ChargeDensityAccumulator

Accumulator used to evaluate the inner product of the particle charge density and the test function required for solving electromagnetic equations.

Overview

In SALAMANDER the charge density $var element = document.getElementById("moose-equation-13d41584-a5a8-44c8-a1cd-c7e4023a7888");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ is defined as

$(1)var element = document.getElementById("moose-equation-225f2cf1-de97-4445-b744-aff6a2d7daf9");katex.render(" \\rho \\left( \\vec{r}\\, \\right) = \\sum_{i=1}^N q_i w_i \\delta \\left( \\vec{r} - \\vec{r}_i \\right),", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-1782df52-027b-44f6-b155-ca0e1c728a6e");katex.render("N", element, {displayMode:false,throwOnError:false});$ is the number of computational particles in the simulation, $var element = document.getElementById("moose-equation-3499e2e9-16c4-47cc-ba69-a558ce92f6ff");katex.render("q_i", element, {displayMode:false,throwOnError:false});$ is the charge of the $var element = document.getElementById("moose-equation-e277c020-9628-4a98-acdb-119282540b92");katex.render("i^\\text{th}", element, {displayMode:false,throwOnError:false});$ particle, $var element = document.getElementById("moose-equation-39ee985c-1d8b-4616-99b2-926b91cb98c5");katex.render("w_i", element, {displayMode:false,throwOnError:false});$ is the weight of the $var element = document.getElementById("moose-equation-6dbe021c-a38d-4529-b206-592b59126f54");katex.render("i^\\text{th}", element, {displayMode:false,throwOnError:false});$ particle, and $var element = document.getElementById("moose-equation-437984ab-2ec9-4652-b61b-31dbe0a853d4");katex.render("\\vec{r}_i", element, {displayMode:false,throwOnError:false});$ is the position at which the $var element = document.getElementById("moose-equation-e7880616-3390-472a-a6ed-f7b8d89ecac7");katex.render("i^\\text{th}", element, {displayMode:false,throwOnError:false});$ computational particle exists.

Electrostatic PIC

In electrostatic PIC simulations the electric field is indirectly solved for by first solving for the electrostatic potential, $var element = document.getElementById("moose-equation-6540f7d5-72d8-4346-be0f-c4001b722d4b");katex.render("\\phi", element, {displayMode:false,throwOnError:false});$ , using Poisson's equation

$(2)var element = document.getElementById("moose-equation-7a60adcc-a0b0-46a3-8e55-58e46b310c6a");katex.render(" -\\nabla^2 \\phi = \\frac{\\rho}{\\varepsilon_0}", element, {displayMode:true,throwOnError:false});$

The weak form of this takes the form

$(3)var element = document.getElementById("moose-equation-620a6ac3-39ef-4f1d-9751-9182bc197585");katex.render(" \\left< - \\varepsilon_0 \\nabla^2 \\phi, \\psi \\right> - \\left< \\rho, \\psi \\right> = 0.", element, {displayMode:true,throwOnError:false});$

The second term of the weak form of Poisson's equation can then be evaluated as

$(4)var element = document.getElementById("moose-equation-805fc529-68b9-448d-a0fb-729ca73dea6d");katex.render(" \\left< \\rho, \\psi_j \\right> = \\sum_{i=1}^{M} q_i \\psi_j \\left( \\vec{r}_i \\right),", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-117b2574-9fd1-48f1-9512-ffe9e59426f9");katex.render("M", element, {displayMode:false,throwOnError:false});$ is the number of particles which exist on the subdomain where the $var element = document.getElementById("moose-equation-ec1f7eaf-74c3-4a70-81d4-5a8c07246000");katex.render("j^\\text{th}", element, {displayMode:false,throwOnError:false});$ test function $var element = document.getElementById("moose-equation-fee297b7-5d57-442e-afa9-202531db0cb6");katex.render("\\psi_j", element, {displayMode:false,throwOnError:false});$ is non-zero. This objects evaluates this source term directly and accumulates the result directly into the residual of the variable representing $var element = document.getElementById("moose-equation-8d20731d-6408-4145-82c4-4589c44255fe");katex.render("\\phi", element, {displayMode:false,throwOnError:false});$ .

