ExtrinsicStaticTrappingMaterial

Overview

This class implements the trapping material class for the case where additional extrinsic trapping sites have previously been created due to the influence of heavy particle bombardment.

Note the transient class exists for cases where traps conitnue to be created over time. This class aims only to maintain the final state after some period of particle implantation is complete and the precise distribution of new traps is required for subsequent transport calculations.

Note there are a number of complimentary classes for use in cases where extrinsic trap creation is taking place or has taken place:

ExtrinsicTransientTrappingMaterial for the case of ongoing bombardment and trap creation
ExtrinsicStaticTrappingMaterial for constant temperature cases after the creation process has ended
ExtrinsicStaticTrappingMaterialRamptingT for cases with a constant temperature ramp after the creation process has ended, for example in the case of thermal desorption

Basic material properties

As with all trapping material classes this object calculates the Diffusion coefficient and trapping/detrapping reaction rates which are required by Achlys kernels. Eq. (1), Eq. (2), and Eq. (3) show the equations implemented to achieve this.

$var element = document.getElementById("moose-equation-9f071f1b-683f-44b7-aa8c-41bf3a9bd1ae");katex.render("D", element, {displayMode:false,throwOnError:false});$ is the diffusivity of the species through some material in units of $var element = document.getElementById("moose-equation-388d65f2-4ff2-43c5-ad67-5c9832fc00fe");katex.render("m^{2}s^{-1}", element, {displayMode:false,throwOnError:false});$ . $(1)var element = document.getElementById("moose-equation-bfbbbd8a-7109-442a-bedc-eb5ea34791ed");katex.render(" D(T) = D_0 \\exp \\left( -E_{diff} / k_{B} T \\right)", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-e741dcb5-fb13-46f0-b237-7a0f0c3ff066");katex.render("\\nu_{m}", element, {displayMode:false,throwOnError:false});$ , in units of $var element = document.getElementById("moose-equation-1c04f679-f429-424b-bfe0-5fa0739e5616");katex.render("m^{3}s^{-1}", element, {displayMode:false,throwOnError:false});$ , is the reaction rate for the trapping process and is modelled by Eq. (2) where $var element = document.getElementById("moose-equation-34ceec52-b080-44f9-a1bc-0fd26d4f689d");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$ is the lattice constant in $var element = document.getElementById("moose-equation-173a0f77-037b-49f3-8231-6ff5b14ab810");katex.render("m", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-2036d765-74b8-461c-9632-39bebc0351f1");katex.render("N_{sol}", element, {displayMode:false,throwOnError:false});$ is the number density of solute sites in the material. $(2)var element = document.getElementById("moose-equation-73f82fb2-6e22-4547-a8db-f8bb15f891cf");katex.render(" \\nu_{m} = \\frac{D(T)}{\\lambda^2 N_{sol}}", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-4cf13416-80af-4818-ac4f-dec04a62de0d");katex.render("\\nu_{i}", element, {displayMode:false,throwOnError:false});$ , in units of $var element = document.getElementById("moose-equation-2cb97b0b-201b-4669-bb4c-61939b5dbd6f");katex.render("s^{-1}", element, {displayMode:false,throwOnError:false});$ , is the reaction rate for the de-trapping process from the $var element = document.getElementById("moose-equation-b6ecbd80-4d00-4c1e-8b87-655895f19b65");katex.render("i", element, {displayMode:false,throwOnError:false});$ -th trapping site. This is modelled by the Arrhenius type equation as given by Equation Eq. (3) where E is the energy barrier a trapped atom must overcome to leave the site and $var element = document.getElementById("moose-equation-780db370-5b63-4c7a-a7f7-5f06637f9a6f");katex.render("\\nu_{0}", element, {displayMode:false,throwOnError:false});$ is referred to as the attempt frequency. $(3)var element = document.getElementById("moose-equation-58763547-0ca0-40f3-ba5b-40a250709e9d");katex.render(" \\nu_{i} = \\nu_0 \\exp \\left( -E_{i} / k_{B} T \\right)", element, {displayMode:true,throwOnError:false});$

