Fuel Cycle

This demonstration re-creates the tritium fuel cycle model described by Abdou et al. (2021). It is also described in Simon et al. (2025).

Generating the Input File

First, we instantiate a mesh

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 1
  nx = 1
[]

For our purposes this does nothing, but MOOSE requires a defined mesh as a placeholder to run the rest of the simulation.

Next, we need to define our system. Following the convention in Abdou et al. (2021), we have 11 modeled systems, each with their own ODE and tritium inventory:

Table 1: Systems and labels used in this example.

System Name	System number	Tritium inventory variable	system equation
Breeding zone	1	`T_01_BZ`	Eq. (1)
Tritium Extraction System	2	`T_02_TES`	Eq. (2)
First Wall	3	`T_03_FW`	Eq. (3)
Divertor	4	`T_04_DIV`	Eq. (4)
Heat Exchanger	5	`T_05_HX`	Eq. (5)
Coolant Purification System	6	`T_06_CPS`	Eq. (6)
Vaccum Pump	7	`T_07_vacuum`	Eq. (7)
Fuel Clean-up	8	`T_08_FCU`	Eq. (8)
Isotope Separation System	9	`T_09_ISS`	Eq. (9)
Exhaust and Water Detritiation System	10	`T_10_exhaust`	Eq. (10)
Storage and Management	11	`T_11_storage`	Eq. (11)

$(1)var element = document.getElementById("moose-equation-098ce896-379a-4ca3-b168-5f462cc8a56d");katex.render(" \\frac{dI_1}{dt} = \\Lambda \\dot{N}^{-} + (1-\\eta_2)\\frac{I_2}{\\tau_2} - \\frac{I_1}{\\tau_1}- \\frac{I_1\\varepsilon_1}{\\tau_1} - I_1\\lambda", element, {displayMode:true,throwOnError:false});$

$(2)var element = document.getElementById("moose-equation-07ab9fd9-64e7-4e89-bdfc-c61c1c8107e9");katex.render(" \\frac{dI_2}{dt} = (1-f_{1-5})\\frac{I_1}{\\tau_1} - \\frac{I_2}{\\tau_2} - \\frac{I_2\\varepsilon_2}{\\tau_2} - I_2\\lambda", element, {displayMode:true,throwOnError:false});$

$(3)var element = document.getElementById("moose-equation-876b8437-7417-452c-933b-f40fa38c8ee3");katex.render(" \\frac{dI_3}{dt} = f_{p-3}\\frac{\\dot{N}^{-}}{\\eta_f f_b} + f_{5-3}(1-f_{5-6})(1-f_{5-10})\\frac{I_5}{\\tau_5} + f_{6-3}(1-\\eta_6)\\frac{I_6}{\\tau_6} - \\frac{I_3}{\\tau_3} - \\frac{I_3\\varepsilon_3}{\\tau_3} - I_3\\lambda", element, {displayMode:true,throwOnError:false});$

$(4)var element = document.getElementById("moose-equation-0346400d-cdde-4c86-987c-4522ad63dd36");katex.render(" \\frac{dI_4}{dt} = f_{p-4}\\frac{\\dot{N}^{-}}{\\eta_f f_b} + (1-f_{5-3})(1-f_{5-6})(1-f_{5-10})\\frac{I_5}{\\tau_5} + (1-f_{6-3})(1-\\eta_6)\\frac{I_6}{\\tau_6} - \\frac{I_4}{\\tau_4} - \\frac{I_4\\varepsilon_4}{\\tau_4} - I_4\\lambda", element, {displayMode:true,throwOnError:false});$

$(5)var element = document.getElementById("moose-equation-977c33bf-c723-4cac-8b41-cfa97723f383");katex.render(" \\frac{dI_5}{dt} = f_{1-5}\\frac{I_1}{\\tau_1} + \\frac{I_3}{\\tau_3} + \\frac{I_4}{\\tau_4} - \\frac{I_5}{\\tau_5} -\\frac{I_5\\varepsilon_5}{\\tau_5} - I_5\\lambda", element, {displayMode:true,throwOnError:false});$

$(6)var element = document.getElementById("moose-equation-3a5b6efb-8920-4d48-b143-46d5287ae2cb");katex.render(" \\frac{dI_6}{dt} = f_{5-6}(1-f_{5-10})\\frac{I_5}{\\tau_5} - \\frac{I_6}{\\tau_6} - \\frac{I_6\\varepsilon_6}{\\tau_6} - I_6\\lambda", element, {displayMode:true,throwOnError:false});$

$(7)var element = document.getElementById("moose-equation-14a779dd-3fa4-4b5e-ab9f-3b2baef3399b");katex.render(" \\frac{dI_7}{dt} = (1-\\eta_f f_b - f_{p-3} - f_{p-4})\\frac{\\dot{N}^{-}}{\\eta_f f_b} - \\frac{I_7}{\\tau_7} - \\frac{I_7\\varepsilon_7}{\\tau_7} - I_7\\lambda", element, {displayMode:true,throwOnError:false});$

$(8)var element = document.getElementById("moose-equation-3eeb8478-c462-4594-9df7-7d261d18f849");katex.render(" \\frac{dI_8}{dt} = \\frac{I_7}{\\tau_7} - \\frac{I_8}{\\tau_8} - \\frac{I_8\\varepsilon_8}{\\tau_8} - I_8\\lambda", element, {displayMode:true,throwOnError:false});$

$(9)var element = document.getElementById("moose-equation-7e816f4f-bf64-4db0-abf6-410c036dba2b");katex.render(" \\frac{dI_9}{dt} = (1-f_{8-11})\\frac{I_8}{\\tau_8} + \\frac{I_{10}}{\\tau_{10}} + \\eta_2 \\frac{I_2}{\\tau_2} + \\eta_6 \\frac{I_6}{\\tau_6} - \\frac{I_9\\varepsilon_9}{\\tau_9} - \\frac{I_9}{\\tau_9} - I_9\\lambda", element, {displayMode:true,throwOnError:false});$ $(10)var element = document.getElementById("moose-equation-b004220f-fc7b-4372-843e-1f4cfdb703e1");katex.render(" \\frac{dI_{10}}{dt} = f_{5-10}\\frac{I_5}{\\tau_5} + f_{9-10}\\frac{I_9}{\\tau_9} - \\frac{I_{10}}{\\tau_{10}} - \\frac{I_{10}\\varepsilon_{10}}{\\tau_{10}} - I_{10}\\lambda", element, {displayMode:true,throwOnError:false});$ $(11)var element = document.getElementById("moose-equation-3c3fbd15-526a-42f1-81ef-855277c790e5");katex.render(" \\frac{dI_{11}}{dt} = f_{8-11}\\frac{I_8}{\\tau_8} + (1-f_{9-10})\\frac{I_9}{\\tau_9} - \\frac{\\dot{N}^{-}}{\\eta_f f_b} - I_{11}\\lambda", element, {displayMode:true,throwOnError:false});$

For an interpretation of these equations and explanations about the notations, readers should refer to Abdou et al. (2021) (Appendix). We instantiate the variables in the typical Variables block, making sure to set the "family" attribute to SCALAR for each variable. The default initial condition is zero.

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [T_01_BZ]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_02_TES]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_03_FW]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_04_DIV]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_05_HX]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_06_CPS]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_07_vacuum]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_08_FCU]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_09_ISS]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_10_exhaust]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_11_storage]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 225.4215
  []
[]

Next we initiate the ScalarKernels block. We can model the time-dependent terms with ODETimeDerivative objects and the other terms can be lumped in ParsedODEKernel objects. We should have one ODETimeDerivative and one (or more) ParsedODEKernel object(s) per equation above. Internally, TMAP8 will sum the contributions of each object, so we need to negate the ParsedODEKernel equation from its representation above (move it to the left hand side). We use Postprocessors to re-use the recurring variables.

