numerical_equilibrium_m Module

Defines the numerical equilibrium subclass N.b. this is axisymmetric; phi, when required, is not used.

The object structure is quite large -- it is designed to be fully self-descriptive, such that multiple equilibria may be developed independently, without resulting in conflicts between the equilibria objects. As a result, most variables are stored within the object (i.e. as object%variable) rather than shared across the module.

The numerical equilibrium object develops an equilibrium object from a NetCDF, specified in the params.in file, as "/.nc". This file should define

  • Global attributes "description", "history", "author"
  • A group "Magnetic_geometry" with
    • dimensions "R", "Z"
    • variables "R", "Z" (corresponding dimension values) and "psi" (R,Z grid). The "btor" (R,Z grid) variable is optional (unused) if use_spline_for_btor == .false. (in params.in), required if use_spline_for_btor == .true.
    • attributes "magnetic_axis_R", "magnetic_axis_Z", "x_point_R", "x_point_Z", "axis_Btor"
  • A group "Psi_limits" with
    • attributes "global_min" and "global_min"
    • subgroups (name not used) corresponding to regions (polygons) where a different psi limit should be applied. Each subgroup should have
      • attributes "local_min" and "local_max", which may be NaN (IEEE conformant) if undefined
      • a nc_polygon (see below)
  • A group "Box_limits" with a corresponding nc_polygon
  • A group "FW_and_divertor_polygon" with a corresponding nc_polygon
  • A group "Shadow_polygon" with a corresponding nc_polygon

Groups which contain a nc_polygon should have the following information * dimension "N_points" which gives the number of polygon points * variables "R_points" and "Z_points" which gives the (R, Z) points Note that the R_points and Z_points will be automatically normalised to the magnetic_axis_R

N.b. this module relies on bspline_fortran module from https://github.com/jacobwilliams/bspline-fortran


Uses

  • module~~numerical_equilibrium_m~~UsesGraph module~numerical_equilibrium_m numerical_equilibrium_m bspline_module bspline_module module~numerical_equilibrium_m->bspline_module iso_fortran_env iso_fortran_env module~numerical_equilibrium_m->iso_fortran_env module~comm_handling_m comm_handling_m module~numerical_equilibrium_m->module~comm_handling_m module~constants_m constants_m module~numerical_equilibrium_m->module~constants_m module~descriptors_m descriptors_m module~numerical_equilibrium_m->module~descriptors_m module~divertor_equilibrium_m divertor_equilibrium_m module~numerical_equilibrium_m->module~divertor_equilibrium_m module~elementary_functions_m elementary_functions_m module~numerical_equilibrium_m->module~elementary_functions_m module~polygon_m polygon_m module~numerical_equilibrium_m->module~polygon_m module~precision_m precision_m module~numerical_equilibrium_m->module~precision_m module~screen_io_m screen_io_m module~numerical_equilibrium_m->module~screen_io_m netcdf netcdf module~numerical_equilibrium_m->netcdf mpi mpi module~comm_handling_m->mpi module~constants_m->module~precision_m module~descriptors_m->module~screen_io_m module~divertor_equilibrium_m->module~descriptors_m module~divertor_equilibrium_m->module~polygon_m module~divertor_equilibrium_m->module~precision_m module~divertor_equilibrium_m->module~screen_io_m module~equilibrium_m equilibrium_m module~divertor_equilibrium_m->module~equilibrium_m module~error_handling_m error_handling_m module~divertor_equilibrium_m->module~error_handling_m module~status_codes_m status_codes_m module~divertor_equilibrium_m->module~status_codes_m module~elementary_functions_m->module~precision_m module~polygon_m->iso_fortran_env module~polygon_m->module~comm_handling_m module~polygon_m->module~descriptors_m module~polygon_m->module~precision_m module~polygon_m->module~screen_io_m module~polygon_m->netcdf ieee_arithmetic ieee_arithmetic module~polygon_m->ieee_arithmetic module~polygon_m->mpi module~precision_m->iso_fortran_env module~precision_m->netcdf iso_c_binding iso_c_binding module~precision_m->iso_c_binding module~precision_m->mpi module~screen_io_m->iso_fortran_env module~screen_io_m->module~precision_m module~screen_io_m->netcdf module~equilibrium_m->module~precision_m module~error_handling_m->module~comm_handling_m module~error_handling_m->module~precision_m module~error_handling_m->module~screen_io_m module~error_handling_m->netcdf module~error_handling_m->module~status_codes_m module~error_handling_m->mpi