Trap creation

The rate of extrinsic trap creation in Tungsten irradiated with a particle fluence above $var element = document.getElementById("moose-equation-2db6193d-ddc7-42e7-91f6-e602ab0516c0");katex.render("1 \\times 10^{18} \\text{D \\:m}^{2}\\text{s}^{-1}", element, {displayMode:false,throwOnError:false});$ is given by Bonnin et al. (2015) and Ogorodnikova et al. (2003) as shown in equation Eq. (4). This accounts for 2 trap-creation processes each parameterised by a creation rate, $var element = document.getElementById("moose-equation-adb1d118-fe80-45a7-b1e1-db64530bdd0e");katex.render("\\eta_i", element, {displayMode:false,throwOnError:false});$ , and a maximum trap density, $var element = document.getElementById("moose-equation-10831a62-127d-4bfe-9a54-2a54408f938a");katex.render("n_i", element, {displayMode:false,throwOnError:false});$ .

$(4)var element = document.getElementById("moose-equation-a40e9c58-392c-44e5-9105-1039505c08e6");katex.render("\\frac{dN_{3}}{dt} = (1 - r) \\phi \\left[ \\left(1-\\frac{N_3}{n_{3a,max}}\\right)\\eta_a f(x) + \\left(1-\\frac{N_3}{n_{3b,max}}\\right)\\eta_b\\theta(x) \\right] ", element, {displayMode:true,throwOnError:false});$

This is implemented in the Extrinsic Trapping Material classes according to Eq. (5)

$(5)var element = document.getElementById("moose-equation-09fdc5d6-9c5f-4a3f-a422-acc708fb0992");katex.render("N(x,t) = A\\left[ 1-\\exp\\left( -(1-r)\\phi \\left[ \\frac{\\eta_a f(x)}{n_{a,max}} + \\frac{\\eta_b \\theta(x)}{n_{b,max}} \\right] t \\right) \\right] ", element, {displayMode:true,throwOnError:false});$

Where the factor, $var element = document.getElementById("moose-equation-d203db18-4253-470a-a4f6-f96259b17c3e");katex.render("A", element, {displayMode:false,throwOnError:false});$ , in Eq. (5) is given by the expression in Eq. (6)

$(6)var element = document.getElementById("moose-equation-2e56f962-681b-4bce-9f5e-3e9d889b8657");katex.render("A = \\frac{n_{a,max}n_{b,max} \\left(f(x)\\eta_a + \\theta(x)\\eta_b \\right)}{n_{a,max}\\theta(x)\\eta_b + n_{b,max}f(x)\\eta_a} ", element, {displayMode:true,throwOnError:false});$

Table 1: Symbol meanings

Parameter Name	Symbol(s)	Unit
Trap Concentration	$var element = document.getElementById("moose-equation-8cea0741-d278-42a2-b54f-bbbb2c5fd7bf");katex.render("N_i", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-58e39af7-009f-42b6-b242-011cd6d40a19");katex.render("m^{-3}", element, {displayMode:false,throwOnError:false});$
Flux	$var element = document.getElementById("moose-equation-751522fe-2f63-4c94-9604-b2af2e8a0a82");katex.render("\\phi", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-d307f9a9-22c6-450c-b709-3b1505a4816e");katex.render("m^{-2}\\:s^{-1}", element, {displayMode:false,throwOnError:false});$
Flux reflection fraction	$var element = document.getElementById("moose-equation-21847d51-6e21-4dd0-be70-c79a2bfa868d");katex.render("r", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-a9caca85-22cf-4c8f-9902-58cf5cbb37a7");katex.render("[]", element, {displayMode:false,throwOnError:false});$
Flux distribution function	$var element = document.getElementById("moose-equation-f9bbb6d4-83cd-4214-8357-82140f3c259d");katex.render("f(x)", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-fbabbbbf-34dd-4902-9487-42b436e81db3");katex.render("m^{-3} / m^{-2}", element, {displayMode:false,throwOnError:false});$
Trap creation rate	$var element = document.getElementById("moose-equation-73560772-e8f9-461d-a8b8-350212fe9cb8");katex.render("\\eta_{i}", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-583d3baa-03da-48ac-8eb8-e4e646a722b8");katex.render("s^{-1}", element, {displayMode:false,throwOnError:false});$
Plastic deformation depth	$var element = document.getElementById("moose-equation-8a0866a1-4f17-47ad-8501-a7a435da0f7c");katex.render("x_p", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-9d4c50a3-0cef-4776-85ce-c2d78a4d93dc");katex.render("m", element, {displayMode:false,throwOnError:false});$
Plastic deformation function	$var element = document.getElementById("moose-equation-54dd4849-b3c4-40d1-a6f2-87301a548569");katex.render("\\theta(x)", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-4bf0866b-8378-496b-b252-321ca43cc42d");katex.render("m^{-1}", element, {displayMode:false,throwOnError:false});$