[ScalarKernels<<<{"href": "../../syntax/ScalarKernels/index.html"}>>>]
  [I1t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_01_BZ
  []
  [I2t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_02_TES
  []
  [I3t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_03_FW
  []
  [I4t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_04_DIV
  []
  [I5t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_05_HX
  []
  [I6t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_06_CPS
  []
  [I7t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_07_vacuum
  []
  [I8t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_08_FCU
  []
  [I9t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_09_ISS
  []
  [I10t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_10_exhaust
  []
  [I11t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_11_storage
  []
  [I1]
    # Breeding Zone
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(tritium_burn_rate * TBR + (1 - TES_efficiency)*T_02_TES/residence2 - T_01_BZ/residence1 - T_01_BZ*epsilon1/residence1 - T_01_BZ*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_01_BZ'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_02_TES'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'TBR tritium_burn_rate TES_efficiency residence1 residence2 tdecay epsilon1'
  []
  [I2]
    #Tritium Extraction System
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-((1 - BZ_HX_leak_fraction)*T_01_BZ/residence1 - T_02_TES/residence2 - T_02_TES*epsilon2/residence2 - T_02_TES*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_02_TES'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_01_BZ'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'BZ_HX_leak_fraction residence1 residence2 tdecay epsilon2'
  []
  [I3]
    #First Wall
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(P_FW_leak_fraction*tritium_burn_rate /tritium_burn_fraction / tritium_fueling_efficiency + HX_FW_leak_fraction * (1 - HX_CPS_leak_fraction) * (1 - HX_EXO_leak_fraction)
                  * T_05_HX/residence5 + CPS_FW_leak_fraction * (1 - CPS_efficiency) * T_06_CPS/residence6 - T_03_FW/residence3 - T_03_FW*epsilon3/residence3 - T_03_FW*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_03_FW'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_05_HX T_06_CPS'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'P_FW_leak_fraction tritium_burn_rate tritium_burn_fraction tritium_fueling_efficiency HX_FW_leak_fraction HX_CPS_leak_fraction HX_EXO_leak_fraction residence5 CPS_FW_leak_fraction CPS_efficiency residence6 residence3 tdecay epsilon3'
  []
  [I4]
    #Divertor
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(P_DIV_leak_fraction * tritium_burn_rate/tritium_burn_fraction / tritium_fueling_efficiency + (1-HX_FW_leak_fraction)*
                  (1-HX_CPS_leak_fraction)*(1-HX_EXO_leak_fraction)* T_05_HX/residence5 + (1-CPS_FW_leak_fraction)*(1 - CPS_efficiency) * T_06_CPS/residence6  - T_04_DIV*epsilon4/residence4 - T_04_DIV/residence4 - T_04_DIV*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_04_DIV'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_06_CPS T_05_HX'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'P_DIV_leak_fraction tritium_burn_rate tritium_burn_fraction tritium_fueling_efficiency HX_FW_leak_fraction HX_CPS_leak_fraction HX_EXO_leak_fraction residence5 CPS_FW_leak_fraction CPS_efficiency residence6 residence4 tdecay epsilon4'
  []
  [I5]
    #Heat eXchanger
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(BZ_HX_leak_fraction * T_01_BZ/residence1 + T_03_FW/residence3 + T_04_DIV/residence4 - T_05_HX/residence5 - T_05_HX*epsilon5/residence5 -T_05_HX*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_05_HX'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_01_BZ T_03_FW T_04_DIV'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'BZ_HX_leak_fraction residence1 residence3 residence4 residence5 tdecay epsilon5'
  []
  [I6]
    #Coolant Purification System
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(HX_CPS_leak_fraction * (1 - HX_EXO_leak_fraction)*T_05_HX/residence5 - T_06_CPS/residence6 - T_06_CPS*epsilon6/residence6 - T_06_CPS*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_06_CPS'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_05_HX'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'HX_CPS_leak_fraction HX_EXO_leak_fraction residence5 residence6 tdecay epsilon6'
  []
  [I7]
    #Vacuum Pump
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-((1-tritium_burn_fraction*tritium_fueling_efficiency - P_FW_leak_fraction - P_DIV_leak_fraction)*
                  tritium_burn_rate/(tritium_burn_fraction * tritium_fueling_efficiency) - T_07_vacuum/residence7 - T_07_vacuum*epsilon7/residence7 - T_07_vacuum*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_07_vacuum'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'tritium_burn_rate tritium_fueling_efficiency P_FW_leak_fraction P_DIV_leak_fraction tritium_burn_fraction residence7 tdecay epsilon7'
  []
  [I8]
    #Fuel clean-up
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(T_07_vacuum/residence7 - T_08_FCU/residence8 - T_08_FCU*epsilon8/residence8 - T_08_FCU*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_08_FCU'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'residence7 residence8 tdecay epsilon8'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_07_vacuum'
  []
  [I9]
    #Isotope Separation System
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-((1-FCU_STO_fraction)*T_08_FCU/residence8 + T_10_exhaust/residence10 + TES_efficiency*T_02_TES/residence2 + CPS_efficiency*T_06_CPS/residence6 - T_09_ISS/residence9 - T_09_ISS*epsilon9/residence9 - T_09_ISS*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_09_ISS'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_08_FCU T_10_exhaust T_02_TES T_06_CPS'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'FCU_STO_fraction residence8 residence10 TES_efficiency residence2 CPS_efficiency residence6 residence9 tdecay epsilon9'
  []
  [I10]
    #Exhaust and Water Detritiation System (EXO)
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(HX_EXO_leak_fraction * T_05_HX/residence5 + ISS_EXO_leak_fraction*T_09_ISS/residence9 - T_10_exhaust/residence10 - T_10_exhaust*epsilon10/residence10 - T_10_exhaust*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_10_exhaust'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_05_HX T_09_ISS'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'HX_EXO_leak_fraction residence5 ISS_EXO_leak_fraction residence9 residence10 tdecay epsilon10'
  []
  [I11]
    #Storage and Management (STO)
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(FCU_STO_fraction * T_08_FCU/residence8 + (1-ISS_EXO_leak_fraction)*T_09_ISS/residence9 - tritium_burn_rate/tritium_burn_fraction/tritium_fueling_efficiency - T_11_storage*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_11_storage'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_08_FCU T_09_ISS'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'FCU_STO_fraction residence8 ISS_EXO_leak_fraction residence9 tritium_burn_rate tritium_burn_fraction tritium_fueling_efficiency tdecay'
  []
[]

Finally, we define the Postprocessors and set their values to those referenced in Abdou et al. (2021). Because the Postprocessors are inputs, not outputs, we must be careful to properly set the "execute_on" parameter. We also gather the values of the different variables in separate Postprocessors and take their sum to obtain the total tritium inventory.

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [BZ_HX_leak_fraction]
    #f_{1-5}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-2
  []
  [CPS_FW_leak_fraction]
    #f_{6-3}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.6
  []
  [CPS_efficiency]
    #eta_6
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.95
  []
  [FCU_STO_fraction]
    #f_{8-11}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [HX_CPS_leak_fraction]
    #f_{5-6}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-2
  []
  [HX_EXO_leak_fraction]
    #f_{5-10}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [HX_FW_leak_fraction]
    #f_{5-3}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.6
  []
  [ISS_EXO_leak_fraction]
    #f_{9-10}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-1
  []
  [P_DIV_leak_fraction]
    #f_{P-4}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [P_FW_leak_fraction]
    #f_{P_3}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [TES_efficiency]
    #eta_2
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.95
  []
  [TBR]
    #According to the PhD Thesis referenced in the paper,
    # this is the required Tritium Breeding Ratio (TBR)
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1.9247
  []
  [epsilon1]
    #BZ
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [epsilon2]
    #TES
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon3]
    #FW
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [epsilon4]
    #DIV
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [epsilon5]
    #HX
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon6]
    #CPS
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon7]
    #Vac
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon8]
    #FCU
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon9]
    #ISS
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon10]
    #EXO
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon11]
    #STO
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [residence1]
    #BZ
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 86400 #1 day, Abdou
    #value = 8640-86400 EXOTIC-6-7-8
  []
  [residence2]
    #TES
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 86400 # Abdou
    #value = 86400-432000 Riva
  []
  [residence3]
    #FW
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1000 #Riva
  []
  [residence4]
    #DIV
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1000 #Riva
  []
  [residence5]
    #HX
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1000 # Abdou 2021 paper chosen for analysis
  []
  [residence6]
    #CPS
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 864000 #Abdou analysis case
    #value 8640000 Abdou 1,4
  []
  [residence7]
    #Vac
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1
    #value = 1800 # 30 minutes (20-30 minutes)
  []
  [residence8]
    #FCU
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1
    #value = 4680 # 1.3 h as per Day
    #value = 5 h Coleman
    #value = 8640 Abdou
    #value = 86400 Abdou
  []
  [residence9]
    #ISS
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 14400
    #value = 7920 #(for four hour overall residence time in inner loop)
  []
  [residence10]
    #EXO
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 3600 # Day et al
    #value = 72000 #Coleman et al
  []
  [tdecay]
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1.7828336471961835e-9
  []
  [tritium_burn_fraction]
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.0036
  []
  [tritium_burn_rate]
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 5.3125e-6 # 0.459 kg/day
  []
  [tritium_fueling_efficiency]
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.25
  []
  # These postprocessors exist to sum up the tritium inventory
  #  across the entirety of the system
  [T_BZ]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_01_BZ
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_TES]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_02_TES
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_FW]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_03_FW
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_DIV]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_04_DIV
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_HX]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_05_HX
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_CPS]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_06_CPS
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_VAC]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_07_vacuum
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_FCU]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_08_FCU
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_ISS]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_09_ISS
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_EXO]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_10_exhaust
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_STO]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_11_storage
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [total_tritium]
    type = SumPostprocessor<<<{"description": "Sums the values of several postprocessors", "href": "../../source/postprocessors/SumPostprocessor.html"}>>>
    values<<<{"description": "List of postprocessors to add"}>>> = 'T_BZ T_TES T_FW T_DIV T_HX T_CPS T_VAC T_FCU T_ISS T_EXO T_STO'
  []
[]

Finally, we can set the Executioner block. In this case, we ask for a simple Transient executioner with an exponentially growing TimeStepper, IterationAdaptiveDT.

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Transient
  start_time = 0
  dtmin = 1
  end_time = 946080000.0
  [TimeStepper<<<{"href": "../../syntax/Executioner/TimeStepper/index.html"}>>>]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
    #timestep_limiting_function = 'catch_five_year'
    #max_function_change = 0.5
    #force_step_every_function_point = true
  []
  solve_type = 'PJFNK'
  nl_rel_tol = 1e-08
  nl_abs_tol = 1e-14
[]

With these blocks set, we can now run the simulation and track tritium inventory.

Implementing a high-fidelity model to replace the default values of specific postprocessors or to more accurately model specific components is an exercise left for a later date.

Comparing Results Against Literature

In order to compare against Abdou et al. (2021), we need to make a few assumptions. First, we set the residence times and other parameters to the values listed in Tables 1-3 of Abdou et al. (2021) (the underlined value if there are multiple options). Here we also assume that the "Fuel clean-up and isotope separation system" total residence time of 4 hours as specified in the paper refers to a residence time of 4 hours for the isotope separation system, and negligible (1 second) residence times for the vacuum pump and fuel clean-up system.

