leq_type – GS2

type, public, extends(abstract_geo_type) :: leq_type

Type-Bound Procedures

initialise gradient calculate_gradients rhofun derm invR eqdbish eqdcart dealloc_common_arrays alloc_common_arrays hahm_burrell dealloc_arrays alloc_arrays alloc_special_arrays dealloc_special_arrays read_and_set finalise finish_setup qfun dbtori btori diameter rcenter zpos rpos eqitem rfun psi betafun dpfun pfun geo_FourierSeries geo_generalizedElongation geo_global geo_Miller geo_MillerExtendedHarmonic

Source Code

leq_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 $(\hat{e}_R, \hat{e}_Z, \hat{e}_\zeta)$
real,	public,	allocatable, dimension (:,:,:)	::	dtcart			Theta gradient in cylindrical coordinates $(\hat{e}_R, \hat{e}_Z, \hat{e}_\zeta)$
real,	public,	allocatable, dimension (:,:,:)	::	dbcart			B gradient in cylindrical coordinates $(\hat{e}_R, \hat{e}_Z, \hat{e}_\zeta)$
real,	public,	allocatable, dimension (:,:,:)	::	dpbish			Minor radius gradient in Bishop coordinates $(\hat{e}_{r_\psi}, \hat{e}_l, \hat{e}_\zeta)$
real,	public,	allocatable, dimension (:,:,:)	::	dtbish			Theta gradient in Bishop coordinates $(\hat{e}_{r_\psi}, \hat{e}_l, \hat{e}_\zeta)$
real,	public,	allocatable, dimension (:,:,:)	::	dbbish			B gradient in Bishop coordinates $(\hat{e}_{r_\psi}, \hat{e}_l, \hat{e}_\zeta)$
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
real,	public		::	thetaShift			Used to translate definition of the poloidal angle such that the location of the maximium magnetic field is at pi (see section 3.2.3 of Ball MIT Masters thesis or section 2.4 of "GS2 analytic geometry specification")
type(flux_surface_type),	public		::	surf

Type-Bound Procedures

procedure, public, :: initialise

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

Arguments

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

procedure, public, :: rhofun => rhofun_null

public function rhofun_null(self, pbar) result(rhofun)

Arguments

Type	Intent	Optional	Attributes		Name
class(abstract_geo_type),	intent(in)			::	self
real,	intent(in)			::	pbar

Return Value real

procedure, public, :: derm

public pure subroutine derm(self, f, dfm, char)

Calculate the derivative of f w.r.t to the radial and poloidal indexes (i.e. calculate the finite differences without dividing by delta psi and delta theta). - dfm(:,:,1) is the psi derivative - dfm(:,:,2) is the theta derivative - char specifies the periodicity in theta - 'E', 'O' mean continuous at theta = +/- pi - 'T' means a jump of 2 pi at theta = +/- pi

Arguments

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

procedure, public, :: invR

public function invR(self, r, theta)

Arguments

Type	Intent		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	Intent	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	Intent	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

public pure subroutine dealloc_common_arrays(self)

Arguments

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

procedure, public, :: alloc_common_arrays

public pure subroutine alloc_common_arrays(self)

Arguments

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

procedure, public, :: hahm_burrell

public subroutine hahm_burrell(self, a)

FIXME : Add documentation

Arguments

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

procedure, public, :: dealloc_arrays

public pure subroutine dealloc_arrays(self)

Arguments

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

procedure, public, :: alloc_arrays

public pure subroutine alloc_arrays(self)

Arguments

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

procedure, public, :: alloc_special_arrays => alloc_special_arrays_null

public pure subroutine alloc_special_arrays_null(self)

Arguments

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

procedure, public, :: dealloc_special_arrays => dealloc_special_arrays_null

public pure subroutine dealloc_special_arrays_null(self)

Arguments

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

procedure, public, :: read_and_set

private subroutine read_and_set(self, inputs)

Set module-level parameters and initialise the leq module

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(inout)			::	self
type(geo_input_type),	intent(in)			::	inputs

procedure, public, :: finalise

private pure subroutine finalise(self)

Finalise leq module

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(inout)			::	self

procedure, public, :: finish_setup

private pure subroutine finish_setup(self)

Finish the leq setup

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(inout)			::	self

procedure, public, :: qfun

private pure function qfun(self, pbar)

FIXME : Add documentation

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(in)			::	self
real,	intent(in)			::	pbar

