oft_gs Module Reference

Detailed Description

Grad-Shafranov implementation for TokaMaker.

Authors

Chris Hansen

Date

August 2011

Data Types
type	circular_curr
	Interpolation class for uniform source with simple tokamak representation. More...
type	coil_region
	Internal coil region structure. More...
type	cond_region
	Internal wall region structure. More...
interface	flux_cofs_get
	Needs Docs. More...
interface	flux_cofs_set
	Needs Docs. More...
type	flux_func
	Abstract flux function prototype. More...
interface	flux_func_eval
	Needs Docs. More...
interface	flux_func_update
	Needs Docs. More...
type	gs_b_interp
	Interpolate magnetic field for a G-S solution. More...
type	gs_curvature_interp
	Interpolate magnetic field for a G-S solution. More...
type	gs_eq
	Grad-Shafranov equilibrium object. More...
type	gs_j_interp
	Interpolate magnetic field for a G-S solution. More...
type	gs_prof_interp
	Interpolate G-S profiles at a specific point in space. More...
type	gs_region_info
	Information for non-continuous regions. More...
type	gsinv_interp
	Need docs. More...
type	oft_gs_zerob
	Zero scalar Lagrange FE field on all boundary nodes and all nodes outside the plasma. More...

Functions/Subroutines
subroutine	build_dels (mat, self, bc, dt, scale)
	Construct \( \frac{1}{R} \Delta^* \) operator, with or without time-dependence.
subroutine	build_mrop (fe_rep, mat, bc)
	Construct mass matrix for a boundary Lagrange scalar representation.
subroutine	circle_interp (self, cell, f, gop, val)
	Evaluate uniform source over simple plasma cross-section.
subroutine	compute_bcmat (self)
	Compute boundary condition matrix for free-boundary case.
real(r8) function	dummy_fpp (self, psi)
subroutine	get_olbp (smesh, olbp)
	Generate oriented loop from boundary points.
subroutine	gs_analyze_saddles (self, o_point, o_psi, x_point, x_psi)
	Needs Docs.
subroutine	gs_b_interp_apply (self, cell, f, gop, val)
	Reconstruct magnetic field from a Grad-Shafranov solution.
subroutine	gs_bcrosskappa (self, bcross_kappa)
	Needs docs.
subroutine	gs_coil_mutual (self, icoil, b, mutual)
	Compute inductance between coil and given poloidal flux.
subroutine	gs_coil_mutual_distributed (self, icoil, b, curr_dist, mutual)
	Compute inductance between a coil with non-uniform current distribution and given poloidal flux.
subroutine	gs_coil_source (self, icoil, b)
	Calculates coil current source for given coil.
subroutine	gs_coil_source_distributed (self, icoil, b, curr_dist)
	Calculates coil current source for given coil with non-uniform current distribution.
subroutine	gs_curvature (self, br, bt, bz, solver_in)
	Needs docs.
subroutine	gs_curvature_apply (self, cell, f, gop, val)
	Reconstruct magnetic field from a Grad-Shafranov solution.
subroutine	gs_destroy (self)
	Destroy internal storage and nullify references for Grad-Shafranov object.
real(8) function	gs_dflux (self)
	Compute diamagentic flux.
character(len=40) function	gs_err_reason (ierr)
	Compute Grad-Shafranov solution for current flux definitions.
subroutine	gs_find_saddle (self, psi_scale_len, psi_x, pt, stype)
	Needs Docs.
subroutine	gs_fit_isoflux (self, psi_full, ierr)
	Compute coil currents to best fit isoflux, flux, and saddle targets at current solution.
subroutine	gs_fixed_vflux (self, pts, fluxes)
	Compute required vacuum flux for fixed boundary equilibrium.
subroutine	gs_gen_source (self, source_fun, b)
	Compute RHS source from an arbitrary current distribution \( J_{\phi} \).
subroutine	gs_get_chi (self)
	Compute toroidal flux potential from Grad-Shafranov solution.
subroutine	gs_get_cond_scales (self, vals, skip_fixed)
	Needs Docs.
subroutine	gs_get_cond_weights (self, vals, skip_fixed)
	Needs Docs.
subroutine	gs_get_qprof (gseq, nr, psi_q, prof, dl, rbounds, zbounds, ravgs)
