dommaschk_equilibrium_m Module

[*] W. Dommaschk, "Representations for vacuum potentials in stellarators", Computer Physics Communications 40, pg. 203 (1986)

Definition of Dommaschk potentials [*]. Fully 3D equilibrium


Uses

  • module~~dommaschk_equilibrium_m~~UsesGraph module~dommaschk_equilibrium_m dommaschk_equilibrium_m module~constants_m constants_m module~dommaschk_equilibrium_m->module~constants_m module~descriptors_m descriptors_m module~dommaschk_equilibrium_m->module~descriptors_m module~elementary_functions_m elementary_functions_m module~dommaschk_equilibrium_m->module~elementary_functions_m module~equilibrium_m equilibrium_m module~dommaschk_equilibrium_m->module~equilibrium_m module~error_handling_m error_handling_m module~dommaschk_equilibrium_m->module~error_handling_m module~euclidean_geo_m euclidean_geo_m module~dommaschk_equilibrium_m->module~euclidean_geo_m module~fieldline_tracer_m fieldline_tracer_m module~dommaschk_equilibrium_m->module~fieldline_tracer_m module~interpolation_m interpolation_m module~dommaschk_equilibrium_m->module~interpolation_m module~kisslinger_m kisslinger_m module~dommaschk_equilibrium_m->module~kisslinger_m module~params_equi_dommaschk_m params_equi_dommaschk_m module~dommaschk_equilibrium_m->module~params_equi_dommaschk_m module~polygon_m polygon_m module~dommaschk_equilibrium_m->module~polygon_m module~precision_m precision_m module~dommaschk_equilibrium_m->module~precision_m module~screen_io_m screen_io_m module~dommaschk_equilibrium_m->module~screen_io_m module~status_codes_m status_codes_m module~dommaschk_equilibrium_m->module~status_codes_m module~constants_m->module~precision_m module~descriptors_m->module~screen_io_m module~elementary_functions_m->module~precision_m module~equilibrium_m->module~precision_m module~error_handling_m->module~precision_m module~error_handling_m->module~screen_io_m module~error_handling_m->module~status_codes_m module~comm_handling_m comm_handling_m module~error_handling_m->module~comm_handling_m mpi mpi module~error_handling_m->mpi netcdf netcdf module~error_handling_m->netcdf module~euclidean_geo_m->module~precision_m module~fieldline_tracer_m->module~equilibrium_m module~fieldline_tracer_m->module~error_handling_m module~fieldline_tracer_m->module~precision_m module~fieldline_tracer_m->module~screen_io_m module~fieldline_tracer_m->module~status_codes_m dop853_constants dop853_constants module~fieldline_tracer_m->dop853_constants dop853_module dop853_module module~fieldline_tracer_m->dop853_module module~fieldline_tracer_m->module~comm_handling_m module~interpolation_m->module~descriptors_m module~interpolation_m->module~error_handling_m module~interpolation_m->module~precision_m module~interpolation_m->module~screen_io_m module~interpolation_m->module~status_codes_m module~kisslinger_m->module~constants_m module~kisslinger_m->module~error_handling_m module~kisslinger_m->module~precision_m module~kisslinger_m->module~screen_io_m module~kisslinger_m->module~status_codes_m module~list_operations_m list_operations_m module~kisslinger_m->module~list_operations_m module~params_equi_dommaschk_m->module~error_handling_m module~params_equi_dommaschk_m->module~precision_m module~params_equi_dommaschk_m->module~screen_io_m module~params_equi_dommaschk_m->module~status_codes_m iso_fortran_env iso_fortran_env module~params_equi_dommaschk_m->iso_fortran_env parallax_build_info_m parallax_build_info_m module~params_equi_dommaschk_m->parallax_build_info_m module~polygon_m->module~descriptors_m module~polygon_m->module~precision_m module~polygon_m->module~screen_io_m ieee_arithmetic ieee_arithmetic module~polygon_m->ieee_arithmetic module~polygon_m->iso_fortran_env module~polygon_m->module~comm_handling_m module~polygon_m->mpi module~polygon_m->netcdf iso_c_binding iso_c_binding module~precision_m->iso_c_binding module~precision_m->iso_fortran_env module~precision_m->mpi module~precision_m->netcdf module~screen_io_m->module~precision_m module~screen_io_m->iso_fortran_env module~screen_io_m->netcdf module~comm_handling_m->mpi module~list_operations_m->module~precision_m module~list_operations_m->module~screen_io_m