Return Value real

procedure, public, :: dbtori

private pure function dbtori(self, pbar)

FIXME : Add documentation

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(in)			::	self
real,	intent(in)			::	pbar

Return Value real

procedure, public, :: btori

private pure function btori(self, pbar)

FIXME : Add documentation

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(in)			::	self
real,	intent(in)			::	pbar

Return Value real

procedure, public, :: diameter

private pure function diameter(self, rp)

FIXME : Add documentation

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(in)			::	self
real,	intent(in)			::	rp

Return Value real

procedure, public, :: rcenter

private pure function rcenter(self, rp)

Return the major radius of the centre of the flux surface

Note

rcenter for other geo types returns the major radius of the LCFS which is named R_geo in geometry. We do store R_geo here so could return that?

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(in)			::	self
real,	intent(in)			::	rp

Return Value real

procedure, public, :: zpos => Zpos

private pure function Zpos(self, r, theta)

Return the axial coordinate at $(r, \theta)$

Arguments

Type	Intent		Name
class(leq_type),	intent(in)	::	self
real,	intent(in)	::	r
real,	intent(in)	::	theta

Return Value real

procedure, public, :: rpos => Rpos

private pure function Rpos(self, r, theta)

Return the major radius at $(r, \theta)$

Arguments

Type	Intent		Name
class(leq_type),	intent(in)	::	self
real,	intent(in)	::	r
real,	intent(in)	::	theta

Return Value real

procedure, public, :: eqitem

private pure function eqitem(self, r_in, theta_in, f, char) result(fstar)

Calculates fstar which is f interpolated at the location theta_in

Arguments

Type	Intent	Attributes		Name
class(leq_type),	intent(in)		::	self
real,	intent(in)		::	r_in
real,	intent(in)		::	theta_in	Desired theta location
real,	intent(in),	dimension(:, :)	::	f	Array to interpolate
character(len=1),	intent(in)		::	char	FIXME: Unused

Return Value real

procedure, public, :: rfun

private pure function rfun(self, r, theta)

FIXME : Add documentation | Should this be equivalent to psi as in others?

Arguments

Type	Intent		Name
class(leq_type),	intent(in)	::	self
real,	intent(in)	::	r
real,	intent(in)	::	theta

Return Value real

procedure, public, :: psi

private pure function psi(self, r, theta)

FIXME : Add documentation

Arguments

Type	Intent		Name
class(leq_type),	intent(in)	::	self
real,	intent(in)	::	r
real,	intent(in)	::	theta

Return Value real

procedure, public, :: betafun

private pure function betafun(self, pbar)

FIXME : Add documentation

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(in)			::	self
real,	intent(in)			::	pbar

Return Value real

procedure, public, :: dpfun

private pure function dpfun(self, pbar)

FIXME : Add documentation

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(in)			::	self
real,	intent(in)			::	pbar

Return Value real

procedure, public, :: pfun

private pure function pfun(self, pbar)

FIXME : Add documentation

Arguments

Type	Intent	Optional	Attributes		Name
class(leq_type),	intent(in)			::	self
real,	intent(in)			::	pbar

Return Value real

procedure, public, :: geo_FourierSeries

private pure subroutine geo_FourierSeries(self, r, theta, Rpos, Zpos)

Calculate the cylindrical $(R, Z)$ at $(r, \theta)$ for the Fourier model

See section 5.1.1 of Ball Oxford PhD thesis or section 2.1.4 of "GS2 analytic geometry specification"

Arguments

Type	Intent		Name
class(leq_type),	intent(in)	::	self
real,	intent(in)	::	r
real,	intent(in)	::	theta
real,	intent(out)	::	Rpos
real,	intent(out)	::	Zpos

procedure, public, :: geo_generalizedElongation

private pure subroutine geo_generalizedElongation(self, r, theta, Rpos, Zpos)

Calculate the cylindrical $(R, Z)$ at $(r, \theta)$ for the generalised elongation model

See section 5.1.2 of Ball Oxford PhD thesis or section 2.1.3 of "GS2 analytic geometry specification"

Arguments

Type	Intent		Name
class(leq_type),	intent(in)	::	self
real,	intent(in)	::	r
real,	intent(in)	::	theta
real,	intent(out)	::	Rpos
real,	intent(out)	::	Zpos

procedure, public, :: geo_global

private pure subroutine geo_global(self, r, theta, Rpos, Zpos)

Calculate the cylindrical $(R, Z)$ at $(r, \theta)$ for the global MHD model

See section 2.1.2 of "GS2 analytic geometry specification"

