smod_equil_RTI_theta_pinch Submodule

This submodule defines Rayleigh-Taylor instabilities in rotating theta pinches. The straight cylinder approximation is used with a constant angular frequency. Density and pressure profiles decrease over the domain, with a uni-directional increasing magnetic field profile. Mode numbers $k = 0$ correspond to HD Rayleigh-Taylor instabilities, while $k \neq 0$ represent MHD RTIs. The geometry is hardcoded to 'cylindrical', the domain is forced to $0 <= r <= 1$ through division by x_end.

This equilibrium is taken from section IV in Goedbloed, J. P. "The Spectral Web of stationary plasma equilibria. II. Internal modes." Physics of Plasmas 25.3 (2018): 032110. and also appears in section 13.4, figs. 13.11 to 13.15 in Goedbloed, H., Keppens, R., & Poedts, S. (2019). Magnetohydrodynamics of Laboratory and Astrophysical Plasmas. Cambridge University Press. DOI.

Contents

Variables

width B_inf bigO

Functions

fx dfx rho0 drho0 T0 v02 dv02 B03 dB03

Module Procedures

RTI_theta_pinch_eq

Variables

Type	Visibility	Attributes		Name		Initial
real(kind=dp),	private		::	width
real(kind=dp),	private		::	B_inf
real(kind=dp),	private		::	bigO

Functions

function fx(r)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	r

Return Value real(kind=dp)

function dfx(r)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	r

Return Value real(kind=dp)

function rho0(r)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	r

Return Value real(kind=dp)

function drho0(r)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	r

Return Value real(kind=dp)

function T0()

Arguments

None

Return Value real(kind=dp)

function v02(r)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	r

Return Value real(kind=dp)

function dv02()

Arguments

None

Return Value real(kind=dp)

function B03(r)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	r

Return Value real(kind=dp)

function dB03(r)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	r

Return Value real(kind=dp)

Module Procedures

module procedure RTI_theta_pinch_eq module module subroutine RTI_theta_pinch_eq(settings, grid, background, physics) Interface →

Arguments

Type	Intent	Optional	Attributes		Name
type(settings_t),	intent(inout)			::	settings
type(grid_t),	intent(inout)			::	grid
type(background_t),	intent(inout)			::	background
type(physics_t),	intent(inout)			::	physics