Utilities needed for a particle in cell code. More...

#include <numbers>
#include <bit>
#include "piecewise.hpp"
#include "workflow.hpp"
#include "random.hpp"
#include "logical.hpp"

Go to the source code of this file.

Classes
class	graph::apply_u_node< T >
	U Collision node. More...

class	graph::apply_xi_node< T >
	Xi Collision node. More...

class	pic::characteristics< T >
	Characteristic factors. More...

class	pic::parameters< T >
	Parameter Class. More...

class	pic::ion< T >
	ion class. More...

class	pic::mesh< T >
	Mesh class. More...

Namespaces
namespace	graph
	Name space for graph nodes.

Typedefs
template<std::floating_point T>
using	graph::shared_apply_u = std::shared_ptr< apply_u_node< T > >
	Convenience type alias for shared sqrt nodes.

template<std::floating_point T>
using	graph::shared_apply_xi = std::shared_ptr< apply_xi_node< T > >
	Convenience type alias for shared sqrt nodes.

Enumerations
enum	pic::model { pic::hinton , pic::chen }
	Model for coulomb scattering operators. More...

Functions
template<std::floating_point T>
shared_leaf< T >	graph::apply_u (shared_leaf< T > x, shared_leaf< T > i, shared_leaf< T > rand, shared_leaf< T > mof, shared_leaf< T > tbnu_e_dt, shared_leaf< T > A, shared_leaf< T > B)
	Build apply_u node.

template<std::floating_point T>
shared_apply_u< T >	graph::apply_u_cast (shared_leaf< T > x)
	Cast to a apply_u node.

template<std::floating_point T>
shared_leaf< T >	graph::apply_xi (shared_leaf< T > x, shared_leaf< T > i, shared_leaf< T > rand, shared_leaf< T > nu_D_dt)
	Build apply_xi node.

template<std::floating_point T>
shared_apply_xi< T >	graph::apply_xi_cast (shared_leaf< T > x)
	Cast to a apply_u node.

template<std::floating_point T>
std::array< graph::shared_leaf< T >, 3 >	pic::cartesian_to_sphereical (graph::shared_leaf< T > x, graph::shared_leaf< T > y)
	Convert from cartesian to sphereical coordinates.

template<std::floating_point T>
std::array< graph::shared_leaf< T >, 2 >	pic::sphereical_to_cartesian (graph::shared_leaf< T > w, graph::shared_leaf< T > xi, graph::shared_leaf< T > sinphi)
	Convert from sphereical to cartesian coordinates.

template<std::floating_point T, model M>
graph::shared_leaf< T >	pic::build_colision_rate (graph::shared_leaf< T > xab, const T mass_a, const T mass_b, graph::shared_leaf< T > gb, graph::shared_leaf< T > nuab0, graph::shared_leaf< T > erfp_xab)
	Calculate ν_{E}.

template<std::floating_point T, model M>
std::array< graph::shared_leaf< T >, 2 >	pic::build_ion_ion_collision (const ion< T > &ion_a, const ion< T > &ion_b, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params, graph::shared_leaf< T > total_density, graph::shared_leaf< T > total_flux, const graph::shared_random_state< T > state)
	Build ion ion collision.

template<std::floating_point T, model M>
std::array< graph::shared_leaf< T >, 2 >	pic::build_ion_electron_collision (const ion< T > &ion_a, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params, graph::shared_leaf< T > total_density, graph::shared_leaf< T > total_flux, const graph::shared_random_state< T > state)
	Build ion electron collision.

template<std::floating_point T, model M>
std::array< graph::shared_leaf< T >, 2 >	pic::build_common_collision (const ion< T > &ion_a, const characteristics< T > &norms, graph::shared_leaf< T > uxb, graph::shared_leaf< T > tb, graph::shared_leaf< T > nb, const T mass_b, const uint8_t zb2, const T dt, const graph::shared_random_state< T > state)
	Build common collisions graphs for all species.

template<std::floating_point T>
std::array< graph::shared_leaf< T >, 3 >	pic::build_initialization (const pic::ion< T > &ion, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params, const graph::shared_random_state< T > state)
	Build initialization.

template<std::floating_point T>
std::array< graph::shared_leaf< T >, 3 >	pic::build_reinjection (const ion< T > &ion, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params, const graph::shared_random_state< T > state)
	Build reinjected expressions.