This object was verified with the test case found in (test/tests/userobjects/particle_quantity_accumulation/simple_potential_solve.i). This is the same verification case as presented in Gall et al. (2024) only the inner product of the charge density source term and the finite element test function is evaluated directly.

note

This representation of the charge density means that direct knowledge of the charge density is lost and only the inner product can be evaluated.

note

The execute_on parameter of this object is set to PRE_KERNELS and is not available to be set by the user.

Example Input Syntax

[UserObjects<<<{"href": "../../syntax/UserObjects/index.html"}>>>]
  [stepper]
    type = TestSimpleStepper
  []

  [initializer]
    type = TestPlacedParticleInitializer
    start_points = '0 0 0
                    0.25 0 0
                    0.5 0 0
                    0.75 0 0
                    1 0 0'
    start_velocities = '0 0 0
                        0 0 0
                        0 0 0
                        0 0 0
                        0 0 0'
    charge = 0.5
    weight = 1
  []

  [study]
    type = TestInitializedPICStudy
    stepper = stepper
    initializer = initializer
    use_custom_rayids = false
    always_cache_traces = true
    data_on_cache_traces = true
    execute_on = 'TIMESTEP_BEGIN'
  []

  [accumulator]
    type = ChargeDensityAccumulator<<<{"description": "Accumulator used to evaluate the inner product of the particle charge density and the test function required for solving electromagnetic equations.", "href": "ChargeDensityAccumulator.html"}>>>
    study<<<{"description": "The PICStudy that owns the charged particles"}>>> = study
    variable<<<{"description": "The variable to contribute to the residual of"}>>> = phi
    extra_vector_tags<<<{"description": "The extra tags for the vectors this Kernel should fill"}>>> = dump_value
  []
[]

Input Parameters

studyThe PICStudy that owns the charged particles
C++ Type:UserObjectName
Controllable:No
Description:The PICStudy that owns the charged particles
variableThe variable to contribute to the residual of
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The variable to contribute to the residual of

Required Parameters

matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/userobjects/particle_initializer/per_element/errors/errors.i)
(test/tests/userobjects/particle_initializer/per_element/elements/initializer_base.i)
(test/tests/benchmarking/lieberman.i)
(test/tests/userobjects/particle_quantity_accumulation/simple_potential_solve.i)

References

Grayson S. Gall, Logan H. Harbour, Casey T. Icenhour, Pierre-Clement A. Simon, Derek Gaston, and Amanda M. Lietz. Kinetic plasma simulation in the moose framework: verification of electrostatic particle in cell capabilities. ANS Transactions, 2024.

@article{gall2024verification,
    author = "Gall, Grayson S. and Harbour, Logan H. and Icenhour, Casey T. and Simon, Pierre-Clement A. and Gaston, Derek and Lietz, Amanda M.",
    title = "Kinetic Plasma Simulation in the MOOSE Framework: Verification of Electrostatic Particle In Cell Capabilities",
    journal = "ANS Transactions",
    year = "2024",
    publisher = "ANS PBNC Conference"
}

(test/tests/userobjects/particle_quantity_accumulation/simple_potential_solve.i)

[Mesh/gmg]
  type = GeneratedMeshGenerator
  dim = 1
  nx = 4
  xmax = 1
[]

[Problem]
  extra_tag_vectors = dump_value
[]

[Variables]
  [phi]
  []
[]

[Kernels]
  [poissons]
    type = ADMatDiffusion
    diffusivity = 1
    variable = phi
  []
[]

[BCs/zero]
  type = DirichletBC
  variable = phi
  value = 0
  boundary = 'left right'
  preset = false
[]

[AuxVariables/dump_value]
[]

[AuxKernels/dump_value]
  type = TagVectorAux
  variable = dump_value
  vector_tag = dump_value
  v = phi
[]

[UserObjects]
  [stepper]
    type = TestSimpleStepper
  []

  [initializer]
    type = TestPlacedParticleInitializer
    start_points = '0 0 0
                    0.25 0 0
                    0.5 0 0
                    0.75 0 0
                    1 0 0'
    start_velocities = '0 0 0
                        0 0 0
                        0 0 0
                        0 0 0
                        0 0 0'
    charge = 0.5
    weight = 1
  []