Example Input File Syntax

[Variables]
  [./Mobile]
    initial_condition = 0.0
  [../]
  [./Trapped_1]
    initial_condition = 0.0
  [../]
  [./Trapped_2]
    initial_condition = 0.0
  []
  [./Trapped_3]
    initial_condition = 0.0
  []
[]

[Materials]
  [./implant]
    type = ExtrinsicStaticTrappingMaterial
    # Energies
    E_diff = 0.39
    E1 = 0.87
    E2 = 1.0
    E3 = 1.5
    k_boltz = 8.617333E-5
    # pre-exponential rate constants
    v0 = 1.0E13
    D0 = 4.1E-7
    lambda = 1.1E-10
    # unused
    rho = 1 # unecessary scaling factor, do not use
    # site densities
    n_sol = 6
    n1 = 1E-3 #1.0E25
    n2 = 4e-4
    n3a_max = 1e-1
    n3b_max = 1e-2
    # trap creation rates
    eta_a = 6e-4
    eta_b = 2e-4
    trap_evolution_time = 400
    # flux distribution parameters
    flux = 4e-10
    function = Gaussian_implant
    xp = 1e-6
    #Temperature
    const_T = 300
    block = 'Tungsten' #'Implantation_region'
    # thermal properties
    conductivity = 150 # W/K
    Cp = 137 # J/(kg K)
    density = 19300 # kg/m3
  [../]
[]

[Functions]
  [./Gaussian_implant]
    type = ParsedFunction
    value = 'scale * exp( -0.5 * ((x - mean) / sd)^2)'
    vars = 'scale mean sd'
    vals = '0.93e8 4.5e-9 4.5e-9'
  [../]
[]

Input Parameters

CpSpecific heat in J/kg/K
C++ Type:double
Options:
Description:Specific heat in J/kg/K
D0The diffusion pre-exponential factor
C++ Type:double
Options:
Description:The diffusion pre-exponential factor
E1Trap detrapping energy in eV
C++ Type:double
Options:
Description:Trap detrapping energy in eV
E2Trap detrapping energy in eV
C++ Type:double
Options:
Description:Trap detrapping energy in eV
E3Trap detrapping energy in eV
C++ Type:double
Options:
Description:Trap detrapping energy in eV
E_diffdiffusion energy in eV
C++ Type:double
Options:
Description:diffusion energy in eV
conductivityThermal conductivity in W/K
C++ Type:double
Options:
Description:Thermal conductivity in W/K
const_Tplaceholder for temperature
C++ Type:double
Options:
Description:placeholder for temperature
densityMaterial density in kg/m3
C++ Type:double
Options:
Description:Material density in kg/m3
eta_aTrap creation rate - "a" type
C++ Type:double
Options:
Description:Trap creation rate - "a" type
eta_bTrap creation rate - "b" type
C++ Type:double
Options:
Description:Trap creation rate - "b" type
fluxScaled implantation flux
C++ Type:double
Options:
Description:Scaled implantation flux
k_boltzBoltzman constant
C++ Type:double
Options:
Description:Boltzman constant
lambdaLattice constant in m-1
C++ Type:double
Options:
Description:Lattice constant in m-1
n1possible trapping sites
C++ Type:double
Options:
Description:possible trapping sites
n2possible trapping sites
C++ Type:double
Options:
Description:possible trapping sites
n3a_maxMaximum trap density - "a" type
C++ Type:double
Options:
Description:Maximum trap density - "a" type
n3b_maxMaximum attainted trap density - "b" type
C++ Type:double
Options:
Description:Maximum attainted trap density - "b" type
n_soldensity of interstitial sites
C++ Type:double
Options:
Description:density of interstitial sites
rhomaterial density in m^-3
C++ Type:double
Options:
Description:material density in m^-3
trap_evolution_timePrevious flux exposure time for trap distribution calculation
C++ Type:double
Options:
Description:Previous flux exposure time for trap distribution calculation
v0pre-exponential detrapping factor in Arrhenious eq.
C++ Type:double
Options:
Description:pre-exponential detrapping factor in Arrhenious eq.
xpregion where trap3 exists
C++ Type:double
Options:
Description:region where trap3 exists