template<std::floating_point T>
graph::shared_leaf< T >	pic::build_magnetic_field (graph::shared_leaf< T > x, const characteristics< T > &norms, const parameters< T > &params)
	Build a magnetic field.

template<std::floating_point T, size_t I = 0, mesh< T >::offset O = mesh<T>::center>
graph::shared_leaf< T >	pic::build_density (graph::shared_leaf< T > x, const ion< T > &ion, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params)
	Build expressions for the density.

template<std::floating_point T, size_t I = 0, mesh< T >::offset O = mesh<T>::center>
graph::shared_leaf< T >	pic::build_density_gradient (graph::shared_leaf< T > x, const ion< T > &ion, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params)
	Build expressions for the density gradient.

template<std::floating_point T>
graph::shared_leaf< T >	pic::build_electron_temperature (graph::shared_leaf< T > x, const characteristics< T > &norms)
	Build Expressions for Electron temperature.

template<std::floating_point T, mesh< T >::offset O = mesh<T>::center>
graph::shared_leaf< T >	pic::build_electric_efield (graph::shared_leaf< T > x, const ion< T > &ion, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params)
	Build expressions for the electric field.

template<std::floating_point T>
graph::shared_leaf< T >	pic::build_interpolate_efield (graph::shared_leaf< T > x, const ion< T > &ion, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params)
	Build interpolation expression.

template<std::floating_point T>
std::array< graph::shared_leaf< T >, 3 >	pic::build_F_expressions (const std::array< graph::shared_leaf< T >, 3 > z, const ion< T > &ion, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params)
	Build F expressions.

template<std::floating_point T>
std::array< graph::shared_leaf< T >, 3 >	pic::build_rk4_step (const ion< T > &ion, const mesh< T > &mesh, const characteristics< T > &norms, const parameters< T > &params)
	Build Runga Kutta step update.

Variables
template<std::floating_point T>
constexpr T	pic::c = static_cast<T> (299792458.0)
	Speed of light m/s.

template<std::floating_point T>
constexpr T	pic::epsilon0 = static_cast<T> (8.8541878188E-12)
	Vacuum permitivity F/m.

template<std::floating_point T>
constexpr T	pic::q = static_cast<T> (1.602176634E-19)
	Fundamental charge coulombs.

template<std::floating_point T>
constexpr T	pic::m_hydrogen = static_cast<T> (1.67362192595E-27)
	Hydrogen mass kg.

template<std::floating_point T>
constexpr T	pic::m_atomic = static_cast<T> (1.66053906892E-27)
	Atomic mass.

template<std::floating_point T>
constexpr T	pic::m_electron = static_cast<T> (9.1093837139E-31)
	Electron mass kg.

template<std::floating_point T>
constexpr T	pic::kb = static_cast<T> (1.380649E-23)
	Boltzman constant.

Detailed Description

Utilities needed for a particle in cell code.

Defines graphs for use in Particle In Cell (PIC) codes.

Enumeration Type Documentation

◆ model

enum pic::model

Model for coulomb scattering operators.

Enumerator
hinton	From Hinton 1983 EQ 92 and T.S. Chen 1988 EQ 50.
chen	From T.S. Chen 1988 Report EQ 57 commonly used for NBI.

Function Documentation

◆ build_colision_rate()

template<std::floating_point T, model M>

graph::shared_leaf< T > pic::build_colision_rate	(	graph::shared_leaf< T >	xab,
		const T	mass_a,
		const T	mass_b,
		graph::shared_leaf< T >	gb,
		graph::shared_leaf< T >	nuab0,
		graph::shared_leaf< T >	erfp_xab
	)

Calculate ν_{E}.

Template Parameters

T	Base type of the calculation.
M	The pic::model of the calculation.

Parameters

[in]	xab
[in]	mass_a	Mass of particle a.
[in]	mass_b	Mass of particle b.
[in]	gb
[in]	nuab0
[in]	erfp_xab	Derivaive of error function.

Returns: ν_{E}.