  [study]
    type = TestInitializedPICStudy
    stepper = stepper
    initializer = initializer
    use_custom_rayids = false
    always_cache_traces = true
    data_on_cache_traces = true
    execute_on = 'TIMESTEP_BEGIN'
  []

  [accumulator]
    type = ChargeDensityAccumulator
    study = study
    variable = phi
    extra_vector_tags = dump_value
  []
[]

[RayKernels]
  [null]
    type = NullRayKernel
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(test/tests/userobjects/particle_quantity_accumulation/simple_potential_solve.i)

[Mesh/gmg]
  type = GeneratedMeshGenerator
  dim = 1
  nx = 4
  xmax = 1
[]

[Problem]
  extra_tag_vectors = dump_value
[]

[Variables]
  [phi]
  []
[]

[Kernels]
  [poissons]
    type = ADMatDiffusion
    diffusivity = 1
    variable = phi
  []
[]

[BCs/zero]
  type = DirichletBC
  variable = phi
  value = 0
  boundary = 'left right'
  preset = false
[]

[AuxVariables/dump_value]
[]

[AuxKernels/dump_value]
  type = TagVectorAux
  variable = dump_value
  vector_tag = dump_value
  v = phi
[]

[UserObjects]
  [stepper]
    type = TestSimpleStepper
  []

  [initializer]
    type = TestPlacedParticleInitializer
    start_points = '0 0 0
                    0.25 0 0
                    0.5 0 0
                    0.75 0 0
                    1 0 0'
    start_velocities = '0 0 0
                        0 0 0
                        0 0 0
                        0 0 0
                        0 0 0'
    charge = 0.5
    weight = 1
  []

  [study]
    type = TestInitializedPICStudy
    stepper = stepper
    initializer = initializer
    use_custom_rayids = false
    always_cache_traces = true
    data_on_cache_traces = true
    execute_on = 'TIMESTEP_BEGIN'
  []

  [accumulator]
    type = ChargeDensityAccumulator
    study = study
    variable = phi
    extra_vector_tags = dump_value
  []
[]

[RayKernels]
  [null]
    type = NullRayKernel
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(test/tests/userobjects/particle_initializer/per_element/errors/errors.i)

[Problem]
  solve = false
[]

[GlobalParams]
  particles_per_element = 10
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Distributions]
  [zero]
    type = Constant
    value = 0.0
  []
[]

[UserObjects]
  [initializer]
    type = PerElementParticleInitializer
    mass = 1
    charge = 1
    number_density = 2
    velocity_distributions = 'zero zero zero'
  []

  [stepper]
    type = TestSimpleStepper
  []

  [study]
    type = TestInitializedPICStudy
    initializer = initializer
    stepper = stepper
    always_cache_traces = true
    data_on_cache_traces = true
    execute_on=TIMESTEP_BEGIN
  []

  [potential_accumulator]
    type = ChargeDensityAccumulator
    study = study
    variable = phi
    extra_vector_tags = dump_value
  []

  [density_accumulator]
    type = ChargeDensityAccumulator
    study = study
    variable = n
  []
[]


[RayKernels]
  [null]
    type = NullRayKernel
  []
[]

[Executioner]
  type = Steady
[]

(test/tests/userobjects/particle_initializer/per_element/elements/initializer_base.i)

# the number of computational particles to be put in each element
particles_per_element = 10
# the analytic solution for the charge density
# set by cli args for each case since it is needed by all
# tests but changes based on the dimension of the problem
charge_density = 0

[GlobalParams]
  particles_per_element = ${particles_per_element}
[]

[Problem]
  extra_tag_vectors = dump_value
[]

[Variables]
  [phi]
  []

  [n]
  []
[]

[Kernels]
  [poissons]
    type = ADMatDiffusion
    diffusivity = 1
    variable = phi
  []

  [projection]
    type = ProjectionKernel
    variable = n
  []
[]


[AuxVariables]
  [dump_value]
  []
[]

