deq_type Derived Type

type, public, extends(abstract_eqfile_cart_geo_type) :: deq_type


Contents

Variables

Type-Bound Procedures

Source Code

deq_type

Components

Type Visibility Attributes Name Initial
character(len=:), public, allocatable :: type_name

Name of the specific implementation
logical, public :: initialised = .false.

Has this instance been initialised
logical, public :: has_full_theta_range = .false.

Does this implementation have the full or half theta grid? If only half then we assume up-down symmetry and use this to set gradients etc.
integer, public :: nr

Typically the number of radial and theta grid points.
integer, public :: nt

Typically the number of radial and theta grid points.
real, public :: psi_0
real, public :: psi_a
real, public :: B_T
real, public :: beta_0
real, public :: R_mag
real, public :: Z_mag
real, public :: aminor
real, public, allocatable, dimension(:,:) :: R_psi

2D map of co-ordinates to R, Z or B
real, public, allocatable, dimension(:,:) :: Z_psi

2D map of co-ordinates to R, Z or B
real, public, allocatable, dimension(:,:) :: B_psi

2D map of co-ordinates to R, Z or B
real, public, allocatable, dimension(:,:) :: eqth

2D maps of theta and eqpsi
real, public, allocatable, dimension(:,:) :: eqpsi_2d

2D maps of theta and eqpsi
real, public, allocatable, dimension (:,:,:) :: dpcart

Minor radius gradient in cylindrical coordinates

real, public, allocatable, dimension (:,:,:) :: dtcart

Theta gradient in cylindrical coordinates

real, public, allocatable, dimension (:,:,:) :: dbcart

B gradient in cylindrical coordinates

real, public, allocatable, dimension (:,:,:) :: dpbish

Minor radius gradient in Bishop coordinates

real, public, allocatable, dimension (:,:,:) :: dtbish

Theta gradient in Bishop coordinates

real, public, allocatable, dimension (:,:,:) :: dbbish

B gradient in Bishop coordinates

real, public, allocatable, dimension(:) :: eqpsi

Equilibrium psi (not normalised) and pressure grids
real, public, allocatable, dimension(:) :: pressure

Equilibrium psi (not normalised) and pressure grids
real, public, allocatable, dimension(:) :: psi_bar

Normalised psi, fp, q, beta, diameter and R_centre values on grid
real, public, allocatable, dimension(:) :: fp

Normalised psi, fp, q, beta, diameter and R_centre values on grid
real, public, allocatable, dimension(:) :: qsf

Normalised psi, fp, q, beta, diameter and R_centre values on grid
real, public, allocatable, dimension(:) :: beta

Normalised psi, fp, q, beta, diameter and R_centre values on grid
real, public, allocatable, dimension(:) :: diam

Normalised psi, fp, q, beta, diameter and R_centre values on grid
real, public, allocatable, dimension(:) :: rc

Normalised psi, fp, q, beta, diameter and R_centre values on grid
character(len=EQFILE_LENGTH), public :: filename
type(spline), public :: btori_spl
type(spline), public :: qsf_spl
type(spline), public :: pressure_spl
type(spline), public :: beta_spl
type(spline), public :: diam_spl
type(spline), public :: rcenter_spl
integer, public :: nw
integer, public :: nh
real, public, allocatable, dimension(:) :: thetab
real, public, allocatable, dimension(:) :: r_bound
real, public, allocatable, dimension(:) :: eq_R
real, public, allocatable, dimension(:) :: eq_Z
type(periodic_spline), public :: rbound_spl
real, private, allocatable, dimension(:) :: rho_mid
real, private, allocatable, dimension(:) :: psi_mid
type(spline), private :: rho_spl