	Get q profile for equilibrium.
subroutine	gs_helicity (self, ener, helic)
	Compute the magnetic energy and helicity of a fixed boundary equilibrium.
subroutine	gs_init (self)
	Initialize Grad-Shafranov object by computing operators and allocating storage.
subroutine	gs_init_psi (self, ierr, r0, a, kappa, delta, curr_source)
	Initialize \( \psi \).
real(8) function	gs_itor (self, psi_vec)
	Compute toroidal current for Grad-Shafranov equilibrium.
subroutine	gs_itor_nl (self, itor, centroid)
	Compute toroidal current for Grad-Shafranov equilibrium.
subroutine	gs_j_interp_apply (self, cell, f, gop, val)
	Reconstruct magnetic field from a Grad-Shafranov solution.
subroutine	gs_j_interp_delete (self)
	Destroy temporary internal storage and nullify references.
subroutine	gs_j_interp_setup (self, gs)
	Needs Docs.
subroutine	gs_lin_solve (self, adjust_r0, ierr)
	Compute solution to linearized Grad-Shafranov without updating \( \psi \) for RHS.
subroutine	gs_load_limiters (self)
	Needs Docs.
subroutine	gs_mat_create (fe_rep, new)
	Create G-S matrix with necessary augmentations for free-boundary BC.
subroutine	gs_plasma_mutual (self, b, mutual, itor)
	Compute inductance between plasma current and given poloidal flux.
subroutine	gs_prof_interp_apply (self, cell, f, gop, val)
	Reconstruct a component of a Grad-Shafranov solution.
subroutine	gs_prof_interp_delete (self)
	Destroy temporary internal storage and nullify references.
subroutine	gs_prof_interp_setup (self, gs)
	Needs Docs.
subroutine	gs_project_b (self, br, bt, bz, solver_in, normalized)
	Needs Docs.
subroutine	gs_psi2pt (self, psi_target, pt, pt_con, vec, psi_int)
	Find position of psi along a vector search direction.
subroutine	gs_psi2r (self, psi_target, pt, psi_int)
	Find position of psi along a radial chord.
subroutine	gs_save_fields (self, pts, npts, filename)
	Compute magnetic fields from Grad-Shafranov equilibrium.
subroutine	gs_save_mug (self, filename, legacy)
	Needs Docs.
subroutine	gs_save_prof (self, filename, mpsi_sample)
	Needs Docs.
subroutine	gs_set_cond_weights (self, vals, skip_fixed)
	Needs Docs.
subroutine	gs_setup (self, ml_lag_2d)
	Needs Docs.
subroutine	gs_setup_walls (self, skip_load, make_plot)
	Needs Docs.
subroutine	gs_solve (self, ierr)
	Compute Grad-Shafranov solution for current flux function definitions and targets.
subroutine	gs_source (self, a, b, b2, b3, itor_alam, itor_press, estore)
	Compute plasma component of RHS source for Grad-Shafranov equation.
logical function	gs_test_bounds (self, pt)
	Test whether a point is inside the LCFS.
subroutine	gs_trace_surf (gseq, psi_in, points, npoints)
	Trace a single specified flux surface.
subroutine	gs_update_bounds (self, track_opoint)
	Needs Docs.
subroutine	gs_vac_solve (self, psi_sol, rhs_source, ierr)
	Compute Grad-Shafranov solution for vacuum (no plasma)
subroutine	gs_vacuum_solve (self, pol_flux, source, ierr)
	Solve for \( \psi \) in vacuum for a given source \( \int \phi^T J_{\phi} dA \).
subroutine	gs_wall_source (self, dpsi_dt, b)
	Calculate RHS source for quasi-static solve from previous \( \psi \).
subroutine	gsinv_apply (self, cell, f, gop, val)
	Needs Docs.
subroutine	gsinv_destroy (self)
	Needs Docs.
subroutine	gsinv_setup (self, lag_rep)
	Needs Docs.
subroutine	psi2pt_error (m, n, cofs, err, iflag)
	Needs docs.
subroutine	psimax_error (m, n, cofs, err, iflag)
	Needs docs.
subroutine	psimax_error_grad (m, n, cofs, err, jac_mat, ldjac_mat, iflag)
	Needs docs.
subroutine	set_bcmat (self, mat)
	Add boundary condition terms for free-boundary case to matrix.
subroutine	zerob_apply (self, a)
	Zero a 2D Lagrange scalar field at all nodes outside the plasma or on the global boundary.
subroutine	zerob_delete (self)
	Destroy temporary internal storage and nullify references.