◆ build_common_collision()

template<std::floating_point T, model M>

std::array< graph::shared_leaf< T >, 2 > pic::build_common_collision	(	const ion< T > &	ion_a,
		const characteristics< T > &	norms,
		graph::shared_leaf< T >	uxb,
		graph::shared_leaf< T >	tb,
		graph::shared_leaf< T >	nb,
		const T	mass_b,
		const uint8_t	zb2,
		const T	dt,
		const graph::shared_random_state< T >	state
	)

Build common collisions graphs for all species.

Template Parameters

T	Base type of the calculation.
M	The pic::model of the calculation.

Parameters

[in]	ion_a	Ions for species a.
[in]	norms	A pic::characteristics object.
[in]	uxb
[in]	tb	Temperature of species b.
[in]	nb	Density of species b.
[in]	mass_b	Mass of species b.
[in]	zb2	Z effective squared.
[in]	dt	Time step.
[in]	state	Random state node.

◆ build_density()

template<std::floating_point T, size_t I = 0, mesh< T >::offset O = mesh<T>::center>

graph::shared_leaf< T > pic::build_density	(	graph::shared_leaf< T >	x,
		const ion< T > &	ion,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params
	)

Build expressions for the density.

Template Parameters

T	Base type of the calculation.
I	Mesh index.
O	Mesh offset.

Parameters

[in]	x	The x position.
[in]	ion	A pic::ion object.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.

Returns: The expression for the density.

◆ build_density_gradient()

template<std::floating_point T, size_t I = 0, mesh< T >::offset O = mesh<T>::center>

graph::shared_leaf< T > pic::build_density_gradient	(	graph::shared_leaf< T >	x,
		const ion< T > &	ion,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params
	)

Build expressions for the density gradient.

Template Parameters

T	Base type of the calculation.
I	Mesh index.
O	Mesh offset.

Parameters

[in]	x	The x position.
[in]	ion	A pic::ion object.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.

Returns: The expression for the density.

◆ build_electric_efield()

template<std::floating_point T, mesh< T >::offset O = mesh<T>::center>

graph::shared_leaf< T > pic::build_electric_efield	(	graph::shared_leaf< T >	x,
		const ion< T > &	ion,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params
	)

Build expressions for the electric field.

Template Parameters

T	Base type of the calculation.
O	Mesh offset.

Parameters

[in]	x	The x position.
[in]	ion	A pic::ion object.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.

◆ build_electron_temperature()

template<std::floating_point T>

graph::shared_leaf< T > pic::build_electron_temperature	(	graph::shared_leaf< T >	x,
		const characteristics< T > &	norms
	)

Build Expressions for Electron temperature.

Template Parameters

T	Base type of the calculation.

Parameters

[in]	x	The x position.
[in]	norms	A pic::characteristics object.

Returns: The expressions for the electron temperature.

◆ build_F_expressions()

template<std::floating_point T>

std::array< graph::shared_leaf< T >, 3 > pic::build_F_expressions	(	const std::array< graph::shared_leaf< T >, 3 >	z,
		const ion< T > &	ion,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params
	)

Build F expressions.

Template Parameters

T	Base type of the calculation.

Parameters

[in]	z	Runga Kutta substep.
[in]	ion	A pic::ion object.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.

Returns: the Forces on the particles.

◆ build_initialization()

template<std::floating_point T>

std::array< graph::shared_leaf< T >, 3 > pic::build_initialization	(	const pic::ion< T > &	ion,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params,
		const graph::shared_random_state< T >	state
	)

Build initialization.

Template Parameters

T	Base type of the calculation.

Parameters

[in]	ion	A pic::ion object.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.
[in]	state	Random state node.

Returns: Initialized normalized values for x, v||, and v⟂

◆ build_interpolate_efield()

template<std::floating_point T>

graph::shared_leaf< T > pic::build_interpolate_efield	(	graph::shared_leaf< T >	x,
		const ion< T > &	ion,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params
	)

Build interpolation expression.

Template Parameters

T	Base type of the calculation.

Parameters

[in]	x	The x position.
[in]	ion	A pic::ion object.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.

Returns: The interpolated mesh quantity.

◆ build_ion_electron_collision()

template<std::floating_point T, model M>

std::array< graph::shared_leaf< T >, 2 > pic::build_ion_electron_collision	(	const ion< T > &	ion_a,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params,
		graph::shared_leaf< T >	total_density,
		graph::shared_leaf< T >	total_flux,
		const graph::shared_random_state< T >	state
	)

Build ion electron collision.