Type-Bound Procedures

procedure, public, :: initialise

  • public subroutine initialise(self, inputs, psi_0_out, psi_a_out, rmaj, B_T0, avgrmid)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_geo_type), intent(inout) :: self
    type(geo_input_type), intent(in) :: inputs
    real, intent(out) :: psi_0_out
    real, intent(out) :: psi_a_out
    real, intent(out) :: rmaj
    real, intent(out) :: B_T0
    real, intent(out) :: avgrmid

procedure, public, :: gradient

Calculate the derivative of rp w.r.t. R and Z and return the modulus sqrt(drp/dR ^ 2 + drp/dZ^2). I.e. return |grad rp|. Parameters are: - rgrid: Submodule radial grid (r_circ for EFIT, rp otherwise) - theta: grid of theta - gradf(:,1): |grad psi| - gradf(:,2): 0.0 - char: if char = 'R', return |grad pressure| instead - char: if char = 'T', then return theta gradient in bishop form - gradf(:,1): (dtheta/dZ d rp/dR - dtheta/dR drp/dZ)/ |grad rp| - gradf(:,2): (dtheta/dR d rp/dR + dtheta/dZ drp/dZ)/ |grad rp| - rp: value of rp on the flux surface where we want the grad - nth: number of theta points - ntgrid: lower index of theta array is -ntgrid

  • public subroutine gradient(self, rgrid, theta, grad, char, rp, nth_used, ntm, use_bishop)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_geo_type), intent(in) :: self
    real, intent(in), dimension (-ntm:) :: rgrid
    real, intent(in), dimension (-ntm:) :: theta
    real, intent(out), dimension (-ntm:,:) :: grad
    character(len=1), intent(in) :: char
    real, intent(in) :: rp
    integer, intent(in) :: nth_used
    integer, intent(in) :: ntm
    logical, intent(in) :: use_bishop

procedure, public, :: calculate_gradients

  • public pure subroutine calculate_gradients(self)

    Given theta, R, Z, B and psi on 2D grids calculate the index space derivatives in the two grid dimensions and use these to find gradients in cartesian and Bishop space.

    Arguments

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

procedure, public, :: invR

  • public function invR(self, r, theta)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_geo_type), intent(in) :: self
    real, intent(in) :: r
    real, intent(in) :: theta

    Return Value real

procedure, public, :: eqdbish

  • public pure subroutine eqdbish(self, dcart, dpcart, dbish)

    Convert gradients of a function f w.r.t. R,Z into bishop form. Note that dbish(1, :, :) is not valid

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_geo_type), intent(in) :: self
    real, intent(in), dimension(:, :, :) :: dcart

    dcart(:,:,1) is gradient of f w.r.t. R; dcart(:,:,2) is gradient of f w.r.t. Z
    real, intent(in), dimension(:, :, :) :: dpcart

    dcart(:,:,1) is gradient of f w.r.t. R; dcart(:,:,2) is gradient of f w.r.t. Z
    real, intent(out), dimension(:, :, :) :: dbish

    dbish(:,:,1) is set to (df/dR dpsi/dR + df/dZ dpsi/dZ)/|grad psi|; dbish(:,:,2) is set to (-df/dR dpsi/dZ + df/dZ dpsi/dR)/|grad psi|. Note that in the special case where f=psi: dbish(:,:,1) is |grad psi|; dbish(:,:,2) is 0

procedure, public, :: eqdcart

  • public pure subroutine eqdcart(self, dfm, drm, dzm, dfcart)

    Converts derivatives w.r.t. (psi_index,theta_index) to derivatives w.r.t. (R,Z). Note that dfcart(1, :, :) is not valid

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_geo_type), intent(in) :: self
    real, intent(in), dimension (:,:,:) :: dfm

    dfm(:,:,1) is deriv w.r.t. psi_index (i.e. (df/dpsi)_theta * delta psi); dfm(:,:,2) is deriv w.r.t. theta_index
    real, intent(in), dimension (:,:,:) :: drm

    dfm(:,:,1) is deriv w.r.t. psi_index (i.e. (df/dpsi)_theta * delta psi); dfm(:,:,2) is deriv w.r.t. theta_index
    real, intent(in), dimension (:,:,:) :: dzm

    dfm(:,:,1) is deriv w.r.t. psi_index (i.e. (df/dpsi)_theta * delta psi); dfm(:,:,2) is deriv w.r.t. theta_index
    real, intent(out), dimension (:,:,:) :: dfcart

    dfcart(:,:,1) is deriv w.r.t. R; dfcart(:,:,2) is deriv w.r.t. Z

procedure, public, :: dealloc_common_arrays

procedure, public, :: alloc_common_arrays

procedure, public, :: hahm_burrell

  • public subroutine hahm_burrell(self, a)