Variables
integer(i4)	cell_active = 0
real(r8), parameter	gs_epsilon = 1.d-12
	Epsilon used for radial coordinate.
integer(4), parameter	max_xpoints = 20
type(oft_lag_brinterp), pointer	psi_eval_active => NULL()
type(oft_lag_bg2interp), pointer	psi_g2eval_active => NULL()
type(oft_lag_bginterp), pointer	psi_geval_active => NULL()
real(r8)	psi_target_active = 0.d0
real(r8), dimension(2)	pt_con_active = [0.d0,0.d0]
real(r8)	qp_int_tol = 1.d-12
real(r8), dimension(2)	vec_con_active = [0.d0,0.d0]

Function/Subroutine Documentation

build_dels()

subroutine build_dels	(	class(oft_matrix), intent(inout), pointer	mat,
		class(gs_eq), intent(inout)	self,
		character(len=*), intent(in)	bc,
		real(8), intent(in), optional	dt,
		real(8), intent(in), optional	scale
	)

Construct \( \frac{1}{R} \Delta^* \) operator, with or without time-dependence.

Supported boundary conditions

• ‘'none’Full matrix -'zerob'Dirichlet for all boundary DOF -'grnd'` Dirichlet for only groundin point

  Parameters

  [in,out]	mat	Matrix object
  [in,out]	self	G-S object
  [in]	bc	Boundary condition
  [in]	dt	Timestep size for time-dependent version
  [in]	scale	Global scale factor

build_mrop()

subroutine build_mrop	(	type(oft_scalar_bfem), intent(inout)	fe_rep,
		class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct mass matrix for a boundary Lagrange scalar representation.

Supported boundary conditions

• ‘'none’Full matrix -'zerob'` Dirichlet for all boundary DOF

  Parameters

  [in,out]	fe_rep	2D Lagrange FE representation
  [in,out]	mat	Matrix object
  [in]	bc	Boundary condition

circle_interp()

subroutine circle_interp	(	class(circular_curr), intent(inout)	self,
		integer(4), intent(in)	cell,
		real(8), dimension(:), intent(in)	f,
		real(8), dimension(3,3), intent(in)	gop,
		real(8), dimension(:), intent(out)	val
	)

Evaluate uniform source over simple plasma cross-section.

Parameters

[in,out]	self	Interpolation object
[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [3]
[in]	gop	Logical gradient vectors at f [3,3]
[out]	val	Reconstructed field at f [1]

compute_bcmat()

subroutine compute_bcmat

(

class(gs_eq), intent(inout)

self

)

Compute boundary condition matrix for free-boundary case.

dummy_fpp()

real(r8) function dummy_fpp	(	class(flux_func), intent(inout)	self,
		real(r8), intent(in)	psi
	)

get_olbp()

subroutine get_olbp	(	class(oft_bmesh), intent(inout)	smesh,
		integer(4), dimension(:), intent(out)	olbp
	)

Generate oriented loop from boundary points.

gs_analyze_saddles()

subroutine gs_analyze_saddles	(	class(gs_eq), intent(inout)	self,
		real(8), dimension(2), intent(inout)	o_point,
		real(8), intent(inout)	o_psi,
		real(8), dimension(2,max_xpoints), intent(out)	x_point,
		real(8), dimension(max_xpoints), intent(out)	x_psi
	)

Needs Docs.

gs_b_interp_apply()

subroutine gs_b_interp_apply	(	class(gs_b_interp), intent(inout)	self,
		integer(4), intent(in)	cell,
		real(8), dimension(:), intent(in)	f,
		real(8), dimension(3,3), intent(in)	gop,
		real(8), dimension(:), intent(out)	val
	)

Reconstruct magnetic field from a Grad-Shafranov solution.

Parameters

[in,out]	self	Interpolation object
[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [3]
[in]	gop	Logical gradient vectors at f [3,3]
[out]	val	Reconstructed field at f [3]

gs_bcrosskappa()

subroutine gs_bcrosskappa	(	class(gs_eq), intent(inout), target	self,
		class(oft_vector), intent(inout), target	bcross_kappa
	)

Needs docs.

gs_coil_mutual()

subroutine gs_coil_mutual	(	class(gs_eq), intent(inout)	self,
		integer(4), intent(in)	icoil,
		class(oft_vector), intent(inout)	b,
		real(8), intent(out)	mutual
	)

Compute inductance between coil and given poloidal flux.

Parameters

[in,out]	self	G-S object
[in]	icoil	Coil index
[in,out]	b	\( \psi \) for mutual calculation
[out]	mutual	Mutual inductance \( \int I_C \psi dV / I_C \)

gs_coil_mutual_distributed()

subroutine gs_coil_mutual_distributed	(	class(gs_eq), intent(inout)	self,
		integer(4), intent(in)	icoil,
		class(oft_vector), intent(inout)	b,
		real(8), dimension(:), intent(in), pointer	curr_dist,
		real(8), intent(out)	mutual
	)

Compute inductance between a coil with non-uniform current distribution and given poloidal flux.