Targeting the black lines of Figure 3 of Abdou et al. (2021), we also need to determine the appropriate reserve inventory $var element = document.getElementById("moose-equation-6eb79ff8-1506-4e48-8176-b98b2404eff4");katex.render("\\frac{\\dot{N}^-}{\\eta_f f_b}t_r q", element, {displayMode:false,throwOnError:false});$ , which, given $var element = document.getElementById("moose-equation-ecf1f141-3d13-4305-a3ad-24b21fb3501f");katex.render("q=0.25", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-b1f479d4-0a10-4eb6-8aa3-3fb76eae8938");katex.render("t_r=1\\ \\text{day}", element, {displayMode:false,throwOnError:false});$ comes out to 127.5 kg. With this constraint, we can determine the relevant TBR to obtain a doubling time of 5 years, and iterating by hand, a value of 1.9247 yields a doubling time of 5 years to three decimal places if T_11_storage is given an initial condition of 225.4215 as shown in Table 2.

Table 2: Assumptions and iteratively obtained conditions used for this example.

Parameter	Value
`residence7` ( $var element = document.getElementById("moose-equation-63e747c0-ad00-4c83-89c9-204def0c6c09");katex.render("\\tau_7", element, {displayMode:false,throwOnError:false});$ )	1 s
`residence8` ( $var element = document.getElementById("moose-equation-be6f3c4c-55c3-4922-9eeb-c6163a6f281c");katex.render("\\tau_8", element, {displayMode:false,throwOnError:false});$ )	1 s
`residence9` ( $var element = document.getElementById("moose-equation-f8bdff69-8791-4061-90c8-802f023d9f0d");katex.render("\\tau_9", element, {displayMode:false,throwOnError:false});$ )	14400 s
`TBR` ( $var element = document.getElementById("moose-equation-03e24cb8-3efa-48b8-a82f-8a84ec941e6b");katex.render("\\Lambda", element, {displayMode:false,throwOnError:false});$ )	1.9247
Initial value for `T_11_storage`	225.4215 kg

We compare our results with those from the black lines in Figure 3 from Abdou et al. (2021) in Figure 1. The lighter lines are estimates of the values shown in the paper, and the darker lines are the results from the model. The agreement is quite good, with only a slight deviation for the tritium extraction system inventory as it transitions to a steady-state value.

Figure 1: Tritium inventories of specific systems as a function of time. Shaded regions are best estimate of Figure 3 in Abdou et al. (2021).

# This input file re-creates the deuterium-tritium fuel cycle model
# described by Abdou et al (2021).
# "Physics and technology considerations for the deuterium-tritium fuel cycle
#   and conditions for tritium fuel self sufficiency" M Abdou & M Riva & A Ying
#   & C Day & A Loarte & L R Baylor & P Humrickhouse & T F Fuerst & S Cho
#   Nucl. Fusion 61 (2021) https://doi.org/10.1088/1741-4326/abbf35

# Since this is a 0D simulation, the mesh is only a single point. If high-fidelity
# models of specific components are required, the scalar variables can be coupled to
# "Field" variables which can vary spatially across the mesh, or could be co-ordinated
# with sub-apps.

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 1
  nx = 1
[]

# One variable for each inventory of tritium is generated. All variables
# are defined as "SCALAR", meaning that they are a single value and are
# disconnected from any specific geometry

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [T_01_BZ]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_02_TES]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_03_FW]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_04_DIV]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_05_HX]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_06_CPS]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_07_vacuum]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_08_FCU]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_09_ISS]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_10_exhaust]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
  []
  [T_11_storage]
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable"}>>> = SCALAR
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 225.4215
  []
[]

# Tritium burn fraction is going to be small. Much
# will be lost to the scrape-off-layer (SOL) and
# recycled.

# TES - tritium extraction system pulls tritium from
# the blanket

# CPS - Coolant purification system pulls tritium from
# the coolant

# An ODE is defined in TMAP8 such that all of the terms must
# be on the left hand side. The terms can be split
# across multiple "ScalarKernels", which are additive,
# so that we have one ODETimeDerivative for each tritium
# inventory and a ParsedODEKernel for the rest of the
# terms. These equations should reflect those described
# in Appendix A of the paper (A.1-A.13), with negation
# on the ParsedODEKernels due to moving the terms to the
# left hand side.

[ScalarKernels<<<{"href": "../../syntax/ScalarKernels/index.html"}>>>]
  [I1t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_01_BZ
  []
  [I2t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_02_TES
  []
  [I3t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_03_FW
  []
  [I4t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_04_DIV
  []
  [I5t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_05_HX
  []
  [I6t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_06_CPS
  []
  [I7t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_07_vacuum
  []
  [I8t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_08_FCU
  []
  [I9t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_09_ISS
  []
  [I10t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_10_exhaust
  []
  [I11t]
    type = ODETimeDerivative<<<{"description": "Returns the time derivative contribution to the residual for a scalar variable.", "href": "../../source/scalarkernels/ODETimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = T_11_storage
  []
  [I1] # Breeding Zone
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(tritium_burn_rate * TBR + (1 - TES_efficiency)*T_02_TES/residence2 - T_01_BZ/residence1 - T_01_BZ*epsilon1/residence1 - T_01_BZ*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_01_BZ'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_02_TES'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'TBR tritium_burn_rate TES_efficiency residence1 residence2 tdecay epsilon1'
  []
  [I2] #Tritium Extraction System
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-((1 - BZ_HX_leak_fraction)*T_01_BZ/residence1 - T_02_TES/residence2 - T_02_TES*epsilon2/residence2 - T_02_TES*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_02_TES'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_01_BZ'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'BZ_HX_leak_fraction residence1 residence2 tdecay epsilon2'
  []
  [I3] #First Wall
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(P_FW_leak_fraction*tritium_burn_rate /tritium_burn_fraction / tritium_fueling_efficiency + HX_FW_leak_fraction * (1 - HX_CPS_leak_fraction) * (1 - HX_EXO_leak_fraction)
                  * T_05_HX/residence5 + CPS_FW_leak_fraction * (1 - CPS_efficiency) * T_06_CPS/residence6 - T_03_FW/residence3 - T_03_FW*epsilon3/residence3 - T_03_FW*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_03_FW'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_05_HX T_06_CPS'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'P_FW_leak_fraction tritium_burn_rate tritium_burn_fraction tritium_fueling_efficiency HX_FW_leak_fraction HX_CPS_leak_fraction HX_EXO_leak_fraction residence5 CPS_FW_leak_fraction CPS_efficiency residence6 residence3 tdecay epsilon3'
  []
  [I4] #Divertor
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(P_DIV_leak_fraction * tritium_burn_rate/tritium_burn_fraction / tritium_fueling_efficiency + (1-HX_FW_leak_fraction)*
                  (1-HX_CPS_leak_fraction)*(1-HX_EXO_leak_fraction)* T_05_HX/residence5 + (1-CPS_FW_leak_fraction)*(1 - CPS_efficiency) * T_06_CPS/residence6  - T_04_DIV*epsilon4/residence4 - T_04_DIV/residence4 - T_04_DIV*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_04_DIV'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_06_CPS T_05_HX'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'P_DIV_leak_fraction tritium_burn_rate tritium_burn_fraction tritium_fueling_efficiency HX_FW_leak_fraction HX_CPS_leak_fraction HX_EXO_leak_fraction residence5 CPS_FW_leak_fraction CPS_efficiency residence6 residence4 tdecay epsilon4'
  []
  [I5] #Heat eXchanger
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(BZ_HX_leak_fraction * T_01_BZ/residence1 + T_03_FW/residence3 + T_04_DIV/residence4 - T_05_HX/residence5 - T_05_HX*epsilon5/residence5 -T_05_HX*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_05_HX'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_01_BZ T_03_FW T_04_DIV'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'BZ_HX_leak_fraction residence1 residence3 residence4 residence5 tdecay epsilon5'
  []
  [I6] #Coolant Purification System
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(HX_CPS_leak_fraction * (1 - HX_EXO_leak_fraction)*T_05_HX/residence5 - T_06_CPS/residence6 - T_06_CPS*epsilon6/residence6 - T_06_CPS*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_06_CPS'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_05_HX'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'HX_CPS_leak_fraction HX_EXO_leak_fraction residence5 residence6 tdecay epsilon6'
  []
  [I7] #Vacuum Pump
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-((1-tritium_burn_fraction*tritium_fueling_efficiency - P_FW_leak_fraction - P_DIV_leak_fraction)*
                  tritium_burn_rate/(tritium_burn_fraction * tritium_fueling_efficiency) - T_07_vacuum/residence7 - T_07_vacuum*epsilon7/residence7 - T_07_vacuum*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_07_vacuum'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'tritium_burn_rate tritium_fueling_efficiency P_FW_leak_fraction P_DIV_leak_fraction tritium_burn_fraction residence7 tdecay epsilon7'
  []
  [I8] #Fuel clean-up
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(T_07_vacuum/residence7 - T_08_FCU/residence8 - T_08_FCU*epsilon8/residence8 - T_08_FCU*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_08_FCU'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'residence7 residence8 tdecay epsilon8'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_07_vacuum'
  []
  [I9] #Isotope Separation System
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-((1-FCU_STO_fraction)*T_08_FCU/residence8 + T_10_exhaust/residence10 + TES_efficiency*T_02_TES/residence2 + CPS_efficiency*T_06_CPS/residence6 - T_09_ISS/residence9 - T_09_ISS*epsilon9/residence9 - T_09_ISS*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_09_ISS'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_08_FCU T_10_exhaust T_02_TES T_06_CPS'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'FCU_STO_fraction residence8 residence10 TES_efficiency residence2 CPS_efficiency residence6 residence9 tdecay epsilon9'
  []
  [I10] #Exhaust and Water Detritiation System (EXO)
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(HX_EXO_leak_fraction * T_05_HX/residence5 + ISS_EXO_leak_fraction*T_09_ISS/residence9 - T_10_exhaust/residence10 - T_10_exhaust*epsilon10/residence10 - T_10_exhaust*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_10_exhaust'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_05_HX T_09_ISS'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'HX_EXO_leak_fraction residence5 ISS_EXO_leak_fraction residence9 residence10 tdecay epsilon10'
  []
  [I11] #Storage and Management (STO)
    type = ParsedODEKernel<<<{"description": "Parsed expression ODE kernel.", "href": "../../source/scalarkernels/ParsedODEKernel.html"}>>>
    expression<<<{"description": "function expression"}>>> = '-(FCU_STO_fraction * T_08_FCU/residence8 + (1-ISS_EXO_leak_fraction)*T_09_ISS/residence9 - tritium_burn_rate/tritium_burn_fraction/tritium_fueling_efficiency - T_11_storage*tdecay)'
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'T_11_storage'
    coupled_variables<<<{"description": "Scalar variables coupled in the parsed expression."}>>> = 'T_08_FCU T_09_ISS'
    postprocessors<<<{"description": "Vector of postprocessor names used in the function expression"}>>> = 'FCU_STO_fraction residence8 ISS_EXO_leak_fraction residence9 tritium_burn_rate tritium_burn_fraction tritium_fueling_efficiency tdecay'
  []
[]