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Options:
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this boundary condition applies
C++ Type:std::vector<BoundaryName>
Options:
Description:The list of boundaries (ids or names) from the mesh where this boundary condition applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Options:
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Options:
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
function0The function describing the implantation flux distribution
Default:0
C++ Type:FunctionName
Options:
Description:The function describing the implantation flux distribution
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
Options:
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.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
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
Options:
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

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Options:
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

Input Files

(problems/thermal_desorption/ogorodnikova/tds_multiapp/resting_multi.i)

References

X. Bonnin, E. Hodille, N. Ning, C. Sang, and Ch. Grisolia. Rate equations modeling for hydrogen inventory studies during a real tokamak material thermal cycle. Journal of Nuclear Materials, 463:970–973, 2015. PLASMA-SURFACE INTERACTIONS 21. URL: https://www.sciencedirect.com/science/article/pii/S0022311514007375, doi:https://doi.org/10.1016/j.jnucmat.2014.10.053.

@article{BONNIN2015,
    author = "Bonnin, X. and Hodille, E. and Ning, N. and Sang, C. and Grisolia, Ch.",
    title = "Rate equations modeling for hydrogen inventory studies during a real tokamak material thermal cycle",
    journal = "Journal of Nuclear Materials",
    volume = "463",
    pages = "970-973",
    year = "2015",
    note = "PLASMA-SURFACE INTERACTIONS 21",
    issn = "0022-3115",
    doi = "https://doi.org/10.1016/j.jnucmat.2014.10.053",
    url = "https://www.sciencedirect.com/science/article/pii/S0022311514007375",
    abstract = "Prediction and control of tritium inventory in plasma-facing components (PFCs) is a critical nuclear safety issue for ITER and future fusion devices. This goal can be achieved through rate equations models as presented here. We calibrate our models with thermal desorption spectrometry results to obtain a validated set of material parameters relevant to hydrogen inventory processes in bulk tungsten. The best fits are obtained with two intrinsic trap types, deep and shallow, and an extrinsic trap created by plasma irradiation and plastic deformation of the tungsten matrix associated with blister formation. We then consider a realistic cycle of plasma discharges consisting of 400s of plasma exposure followed by a resting period of 1000s, repeating for several hours. This cycle is then closed by a long “overnight” period, thus providing an estimate of the amount of tritium retained in the PFCs after a full day of standard operation."
}

O.V Ogorodnikova, J Roth, and M Mayer. Deuterium retention in tungsten in dependence of the surface conditions. Journal of Nuclear Materials, 313-316:469–477, 2003. Plasma-Surface Interactions in Controlled Fusion Devices 15. URL: https://www.sciencedirect.com/science/article/pii/S0022311502013752, doi:https://doi.org/10.1016/S0022-3115(02)01375-2.

@article{OGOROD2003,
    author = "Ogorodnikova, O.V and Roth, J and Mayer, M",
    title = "Deuterium retention in tungsten in dependence of the surface conditions",
    journal = "Journal of Nuclear Materials",
    volume = "313-316",
    pages = "469-477",
    year = "2003",
    note = "Plasma-Surface Interactions in Controlled Fusion Devices 15",
    issn = "0022-3115",
    doi = "https://doi.org/10.1016/S0022-3115(02)01375-2",
    url = "https://www.sciencedirect.com/science/article/pii/S0022311502013752",
    keywords = "Deuterium, Tungsten, Retention, Implantation",
    abstract = "The paper reviews hydrogen isotope retention and migration in tungsten (W). Due to a large scatter of the deuterium (D) retention database, new measurements of ion-driven D retention in polycrystalline W foil have been performed to clarify the mechanism of hydrogen isotope inventory in W. Deuterium retention has been investigated as a function of ion fluence, implantation temperature, incident energy and surface conditions. Special attention has been given on the investigation of D retention in thin films of tungsten carbide and tungsten oxide which can be formed on W surface in a fusion device. Such kinds of films increase the D retention in W. Several points are reviewed: (i) inventory in pure W, (ii) inventory in W pre-implanted by carbon ions and (iii) inventory in tungsten oxide."
}

