dispersion::cold_plasma< T, SAFE_MATH > Class Template Reference

Cold Plasma Disperison function. More...

#include <dispersion.hpp>

Inheritance diagram for dispersion::cold_plasma< T, SAFE_MATH >:

Public Member Functions
virtual graph::shared_leaf< T, SAFE_MATH >	D (graph::shared_leaf< T, SAFE_MATH > w, graph::shared_leaf< T, SAFE_MATH > kx, graph::shared_leaf< T, SAFE_MATH > ky, graph::shared_leaf< T, SAFE_MATH > kz, graph::shared_leaf< T, SAFE_MATH > x, graph::shared_leaf< T, SAFE_MATH > y, graph::shared_leaf< T, SAFE_MATH > z, graph::shared_leaf< T, SAFE_MATH > t, equilibrium::shared< T, SAFE_MATH > &eq)
	Cold Plasma Disperison function.

Additional Inherited Members
Public Types inherited from dispersion::dispersion_function< T, SAFE_MATH >
typedef T	base
	Type def to retrieve the backend base type.
Static Public Attributes inherited from dispersion::dispersion_function< T, SAFE_MATH >
static constexpr bool	safe_math = SAFE_MATH
	Retrieve template parameter of safe math.
Protected Attributes inherited from dispersion::physics< T, SAFE_MATH >
const T	epsion0 = 8.8541878138E-12
	Vacuum permitivity.
const T	mu0 = M_PI*4.0E-7
	Vacuum permeability.
const T	q = 1.602176634E-19
	Fundamental charge.
const T	me = 9.1093837015E-31
	Electron mass.
const T	c = static_cast<T> (1.0)/std::sqrt(epsion0*mu0)
	Speed of light.

Detailed Description

template<jit::float_scalar T, bool SAFE_MATH = false>
class dispersion::cold_plasma< T, SAFE_MATH >

Cold Plasma Disperison function.

Template Parameters

T	Base type of the calculation.
SAFE_MATH	Use Safe Math operations.

Member Function Documentation

D()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual graph::shared_leaf< T, SAFE_MATH > dispersion::cold_plasma< T, SAFE_MATH >::D ( graph::shared_leaf< T, SAFE_MATH >  w, graph::shared_leaf< T, SAFE_MATH >  kx, graph::shared_leaf< T, SAFE_MATH >  ky, graph::shared_leaf< T, SAFE_MATH >  kz, graph::shared_leaf< T, SAFE_MATH >  x, graph::shared_leaf< T, SAFE_MATH >  y, graph::shared_leaf< T, SAFE_MATH >  z, graph::shared_leaf< T, SAFE_MATH >  t, equilibrium::shared< T, SAFE_MATH > &  eq  )

inlinevirtual

Cold Plasma Disperison function.

D = Det[ϵ + nn - n^2I] (1)

[  ϵ_11 ϵ_12 0    ]

ϵ = [ -ϵ_12 ϵ_11 0 ] (2) [ 0 0 ϵ_33 ]

s represents each plasma species.

ϵ_11 = 1 - Σ_s ɑ(s)^2/(1 - ɣ(s)^2) (3) ϵ_12 = -iΣ_s ɣ(s)ɑ(s)^2/(1 - ɣ(s)^2) (4) ϵ_33 = 1 - Σ_s ɑ(s)^2

ɑ(s) is the normalized plasma frequency for a plasma species and ɣ(s) is the normalized cyclotron frequency for each species. Note that electrons have a negative charge.

ɑ = ⍵_p/⍵ (5) ɣ = Ω_c/⍵ (6)

The plasma frequency is defined as

⍵_p^2 = n*q^2/ϵ0m (7) Ω_c = qB/m (8)

Parameters

[in]	w	Omega variable.
[in]	kx	Kx variable.
[in]	ky	Ky variable.
[in]	kz	Kz variable.
[in]	x	x variable.
[in]	y	y variable.
[in]	z	z variable.
[in]	t	Current time.
[in]	eq	The plasma equilibrium.

Implements dispersion::dispersion_function< T, SAFE_MATH >.

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The documentation for this class was generated from the following file:

• graph_framework/dispersion.hpp