# These postprocessors define the constants referenced in
# the equations above. The value of any of these constants
# could be informed by more detailed models (using sub-apps
# and transfers), but it is important that the postprocessor
# is evaluated before the executioner attempts to solve the
# ODE, which is not the default behavior.
[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [BZ_HX_leak_fraction] #f_{1-5}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-2
  []
  [CPS_FW_leak_fraction] #f_{6-3}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.6
  []
  [CPS_efficiency] #eta_6
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.95
  []
  [FCU_STO_fraction] #f_{8-11}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [HX_CPS_leak_fraction] #f_{5-6}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-2
  []
  [HX_EXO_leak_fraction] #f_{5-10}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [HX_FW_leak_fraction] #f_{5-3}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.6
  []
  [ISS_EXO_leak_fraction] #f_{9-10}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-1
  []
  [P_DIV_leak_fraction] #f_{P-4}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [P_FW_leak_fraction] #f_{P_3}
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [TES_efficiency] #eta_2
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.95
  []
  [TBR] #According to the PhD Thesis referenced in the paper,
        # this is the required Tritium Breeding Ratio (TBR)
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1.9247
  []
  [epsilon1] #BZ
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [epsilon2] #TES
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon3] #FW
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [epsilon4] #DIV
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [epsilon5] #HX
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon6] #CPS
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon7] #Vac
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon8] #FCU
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> =  1e-4
  []
  [epsilon9] #ISS
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon10] #EXO
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1e-4
  []
  [epsilon11] #STO
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0
  []
  [residence1] #BZ
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 86400 #1 day, Abdou
    #value = 8640-86400 EXOTIC-6-7-8
  []
  [residence2] #TES
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 86400 # Abdou
    #value = 86400-432000 Riva
  []
  [residence3] #FW
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1000 #Riva
  []
  [residence4] #DIV
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1000 #Riva
  []
  [residence5] #HX
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1000 # Abdou 2021 paper chosen for analysis
  []
  [residence6] #CPS
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 864000 #Abdou analysis case
    #value 8640000 Abdou 1,4
  []
  [residence7] #Vac
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1
    #value = 1800 # 30 minutes (20-30 minutes)
  []
  [residence8] #FCU
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1
    #value = 4680 # 1.3 h as per Day
    #value = 5 h Coleman
    #value = 8640 Abdou
    #value = 86400 Abdou
  []
  [residence9] #ISS
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 14400
    #value = 7920 #(for four hour overall residence time in inner loop)
  []
  [residence10] #EXO
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 3600 # Day et al
    #value = 72000 #Coleman et al
  []
  [tdecay]
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 1.7828336471961835e-9
  []
  [tritium_burn_fraction]
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.0036
  []
  [tritium_burn_rate]
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 5.3125e-6 # 0.459 kg/day
  []
  [tritium_fueling_efficiency]
    type = ConstantPostprocessor<<<{"description": "Postprocessor that holds a constant value", "href": "../../source/postprocessors/ConstantPostprocessor.html"}>>>
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value<<<{"description": "The value"}>>> = 0.25
  []
  # These postprocessors exist to sum up the tritium inventory
  #  across the entirety of the system
  [T_BZ]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_01_BZ
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_TES]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_02_TES
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_FW]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_03_FW
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_DIV]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_04_DIV
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_HX]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_05_HX
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_CPS]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_06_CPS
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_VAC]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_07_vacuum
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_FCU]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_08_FCU
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_ISS]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_09_ISS
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_EXO]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_10_exhaust
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [T_STO]
    type = ScalarVariable<<<{"description": "Returns the value of a scalar variable as a postprocessor value.", "href": "../../source/postprocessors/ScalarVariable.html"}>>>
    variable<<<{"description": "Name of the variable"}>>> = T_11_storage
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = TIMESTEP_END
  []
  [total_tritium]
    type = SumPostprocessor<<<{"description": "Sums the values of several postprocessors", "href": "../../source/postprocessors/SumPostprocessor.html"}>>>
    values<<<{"description": "List of postprocessors to add"}>>> = 'T_BZ T_TES T_FW T_DIV T_HX T_CPS T_VAC T_FCU T_ISS T_EXO T_STO'
  []
[]
[UserObjects<<<{"href": "../../syntax/UserObjects/index.html"}>>>]
  [terminator]
    type = Terminator<<<{"description": "Requests termination of the current solve based on the evaluation of a parsed logical expression of the Postprocessor value(s).", "href": "../../source/userobjects/Terminator.html"}>>>
    expression<<<{"description": "FParser expression to process Postprocessor values into a boolean value. Termination of the simulation occurs when this returns true."}>>> = 'T_STO < 0'
    fail_mode<<<{"description": "Abort entire simulation (HARD), just the current time step (SOFT), or not at all (NONE)."}>>> = 'HARD'
    message<<<{"description": "An optional message to be output instead of the default message when the termination condition is triggered"}>>> = 'Tritium in storage has been depleted'
  []
  [terminator2]
    type = Terminator<<<{"description": "Requests termination of the current solve based on the evaluation of a parsed logical expression of the Postprocessor value(s).", "href": "../../source/userobjects/Terminator.html"}>>>
    expression<<<{"description": "FParser expression to process Postprocessor values into a boolean value. Termination of the simulation occurs when this returns true."}>>> = 'total_tritium < 0'
    fail_mode<<<{"description": "Abort entire simulation (HARD), just the current time step (SOFT), or not at all (NONE)."}>>> = 'HARD'
    message<<<{"description": "An optional message to be output instead of the default message when the termination condition is triggered"}>>> = 'Tritium in system has been depleted'
  []
[]
# The tritium breeding ratio is not directly given in the paper,
# but is specified as a "five year" doubling time from the initial
# inventory. As such, it may be necessary to force the simulation to
# record a timestep at exactly five years, or whatever doubling time
# is wanted, to dial in the tritium breeding ratio. This can be done
# using the IterationAdaptiveDT settings commented out below along
# with this function.
#
#[Functions]
#  [catch_five_year]
#    type = PiecewiseLinear
#    x = '0 157680000 157680100 864000000.0'
#    y = '0 0 1 1'
#  []
#[]

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Transient
  start_time = 0
  dtmin = 1
  end_time = 946080000.0
  [TimeStepper<<<{"href": "../../syntax/Executioner/TimeStepper/index.html"}>>>]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
    #timestep_limiting_function = 'catch_five_year'
    #max_function_change = 0.5
    #force_step_every_function_point = true
  []
  solve_type = 'PJFNK'
  nl_rel_tol = 1e-08
  nl_abs_tol = 1e-14
[]
[Outputs<<<{"href": "../../syntax/Outputs/index.html"}>>>]
  hide<<<{"description": "A list of the variables and postprocessors that should NOT be output to the Exodus file (may include Variables, ScalarVariables, and Postprocessor names)."}>>> = "BZ_HX_leak_fraction CPS_FW_leak_fraction CPS_efficiency FCU_STO_fraction HX_CPS_leak_fraction HX_EXO_leak_fraction HX_FW_leak_fraction ISS_EXO_leak_fraction P_DIV_leak_fraction P_FW_leak_fraction TBR TES_efficiency T_BZ T_CPS T_DIV T_EXO T_FCU T_FW T_HX T_ISS T_STO T_TES T_VAC epsilon1 epsilon10 epsilon11 epsilon2 epsilon3 epsilon4 epsilon5 epsilon6 epsilon7 epsilon8 epsilon9 residence1 residence10 residence2 residence3 residence4 residence5 residence6 residence7 residence8 residence9 tdecay tritium_burn_fraction tritium_burn_rate tritium_fueling_efficiency"
  csv<<<{"description": "Output the scalar variable and postprocessors to a *.csv file using the default CSV output."}>>> = true
  console<<<{"description": "Output the results using the default settings for Console output"}>>> = false
[]

Python-based Interactive Script

A python-based graphical interactive script is available at (test/tests/fuel_cycle_Abdou/fuel_cycle_gui.py) as a demonstration of the various effects of individual parameters. To use it, navigate to the scripts directory and run the script. All of the input parameters for the model can be changed by editing the associated entry, then clicking the "Run" button. Once the simulation has run, checkboxes will appear for each system-level tritium inventory. Time units can also be adjusted by selecting the appropriate timescale.