Parameters

[in,out]	self	G-S object
[in]	icoil	Coil index
[in,out]	b	\( \psi \) for mutual calculation
[in]	curr_dist	Relative current density
[out]	mutual	Mutual inductance \( \int I_C \psi dV / I_C \)

gs_coil_source()

subroutine gs_coil_source	(	class(gs_eq), intent(inout)	self,
		integer(4), intent(in)	icoil,
		class(oft_vector), intent(inout)	b
	)

Calculates coil current source for given coil.

Parameters

[in,out]	self	G-S Object
[in]	icoil	Coil index
[in,out]	b	Resulting source field

gs_coil_source_distributed()

subroutine gs_coil_source_distributed	(	class(gs_eq), intent(inout)	self,
		integer(4), intent(in)	icoil,
		class(oft_vector), intent(inout)	b,
		real(8), dimension(:), intent(in), pointer	curr_dist
	)

Calculates coil current source for given coil with non-uniform current distribution.

Parameters

[in,out]	self	G-S object
[in]	icoil	Coil index
[in,out]	b	Resulting source field
[in]	curr_dist	Relative current density

gs_curvature()

subroutine gs_curvature	(	class(gs_eq), intent(inout), target	self,
		class(oft_vector), intent(inout), target	br,
		class(oft_vector), intent(inout), target	bt,
		class(oft_vector), intent(inout), target	bz,
		class(oft_solver), intent(inout), optional, target	solver_in
	)

Needs docs.

gs_curvature_apply()

subroutine gs_curvature_apply	(	class(gs_curvature_interp), intent(inout)	self,
		integer(4), intent(in)	cell,
		real(8), dimension(:), intent(in)	f,
		real(8), dimension(3,3), intent(in)	gop,
		real(8), dimension(:), intent(out)	val
	)

Reconstruct magnetic field from a Grad-Shafranov solution.

Parameters

[in,out]	self	Interpolation object
[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [3]
[in]	gop	Logical gradient vectors at f [3,3]
[out]	val	Reconstructed field at f [3]

gs_destroy()

subroutine gs_destroy

(

class(gs_eq), intent(inout)

self

)

Destroy internal storage and nullify references for Grad-Shafranov object.

Parameters

[in,out]

self

G-S object

gs_dflux()

real(8) function gs_dflux

(

class(gs_eq), intent(inout)

self

)

Compute diamagentic flux.

Parameters

[in,out]

self

G-S object

Returns

Toroidal flux increment due to plasma

gs_err_reason()

character(len=40) function gs_err_reason

(

integer(4), intent(in)

ierr

)

Compute Grad-Shafranov solution for current flux definitions.

Parameters

[in]

ierr

Error flag

Returns

String representation of error

gs_find_saddle()

subroutine gs_find_saddle	(	class(gs_eq), intent(inout)	self,
		real(8), intent(in)	psi_scale_len,
		real(8), intent(inout)	psi_x,
		real(8), dimension(2), intent(inout)	pt,
		integer(4), intent(out)	stype
	)

Needs Docs.

gs_fit_isoflux()

subroutine gs_fit_isoflux	(	class(gs_eq), intent(inout)	self,
		class(oft_vector), intent(inout), target	psi_full,
		integer(4), intent(out)	ierr
	)

Compute coil currents to best fit isoflux, flux, and saddle targets at current solution.

Parameters

[in,out]	self	G-S object
[in,out]	psi_full	Current \( \psi \)
[out]	ierr	Error flag

gs_fixed_vflux()

subroutine gs_fixed_vflux	(	class(gs_eq), intent(inout)	self,
		real(8), dimension(:,:), intent(inout), pointer	pts,
		real(8), dimension(:), intent(inout), pointer	fluxes
	)

Compute required vacuum flux for fixed boundary equilibrium.

Parameters

[in,out]	self	G-S object
[in,out]	pts	Locations of boundary points
[in,out]	fluxes	Required flux at each point

gs_gen_source()

subroutine gs_gen_source	(	class(gs_eq), intent(inout)	self,
		class(bfem_interp), intent(inout)	source_fun,
		class(oft_vector), intent(inout)	b
	)

Compute RHS source from an arbitrary current distribution \( J_{\phi} \).