Template Parameters

T	Base type of the calculation.
M	The pic::model of the calculation.

Parameters

[in]	ion_a	Ions for species a.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.
[in]	total_density	Accumulated density.
[in]	total_flux	Accumulated total_flux.
[in]	state	Random state node.

◆ build_ion_ion_collision()

template<std::floating_point T, model M>

std::array< graph::shared_leaf< T >, 2 > pic::build_ion_ion_collision	(	const ion< T > &	ion_a,
		const ion< T > &	ion_b,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params,
		graph::shared_leaf< T >	total_density,
		graph::shared_leaf< T >	total_flux,
		const graph::shared_random_state< T >	state
	)

Build ion ion collision.

Template Parameters

T	Base type of the calculation.
M	The pic::model of the calculation.

Parameters

[in]	ion_a	Ions for species a.
[in]	ion_b	Ions for species b.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.
[in,out]	total_density	Accumulated density.
[in,out]	total_flux	Accumulated total_flux.
[in]	state	Random state node.

◆ build_magnetic_field()

template<std::floating_point T>

graph::shared_leaf< T > pic::build_magnetic_field	(	graph::shared_leaf< T >	x,
		const characteristics< T > &	norms,
		const parameters< T > &	params
	)

Build a magnetic field.

Template Parameters

T	Base type of the calculation.

Parameters

[in]	x	The x position.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.

Returns: The expression for the magnetic field.

◆ build_reinjection()

template<std::floating_point T>

std::array< graph::shared_leaf< T >, 3 > pic::build_reinjection	(	const ion< T > &	ion,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params,
		const graph::shared_random_state< T >	state
	)

Build reinjected expressions.

If the particles leave the mesh, reinitalize them using the same initialization.

Template Parameters

T	Base type of the calculation.

Parameters

[in]	ion	A pic::ion object.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.
[in]	state	Random state node.

Returns: Reinjected values for x, v||, and v⟂

◆ build_rk4_step()

template<std::floating_point T>

std::array< graph::shared_leaf< T >, 3 > pic::build_rk4_step	(	const ion< T > &	ion,
		const mesh< T > &	mesh,
		const characteristics< T > &	norms,
		const parameters< T > &	params
	)

Build Runga Kutta step update.

Template Parameters

T	Base type of the calculation.

Parameters

[in]	ion	A pic::ion object.
[in]	mesh	A pic::mesh object.
[in]	norms	A pic::characteristics object.
[in]	params	A pic::parameters object.

Returns: Step update expressions for x, v_para, and x_perp.

◆ cartesian_to_sphereical()

template<std::floating_point T>

std::array< graph::shared_leaf< T >, 3 > pic::cartesian_to_sphereical	(	graph::shared_leaf< T >	x,
		graph::shared_leaf< T >	y
	)

Convert from cartesian to sphereical coordinates.

Template Parameters

T	Base type of the calculation.

Parameters

[in]	x
[in]	y

Returns: The coordinates as sphereical coordinates.

◆ sphereical_to_cartesian()

template<std::floating_point T>

std::array< graph::shared_leaf< T >, 2 > pic::sphereical_to_cartesian	(	graph::shared_leaf< T >	w,
		graph::shared_leaf< T >	xi,
		graph::shared_leaf< T >	sinphi
	)

Convert from sphereical to cartesian coordinates.

Template Parameters

T	Base type of the calculation.

Parameters

[in]	w
[in]	xi
[in]	sinphi

Returns: The coordinates as cartesian coordinates.

Classes

Namespaces

Typedefs

Enumerations

Functions

Variables

Detailed Description

Enumeration Type Documentation

◆ model

Function Documentation

◆ build_colision_rate()

◆ build_common_collision()

◆ build_density()

◆ build_density_gradient()

◆ build_electric_efield()

◆ build_electron_temperature()

◆ build_F_expressions()

◆ build_initialization()

◆ build_interpolate_efield()

◆ build_ion_electron_collision()

◆ build_ion_ion_collision()

◆ build_magnetic_field()

◆ build_reinjection()

◆ build_rk4_step()

◆ cartesian_to_sphereical()

◆ sphereical_to_cartesian()