References

Mohamed Abdou, Marco Riva, Alice Ying, Christian Day, Alberto Loarte, Larry R. Baylor, Paul Humrickhouse, Thomas F. Fuerst, and Seungyon Cho. Physics and technology considerations for the deuterium–tritium fuel cycle and conditions for tritium fuel self sufficiency. Nuclear Fusion, 61(1):013001, 2021. URL: https://dx.doi.org/10.1088/1741-4326/abbf35, doi:10.1088/1741-4326/abbf35.

@article{Abdou2021,
    author = "Abdou, Mohamed and Riva, Marco and Ying, Alice and Day, Christian and Loarte, Alberto and Baylor, Larry R. and Humrickhouse, Paul and Fuerst, Thomas F. and Cho, Seungyon",
    doi = "10.1088/1741-4326/abbf35",
    url = "https://dx.doi.org/10.1088/1741-4326/abbf35",
    year = "2021",
    publisher = "IOP Publishing",
    volume = "61",
    number = "1",
    pages = "013001",
    title = "Physics and technology considerations for the deuterium–tritium fuel cycle and conditions for tritium fuel self sufficiency",
    journal = "Nuclear Fusion"
}

Pierre-Clément A. Simon, Casey T. Icenhour, Gyanender Singh, Alexander D Lindsay, Chaitanya Vivek Bhave, Lin Yang, Adriaan Anthony Riet, Yifeng Che, Paul Humrickhouse, Masashi Shimada, and Pattrick Calderoni. MOOSE-based tritium migration analysis program, version 8 (TMAP8) for advanced open-source tritium transport and fuel cycle modeling. Fusion Engineering and Design, 214:114874, May 2025. doi:10.1016/j.fusengdes.2025.114874.

@article{Simon2025,
    author = "Simon, Pierre-Clément A. and Icenhour, Casey T. and Singh, Gyanender and Lindsay, Alexander D and Bhave, Chaitanya Vivek and Yang, Lin and Riet, Adriaan Anthony and Che, Yifeng and Humrickhouse, Paul and Shimada, Masashi and Calderoni, Pattrick",
    title = "{MOOSE}-based Tritium Migration Analysis Program, Version 8 ({TMAP8}) for Advanced Open-Source Tritium Transport and Fuel Cycle Modeling",
    journal = "Fusion Engineering and Design",
    publisher = "Elsevier",
    volume = "214",
    pages = "114874",
    year = "2025",
    month = "May",
    issn = "0920-3796",
    doi = "10.1016/j.fusengdes.2025.114874"
}

(test/tests/fuel_cycle_Abdou/fuel_cycle.i)

# This input file re-creates the deuterium-tritium fuel cycle model
# described by Abdou et al (2021).
# "Physics and technology considerations for the deuterium-tritium fuel cycle
#   and conditions for tritium fuel self sufficiency" M Abdou & M Riva & A Ying
#   & C Day & A Loarte & L R Baylor & P Humrickhouse & T F Fuerst & S Cho
#   Nucl. Fusion 61 (2021) https://doi.org/10.1088/1741-4326/abbf35

# Since this is a 0D simulation, the mesh is only a single point. If high-fidelity
# models of specific components are required, the scalar variables can be coupled to
# "Field" variables which can vary spatially across the mesh, or could be co-ordinated
# with sub-apps.

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 1
  nx = 1
[]

# One variable for each inventory of tritium is generated. All variables
# are defined as "SCALAR", meaning that they are a single value and are
# disconnected from any specific geometry

[Variables]
  [T_01_BZ]
    family = SCALAR
  []
  [T_02_TES]
    family = SCALAR
  []
  [T_03_FW]
    family = SCALAR
  []
  [T_04_DIV]
    family = SCALAR
  []
  [T_05_HX]
    family = SCALAR
  []
  [T_06_CPS]
    family = SCALAR
  []
  [T_07_vacuum]
    family = SCALAR
  []
  [T_08_FCU]
    family = SCALAR
  []
  [T_09_ISS]
    family = SCALAR
  []
  [T_10_exhaust]
    family = SCALAR
  []
  [T_11_storage]
    family = SCALAR
    initial_condition = 225.4215
  []
[]

# Tritium burn fraction is going to be small. Much
# will be lost to the scrape-off-layer (SOL) and
# recycled.

# TES - tritium extraction system pulls tritium from
# the blanket

# CPS - Coolant purification system pulls tritium from
# the coolant

# An ODE is defined in TMAP8 such that all of the terms must
# be on the left hand side. The terms can be split
# across multiple "ScalarKernels", which are additive,
# so that we have one ODETimeDerivative for each tritium
# inventory and a ParsedODEKernel for the rest of the
# terms. These equations should reflect those described
# in Appendix A of the paper (A.1-A.13), with negation
# on the ParsedODEKernels due to moving the terms to the
# left hand side.


[ScalarKernels]
  [I1t]
    type = ODETimeDerivative
    variable = T_01_BZ
  []
  [I2t]
    type = ODETimeDerivative
    variable = T_02_TES
  []
  [I3t]
    type = ODETimeDerivative
    variable = T_03_FW
  []
  [I4t]
    type = ODETimeDerivative
    variable = T_04_DIV
  []
  [I5t]
    type = ODETimeDerivative
    variable = T_05_HX
  []
  [I6t]
    type = ODETimeDerivative
    variable = T_06_CPS
  []
  [I7t]
    type = ODETimeDerivative
    variable = T_07_vacuum
  []
  [I8t]
    type = ODETimeDerivative
    variable = T_08_FCU
  []
  [I9t]
    type = ODETimeDerivative
    variable = T_09_ISS
  []
  [I10t]
    type = ODETimeDerivative
    variable = T_10_exhaust
  []
  [I11t]
    type = ODETimeDerivative
    variable = T_11_storage
  []
  [I1] # Breeding Zone
    type = ParsedODEKernel
    expression = '-(tritium_burn_rate * TBR + (1 - TES_efficiency)*T_02_TES/residence2 - T_01_BZ/residence1 - T_01_BZ*epsilon1/residence1 - T_01_BZ*tdecay)'
    variable = 'T_01_BZ'
    coupled_variables = 'T_02_TES'
    postprocessors = 'TBR tritium_burn_rate TES_efficiency residence1 residence2 tdecay epsilon1'
  []
  [I2] #Tritium Extraction System
    type = ParsedODEKernel
    expression = '-((1 - BZ_HX_leak_fraction)*T_01_BZ/residence1 - T_02_TES/residence2 - T_02_TES*epsilon2/residence2 - T_02_TES*tdecay)'
    variable = 'T_02_TES'
    coupled_variables = 'T_01_BZ'
    postprocessors = 'BZ_HX_leak_fraction residence1 residence2 tdecay epsilon2'
  []
  [I3] #First Wall
    type = ParsedODEKernel
    expression = '-(P_FW_leak_fraction*tritium_burn_rate /tritium_burn_fraction / tritium_fueling_efficiency + HX_FW_leak_fraction * (1 - HX_CPS_leak_fraction) * (1 - HX_EXO_leak_fraction)
                  * T_05_HX/residence5 + CPS_FW_leak_fraction * (1 - CPS_efficiency) * T_06_CPS/residence6 - T_03_FW/residence3 - T_03_FW*epsilon3/residence3 - T_03_FW*tdecay)'
    variable = 'T_03_FW'
    coupled_variables = 'T_05_HX T_06_CPS'
    postprocessors = 'P_FW_leak_fraction tritium_burn_rate tritium_burn_fraction tritium_fueling_efficiency HX_FW_leak_fraction HX_CPS_leak_fraction HX_EXO_leak_fraction residence5 CPS_FW_leak_fraction CPS_efficiency residence6 residence3 tdecay epsilon3'
  []
  [I4] #Divertor
    type = ParsedODEKernel
    expression = '-(P_DIV_leak_fraction * tritium_burn_rate/tritium_burn_fraction / tritium_fueling_efficiency + (1-HX_FW_leak_fraction)*
                  (1-HX_CPS_leak_fraction)*(1-HX_EXO_leak_fraction)* T_05_HX/residence5 + (1-CPS_FW_leak_fraction)*(1 - CPS_efficiency) * T_06_CPS/residence6  - T_04_DIV*epsilon4/residence4 - T_04_DIV/residence4 - T_04_DIV*tdecay)'
    variable = 'T_04_DIV'
    coupled_variables = 'T_06_CPS T_05_HX'
    postprocessors = 'P_DIV_leak_fraction tritium_burn_rate tritium_burn_fraction tritium_fueling_efficiency HX_FW_leak_fraction HX_CPS_leak_fraction HX_EXO_leak_fraction residence5 CPS_FW_leak_fraction CPS_efficiency residence6 residence4 tdecay epsilon4'
  []
  [I5] #Heat eXchanger
    type = ParsedODEKernel
    expression = '-(BZ_HX_leak_fraction * T_01_BZ/residence1 + T_03_FW/residence3 + T_04_DIV/residence4 - T_05_HX/residence5 - T_05_HX*epsilon5/residence5 -T_05_HX*tdecay)'
    variable = 'T_05_HX'
    coupled_variables = 'T_01_BZ T_03_FW T_04_DIV'
    postprocessors = 'BZ_HX_leak_fraction residence1 residence3 residence4 residence5 tdecay epsilon5'
  []
  [I6] #Coolant Purification System
    type = ParsedODEKernel
    expression = '-(HX_CPS_leak_fraction * (1 - HX_EXO_leak_fraction)*T_05_HX/residence5 - T_06_CPS/residence6 - T_06_CPS*epsilon6/residence6 - T_06_CPS*tdecay)'
    variable = 'T_06_CPS'
    coupled_variables = 'T_05_HX'
    postprocessors = 'HX_CPS_leak_fraction HX_EXO_leak_fraction residence5 residence6 tdecay epsilon6'
  []
  [I7] #Vacuum Pump
    type = ParsedODEKernel
    expression = '-((1-tritium_burn_fraction*tritium_fueling_efficiency - P_FW_leak_fraction - P_DIV_leak_fraction)*
                  tritium_burn_rate/(tritium_burn_fraction * tritium_fueling_efficiency) - T_07_vacuum/residence7 - T_07_vacuum*epsilon7/residence7 - T_07_vacuum*tdecay)'
    variable = 'T_07_vacuum'
    postprocessors = 'tritium_burn_rate tritium_fueling_efficiency P_FW_leak_fraction P_DIV_leak_fraction tritium_burn_fraction residence7 tdecay epsilon7'
  []
  [I8] #Fuel clean-up
    type = ParsedODEKernel
    expression = '-(T_07_vacuum/residence7 - T_08_FCU/residence8 - T_08_FCU*epsilon8/residence8 - T_08_FCU*tdecay)'
    variable = 'T_08_FCU'
    postprocessors = 'residence7 residence8 tdecay epsilon8'
    coupled_variables = 'T_07_vacuum'
  []
  [I9] #Isotope Separation System
    type = ParsedODEKernel
    expression = '-((1-FCU_STO_fraction)*T_08_FCU/residence8 + T_10_exhaust/residence10 + TES_efficiency*T_02_TES/residence2 + CPS_efficiency*T_06_CPS/residence6 - T_09_ISS/residence9 - T_09_ISS*epsilon9/residence9 - T_09_ISS*tdecay)'
    variable = 'T_09_ISS'
    coupled_variables = 'T_08_FCU T_10_exhaust T_02_TES T_06_CPS'
    postprocessors = 'FCU_STO_fraction residence8 residence10 TES_efficiency residence2 CPS_efficiency residence6 residence9 tdecay epsilon9'
  []
  [I10] #Exhaust and Water Detritiation System (EXO)
    type = ParsedODEKernel
    expression = '-(HX_EXO_leak_fraction * T_05_HX/residence5 + ISS_EXO_leak_fraction*T_09_ISS/residence9 - T_10_exhaust/residence10 - T_10_exhaust*epsilon10/residence10 - T_10_exhaust*tdecay)'
    variable = 'T_10_exhaust'
    coupled_variables = 'T_05_HX T_09_ISS'
    postprocessors = 'HX_EXO_leak_fraction residence5 ISS_EXO_leak_fraction residence9 residence10 tdecay epsilon10'
  []
  [I11] #Storage and Management (STO)
    type = ParsedODEKernel
    expression = '-(FCU_STO_fraction * T_08_FCU/residence8 + (1-ISS_EXO_leak_fraction)*T_09_ISS/residence9 - tritium_burn_rate/tritium_burn_fraction/tritium_fueling_efficiency - T_11_storage*tdecay)'
    variable = 'T_11_storage'
    coupled_variables = 'T_08_FCU T_09_ISS'
    postprocessors = 'FCU_STO_fraction residence8 ISS_EXO_leak_fraction residence9 tritium_burn_rate tritium_burn_fraction tritium_fueling_efficiency tdecay'
  []
[]