Parameters

[in,out]	self	G-S object
[in,out]	source_fun	Interpolation object for \( J_{\phi} \)
[in,out]	b	Resulting source field

gs_get_chi()

subroutine gs_get_chi

(

class(gs_eq), intent(inout)

self

)

Compute toroidal flux potential from Grad-Shafranov solution.

Parameters

[in,out]

self

G-S object

gs_get_cond_scales()

subroutine gs_get_cond_scales	(	class(gs_eq), intent(inout)	self,
		real(8), dimension(:), intent(inout)	vals,
		logical, intent(in)	skip_fixed
	)

Needs Docs.

gs_get_cond_weights()

subroutine gs_get_cond_weights	(	class(gs_eq), intent(inout)	self,
		real(8), dimension(:), intent(inout)	vals,
		logical, intent(in)	skip_fixed
	)

Needs Docs.

gs_get_qprof()

subroutine gs_get_qprof	(	class(gs_eq), intent(inout)	gseq,
		integer(4), intent(in)	nr,
		real(8), dimension(nr), intent(in)	psi_q,
		real(8), dimension(nr), intent(out)	prof,
		real(8), intent(out), optional	dl,
		real(8), dimension(2,2), intent(out), optional	rbounds,
		real(8), dimension(2,2), intent(out), optional	zbounds,
		real(8), dimension(nr,3), intent(out), optional	ravgs
	)

Get q profile for equilibrium.

Parameters

[in,out]	gseq	G-S object
[in]	nr	Number of flux surfaces to sample
[in]	psi_q	Locations to sample in normalized flux
[out]	prof	q value at each sampling location
[out]	dl	Arc length of surface psi_q(1) (should be LCFS)
[out]	rbounds	Radial bounds of surface psi_q(1) (should be LCFS)
[out]	zbounds	Vertical bounds of surface psi_q(1) (should be LCFS)
[out]	ravgs	Flux surface averages <R>, <1/R>, and dV/dPsi

gs_helicity()

subroutine gs_helicity	(	class(gs_eq), intent(inout)	self,
		real(8), intent(out)	ener,
		real(8), intent(out)	helic
	)

Compute the magnetic energy and helicity of a fixed boundary equilibrium.

Note

Helicity computed by this subroutine is only valid for equilibria with no normal field on the boundary

Parameters

[in,out]	self	G-S object
[out]	ener	Total magnetic energy
[out]	helic	Total magnetic helicity

gs_init()

subroutine gs_init

(

class(gs_eq), intent(inout)

self

)

Initialize Grad-Shafranov object by computing operators and allocating storage.

Parameters

[in,out]

self

G-S object

gs_init_psi()

subroutine gs_init_psi	(	class(gs_eq), intent(inout)	self,
		integer(4), intent(out)	ierr,
		real(8), dimension(2), intent(in), optional	r0,
		real(8), intent(in), optional	a,
		real(8), intent(in), optional	kappa,
		real(8), intent(in), optional	delta,
		real(8), dimension(:), intent(in), optional	curr_source
	)

Initialize \( \psi \).

\( \psi \) can be initialized in one of four ways:

1. If no optional arguments are passed a Taylor state is computed and used
2. If r0 < 0.0 is passed a uniform current across the entire plasma region is used
3. If r0 and a, and optionally kappa and delta, are passed then a uniform current across a cross-section defined by those parameters is used
4. If curr_source is passed then the source defined by those values is used

In all cases the solution is scaled to match the target Ip value

Parameters

[in,out]	self	G-S object
[out]	ierr	Error flag
[in]	r0	Center for cross-section initialization
[in]	a	Minor radius for cross-section initialization
[in]	kappa	Elongation for cross-section initialization
[in]	delta	Triangularity for cross-section initialization
[in]	curr_source	Explicit current source

gs_itor()

real(8) function gs_itor	(	class(gs_eq), intent(inout)	self,
		class(oft_vector), intent(inout), optional	psi_vec
	)

Compute toroidal current for Grad-Shafranov equilibrium.

Parameters

[in,out]	self	G-S object
[in,out]	psi_vec	Needs docs

Returns

Toroidal current

gs_itor_nl()

subroutine gs_itor_nl	(	class(gs_eq), intent(inout)	self,
		real(8), intent(out)	itor,
		real(8), dimension(2), intent(out), optional	centroid
	)

Compute toroidal current for Grad-Shafranov equilibrium.