Used by

  • module~~dommaschk_equilibrium_m~~UsedByGraph module~dommaschk_equilibrium_m dommaschk_equilibrium_m module~dommaschk_equilibrium_netcdf_s dommaschk_equilibrium_netcdf_s module~dommaschk_equilibrium_netcdf_s->module~dommaschk_equilibrium_m module~equilibrium_factory_m equilibrium_factory_m module~equilibrium_factory_m->module~dommaschk_equilibrium_m module~map_factory_s map_factory_s module~map_factory_s->module~dommaschk_equilibrium_m program~benchmark_helmholtz_solvers benchmark_helmholtz_solvers program~benchmark_helmholtz_solvers->module~equilibrium_factory_m program~diagnose_poincare diagnose_poincare program~diagnose_poincare->module~equilibrium_factory_m program~test_diffusion test_diffusion program~test_diffusion->module~equilibrium_factory_m

Interfaces

interface

  • public module subroutine read_bndry_polygons(self, filename, variable, phi_array, polygon_vertices)

    Reads in boundary / exclusion polygon data from NetCDF

    Arguments

    Type IntentOptional Attributes Name
    class(dommaschk_t), intent(in) :: self

    Instance of the type
    character(len=*), intent(in) :: filename

    NetCDF filename
    character(len=*), intent(in) :: variable

    NetCDF variable name
    real(kind=FP), dimension(:), allocatable :: phi_array

    Toroidal angles of each polygon
    real(kind=FP), intent(out), dimension(:,:,:), allocatable :: polygon_vertices

    Closed polygon vertices at each toroidal angle

interface

  • public module subroutine read_rho_polygons(self, filename)

    Reads in flux surface polygon data from NetCDF

    Arguments

    Type IntentOptional Attributes Name
    class(dommaschk_t), intent(inout) :: self

    Instance of the type
    character(len=*), intent(in) :: filename

    NetCDF filename

Derived Types

type, public, extends(equilibrium_t) ::  dommaschk_t

Type implementing 3D vacuum fields as described by Dommaschk [*]. These are determined with toroidal mode numbers m, poloidal mode numbers l, the number of field periods, and fitting coefficients which are specific to each magnetic configuration.

Components

Type Visibility Attributes Name Initial
logical, public :: initialized = .false.
real(kind=FP), public :: x0

Magnetic axis x = R/R0 (in normalised units)
real(kind=FP), public :: y0

Magnetic axis y = Z/R0 (in normalised units)
real(kind=FP), public :: phi0 = 0.0_FP

Magnetic axis phi
real(kind=FP), public :: xmin

Box limits
real(kind=FP), public :: xmax

Box limits
real(kind=FP), public :: ymin

Box limits
real(kind=FP), public :: ymax

Box limits
real(kind=FP), public :: rhomax

Global limits for rho (rho = normalised psi, n.b. there may also be region-specific limits defined in equi)
real(kind=FP), public :: rhomin

Global limits for rho (rho = normalised psi, n.b. there may also be region-specific limits defined in equi)
real(kind=FP), public, dimension(:,:,:), allocatable :: CD_r_coef

Coefficients of the R terms of the C^D_{m,k} function. See Eqs. 31 and 32 in [*]
real(kind=FP), public, dimension(:,:,:), allocatable :: CN_r_coef

Coefficients of the R terms of the C^N_{m,k} function. See Eqs. 31 and 32 in [*]
real(kind=FP), public, dimension(:,:,:), allocatable :: C_r_power