(problems/thermal_desorption/ogorodnikova/tds_multiapp/resting_multi.i)

[Mesh]
 [./unlabelled]
    file = /Users/sdixon/projects/blue_kite/problems/thermal_desorption/optimisation/ogorodnikova_1k.msh
    type = FileMeshGenerator
    construct_side_list_from_node_list=true
  [../]
  [./block_1]
    type= AllSideSetsByNormalsGenerator
    input = unlabelled
    #fixed_normal = false
  [../]
[]

[Problem]
  type = FEProblem # This is the "normal" type of Finite Element Problem in MOOSE
  coord_type = XYZ # cartesian
[]

[Variables]
  [./Mobile]
    initial_condition = 0.0
  [../]
  [./Trapped_1]
    initial_condition = 0.0
  [../]
  [./Trapped_2]
    initial_condition = 0.0
  []
  [./Trapped_3]
    initial_condition = 0.0
  []
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    x = '0 1e-4 5e-4 1e-3'
    y = '1e-4 1e-4 5e-4 5e-4'
  [../]
  [./Gaussian_implant]
    type = ParsedFunction
    value = 'scale * exp( -0.5 * ((x - mean) / sd)^2)'
    vars = 'scale mean sd'
    vals = '0.93e8 4.5e-9 4.5e-9'
  [../]
  [./Exponweib_implant]
    type = ParsedFunction
    value = 'peak * (a * c / scale) * (( 1 - exp(-1 * (((x*1e9)-loc)/scale)^c))^(a-1) ) * exp(-1 * (((x*1e9)-loc)/scale)^c)*(((x*1e9)-loc)/scale)^(c-1)'
    vars = 'peak a c loc scale'
    vals = '5.82e8 0.90 1.96 -0.013 4.909'
  [../]
[]

[MultiApps]
  [sub_app]
    type = FullSolveMultiApp
    #app_type = BlueKiteApp
    input_files = 'implant_sub.i'
   # positions = '0   0.029   0
   #              0.015 0.0.029 0
   #              0.015 0.014 0
   #              0.0 0.014 0'
  execute_on = INITIAL
  clone_master_mesh = true
  []
[]

[Transfers]
#   [to_sub] 
#    type = MultiAppCopyTransfer
#    multi_app = sub_app
#    source_variable = 'surface_temp'
#    variable = 'surface_temp'
#    direction = to_multiapp
#  []
  [mobile_transfer]
    type =  MultiAppCopyTransfer #MultiAppScalarToAuxScalarTransfer
    multi_app = sub_app
    source_variable = 'Mobile'
    variable = 'Mobile'
    direction = from_multiapp
  []
  [trap_1_transfer]
    type =  MultiAppCopyTransfer #MultiAppScalarToAuxScalarTransfer
    multi_app = sub_app
    source_variable = 'Trapped_1'
    variable = 'Trapped_1'
    direction = from_multiapp
  []
  [trap_2_transfer]
    type =  MultiAppCopyTransfer #MultiAppScalarToAuxScalarTransfer
    multi_app = sub_app
    source_variable = 'Trapped_2'
    variable = 'Trapped_2'
    direction = from_multiapp
  []
  [trap_3_transfer]
    type =  MultiAppCopyTransfer #MultiAppScalarToAuxScalarTransfer
    multi_app = sub_app
    source_variable = 'Trapped_3'
    variable = 'Trapped_3'
    direction = from_multiapp
  []
[]