    FIXME : Add documentation

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_geo_type), intent(in) :: self
    real, intent(in) :: a

procedure, public, :: dealloc_arrays

procedure, public, :: alloc_arrays

procedure, public, :: alloc_special_arrays => alloc_special_arrays_null

procedure, public, :: finalise => finalise_eqfile

procedure, public, :: finish_setup => finish_setup_eqfile

procedure, public, :: setup_splines => setup_splines_eqfile

procedure, public, :: delete_splines => delete_splines_eqfile

procedure, public, :: dbtori => dbtori_eqfile

  • public function dbtori_eqfile(self, pbar) result(dbtori)

    at the given normalised

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_geo_type), intent(in) :: self
    real, intent(in) :: pbar

    Return Value real

procedure, public, :: btori => btori_eqfile

  • public function btori_eqfile(self, pbar) result(btori)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_geo_type), intent(in) :: self
    real, intent(in) :: pbar

    Return Value real

procedure, public, :: betafun => betafun_eqfile

  • public function betafun_eqfile(self, pbar) result(betafun)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_geo_type), intent(in) :: self
    real, intent(in) :: pbar

    Return Value real

procedure, public, :: qfun => qfun_eqfile

  • public function qfun_eqfile(self, pbar) result(qfun)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_geo_type), intent(in) :: self
    real, intent(in) :: pbar

    Return Value real

procedure, public, :: dpfun => dpfun_eqfile

  • public function dpfun_eqfile(self, pbar) result(dpfun)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_geo_type), intent(in) :: self
    real, intent(in) :: pbar

    Return Value real

procedure, public, :: pfun => pfun_eqfile

  • public function pfun_eqfile(self, pbar) result(pfun)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_geo_type), intent(in) :: self
    real, intent(in) :: pbar

    Return Value real

procedure, public, :: shared_setup => shared_setup_cart

  • public subroutine shared_setup_cart(self, nw_in, nh_in, spsi_bar, sefit_R, sefit_Z, f, p, q, sefit_psi, nbbbs, rbbbs, zbbbs, bcentr, rleft, rwid, zoffset, zhei, big, calc_aminor)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_cart_geo_type), intent(inout) :: self
    integer, intent(in) :: nw_in
    integer, intent(in) :: nh_in
    real, intent(in), dimension(:) :: spsi_bar
    real, intent(in), dimension(:) :: sefit_R
    real, intent(in), dimension(:) :: sefit_Z
    real, intent(in), dimension(:) :: f
    real, intent(in), dimension(:) :: p
    real, intent(in), dimension(:) :: q
    real, intent(in), dimension(:, :) :: sefit_psi
    integer, intent(in) :: nbbbs
    real, intent(inout), dimension(:) :: rbbbs
    real, intent(inout), dimension(:) :: zbbbs
    real, intent(in) :: bcentr
    real, intent(in) :: rleft
    real, intent(in) :: rwid
    real, intent(in) :: zoffset
    real, intent(in) :: zhei
    integer, intent(in) :: big
    logical, intent(in) :: calc_aminor

procedure, public, :: zbrent

  • public function zbrent(self, x1, x2, rootval, thetroot, tol)

    FIXME : Add documentation

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_cart_geo_type), intent(in) :: self
    real, intent(in) :: x1
    real, intent(in) :: x2
    real, intent(in) :: rootval
    real, intent(in) :: thetroot
    real, intent(in) :: tol

    Return Value real

procedure, public, :: rfun

  • public function rfun(self, r, theta)

    Returns the distance to the magnetic axis as a function of rp (the normalised poloidal flux variable) and theta.