# These postprocessors define the constants referenced in
# the equations above. The value of any of these constants
# could be informed by more detailed models (using sub-apps
# and transfers), but it is important that the postprocessor
# is evaluated before the executioner attempts to solve the
# ODE, which is not the default behavior.
[Postprocessors]
  [BZ_HX_leak_fraction] #f_{1-5}
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-2
  []
  [CPS_FW_leak_fraction] #f_{6-3}
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0.6
  []
  [CPS_efficiency] #eta_6
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0.95
  []
  [FCU_STO_fraction] #f_{8-11}
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0
  []
  [HX_CPS_leak_fraction] #f_{5-6}
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-2
  []
  [HX_EXO_leak_fraction] #f_{5-10}
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-4
  []
  [HX_FW_leak_fraction] #f_{5-3}
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0.6
  []
  [ISS_EXO_leak_fraction] #f_{9-10}
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-1
  []
  [P_DIV_leak_fraction] #f_{P-4}
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-4
  []
  [P_FW_leak_fraction] #f_{P_3}
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-4
  []
  [TES_efficiency] #eta_2
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0.95
  []
  [TBR] #According to the PhD Thesis referenced in the paper,
        # this is the required Tritium Breeding Ratio (TBR)
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1.9247
  []
  [epsilon1] #BZ
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0
  []
  [epsilon2] #TES
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-4
  []
  [epsilon3] #FW
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0
  []
  [epsilon4] #DIV
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0
  []
  [epsilon5] #HX
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-4
  []
  [epsilon6] #CPS
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-4
  []
  [epsilon7] #Vac
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-4
  []
  [epsilon8] #FCU
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value =  1e-4
  []
  [epsilon9] #ISS
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-4
  []
  [epsilon10] #EXO
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1e-4
  []
  [epsilon11] #STO
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0
  []
  [residence1] #BZ
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 86400 #1 day, Abdou
    #value = 8640-86400 EXOTIC-6-7-8
  []
  [residence2] #TES
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 86400 # Abdou
    #value = 86400-432000 Riva
  []
  [residence3] #FW
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1000 #Riva
  []
  [residence4] #DIV
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1000 #Riva
  []
  [residence5] #HX
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1000 # Abdou 2021 paper chosen for analysis
  []
  [residence6] #CPS
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 864000 #Abdou analysis case
    #value 8640000 Abdou 1,4
  []
  [residence7] #Vac
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1
    #value = 1800 # 30 minutes (20-30 minutes)
  []
  [residence8] #FCU
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1
    #value = 4680 # 1.3 h as per Day
    #value = 5 h Coleman
    #value = 8640 Abdou
    #value = 86400 Abdou
  []
  [residence9] #ISS
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 14400
    #value = 7920 #(for four hour overall residence time in inner loop)
  []
  [residence10] #EXO
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 3600 # Day et al
    #value = 72000 #Coleman et al
  []
  [tdecay]
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 1.7828336471961835e-9
  []
  [tritium_burn_fraction]
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0.0036
  []
  [tritium_burn_rate]
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 5.3125e-6 # 0.459 kg/day
  []
  [tritium_fueling_efficiency]
    type = ConstantPostprocessor
    execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR'
    value = 0.25
  []
  # These postprocessors exist to sum up the tritium inventory
  #  across the entirety of the system
  [T_BZ]
    type = ScalarVariable
    variable = T_01_BZ
    execute_on = TIMESTEP_END
  []
  [T_TES]
    type = ScalarVariable
    variable = T_02_TES
    execute_on = TIMESTEP_END
  []
  [T_FW]
    type = ScalarVariable
    variable = T_03_FW
    execute_on = TIMESTEP_END
  []
  [T_DIV]
    type = ScalarVariable
    variable = T_04_DIV
    execute_on = TIMESTEP_END
  []
  [T_HX]
    type = ScalarVariable
    variable = T_05_HX
    execute_on = TIMESTEP_END
  []
  [T_CPS]
    type = ScalarVariable
    variable = T_06_CPS
    execute_on = TIMESTEP_END
  []
  [T_VAC]
    type = ScalarVariable
    variable = T_07_vacuum
    execute_on = TIMESTEP_END
  []
  [T_FCU]
    type = ScalarVariable
    variable = T_08_FCU
    execute_on = TIMESTEP_END
  []
  [T_ISS]
    type = ScalarVariable
    variable = T_09_ISS
    execute_on = TIMESTEP_END
  []
  [T_EXO]
    type = ScalarVariable
    variable = T_10_exhaust
    execute_on = TIMESTEP_END
  []
  [T_STO]
    type = ScalarVariable
    variable = T_11_storage
    execute_on = TIMESTEP_END
  []
  [total_tritium]
    type = SumPostprocessor
    values = 'T_BZ T_TES T_FW T_DIV T_HX T_CPS T_VAC T_FCU T_ISS T_EXO T_STO'
  []
[]
[UserObjects]
  [terminator]
    type = Terminator
    expression = 'T_STO < 0'
    fail_mode = 'HARD'
    message = 'Tritium in storage has been depleted'
  []
  [terminator2]
    type = Terminator
    expression = 'total_tritium < 0'
    fail_mode = 'HARD'
    message = 'Tritium in system has been depleted'
  []
[]
# The tritium breeding ratio is not directly given in the paper,
# but is specified as a "five year" doubling time from the initial
# inventory. As such, it may be necessary to force the simulation to
# record a timestep at exactly five years, or whatever doubling time
# is wanted, to dial in the tritium breeding ratio. This can be done
# using the IterationAdaptiveDT settings commented out below along
# with this function.
#
#[Functions]
#  [catch_five_year]
#    type = PiecewiseLinear
#    x = '0 157680000 157680100 864000000.0'
#    y = '0 0 1 1'
#  []
#[]

[Executioner]
  type = Transient
  start_time = 0
  dtmin = 1
  end_time = 946080000.0
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
    #timestep_limiting_function = 'catch_five_year'
    #max_function_change = 0.5
    #force_step_every_function_point = true
  []
  solve_type = 'PJFNK'
  nl_rel_tol = 1e-08
  nl_abs_tol = 1e-14
[]
[Outputs]
  hide = "BZ_HX_leak_fraction CPS_FW_leak_fraction CPS_efficiency FCU_STO_fraction HX_CPS_leak_fraction HX_EXO_leak_fraction HX_FW_leak_fraction ISS_EXO_leak_fraction P_DIV_leak_fraction P_FW_leak_fraction TBR TES_efficiency T_BZ T_CPS T_DIV T_EXO T_FCU T_FW T_HX T_ISS T_STO T_TES T_VAC epsilon1 epsilon10 epsilon11 epsilon2 epsilon3 epsilon4 epsilon5 epsilon6 epsilon7 epsilon8 epsilon9 residence1 residence10 residence2 residence3 residence4 residence5 residence6 residence7 residence8 residence9 tdecay tritium_burn_fraction tritium_burn_rate tritium_fueling_efficiency"
  csv = true
  console = false
[]