[Kernels]
  [./H3_diffusion_eq1]
    type = ADMatDiffusion
    variable = Mobile
    Diffusivity = D
  [../]
  [./mobile_time_deriv]
    type = ADTimeDerivative
    variable = Mobile
  [../]
  [./trapping_equilibrium_equation1]
    type = ADTrappingEquilibriumEquation
    variable = Trapped_1
    v = Mobile
    n_traps = n1
    vi = V1
  [../]
  [./trapping_equilibrium_equation2]
    type = ADTrappingEquilibriumEquation
    variable = Trapped_2
    v = Mobile
    n_traps = n2
    vi = V2
  [../]
  [./trapping_equilibrium_equation3]
    type = ADTrappingEquilibriumEquation
    variable = Trapped_3
    v = Mobile
    n_traps = n3
    vi = V3
  [../]
  [./trapped_time_deriv_couple]
    type = ADCoupledTimeDerivative
    variable = Mobile
    v = Trapped_1
  [../]
  [./trapped_time_deriv_couple2]
    type = ADCoupledTimeDerivative
    variable = Mobile
    v = Trapped_2
  [../]
  [./trapped_time_deriv_couple3]
    type = ADCoupledTimeDerivative
    variable = Mobile
    v = Trapped_3
  [../]
  [./trapped_time_deriv]
    type = ADTimeDerivative
    variable = Trapped_1
  [../]     
  [./trapped_time_deriv2]
    type = ADTimeDerivative
    variable = Trapped_2
  [../]
  [./trapped_time_deriv3]
    type = ADTimeDerivative
    variable = Trapped_3
  [../]
[]

[Postprocessors]
  [/pfc_flux]
    type = ADSideFluxIntegral
    variable = Mobile
    boundary = 1
    diffusivity = D
  [../]
  [/back_flux]
    type = ADSideFluxIntegral
    variable = Mobile
    boundary = 2
    diffusivity = D
  [../]
  [./total_mobile]
    type = VariableIntegral
    variable = Mobile
  [../]
  [./total_trap_1]
    type = VariableIntegral
    variable = Trapped_1
  [../]
    [./total_trap_2]
    type = VariableIntegral
    variable = Trapped_2
  [../]
  [./total_trap_3]
    type = VariableIntegral
    variable = Trapped_3
  [../]
[]

[BCs]
  [./desorption]
    type =  ADDirichletBC
    variable = Mobile
    boundary = 1
    value = 0
  [../]
  [./back_desorption]
    type =  ADDirichletBC
    variable = Mobile
    boundary = 2
    value = 0
  [../]
[]

[Materials]
   [./implant]
    type = ExtrinsicStaticTrappingMaterial
# Energies
    E_diff = 0.39
    E1 = 0.87
    E2 = 1.0
    E3 = 1.5
    k_boltz = 8.617333E-5
# pre-exponential rate constants
    v0 = 1.0E13
    D0 = 4.1E-7
    lambda = 1.1E-10
# unused
    rho = 1 # unecessary scaling factor, do not use
# site densities
    n_sol = 6
    n1 = 1E-3 #1.0E25
    n2 = 4e-4
    n3a_max = 1e-1
    n3b_max = 1e-2
# trap creation rates
    eta_a = 6e-4
    eta_b = 2e-4
    trap_evolution_time = 400
# flux distribution parameters
    flux = 4e-10
    function = Gaussian_implant
    xp = 1e-6
#Temperature
    const_T = 300
    block = 'Tungsten' #'Implantation_region'
# thermal properties
    conductivity = 150 # W/K
    Cp = 137 # J/(kg K)
    density = 19300 # kg/m3
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  scheme = bdf2
  automatic_scaling=True
 compute_scaling-once=False
  scaling_group_variables = 'Trapped_3; Trapped_2; Trapped_1; Mobile'
  resid_vs_jac_scaling_param = 0.8
  l_tol = 1e-4
  l_max_its = 100
  nl_max_funcs = 7
#  nl_rel_tol = 1e-7
  nl_abs_tol = 1e-29

  # Set PETSc parameters to optimize solver efficiency
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_shift_type'
  petsc_options_value = 'bcgs lu  NONZERO'
  end_time = 50
  timestep_tolerance = 0.01
  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 4
    cutback_factor = 0.8
    growth_factor = 1.5
    dt = 0.05
  []
[]


