Modules

This submodule defines a simple, adiabatic homogeneous medium in Cartesian geometry. The geometry can be overridden using the parfile.

This submodule defines an equilibrium in cylindrical geometry with a constant axial current. The geometry can be overridden using the parfile.

This submodule defines a magnetic flux tube embedded in a uniform magnetic environment. In this case the flux tube is under coronal conditions $c_s < c_A < c_{Ae}$ where the subscript e denotes the outer region. More specifically the equilibrium is defined as $c_{Ae} = 5c_s, c_{se} = c_s/2, c_A = 2c_s$. The geometry can be overridden in the parfile, and is cylindrical by default for $r \in [0, 10]$.

This submodule defines a steady plane Couette flow in a Cartesian geometry with flow and viscosity.

This submodule defines an equilibrium in cylindrical geometry with an axial current profile ($\nu = 2$), modelling a solar coronal loop in which discrete Alfvén waves are present. The geometry can be overridden in the parfile.

This submodule defines flow driven instabilities in a Cartesian geometry. This equilibrium can not be called explicitly from the parfile, but rather acts as a "parent setup" for the Rayleigh-Taylor and Kelvin-Helmholtz submodules which use this specific kind of equilibrium but with different parameters. This submodule is called within its implicit children.

This submodule defines a Gold-Hoyle equilibrium in cylindrical geometry. This equilibrium configuration models a filament with a uniform twist such that all fieldlines perform an equal amount of turns around the cylinder axis. The geometry can be overridden in the parfile.

This submodule defines an equilibrium in Cartesian geometry with a stratified equilibrium profile, giving rise to gravito-acoustic waves. No magnetic fields are included, such that this treats the hydrodynamic regime. The geometry can be overridden using the parfile.

This submodule defines an equilibrium in Cartesian geometry with a stratified equilibrium profile, giving rise to gravito-MHD waves. The geometry can be overridden using the parfile.

This submodule defines a resistive equilibrium with tearing modes created by a Harris sheet.

This submodule defines an exponentially stratified medium in Cartesian geometry with a constant gravity term and magnetic shear. The geometry can be overridden in the parfile.

This submodule defines internal kink modes in force-free magnetic fields. The geometry is cylindrical with parabolic density and velocity profiles, The geometry can be overridden in the parfile.

This submodule defines an equilibrium in Cartesian geometry with a stratified equilibrium profile, representing a solar magnetic atmosphere. The equilibrium is isothermal with a constant magnetic field. The scale height is given by $$H = \frac{\text{cte_T0}}{g}$$ The geometry is fixed to Cartesian, boundaries can be overridden using the parfile.

This submodule defines an unperturbed magnetised jet model in cylindrical geometry, giving rise to Kelvin-Helmholtz and current-driven instabilities. The geometry is fixed for this problem; the cylinder wall is dependent on the equilibrium parameters and is given by 2rj.

This submodule defines Kelvin-Helmholtz instabilities in Cartesian geometry. This equilibrium is a specific case of the flow driven instabilities. No magnetic fields are considered in this case (pure HD).

This submodule defines an equilibrium containing magnetothermal instabilities in a cylindrical geometry. The geometry can be overridden in the parfile.

This submodule defines magneto-rotational instabilities in an accretion disk. Due to the special nature of this equilibrium x_start is hardcoded to one and can not be overridden in the parfile, the same goes for the geometry which is hardcoded to 'cylindrical'. The outer edge can be chosen freely. This equilibrium is chosen in such a way that the angular rotation is of order unity, implying Keplerian rotation. The thin-disk approximation is valid with small magnetic fields, but still large enough to yield magneto-rotational instabilities. Gravity is assumed to go like $g \thicksim 1/r^2$.