(test/tests/fuel_cycle_Abdou/fuel_cycle_gui.py)

#! /usr/bin/env python
# -*- coding: utf-8 -*-
"""
Created on Fri Oct 11 15:33:07 2024
This file creates a GUI interface that can be used to adjust the parameters in
the TMAP8 fuel cycle model.
"""
import tempfile
import tkinter as tk
import tkinter.ttk as ttk
import re
import subprocess
from matplotlib.backends.backend_tkagg import (FigureCanvasTkAgg, NavigationToolbar2Tk)
from matplotlib.backend_bases import key_press_handler
from matplotlib.figure import Figure
import numpy as np
import scipy.constants as scc
import atexit
#import asyncio
import os
import shutil
import argparse
import PIL
dir_path = os.path.dirname(os.path.realpath(__file__))
icon_path = os.path.join(dir_path,'..','..','..','doc','content','figures','TMAP8_logo_blue.png')

class fake_tk():
    def __init__(self,x=0,text=None,row=0,column=0,grid=None,textvariable=None,validate=None,validatecommand=None, width=True, height=True,master=None,**kwargs):
        if text is not None:
            self.x = text
            self.text = text
        else:
            self.x = x
        if textvariable is not None:
            self.x = textvariable
        self.__dict__[0] = 1
        self.__dict__.update(**kwargs)
        self._tkcanvas = self
        self.figure = self
        self.bbox = self
        self.width = 1
        self.height = 1
        self.mpl_connect = self
        self.yview = None
        self.columnconfigure = self.rowconfigure = self.create_window = self.configure
        self.bind = self.configure

    def configure(self,*args,**kwargs):
        return True
    def get(self):
        if 'values' in self.__dict__.keys():
            return self.values[0]
        if type(self.x) is type(self):
            return str(self.x)
        else:
            return self.x
    def cget(self,index):
        return self[index]
    def __call__(self,*args,**kwargs):
        pass
    def set(self,x):
        self.x = x
    def grid(self,row=0,column=0,**kwargs):
        return True
    def update(self):
        return True
    def current(self, indice):
        self.x.set(indice)
    def __setitem__(self, key, value):
        setattr(self, key, value)
    def __getitem__(self, key):
        getattr(self, key)
    def trace(self,*args,**kwargs):
        pass
    def draw(self):
        pass
    def __str__(self):
        if type(self.x) is type(self):
            return self.x.__str__()
        else:
            return self.x
    def __repr__(self):
        if type(self.x) is type(self):
            return self.x.__str__()
        else:
            return str(self.x)

class fuel_cycle_form(tk.Tk):
    def __init__(self, interval=1/120,tmap8_path=None,headless=False):
        self.headless = headless
        if not headless:
            super().__init__()
        else:
            self.register = lambda x, *args, **kwargs: True
            self.update = lambda: True
            self.destroy = self.cleanup
        if tmap8_path is None:
            check_paths = [os.path.join(dir_path,'..','..','..','tmap8-opt'),
                           os.path.join(dir_path,'..','..','..','tmap8-dbg'),
                           os.path.join(dir_path,'..','..','..','tmap8-devel'),
                           os.path.join(dir_path,'..','..','..','tmap8-oprof')]
            for check_path in check_paths:
                if tmap8_path is None:
                    if os.path.isfile(check_path) and os.access(check_path, os.X_OK):
                        tmap8_path = check_path
            for check_path in check_paths:
                if tmap8_path is None:
                    tmap8_path = shutil.which(check_path[check_path.rfind('/')+1:])
        self.tmap8_path = tmap8_path
        if tmap8_path is None or not (os.path.isfile(self.tmap8_path) and os.access(self.tmap8_path, os.X_OK)):
            raise OSError('Unable to locate a working TMAP8 executable')
        pattern = re.compile('\\[(?P<variable>[0-9a-zA-Z_]+)\\]\ntype = ConstantPostprocessor\nexecute_on = \'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR\'\nvalue\\s?=\\s*(?P<valnum>[0-9e.-]+)\n\\[]',re.MULTILINE)
        instring = ''
        test_path = os.path.join(dir_path,'fuel_cycle.i')
        self.gold_path = os.path.join(dir_path,'gold','fuel_cycle_out.csv')
        if not os.path.isfile(test_path):
            raise OSError('Unable to locate the fuel cycle input file')
        with open(test_path,'r') as infile:
            instring = infile.read()
        ic_loc = instring.find('initial_condition')
        ic_end = instring.find('\n',ic_loc)
        start = instring.find('Postprocessors]')+len('Postprocessors]\n')
        end = instring.find('  [T_BZ')
        self.top_header = instring[:ic_loc]
        self.bottom_header = instring[ic_end:start]
        self.footer = instring[end:]
        filtstring = [x[:x.find('#')].strip() if '#' in x else x for x in instring[start:end].split('\n')]
        self.filtstring = '\n'.join([x.strip() for x in filtstring if len(x.strip())>1])
        self.matches = [(m.span(), m.groups()) for m in pattern.finditer(self.filtstring)]
        labels = []
        self.entries = []
        self.plot_vars = []
        tvariables = {}
        row_i = 1
        if not headless:
            label = tk.Label(self, text='Variable')
        else:
            label = fake_tk(grid=lambda row, column: True)
        _,self.tmpfile = tempfile.mkstemp(suffix='.i')
        atexit.register(self.cleanup)
        label.grid(row=0,column=0)
        newlabel = tk.Label(self, text='Value')
        newlabel.grid(row=0,column=1)
        newlabel = tk.Label(self, text='Plot')
        newlabel.grid(row=0,column=2)
        self.param_frame = tk.Frame(self,borderwidth=0)
        self.param_frame.grid(row=1,column=0,columnspan=2,rowspan=2,sticky='news')
        self.scroll_can = tk.Canvas(self.param_frame,borderwidth=0)
        self.scrollable = tk.Frame(self.scroll_can)
        scrollbar = tk.Scrollbar(self.param_frame,orient="vertical",command=self.scroll_can.yview)
        self.scroll_can.configure(yscrollcommand=scrollbar.set)
        self.scroll_can.grid(row=0,column=0,sticky='news')
        scrollbar.grid(row=0,column=1,sticky='news')
        self.param_frame.columnconfigure(0,weight=1)
        self.param_frame.rowconfigure(0,weight=1)
        self.scroll_can.create_window((8,4),window=self.scrollable,tags="self.frame",anchor='nw')
        self.scrollable.bind("<Configure>", self.onFrameConfigure)
        output_var = tk.StringVar()
        self.plot_ints = []
        self.checkboxes = []
        self.first_run = True
        label = tk.Label(self.scrollable, text="Initial storage")
        entryval = tk.StringVar()
        self.float_validator = (self.register(self.float_validation), '%d','%i', '%P', '%s', '%S', '%v', '%V', '%W')
        textwidget = tk.Entry(self.scrollable,textvariable=entryval,validate='key', validatecommand=self.float_validator)
        entryval.set("225.4215")
        self.init_storage = textwidget
        labels.append(label)
        label.update()
        textwidget.update()
        row_i = 0
        label.grid(row=row_i, column=0)
        textwidget.grid(row=row_i, column=1)
        row_i+=1
        for match in self.matches:
            label = tk.Label(self.scrollable, text=match[1][0])
            entryval = tk.StringVar()
            textwidget = tk.Entry(self.scrollable, text=match[1][0],textvariable=entryval, validate='key', validatecommand=self.float_validator)
            entryval.set(match[1][1])
            self.entries.append(textwidget)
            labels.append(label)
            label.update()
            textwidget.update()
            label.grid(row=row_i, column=0)
            textwidget.grid(row=row_i, column=1)
            row_i+=1
        self.input_entries = self.entries
        plotlabel = tk.Label(self.scrollable,text='Time Units')
        plotlabel.grid(row=row_i,column=0)
        self.time_unit = tk.StringVar()
        self.time_combobox = ttk.Combobox(self.scrollable,width=20,textvariable=self.time_unit)
        self.time_combobox['values'] = ('seconds','hours','days','months','years')
        self.time_combobox.current(0)
        self.time_divisors = {0:1,'seconds':1,'minutes':scc.minute,'hours':scc.hour,'days':scc.day,'months':scc.year/12,'years':scc.year}
        self.old_timescale = self.time_divisors[self.time_unit.get()]
        self.time_unit.trace('w',self.change_scale)
        if not headless:
            self.update()
        self.entries.append(self.time_combobox)
        self.time_combobox.grid(row=row_i,column=1)
        row_i+=1
        self.labeldict = {}
        for label, x in zip(self.matches, self.input_entries):
            try:
                self.labeldict[label[1][0]]=float(x.get())
            except ValueError:
                x_str = x.get()
                try:
                    self.labeldict[label[1][0]]=float(x.get().replace('e','').replace('-',''))
                except ValueError:
                    raise ValueError('Non-numeric value in parameter definition during creation')
                    self.destroy()

