physics_functions_procedures Submodule

Contains the implementations of various physics routines


Uses


Module Functions

pure module function logLee(Te, ne) result(res)

Calculate Coulomb logarithm for electron-electron collisions (NRL Formulary 2013 page 34 equation a)

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: Te

Electron temperature in eV
real(kind=rk), intent(in) :: ne

Electron density in m^{-3}

Return Value real(kind=rk)

pure module function logLei(Te, ne, Z) result(res)

Calculate Coulomb logarithm for electron-ion collisions (NRL Formulary 2013 page 34 equation b). Assumes Te > TiZm_e/m_i

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: Te

Electron temperature in eV
real(kind=rk), intent(in) :: ne

Electron density in m^{-3}

real(kind=rk), intent(in) :: Z

Ion charge

Return Value real(kind=rk)

pure module function logLii(Z1, Z2, mRatio, n1, n2, T1, T2) result(res)

Calculate Coulomb logarithm for ion-ion collisions (NRL Formulary 2013 page 34 equation c).

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: Z1

Ion charge for first species
real(kind=rk), intent(in) :: Z2

Ion charge for second species
real(kind=rk), intent(in) :: mRatio

Mass ratio m2/m1
real(kind=rk), intent(in) :: n1

First ion species density in m^{-3}

real(kind=rk), intent(in) :: n2

Second ion species density in m^{-3}

real(kind=rk), intent(in) :: T1

First ion temperature in eV
real(kind=rk), intent(in) :: T2

Second ion temperature in eV

Return Value real(kind=rk)

pure module function shPotDrop(massRatio, tempRatio) result(res)

Calculate sheath potential drop for 2 component plasma in units of kTe/e

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: massRatio

Mass ratio me/mi
real(kind=rk), intent(in) :: tempRatio

Ion to electron temperature ratio

Return Value real(kind=rk)

pure module function collTimeei(Te, ne, Z, logL) result(res)

Calculate electron-ion collision time in seconds. This is not the Braginskii time, which can be calculated as this value multiplied by 3 sqrt(pi)/4 .

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: Te

Electron temperature in eV
real(kind=rk), intent(in) :: ne

Electron density in m^{-3}

real(kind=rk), intent(in) :: Z

Ion charge
real(kind=rk), intent(in) :: logL

Coulomb logarithm to be used

Return Value real(kind=rk)

pure module function elPlasmaOscFreq(ne) result(res)

Calculate cold electron plasma oscillation frequency in s^{-1}

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: ne

Electron density in m^{-3}

Return Value real(kind=rk)

pure module function elVthermal(Te) result(res)

Mean thermal electron speed

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: Te

Electron temperature in eV

Return Value real(kind=rk)

pure module function vSonic(Te, Ti, mi, ePolytropic, iPolytropic) result(res)

Sonic speed caclulated as sqrt((ePolyTe + iPolyTi)/mi)

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: Te

Electron temperature in eV
real(kind=rk), intent(in) :: Ti

Ion temperature in eV
real(kind=rk), intent(in) :: mi

Ion mass

real(kind=rk), intent(in) :: ePolytropic

Electron polytropic coefficient
real(kind=rk), intent(in) :: iPolytropic

Ion polytropic coefficient

Return Value real(kind=rk)

pure module function normMaxwellian(n, T, vPoints) result(res)

Returns a normalized stationary Maxwellian evaluated at vPoints. Assumes that velocity and temperature are normalized in such way that m v_0^2/2 = kT_0 , and the returned value is normalized to 1/v_0^(3/2) .

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: n

Density in arbitrary units
real(kind=rk), intent(in) :: T

Temperature in units compatible with velocity grid
real(kind=rk), intent(in), dimension(:) :: vPoints

Velocity grid

Return Value real(kind=rk), allocatable, dimension(:)

pure module function simpleMoment(m, f, vPoints, vWidths, g) result(res)

Returns the m-th moment of passed distribution function harmonic - 4piint(v^(2+m)fdv) . Optionally takes moment of f*g where g conforms to f. The integration is a simple Riemann sum.

Arguments

Type IntentOptional Attributes Name
integer(kind=ik), intent(in) :: m

Moment degree
real(kind=rk), intent(in), dimension(:) :: f

Distribution function to take the moment of
real(kind=rk), intent(in), dimension(:) :: vPoints

Coordinates of cell centres in velocity space
real(kind=rk), intent(in), dimension(:) :: vWidths

Widths of velocity space cells
real(kind=rk), intent(in), optional, dimension(:) :: g

Optional velocity space array to include in moment integral

Return Value real(kind=rk)