Used by

  • module~~numerical_equilibrium_m~~UsedByGraph module~numerical_equilibrium_m numerical_equilibrium_m module~equilibrium_factory_m equilibrium_factory_m module~equilibrium_factory_m->module~numerical_equilibrium_m module~initialise_numerical_equilibrium_s initialise_numerical_equilibrium_s module~initialise_numerical_equilibrium_s->module~numerical_equilibrium_m module~testfunctions_m testfunctions_m module~testfunctions_m->module~numerical_equilibrium_m program~benchmark_helmholtz_solvers benchmark_helmholtz_solvers program~benchmark_helmholtz_solvers->module~equilibrium_factory_m program~benchmark_helmholtz_solvers->module~testfunctions_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

Derived Types

type, public, extends(divertor_equilibrium_t) ::  numerical_t

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)
logical, public :: flip_Z = .false.

Inverts the Z direction, which is equivalent to reversing the field direction Default false, use true to flip the equilibrium vertically (magnetic axis position unchanged).
real(kind=FP), public :: poloidal_field_factor = 1.0_FP

Poloidal field factor, which can be used to reverse the helicity
type(closed_polygon2d_t), public :: divertor_polygon

Closed polygon which defines the divertor
type(closed_polygon2d_t), public :: exclusion_polygon

Closed polygon which marks points as being off the grid

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logical, public :: invert_divertor_polygon

Flips the divertor polygon from being assumed concave to convex.
logical, public :: invert_exclusion_polygon

Flips the exclusion polygon from being assumed concave to convex.
real(kind=FP), public :: axis_Btor

Toroidal field at the the magnetic axis -- used to normalise magnetic field
real(kind=FP), public :: O_point_psi

Poloidal flux of the magnetic axis -- used to define the 0-point of rho
real(kind=FP), public :: X_point_psi

Poloidal flux of the (primary) separatrix -- used to define the 1-point of rho
character(len=:), public, allocatable :: district_definition

Indicates, how districts are defined 'flux': Based on the limiting flux surface rho_max (default) 'wall': Based on divertor and exclusion polygons
real(kind=FP), public :: R0

Type-Bound Procedures

procedure, public, pass(self) :: absb
procedure, public, pass(self) :: bpol
procedure, public :: is_axisymmetric
procedure, public :: rho
procedure, public :: jacobian
procedure, public :: epol
procedure, public :: erad
procedure, public, nopass :: make_polygon
procedure, public :: make_polygon_from_params
procedure, public :: polygon_projection
procedure, public :: in_vessel
procedure, public :: mag_axis_loc
procedure, public :: on_grid
procedure, public :: district
procedure, public :: init

Initialises equilibrium, i.e.~reads any required parameters from file.
procedure, public :: display

Print to console information about the equilibrium
procedure, public :: debug

Print to console extended information about the equilibrium
procedure, public :: psi

Non-normalised poloidal flux function (in Wb=Vs=Tm2)
procedure, public :: bx

Radial field component normalized to on axis field strength.
procedure, public :: by

Vertical field component normalized to on axis field strength.
procedure, public :: btor

Toroidal field component normalized to on axis field strength.
procedure, public :: check_privflux_regions

Returns the equivalent to 'rholimit_privflux' for a given (x,y) point

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