Arguments

Type	Intent		Name
class(leq_type),	intent(in)	::	self
real,	intent(in)	::	r
real,	intent(in)	::	theta
real,	intent(out)	::	Rpos
real,	intent(out)	::	Zpos

procedure, public, :: geo_Miller

private pure subroutine geo_Miller(self, r, theta, Rpos, Zpos)

Calculate the cylindrical $(R, Z)<script type="math/tex; mode=display"> at$ (r, \theta) for the generalised Miller model

See section 3.2.1 of Ball MIT Masters thesis or section 2.1.1 of "GS2 analytic geometry specification"

Arguments

Type	Intent		Name
class(leq_type),	intent(in)	::	self
real,	intent(in)	::	r
real,	intent(in)	::	theta
real,	intent(out)	::	Rpos
real,	intent(out)	::	Zpos

procedure, public, :: geo_MillerExtendedHarmonic

private pure subroutine geo_MillerExtendedHarmonic(self, r, theta, Rpos, Zpos)

Calculate the cylindrical $(R, Z)$ at $(r, \theta)$ for the Miller Extended Harmonic model

See PPCF 63 (2021) 012001 (5pp)

Arguments

Type	Intent		Name
class(leq_type),	intent(in)	::	self
real,	intent(in)	::	r
real,	intent(in)	::	theta
real,	intent(out)	::	Rpos
real,	intent(out)	::	Zpos

Source Code

  type, extends(abstract_geo_type) :: leq_type
     !> Used to translate definition of the poloidal angle such that the location
     !> of the maximium magnetic field is at pi (see section 3.2.3 of Ball MIT
     !> Masters thesis or section 2.4 of "GS2 analytic geometry specification")
     real :: thetaShift
     type(flux_surface_type) :: surf
   contains
     procedure :: finish_setup, finalise, read_and_set
     procedure :: rpos, zpos, rcenter, diameter, btori, dbtori, qfun
     procedure :: pfun, dpfun, betafun, psi, rfun, eqitem
     procedure :: geo_Miller, geo_global, geo_generalizedElongation, geo_FourierSeries
     procedure :: geo_MillerExtendedHarmonic
  end type leq_type

leq_type Derived Type

Contents

Variables

Type-Bound Procedures

Source Code

type, public, extends(abstract_geo_type) :: leq_type

Contents

Variables

Type-Bound Procedures

Source Code

Components

Type-Bound Procedures

procedure, public, :: initialise

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

Arguments

procedure, public, :: gradient

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

Arguments

procedure, public, :: calculate_gradients

public pure subroutine calculate_gradients(self)

Arguments

procedure, public, :: rhofun => rhofun_null

public function rhofun_null(self, pbar) result(rhofun)

Arguments

Return Value real

procedure, public, :: derm

public pure subroutine derm(self, f, dfm, char)

Arguments

procedure, public, :: invR

public function invR(self, r, theta)

Arguments

Return Value real

procedure, public, :: eqdbish

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

Arguments

procedure, public, :: eqdcart

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

Arguments

procedure, public, :: dealloc_common_arrays

public pure subroutine dealloc_common_arrays(self)

Arguments

procedure, public, :: alloc_common_arrays

public pure subroutine alloc_common_arrays(self)

Arguments

procedure, public, :: hahm_burrell

public subroutine hahm_burrell(self, a)

Arguments

procedure, public, :: dealloc_arrays

public pure subroutine dealloc_arrays(self)

Arguments

procedure, public, :: alloc_arrays

public pure subroutine alloc_arrays(self)

Arguments

procedure, public, :: alloc_special_arrays => alloc_special_arrays_null

public pure subroutine alloc_special_arrays_null(self)

Arguments

procedure, public, :: dealloc_special_arrays => dealloc_special_arrays_null

public pure subroutine dealloc_special_arrays_null(self)

Arguments

procedure, public, :: read_and_set

private subroutine read_and_set(self, inputs)

Arguments

procedure, public, :: finalise

private pure subroutine finalise(self)

Arguments

procedure, public, :: finish_setup

private pure subroutine finish_setup(self)

Arguments

procedure, public, :: qfun

private pure function qfun(self, pbar)

Arguments

Return Value real

procedure, public, :: dbtori

private pure function dbtori(self, pbar)

Arguments

Return Value real

procedure, public, :: btori

private pure function btori(self, pbar)

Arguments

Return Value real