        run_button = tk.Button(self,text="Run",command=self.buttonClick)
        run_button.grid(row=3,column=1)
        self.number_rows = row_i
        self.create_plot()
    def float_validation(self,action,index,value_if_allowed, prior_value, text, validation_type, trigger_type, widget_name):
        if value_if_allowed:
            try:
                float(value_if_allowed)
                return True
            except ValueError:
                try:
                    float(value_if_allowed.replace('e','').replace('-',''))
                    return True
                except ValueError:
                    return False
                return False
        else:
            return False

    def onFrameConfigure(self, event):
        self.scroll_can.configure(scrollregion=self.scroll_can.bbox("all"))
    def onListConfigure(self, event):
        self.cbcanvas.configure(scrollregion=self.cbcanvas.bbox("all"))

    def test_compare(self):
        check_one = np.genfromtxt(self.tmpfile[:-2]+'_out.csv',skip_header=1,delimiter=',')
        check_two = np.genfromtxt(self.gold_path,              skip_header=1,delimiter=',')
        if not np.array_equal(check_one, check_two):
            return sum((check_one[-1,:]-check_two[-1,:])**2) < 1e-10
        else:
            return np.array_equal(check_one, check_two)

    def apply_template(self,vals):
        outstring = self.top_header
        pointer = 0
        try:
            ins = float(self.init_storage.get())
            outstring+='initial_condition = {:f}'.format(ins)
        except ValueError:
            try:
                ins=float(self.init_storage.get().replace('e','').replace('-',''))
                outstring+='initial_condition = {:f}'.format(ins)
            except ValueError:
                raise ValueError('Non-numeric value in initial storage definition')
                self.destroy()

        outstring+=self.bottom_header
        for match in self.matches:
            outstring+=self.filtstring[pointer:match[0][0]]
            outstring+='  [{:s}]\n    type = ConstantPostprocessor\n    execute_on = \'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR\'\n'.format(match[1][0])
            try:
                outstring+='    value = '+str(vals[match[1][0]])+'\n  []\n'
            except ValueError:
                try:
                    ins=float(vals[match[1][0]].replace('e','').replace('-',''))
                    outstring+='    value = '+str(ins)+'\n  []\n'
                except ValueError:
                    raise ValueError('Non-numeric value in parameter definition {:s}'.format(match[1][0]))
                    self.destroy()
            pointer = match[0][1]
        outstring+= self.filtstring[pointer:]
        outstring+=self.footer
        return outstring

    def create_plot(self):
        fig = Figure(figsize=(6,4), dpi=150)
        self.ax = fig.add_subplot(111)
        self.canvas = FigureCanvasTkAgg(fig, master=self)
        self.canvas._tkcanvas.grid(row=2,column=2)
        self.canvas.draw()
        self.toolbar = NavigationToolbar2Tk(self.canvas,self,pack_toolbar=False)
        self.toolbar.update()
        self.toolbar.grid(row=3,column=2)
        self.canvas.mpl_connect("key_press_event", self.on_key_press)
        self.lines = self.ax.plot([],[])
        if not self.headless:
            self.ax.set_xlabel('Time [{:s}]'.format(self.time_unit.get()))
            self.ax.set_ylabel('Tritium [kg]')
            self.ax.set_xlim(0,8.64e8/self.time_divisors[self.time_unit.get()])

    def on_key_press(self,event):
        key_press_handler(event,self.canvas,self.toolbar)

    def buttonClick(self):
        output_string = ""
        for label, x in zip(self.matches, self.input_entries):
            try:
                self.labeldict[label[1][0]]=float(x.get())
            except ValueError:
                x_str = x.get()
                try:
                    self.labeldict[label[1][0]]=float(x.get().replace('e','').replace('-',''))
                except ValueError:
                    raise ValueError('Non-numeric value in parameter definition during creation')
                    self.destroy()

        output_string = self.apply_template(self.labeldict)
        with open(self.tmpfile,'w') as outfile:
            outfile.write(output_string)
        self.proc = subprocess.Popen([self.tmap8_path, '-i',self.tmpfile],stdout=subprocess.PIPE,stderr=subprocess.PIPE,cwd=os.path.dirname(self.tmpfile))
        stdout, stderr = self.proc.communicate()
        with open(self.tmpfile[:-2]+'_out.csv','r') as infile:
            self.data_labels = infile.readline()[:-1].split(',')
            self.iz_data = np.genfromtxt(self.tmpfile[:-2]+'_out.csv',skip_header=1,delimiter=',')
        row_i=1
        self.ax.clear()
        if self.first_run:
            self.cbframe = tk.Frame(self,borderwidth=0)
            self.cbframe.rowconfigure(0,weight=1)
            self.cbframe.columnconfigure(0,weight=1)
            self.cbframe.grid(row=1,column=2,sticky='news')
            self.cbcanvas = tk.Canvas(self.cbframe,borderwidth=0)
            self.cblable = tk.Frame(self.cbcanvas)
            scrollbar = tk.Scrollbar(self.cbframe,orient="vertical",command=self.cbcanvas.yview)
            self.cbcanvas.configure(yscrollcommand=scrollbar.set)
            self.cbcanvas.grid(row=0,column=0,sticky='news')
            scrollbar.grid(row=0,column=1,sticky='nws')
            self.cbcanvas.create_window((8,4),window=self.cblable,tags="self.frame",anchor='nw')
            self.cblable.bind("<Configure>", self.onListConfigure)
            for label in self.data_labels[1:]:
                plotint = tk.IntVar()
                checkbutton = tk.Checkbutton(self.cblable,variable=plotint,onvalue=1,offvalue=0,command=self.update_ydata,text=label)
                self.checkboxes.append(checkbutton)
                self.plot_ints.append(plotint)
                checkbutton.grid(row=row_i, column=2)
                self.cbframe.columnconfigure(row_i,weight=1)
                row_i+=1
            self.first_run = False
        self.update_ydata()
        self.update_plot()
        self.update()

    def update_plot(self):
        i=0
        j=1
        count = sum([x.get() for x in self.plot_ints])
        if count > len(self.ax.get_lines()):
            for indice in range(count - len(self.ax.get_lines())):
                self.ax.plot([],[])
        self.lines = self.ax.get_lines()
        maximum = 0
        minimum = 1e9
        for pli in self.plot_ints:
            if pli.get()>0:
                self.lines[i].set_xdata(self.iz_data[:,0]/self.time_divisors[self.time_unit.get()])
                self.lines[i].set_ydata(self.iz_data[:,j])
                self.lines[i].set_label(self.checkboxes[j-1].cget("text"))
                self.ax.set_xlabel('Time [{:s}]'.format(str(self.time_unit.get())))
                self.ax.set_xlim(0, np.max(self.iz_data[:,0]/self.time_divisors[self.time_unit.get()]))
                maximum = max(np.max(self.iz_data[:,j]), maximum)
                minimum = min(np.min(self.iz_data[:,j]), minimum)
                i+=1
            j+=1
        self.ax.set_ylim(minimum, maximum*1.1)
        if not self.ax.get_legend_handles_labels() == ([], []):
            self.ax.legend(loc='best')
        self.canvas.draw()

    def update_ydata(self):
        self.ax.cla()
        self.ax.set_ylabel('Tritium [kg]')
        count = sum([x.get() for x in self.plot_ints])
        self.ax.plot([]*count,[]*count)
        self.update_plot()

    def change_scale(self,*arg):
        xlims = list(self.ax.get_xlim())
        xlims[0] = xlims[0]*self.old_timescale/self.time_divisors[self.time_unit.get()]
        xlims[1] = xlims[1]*self.old_timescale/self.time_divisors[self.time_unit.get()]
        for line in self.lines:
            data = line.get_xdata()*self.old_timescale/self.time_divisors[self.time_unit.get()]
            line.set_xdata(data)
        self.old_timescale = self.time_divisors[self.time_unit.get()]
        self.ax.set_xlim(xlims)
        self.ax.set_xlabel('Time [{:s}]'.format(self.time_unit.get()))
        self.canvas.draw()
        self.ax.set_ylabel('Tritium [kg]')

    def cleanup(self):
        if self.first_run==False:
            if os.path.exists(self.tmpfile[:-2]+'_out.csv'):
                os.remove(self.tmpfile[:-2]+'_out.csv')
        if os.path.exists(self.tmpfile):
            os.remove(self.tmpfile)
parser = argparse.ArgumentParser(
        description='Graphical interface to run the fuel cycle example with different input parameters')
parser.add_argument('--test',help='for use in TMAP8 testing to verify successful script execution\
        No GUI will be shown when using this flag',action='store_true')
parsed_vals = parser.parse_args()
if parsed_vals.test==True:
    tk.Tk = fake_tk
    tk.Frame = fake_tk
    tk.Label = fake_tk
    tk.StringVar = fake_tk
    tk.Entry = fake_tk
    tk.Canvas = fake_tk
    tk.Button = fake_tk
    tk.Scrollbar = fake_tk
    ttk.Combobox = fake_tk
    tk.Checkbutton = fake_tk
    FigureCanvasTkAgg = fake_tk
    NavigationToolbar2Tk = fake_tk
    tk.IntVar = fake_tk
    window = fuel_cycle_form(headless=True)
    window.buttonClick()
    window.update_plot()
    window.plot_ints[0].set(1)
    window.update_plot()
    assert(window.test_compare()==True)
    #window.mainloop()
    window.destroy()
else:
    if __name__ == "__main__":
        window = fuel_cycle_form()
        icon_obj = PIL.ImageTk.PhotoImage(file=icon_path)
        window.wm_iconphoto(False,icon_obj)
        window.columnconfigure(0,weight=1)
        window.columnconfigure(1,weight=1)
        window.columnconfigure(2,weight=3)
        window.title("Tritium Inventory Plot")
        window.rowconfigure(1,weight=1)
        window.rowconfigure(2,weight=1)
        window.mainloop()

References