[AuxKernels]
  [dump_value]
    type = TagVectorAux
    variable = dump_value
    vector_tag = dump_value
    v = phi
  []
[]

[Distributions]
  [zero]
    type = Constant
    value = 0.0
  []
[]

[UserObjects]
  [initializer]
    type = PerElementParticleInitializer
    mass = 1
    charge = 1
    number_density = ${charge_density}
    velocity_distributions = 'zero zero zero'
  []

  [stepper]
    type = TestSimpleStepper
  []

  [study]
    type = TestInitializedPICStudy
    initializer = initializer
    stepper = stepper
    always_cache_traces = true
    data_on_cache_traces = true
    execute_on=TIMESTEP_BEGIN
  []

  [potential_accumulator]
    type = ChargeDensityAccumulator
    study = study
    variable = phi
    extra_vector_tags = dump_value
  []

  [density_accumulator]
    type = ChargeDensityAccumulator
    study = study
    variable = n
  []
[]


[RayKernels]
  [null]
    type = NullRayKernel
  []
[]

[Functions]
  [charge_density]
    type = ParsedFunction
    expression = ${charge_density}
  []
[]


[Postprocessors]
  [potential_l2]
    type = ElementL2Error
    variable = phi
    function = potential
  []

  [density_l2]
    type = ElementL2Error
    variable = n
    function = charge_density
  []

  [particles_per_element]
    type = ConstantPostprocessor
    value = ${particles_per_element}
  []

  [h]
    type = AverageElementSize
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -pc_factor_mat_solver'
  petsc_options_value = 'lu NONZERO 1.e-9 superlu_dists'
  line_search = 'none'
  nl_max_its = 15
  l_max_its = 300
  scheme = 'bdf2'
  automatic_scaling = true
  compute_scaling_once = false
  dt = 1
  num_steps = 1
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    execute_on = TIMESTEP_END
  []
  [rays]
    type = RayTracingExodus
    study = study
    output_data_names = 'charge weight mass'
    execute_on = TIMESTEP_END
  []
[]

(test/tests/benchmarking/lieberman.i)

# The input reproduces the results in Principles of Plasma Discharge and Material Processing
# ISBN 0-471-72001-1 chapter 1, pages 26-27
# the initial uniform number density to represent
# with particles
number_density = 1e16 # [m^-3]
# domain length
l = 0.1 # [m]
# permittivity of free space
eps_0 = 8.85e-12 # [F/m]
# Argon mass
m = 6.64e-26 # [kg]
# particle charge, singly charged ion
q = 1.602e-19 # [C]
# number of elements being used
num_elem = 100
# number of points to sample the potential at
# this should be at every node in the domain
num_samples = ${fparse num_elem + 1}

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = ${num_elem}
    xmax = ${l}
  []
  allow_renumbering = false
[]

[Variables]
  [phi]
  []

  [n]
  []
[]

[Kernels]
  [poissons]
    type = ADMatDiffusion
    diffusivity = ${eps_0}
    variable = phi
  []

  [projection]
    type = ProjectionKernel
    variable = n
  []
[]

[BCs/zero]
  type = DirichletBC
  variable = phi
  boundary = 'left right'
  value = 0
[]

[Functions]
  [potential_ic_func]
    type = ParsedFunction
    symbol_names = 'l q n_i eps_0'
    symbol_values = '${l} ${q} ${number_density} ${eps_0}'
    expression = '0.5 * q * n_i / eps_0 * ((l / 2)^2 - (x-l/2)^2)'
  []
[]

[ICs]
  [potential_ic]
    type = FunctionIC
    variable = phi
    function = 'potential_ic_func'
  []
[]

[AuxVariables]
  [Ex]
    order = CONSTANT
    family = MONOMIAL
  []
  [Ey]
  []
  [Ez]
  []
[]

[AuxKernels]
  [grad_potential]
    type = NegativeVariableGradientComponent
    variable = Ex
    gradient_variable = phi
    component = 0
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Distributions]
  [zero]
    type = Constant
    value = 0
  []
[]

[UserObjects]
  [stepper]
    type = LeapFrogStepper
    field_components = 'Ex Ey Ez'
  []