Powers of the R terms of the C^D_{m,k} and C^N_{m,k} functions. See Eqs. 31 and 32 in [*]
real(kind=FP), public, dimension(:,:,:), allocatable :: CD_lnr_coef

Coefficients of the log(R) terms of the C^D_{m,k} function. See Eqs. 31 and 32 in [*]
real(kind=FP), public, dimension(:,:,:), allocatable :: CN_lnr_coef

Coefficients of the log(R) terms of the C^N_{m,k} function. See Eqs. 31 and 32 in [*]
real(kind=FP), public, dimension(:,:,:), allocatable :: C_lnr_power

Powers of the log(R) terms of the C^D_{m,k} and C^N_{m,k} functions. See Eqs. 31 and 32 in [*]
real(kind=FP), public, dimension(:,:,:), allocatable :: dCD_dR_r_coef

Coefficients of the R terms of the derivative with respect to R of the C^D_{m,k} function
real(kind=FP), public, dimension(:,:,:), allocatable :: dCN_dR_r_coef

Coefficients of the R terms of the derivative with respect to R of the C^N_{m,k} function
real(kind=FP), public, dimension(:,:,:), allocatable :: dC_dR_r_power

Powers of the R terms of the derivatives with respect to R of the C^D_{m,k} and C^N_{m,k} functions. See Eqs. 31 and 32 in [*]
real(kind=FP), public, dimension(:,:,:), allocatable :: dCD_dR_lnr_coef

Coefficients of the log(R) terms of the derivative with respect to R of the C^D_{m,k} function
real(kind=FP), public, dimension(:,:,:), allocatable :: dCN_dR_lnr_coef

Coefficients of the log(R) terms of the derivative with respect to R of the C^N_{m,k} function
real(kind=FP), public, dimension(:,:,:), allocatable :: dC_dR_lnr_power

Powers of the log(R) terms of the derivatives with respect to R of the C^D_{m,k} and C^N_{m,k} functions
real(kind=FP), public, dimension(:,:,:), allocatable :: I_mn_coef

Coefficients of the Z terms of the I_{m,n} function. See Eqs. 3, 8, and 9 in [*]
real(kind=FP), public, dimension(:,:,:), allocatable :: I_mn_power

Powers of the Z terms of the I_{m,n} function. See Eqs. 3, 8, and 9 in [*]
real(kind=FP), public, dimension(:,:,:), allocatable :: dI_dZ_coef

Coefficients of the Z terms of the derivative with respect to Z of the I_{m,n} function
real(kind=FP), public, dimension(:,:,:), allocatable :: dI_dZ_power

Powers of the Z terms of the derivative with respect to Z of the I_{m,n} function.
logical, public :: kiss_boundary_on

True if some boundary description in Kisslinger format is applied

integer, public :: ibnd

Type-Bound Procedures

procedure, public, pass(self) :: absb
procedure, public, pass(self) :: bpol
procedure, public :: get_l_pol
procedure, public :: get_m_tor_consecutive
procedure, public :: get_num_field_periods
procedure, public :: init
procedure, public :: display
procedure, public :: debug
procedure, public :: is_axisymmetric
procedure, public :: rho
procedure, public :: bx
procedure, public :: by
procedure, public :: btor
procedure, public :: jacobian
procedure, public :: epol
procedure, public :: erad
procedure, public :: district
procedure, public :: in_vessel
procedure, public :: mag_axis_loc

Functions

public pure function get_l_pol(self)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self

Return Value integer

public pure function get_m_tor_consecutive(self)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self

Return Value integer

public pure function get_num_field_periods(self)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self

Return Value integer

public function is_axisymmetric(self)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self

Return Value logical

public function rho(self, x, y, phi)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self
real(kind=FP), intent(in) :: x
real(kind=FP), intent(in) :: y
real(kind=FP), intent(in) :: phi

Return Value real(kind=fp)

public function bx(self, x, y, phi)