This submodule defines a magnetic flux tube embedded in a uniform magnetic environment. In this case the flux tube is under photospheric conditions $c_{Ae} < c_s < c_{se} < c_A$ where the subscript e denotes the outer region. More specifically the equilibrium is defined as $c_{Ae} = c_s/2, c_{se} = 3c_s/2, c_A = 2c_s$. The geometry can be overridden in the parfile, and is cylindrical by default for $r \in [0, 10]$.

This submodule defines a simple, homogeneous medium in Cartesian geometry with a constant resistivity value. The geometry can be overridden using the parfile.

This submodule defines an equilibrium in Cartesian geometry with a constant resistivity value. Parameters are taken in such a way as to allow for resistive tearing modes. The geometry can be overridden using the parfile.

This submodule defines an equilibrium in Cartesian geometry with a flow profile and a constant resistivity value. Parameters are taken in such a way as to allow for resistive tearing modes. The geometry can be overridden using the parfile.

This submodule defines an inhomogeneous medium in Cartesian geometry with a constant resistivity value. Two (constant) density profiles are defined which are connected by a sine profile, representing the interface inbetween. This density profile allows for resonant absorption, the geometry can be overridden in the parfile.

This submodule defines a cylindrical equilibrium, resembling a rotating plasma cylinder. The geometry can be overridden using the parfile.

This submodule defines Rayleigh-Taylor instabilities in Cartesian geometry. This equilibrium is a specific case of the flow driven instabilities.

This submodule defines Rayleigh-Taylor and Kelvin-Helmholtz instabilities in Cartesian geometry. This equilibrium is a specific case of the flow driven instabilities.

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 submodule defines a cylindrical equilibrium in which a Suydam surface is present, such that this gives rises to Suydam cluster modes. The geometry can be overriden using the parfile.

This submodule defines a steady Taylor-Couette flow in a cylindrical geometry where a fluid is confined between two (rotating) coaxial cylinders (without a magnetic field).

This submodule defines a steady Taylor-Couette flow in a cylindrical geometry where a plasma is confined between two (rotating) coaxial cylinders with an azimuthal magnetic field and constant resistivity.

Example submodule for numerically-defined equilibria.

Submodule for user-defined equilibria. Look at the examples in the equilibria subdirectory or consult the website for more information.

Main module for the Arnoldi-type solvers. Contains interfaces to the general Arnoldi procedures (general, shift-invert, etc.).

Module containing the implementation for the ARPACK general-type solver, that is, given the general eigenvalue problem $$AX = \omega BX,$$ find $k$ eigenvalues that satisfy a given criterion.

Module containing the implementation for the ARPACK shift-invert-type solver, that is, given the general eigenvalue problem $$AX = \omega BX,$$ choose a shift $\sigma$ and solve the problem $$(A - \sigma B)X = \omega X,$$ thereby finding $k$ eigenvalues of the shifted problem that satisfy a given criterion.

Submodule containing the implementation of the inverse iteration algorithm. TODO more docs

Submodule containing the implementation of the QR-cholesky algorithm. Using LAPACKS's zpbtrf and BLAS's zgbtrs, the original problem is written as a standard eigenvalue problem as $$U^{-H}\mathcal{A}U^{-1}\textbf{Y} = \omega\textbf{Y}\ $$ where $\mathcal{B} = U^HU$ is positive definite and $\textbf{Y}=U\textbf{X}$. Eventually a call to LAPACK's zgeev routine is done to obtain all eigenvalues and eigenvectors.

Submodule containing the implementation of the QR-invert algorithm. The original problem is written as a standard eigenvalue problem through $$\mathcal{B}^{-1}\mathcal{A}\textbf{X} = \omega\textbf{X}\ $$ . This is done using a LU decomposition via LAPACKS's zgbsv. Eventually a call to LAPACK's zgeev routine is done to obtain all eigenvalues and eigenvectors.

Submodule containing the implementation of the QZ-direct algorithm. We keep the general form of the eigenvalue problem $$\mathcal{A}\textbf{X} = \omega\mathcal{B}\textbf{X}\ $$ and solve this directly by calling LAPACK's zggev3 routine.