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_cart_geo_type), intent(in) :: self
    real, intent(in) :: r
    real, intent(in) :: theta

    Return Value real

procedure, public, :: bound => bound_eqfile_cart

  • public function bound_eqfile_cart(self, theta) result(bound)

    Find the value of the major radius on the plasma boundary at given geometric theta.

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_cart_geo_type), intent(in) :: self
    real, intent(in) :: theta

    Return Value real

procedure, public, :: zpos => zpos_eqfile_cart

  • public pure function zpos_eqfile_cart(self, r, theta) result(zpos)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_cart_geo_type), intent(in) :: self
    real, intent(in) :: r
    real, intent(in) :: theta

    Return Value real

procedure, public, :: rpos => rpos_eqfile_cart

  • public pure function rpos_eqfile_cart(self, r, theta) result(rpos)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_cart_geo_type), intent(in) :: self
    real, intent(in) :: r
    real, intent(in) :: theta

    Return Value real

procedure, public, :: psi => psi_eqfile_cart

  • public function psi_eqfile_cart(self, r, theta) result(psi)

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_cart_geo_type), intent(in) :: self
    real, intent(in) :: r
    real, intent(in) :: theta

    Return Value real

procedure, public, :: diameter => diameter_eqfile_cart

procedure, public, :: eqitem => eqitem_cart

  • public function eqitem_cart(self, r_in, theta_in, f, char) result(fstar)

    fstar is f(R,Z) interpolated at the values (r,thetain). The parameter r is the distance to the magnetic axis.

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_cart_geo_type), intent(in) :: self
    real, intent(in) :: r_in
    real, intent(in) :: theta_in
    real, intent(in), dimension(:, :) :: f
    character(len=1), intent(in) :: char

    Return Value real

procedure, public, :: derm => derm_cart

  • public pure subroutine derm_cart(self, f, dfm, char)

    Calculate the derivative of f w.r.t. R, Z - dfm(:,:,1) is deriv w.r.t. R - dfm(:,:,2) is deriv w.r.t. Z

    Arguments

    Type IntentOptional Attributes Name
    class(abstract_eqfile_cart_geo_type), intent(in) :: self
    real, intent(in), dimension(:,:) :: f
    real, intent(out), dimension(:,:,:) :: dfm
    character(len=1), intent(in) :: char

procedure, public, :: delete_special_splines

procedure, public, :: setup_special_splines

procedure, public, :: read_and_set

  • private subroutine read_and_set(self, inputs)

    This subroutine reads an DFIT output file containing the axisymmetric magnetic field geometry on a rectangular domain defined by the coordinates (R,Z).

    Arguments

    Type IntentOptional Attributes Name
    class(deq_type), intent(inout) :: self
    type(geo_input_type), intent(in) :: inputs

procedure, public, :: dealloc_special_arrays

  • private pure subroutine dealloc_special_arrays(self)

    FIXME : Add documentation

    Arguments

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

procedure, public, :: rhofun

  • private function rhofun(self, pbar)

    FIXME : Add documentation

    Arguments

    Type IntentOptional Attributes Name
    class(deq_type), intent(in) :: self
    real, intent(in) :: pbar

    Return Value real

procedure, public, :: rcenter

  • private function rcenter(self, rp)

    FIXME : Add documentation | Not implemented

    Arguments

    Type IntentOptional Attributes Name
    class(deq_type), intent(in) :: self
    real, intent(in) :: rp

    Return Value real

Source Code

  type, extends(abstract_eqfile_cart_geo_type) :: deq_type
     private
     real, allocatable, dimension(:) :: rho_mid, psi_mid
     type(spline) :: rho_spl
   contains
     procedure :: read_and_set, setup_special_splines, delete_special_splines
     procedure :: rcenter, rhofun, dealloc_special_arrays
  end type deq_type