[Outputs]
  #execute_on = 'timestep_end'
  exodus = false # Output Exodus format
  csv = true
[]
[Debug]
  show_material_props = true
  show_var_residual_norms = true
[]

(problems/thermal_desorption/ogorodnikova/tds_multiapp/resting_multi.i)

[Mesh]
 [./unlabelled]
    file = /Users/sdixon/projects/blue_kite/problems/thermal_desorption/optimisation/ogorodnikova_1k.msh
    type = FileMeshGenerator
    construct_side_list_from_node_list=true
  [../]
  [./block_1]
    type= AllSideSetsByNormalsGenerator
    input = unlabelled
    #fixed_normal = false
  [../]
[]

[Problem]
  type = FEProblem # This is the "normal" type of Finite Element Problem in MOOSE
  coord_type = XYZ # cartesian
[]

[Variables]
  [./Mobile]
    initial_condition = 0.0
  [../]
  [./Trapped_1]
    initial_condition = 0.0
  [../]
  [./Trapped_2]
    initial_condition = 0.0
  []
  [./Trapped_3]
    initial_condition = 0.0
  []
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    x = '0 1e-4 5e-4 1e-3'
    y = '1e-4 1e-4 5e-4 5e-4'
  [../]
  [./Gaussian_implant]
    type = ParsedFunction
    value = 'scale * exp( -0.5 * ((x - mean) / sd)^2)'
    vars = 'scale mean sd'
    vals = '0.93e8 4.5e-9 4.5e-9'
  [../]
  [./Exponweib_implant]
    type = ParsedFunction
    value = 'peak * (a * c / scale) * (( 1 - exp(-1 * (((x*1e9)-loc)/scale)^c))^(a-1) ) * exp(-1 * (((x*1e9)-loc)/scale)^c)*(((x*1e9)-loc)/scale)^(c-1)'
    vars = 'peak a c loc scale'
    vals = '5.82e8 0.90 1.96 -0.013 4.909'
  [../]
[]

[MultiApps]
  [sub_app]
    type = FullSolveMultiApp
    #app_type = BlueKiteApp
    input_files = 'implant_sub.i'
   # positions = '0   0.029   0
   #              0.015 0.0.029 0
   #              0.015 0.014 0
   #              0.0 0.014 0'
  execute_on = INITIAL
  clone_master_mesh = true
  []
[]

[Transfers]
#   [to_sub] 
#    type = MultiAppCopyTransfer
#    multi_app = sub_app
#    source_variable = 'surface_temp'
#    variable = 'surface_temp'
#    direction = to_multiapp
#  []
  [mobile_transfer]
    type =  MultiAppCopyTransfer #MultiAppScalarToAuxScalarTransfer
    multi_app = sub_app
    source_variable = 'Mobile'
    variable = 'Mobile'
    direction = from_multiapp
  []
  [trap_1_transfer]
    type =  MultiAppCopyTransfer #MultiAppScalarToAuxScalarTransfer
    multi_app = sub_app
    source_variable = 'Trapped_1'
    variable = 'Trapped_1'
    direction = from_multiapp
  []
  [trap_2_transfer]
    type =  MultiAppCopyTransfer #MultiAppScalarToAuxScalarTransfer
    multi_app = sub_app
    source_variable = 'Trapped_2'
    variable = 'Trapped_2'
    direction = from_multiapp
  []
  [trap_3_transfer]
    type =  MultiAppCopyTransfer #MultiAppScalarToAuxScalarTransfer
    multi_app = sub_app
    source_variable = 'Trapped_3'
    variable = 'Trapped_3'
    direction = from_multiapp
  []
[]