Parameters

[in,out]	self	G-S object
[out]	itor	Toroidal current
[out]	centroid	Current centroid (optional) [2]

gs_j_interp_apply()

subroutine gs_j_interp_apply	(	class(gs_j_interp), intent(inout)	self,
		integer(4), intent(in)	cell,
		real(8), dimension(:), intent(in)	f,
		real(8), dimension(3,3), intent(in)	gop,
		real(8), dimension(:), intent(out)	val
	)

Reconstruct magnetic field from a Grad-Shafranov solution.

Parameters

[in,out]	self	Interpolation object
[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [3]
[in]	gop	Logical gradient vectors at f [3,3]
[out]	val	Reconstructed field at f [3]

gs_j_interp_delete()

subroutine gs_j_interp_delete

(

class(gs_j_interp), intent(inout)

self

)

Destroy temporary internal storage and nullify references.

gs_j_interp_setup()

subroutine gs_j_interp_setup	(	class(gs_j_interp), intent(inout)	self,
		class(gs_eq), intent(inout), target	gs
	)

Needs Docs.

gs_lin_solve()

subroutine gs_lin_solve	(	class(gs_eq), intent(inout)	self,
		logical, intent(in)	adjust_r0,
		integer(4), intent(out), optional	ierr
	)

Compute solution to linearized Grad-Shafranov without updating \( \psi \) for RHS.

Parameters

[in,out]	self	G-S object
[in]	adjust_r0	Needs docs
[out]	ierr	Error flag

gs_load_limiters()

subroutine gs_load_limiters

(

class(gs_eq), intent(inout)

self

)

Needs Docs.

Parameters

[in,out]

self

G-S object

gs_mat_create()

subroutine gs_mat_create	(	class(oft_scalar_bfem), intent(inout)	fe_rep,
		class(oft_matrix), intent(out), pointer	new
	)

Create G-S matrix with necessary augmentations for free-boundary BC.

gs_plasma_mutual()

subroutine gs_plasma_mutual	(	class(gs_eq), intent(inout)	self,
		class(oft_vector), intent(inout)	b,
		real(8), intent(out)	mutual,
		real(8), intent(out)	itor
	)

Compute inductance between plasma current and given poloidal flux.

Parameters

[in,out]	self	G-S solver object
[in,out]	b	\( \psi \) for mutual calculation
[out]	mutual	Mutual inductance \( \int J_p \psi dV / I_p \)
[out]	itor	Plasma toroidal current

gs_prof_interp_apply()

subroutine gs_prof_interp_apply	(	class(gs_prof_interp), intent(inout)	self,
		integer(4), intent(in)	cell,
		real(8), dimension(:), intent(in)	f,
		real(8), dimension(3,3), intent(in)	gop,
		real(8), dimension(:), intent(out)	val
	)

Reconstruct a component of a Grad-Shafranov solution.

Parameters

[in,out]	self	Interpolation object
[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [3]
[in]	gop	Logical gradient vectors at f [3,3]
[out]	val	Reconstructed field at f [1]

gs_prof_interp_delete()

subroutine gs_prof_interp_delete

(

class(gs_prof_interp), intent(inout)

self

)

Destroy temporary internal storage and nullify references.

gs_prof_interp_setup()

subroutine gs_prof_interp_setup	(	class(gs_prof_interp), intent(inout)	self,
		class(gs_eq), intent(inout), target	gs
	)

Needs Docs.

gs_project_b()

subroutine gs_project_b	(	class(gs_eq), intent(inout), target	self,
		class(oft_vector), intent(inout)	br,
		class(oft_vector), intent(inout)	bt,
		class(oft_vector), intent(inout)	bz,
		class(oft_solver), intent(inout), optional, target	solver_in,
		logical, intent(in), optional	normalized
	)

Needs Docs.

gs_psi2pt()

subroutine gs_psi2pt	(	class(gs_eq), intent(inout)	self,
		real(8), intent(in)	psi_target,
		real(8), dimension(2), intent(inout)	pt,
		real(8), dimension(2), intent(in)	pt_con,
		real(8), dimension(2), intent(in)	vec,
		type(oft_lag_brinterp), intent(inout), optional, target	psi_int
	)

Find position of psi along a vector search direction.

Parameters

[in,out]	self	G-S object
[in]	psi_target	Target \( \psi \) value to find
[in,out]	pt	Guess location (input); Closest point found (output) [2]
[in]	pt_con	Location defining origin of search path
[in]	vec	Vector defining direction of search path
[in,out]	psi_int	Interpolation object (created internally if not passed)

gs_psi2r()

subroutine gs_psi2r	(	class(gs_eq), intent(inout)	self,
		real(8), intent(in)	psi_target,
		real(8), dimension(2), intent(inout)	pt,
		type(oft_lag_brinterp), intent(inout), optional, target	psi_int
	)

Find position of psi along a radial chord.