Evaluates the radial component of the vacuum magnetic field B according to B_R = dV/dR

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self
real(kind=FP), intent(in) :: x
real(kind=FP), intent(in) :: y
real(kind=FP), intent(in) :: phi

Return Value real(kind=fp)

public function by(self, x, y, phi)

Evaluates the radial component of the vacuum magnetic field B according to B_Z = dV/dZ

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self
real(kind=FP), intent(in) :: x
real(kind=FP), intent(in) :: y
real(kind=FP), intent(in) :: phi

Return Value real(kind=fp)

public function btor(self, x, y, phi)

Evaluates the poloidal component of the vacuum magnetic field B according to B_phi = 1/R dV/dphi

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self
real(kind=FP), intent(in) :: x
real(kind=FP), intent(in) :: y
real(kind=FP), intent(in) :: phi

Return Value real(kind=fp)

public function jacobian(self, x, y, phi)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self
real(kind=FP), intent(in) :: x
real(kind=FP), intent(in) :: y
real(kind=FP), intent(in) :: phi

Return Value real(kind=fp)

public function district(self, x, y, phi)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self
real(kind=FP), intent(in) :: x
real(kind=FP), intent(in) :: y
real(kind=FP), intent(in) :: phi

Return Value integer

public function in_vessel(self, x, y, phi)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self
real(kind=FP), intent(in) :: x
real(kind=FP), intent(in) :: y
real(kind=FP), intent(in) :: phi

Return Value logical


Subroutines

public subroutine init(self, filename)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(inout) :: self
character(len=*), intent(in), optional :: filename

public subroutine check_fitting_coef(self)

Check fitting_coef for consistency. The first condition (from Eq. 12 in [*]) is strict, while the second and third (from Eq. 13a) only enforce stellarator symmetry, which can be violated. Hence, only a warning is provided there.

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(inout) :: self

public subroutine init_CD_CN(self)

Compute and store C^D_{m,k}(R) and C^N_{m,k}(R) (Eq. 31 and 32)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(inout) :: self

public subroutine init_Imn(self)

Compute and store D_{m,n} and N_{m,n} (as used in Eq. 12 in [*]) via Eq. 3

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(inout) :: self

public subroutine init_B_norm(self)

Determine the magnetic field normalization with the un-normalized value of btor evaluated at the location of the magnetic axis. This is used to normalize all subsequent magnetic field calculations.

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(inout) :: self

public subroutine init_rho_array(self)

Calculates the value of rho for every surface in the given rho file. Used later in rho calculation, to interpolate between surfaces

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(inout) :: self

public subroutine init_mag_axis_loc(self)

Initializes two arrays (equidistant in phi) of x- and y-coordinates of magnetic axis within the first field period calculated via field line tracing. These are used as data points for fast interpolation in 'mag_axis_loc'

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(inout) :: self

Instance of class

public subroutine display(self)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self

public subroutine debug(self)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self

public subroutine epol(self, x, y, phi, epolx, epoly)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self
real(kind=FP), intent(in) :: x
real(kind=FP), intent(in) :: y
real(kind=FP), intent(in) :: phi
real(kind=FP), intent(out) :: epolx
real(kind=FP), intent(out) :: epoly

public subroutine erad(self, x, y, phi, eradx, erady)

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self
real(kind=FP), intent(in) :: x
real(kind=FP), intent(in) :: y
real(kind=FP), intent(in) :: phi
real(kind=FP), intent(out) :: eradx
real(kind=FP), intent(out) :: erady

public subroutine mag_axis_loc(self, phi, axis_x, axis_y)

Returns the coordinates of magnetic axis

Arguments

Type IntentOptional Attributes Name
class(dommaschk_t), intent(in) :: self

Instance of class
real(kind=FP), intent(in) :: phi

Toroidal angle
real(kind=FP), intent(out) :: axis_x

x-coordinate of the magnetic axis
real(kind=FP), intent(out) :: axis_y

y-coordinate of the magnetic axis