[Kernels]
  [./H3_diffusion_eq1]
    type = ADMatDiffusion
    variable = Mobile
    Diffusivity = D
  [../]
  [./mobile_time_deriv]
    type = ADTimeDerivative
    variable = Mobile
  [../]
  [./trapping_equilibrium_equation1]
    type = ADTrappingEquilibriumEquation
    variable = Trapped_1
    v = Mobile
    n_traps = n1
    vi = V1
  [../]
  [./trapping_equilibrium_equation2]
    type = ADTrappingEquilibriumEquation
    variable = Trapped_2
    v = Mobile
    n_traps = n2
    vi = V2
  [../]
  [./trapping_equilibrium_equation3]
    type = ADTrappingEquilibriumEquation
    variable = Trapped_3
    v = Mobile
    n_traps = n3
    vi = V3
  [../]
  [./trapped_time_deriv_couple]
    type = ADCoupledTimeDerivative
    variable = Mobile
    v = Trapped_1
  [../]
  [./trapped_time_deriv_couple2]
    type = ADCoupledTimeDerivative
    variable = Mobile
    v = Trapped_2
  [../]
  [./trapped_time_deriv_couple3]
    type = ADCoupledTimeDerivative
    variable = Mobile
    v = Trapped_3
  [../]
  [./trapped_time_deriv]
    type = ADTimeDerivative
    variable = Trapped_1
  [../]     
  [./trapped_time_deriv2]
    type = ADTimeDerivative
    variable = Trapped_2
  [../]
  [./trapped_time_deriv3]
    type = ADTimeDerivative
    variable = Trapped_3
  [../]
[]

[Postprocessors]
  [/pfc_flux]
    type = ADSideFluxIntegral
    variable = Mobile
    boundary = 1
    diffusivity = D
  [../]
  [/back_flux]
    type = ADSideFluxIntegral
    variable = Mobile
    boundary = 2
    diffusivity = D
  [../]
  [./total_mobile]
    type = VariableIntegral
    variable = Mobile
  [../]
  [./total_trap_1]
    type = VariableIntegral
    variable = Trapped_1
  [../]
    [./total_trap_2]
    type = VariableIntegral
    variable = Trapped_2
  [../]
  [./total_trap_3]
    type = VariableIntegral
    variable = Trapped_3
  [../]
[]

[BCs]
  [./desorption]
    type =  ADDirichletBC
    variable = Mobile
    boundary = 1
    value = 0
  [../]
  [./back_desorption]
    type =  ADDirichletBC
    variable = Mobile
    boundary = 2
    value = 0
  [../]
[]

[Materials]
   [./implant]
    type = ExtrinsicStaticTrappingMaterial
# Energies
    E_diff = 0.39
    E1 = 0.87
    E2 = 1.0
    E3 = 1.5
    k_boltz = 8.617333E-5
# pre-exponential rate constants
    v0 = 1.0E13
    D0 = 4.1E-7
    lambda = 1.1E-10
# unused
    rho = 1 # unecessary scaling factor, do not use
# site densities
    n_sol = 6
    n1 = 1E-3 #1.0E25
    n2 = 4e-4
    n3a_max = 1e-1
    n3b_max = 1e-2
# trap creation rates
    eta_a = 6e-4
    eta_b = 2e-4
    trap_evolution_time = 400
# flux distribution parameters
    flux = 4e-10
    function = Gaussian_implant
    xp = 1e-6
#Temperature
    const_T = 300
    block = 'Tungsten' #'Implantation_region'
# thermal properties
    conductivity = 150 # W/K
    Cp = 137 # J/(kg K)
    density = 19300 # kg/m3
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  scheme = bdf2
  automatic_scaling=True
 compute_scaling-once=False
  scaling_group_variables = 'Trapped_3; Trapped_2; Trapped_1; Mobile'
  resid_vs_jac_scaling_param = 0.8
  l_tol = 1e-4
  l_max_its = 100
  nl_max_funcs = 7
#  nl_rel_tol = 1e-7
  nl_abs_tol = 1e-29

  # Set PETSc parameters to optimize solver efficiency
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_shift_type'
  petsc_options_value = 'bcgs lu  NONZERO'
  end_time = 50
  timestep_tolerance = 0.01
  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 4
    cutback_factor = 0.8
    growth_factor = 1.5
    dt = 0.05
  []
[]


[Outputs]
  #execute_on = 'timestep_end'
  exodus = false # Output Exodus format
  csv = true
[]
[Debug]
  show_material_props = true
  show_var_residual_norms = true
[]

Overview
Basic material properties
Trap creation
Example Input File Syntax
Input Parameters
Input Files
References

Module

Examples

Source Code

Comparison to Analytical Solution

Thermal Desorption Spectrum

Kernels

BCs

Materials

Postprocessors