Parameters

[in,out]	self	G-S object
[in]	psi_target	Target \( \psi \) value to find
[in,out]	pt	Guess location (input); Closest point found, by changing R only (output) [2]

gs_save_fields()

subroutine gs_save_fields	(	class(gs_eq), intent(inout)	self,
		real(8), dimension(2,npts), intent(in)	pts,
		integer(4), intent(in)	npts,
		character(len=*), intent(in)	filename
	)

Compute magnetic fields from Grad-Shafranov equilibrium.

Parameters

[in,out]	self	G-S object
[in]	pts	Sampling locations [2,npts]
[in]	npts	Number of points to sample
[in]	filename	Output file for field data

gs_save_mug()

subroutine gs_save_mug	(	class(gs_eq), intent(inout), target	self,
		character(len=*), intent(in), optional	filename,
		logical, intent(in), optional	legacy
	)

Needs Docs.

gs_save_prof()

subroutine gs_save_prof	(	class(gs_eq), intent(inout), target	self,
		character(len=*), intent(in)	filename,
		integer(4), intent(in), optional	mpsi_sample
	)

Needs Docs.

gs_set_cond_weights()

subroutine gs_set_cond_weights	(	class(gs_eq), intent(inout)	self,
		real(8), dimension(:), intent(in)	vals,
		logical, intent(in)	skip_fixed
	)

Needs Docs.

gs_setup()

subroutine gs_setup	(	class(gs_eq), intent(inout)	self,
		class(oft_ml_fem_type), intent(inout), target	ml_lag_2d
	)

Needs Docs.

Parameters

[in,out]

self

G-S object

gs_setup_walls()

subroutine gs_setup_walls	(	class(gs_eq), intent(inout)	self,
		logical, intent(in), optional	skip_load,
		logical, intent(in), optional	make_plot
	)

Needs Docs.

Parameters

[in,out]

self

G-S object

gs_solve()

subroutine gs_solve	(	class(gs_eq), intent(inout)	self,
		integer(4), intent(out), optional	ierr
	)

Compute Grad-Shafranov solution for current flux function definitions and targets.

Parameters

[in,out]	self	G-S object
[out]	ierr	Error flag

gs_source()

subroutine gs_source	(	class(gs_eq), intent(inout)	self,
		class(oft_vector), intent(inout), target	a,
		class(oft_vector), intent(inout)	b,
		class(oft_vector), intent(inout)	b2,
		class(oft_vector), intent(inout)	b3,
		real(8), intent(out)	itor_alam,
		real(8), intent(out)	itor_press,
		real(8), intent(out)	estore
	)

Compute plasma component of RHS source for Grad-Shafranov equation.

Parameters

[in,out]	self	G-S object
[in,out]	a	\( \psi \)
[in,out]	b	Full RHS source
[in,out]	b2	F*F' component of source (including alam)
[in,out]	b3	P' component of source (without pnorm)

gs_test_bounds()

logical function gs_test_bounds	(	class(gs_eq), intent(inout)	self,
		real(8), dimension(2), intent(in)	pt
	)

Test whether a point is inside the LCFS.

Parameters

[in,out]	self	G-S object
[in]	pt	Location to test in/out of plasma

gs_trace_surf()

subroutine gs_trace_surf	(	class(gs_eq), intent(inout)	gseq,
		real(8), intent(in)	psi_in,
		real(8), dimension(:,:), intent(out), pointer	points,
		integer(4), intent(out)	npoints
	)

Trace a single specified flux surface.

Parameters

[in,out]	gseq	G-S object
[in]	psi_in	Locations of surface to trace in normalized flux
[out]	points	Traced surface
[out]	npoints	Number of points in traced surface

gs_update_bounds()

subroutine gs_update_bounds	(	class(gs_eq), intent(inout)	self,
		logical, intent(in), optional	track_opoint
	)

Needs Docs.

gs_vac_solve()

subroutine gs_vac_solve	(	class(gs_eq), intent(inout)	self,
		class(oft_vector), intent(inout)	psi_sol,
		class(bfem_interp), intent(inout), optional	rhs_source,
		integer(4), intent(out), optional	ierr
	)

Compute Grad-Shafranov solution for vacuum (no plasma)

Parameters

[in,out]	self	G-S object
[in,out]	psi_sol	Input: BCs for \( \psi \), Output: solution
[in,out]	rhs_source	Specified current source (optional)
[out]	ierr	Error flag

gs_vacuum_solve()

subroutine gs_vacuum_solve	(	class(gs_eq), intent(inout)	self,
		class(oft_vector), intent(inout)	pol_flux,
		class(oft_vector), intent(inout)	source,
		integer(4), intent(out), optional	ierr
	)

Solve for \( \psi \) in vacuum for a given source \( \int \phi^T J_{\phi} dA \).