  [initializer]
    type = UniformGridParticleInitializer
    mass = ${m}
    charge = ${q}
    total_particles = 100
    number_density = ${number_density}
    velocity_distributions = 'zero zero zero'
  []

  [study]
    type = TestInitializedPICStudy
    stepper = stepper
    initializer = initializer
    always_cache_traces = true
    data_on_cache_traces = true
    particles_per_element = 1
    execute_on = 'TIMESTEP_BEGIN'
  []

  [charge_accumulator]
    type = ChargeDensityAccumulator
    study = study
    variable = phi
  []

  [density_accumulator]
    type = NumberDensityAccumulator
    study = study
    variable = n
  []
[]

[RayBCs]
  [reflect]
    type = KillRayBC
    boundary = 'left right'
    study = study
  []
[]

[RayKernels]
  [null]
    type = NullRayKernel
  []
[]

[Postprocessors]
  [ray_count]
    type = RayTracingStudyResult
    study = study
    result = 'total_rays_started'
    execute_on = 'TIMESTEP_END'
  []
[]


[VectorPostprocessors]
  [ray_data]
    type = TestParticleDataVectorPostprocessor
    additional_ray_data_outputs = 'mass charge weight'
    study = study
    execute_on = TIMESTEP_END
  []

  [potential]
    type = LineValueSampler
    variable = phi
    start_point = '0 0 0'
    end_point = '${l} 0 0'
    num_points = ${num_samples}
    sort_by = 'x'
    execute_on = TIMESTEP_END
  []
[]


[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -pc_factor_mat_solver'
  petsc_options_value = 'lu NONZERO 1.e-9 superlu_dists'
  line_search = 'none'
  nl_max_its = 15
  l_max_its = 300
  scheme = 'bdf2'
  automatic_scaling = true
  compute_scaling_once = false
  dt = 1e-10
  end_time = 2.6e-8
  # num_steps = 1
[]
[Outputs]
  exodus = true
  [particle_population]
    type = CSV
    file_base = 'lieberman'
    show = 'ray_count'
    execute_on = TIMESTEP_END
  []
  [csv_initial]
    type = CSV
    file_base = 'lieberman_i'
    show = 'ray_data potential'
    end_step = 1
    execute_on = TIMESTEP_END
  []
  [csv_final]
    type = CSV
    file_base = 'lieberman_f'
    show = 'ray_data potential'
    execute_on = FINAL
  []
[]

(test/tests/userobjects/particle_quantity_accumulation/simple_potential_solve.i)

[Mesh/gmg]
  type = GeneratedMeshGenerator
  dim = 1
  nx = 4
  xmax = 1
[]

[Problem]
  extra_tag_vectors = dump_value
[]

[Variables]
  [phi]
  []
[]

[Kernels]
  [poissons]
    type = ADMatDiffusion
    diffusivity = 1
    variable = phi
  []
[]

[BCs/zero]
  type = DirichletBC
  variable = phi
  value = 0
  boundary = 'left right'
  preset = false
[]

[AuxVariables/dump_value]
[]

[AuxKernels/dump_value]
  type = TagVectorAux
  variable = dump_value
  vector_tag = dump_value
  v = phi
[]

[UserObjects]
  [stepper]
    type = TestSimpleStepper
  []

  [initializer]
    type = TestPlacedParticleInitializer
    start_points = '0 0 0
                    0.25 0 0
                    0.5 0 0
                    0.75 0 0
                    1 0 0'
    start_velocities = '0 0 0
                        0 0 0
                        0 0 0
                        0 0 0
                        0 0 0'
    charge = 0.5
    weight = 1
  []

  [study]
    type = TestInitializedPICStudy
    stepper = stepper
    initializer = initializer
    use_custom_rayids = false
    always_cache_traces = true
    data_on_cache_traces = true
    execute_on = 'TIMESTEP_BEGIN'
  []

  [accumulator]
    type = ChargeDensityAccumulator
    study = study
    variable = phi
    extra_vector_tags = dump_value
  []
[]

[RayKernels]
  [null]
    type = NullRayKernel
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

Overview
Electrostatic PIC
Example Input Syntax
Input Parameters
Input Files
References