Source field must already be projected onto the appropriate Lagrange FE basis

Parameters

[in,out]	self	G-S object
[in,out]	pol_flux	\( \psi \) (output)
[in,out]	source	Current source
[out]	ierr	Error flag

gs_wall_source()

subroutine gs_wall_source	(	class(gs_eq), intent(inout)	self,
		class(oft_vector), intent(inout)	dpsi_dt,
		class(oft_vector), intent(inout)	b
	)

Calculate RHS source for quasi-static solve from previous \( \psi \).

Parameters

[in,out]	self	G-S object
[in,out]	dpsi_dt	\( \psi \) at start of step
[in,out]	b	Resulting source field

gsinv_apply()

subroutine gsinv_apply	(	class(gsinv_interp), intent(inout)	self,
		integer(4), intent(in)	cell,
		real(8), dimension(:), intent(in)	f,
		real(8), dimension(3,3), intent(in)	gop,
		real(8), dimension(:), intent(out)	val
	)

Needs Docs.

gsinv_destroy()

subroutine gsinv_destroy

(

class(gsinv_interp), intent(inout)

self

)

Needs Docs.

gsinv_setup()

subroutine gsinv_setup	(	class(gsinv_interp), intent(inout)	self,
		class(oft_afem_type), intent(inout), target	lag_rep
	)

Needs Docs.

psi2pt_error()

subroutine psi2pt_error	(	integer(4), intent(in)	m,
		integer(4), intent(in)	n,
		real(8), dimension(n), intent(in)	cofs,
		real(8), dimension(m), intent(out)	err,
		integer(4), intent(inout)	iflag
	)

Needs docs.

psimax_error()

subroutine psimax_error	(	integer(4), intent(in)	m,
		integer(4), intent(in)	n,
		real(8), dimension(n), intent(in)	cofs,
		real(8), dimension(m), intent(out)	err,
		integer(4), intent(inout)	iflag
	)

Needs docs.

psimax_error_grad()

subroutine psimax_error_grad	(	integer(4), intent(in)	m,
		integer(4), intent(in)	n,
		real(8), dimension(n), intent(in)	cofs,
		real(8), dimension(m), intent(out)	err,
		real(8), dimension(ldjac_mat,n), intent(out)	jac_mat,
		integer(4), intent(in)	ldjac_mat,
		integer(4), intent(in)	iflag
	)

Needs docs.

set_bcmat()

subroutine set_bcmat	(	class(gs_eq), intent(inout)	self,
		class(oft_matrix), intent(inout)	mat
	)

Add boundary condition terms for free-boundary case to matrix.

Parameters

[in,out]	self	G-S object
[in,out]	mat	Matrix object

zerob_apply()

subroutine zerob_apply	(	class(oft_gs_zerob), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero a 2D Lagrange scalar field at all nodes outside the plasma or on the global boundary.

Parameters

[in,out]	self	BC object
[in,out]	a	Field to be zeroed

zerob_delete()

subroutine zerob_delete

(

class(oft_gs_zerob), intent(inout)

self

)

Destroy temporary internal storage and nullify references.

Parameters

[in,out]

self

BC object

Variable Documentation

cell_active

integer(i4) cell_active = 0

gs_epsilon

real(r8), parameter gs_epsilon = 1.d-12

Epsilon used for radial coordinate.

max_xpoints

integer(4), parameter max_xpoints = 20

psi_eval_active

type(oft_lag_brinterp), pointer psi_eval_active => NULL()

psi_g2eval_active

type(oft_lag_bg2interp), pointer psi_g2eval_active => NULL()

psi_geval_active

type(oft_lag_bginterp), pointer psi_geval_active => NULL()

psi_target_active

real(r8) psi_target_active = 0.d0

pt_con_active

real(r8), dimension(2) pt_con_active = [0.d0,0.d0]

qp_int_tol

real(r8) qp_int_tol = 1.d-12

vec_con_active

real(r8), dimension(2) vec_con_active = [0.d0,0.d0]