Module for reading in VMEC input and computing metric elements on the SIESTA (sqrt-flux) radial grid. Computes and stores the real-space metric elements, Jacobian based on square root of fluc splined vmec coordinate system. More...

Functions/Subroutines
subroutine	init_metric_elements ()
	Initialize the metric elements.

subroutine	set_grid_sizes (mpol_in, ntor_in, nfp_in, tor_modes)
	Set grid sizes.

subroutine	surfavg (average, q3d, nsmin, nsmax)
	Surface average a quantity.

subroutine	loadgrid (istat)
	Load the R, Z and lambda arrays from VMEC.

subroutine	rz_to_ijsp (rmn, zmn, lasym)
	Transform from fourier R Z to real space qauntities.

subroutine	half_mesh_metrics (r1_i, ru_i, rv_i, z1_i, zu_i, zv_i)
	Compute the metric elements on the half mesh.

subroutine	full_mesh_metrics
	Gets the full grid metric elements.

subroutine	check_metrics
	@ brief Test to check that we computed the upper metric elements correctly.

subroutine	toupper (xsubsij, xsubuij, xsubvij,
	Converts to contravariant component full grid.

subroutine	tolowerh (xsupsij, xsupuij, xsupvij,
	Converts to covariant component half grid.

subroutine	tolowerf (xsupsij, xsupuij, xsupvij,
	Converts to covariant component full grid.

subroutine	cleanup_metric_elements
	Deallocate memory containing metric elements on the half mesh.

subroutine	dealloc_full_lower_metrics
	Deallocate memory containing metric elements on the full mesh.

Variables
real(dp), dimension(:,:), allocatable	sqrtg
	Jacobian on half grid.

real(dp), dimension(:,:), allocatable	gss
	Lower metric tensor half grid. e_s . e_s.

real(dp), dimension(:,:), allocatable	gsu
	Lower metric tensor half grid. e_s . e_u.

real(dp), dimension(:,:), allocatable	gsv
	Lower metric tensor half grid. e_s . e_v.

real(dp), dimension(:,:), allocatable	guu
	Lower metric tensor half grid. e_u . e_u.

real(dp), dimension(:,:), allocatable	guv
	Lower metric tensor half grid. e_u . e_v.

real(dp), dimension(:,:), allocatable	gvv
	Lower metric tensor half grid. e_v . e_v.

real(dp), dimension(:,:), allocatable	hss
	Upper metric tensor half grid. e^s . e^s.

real(dp), dimension(:,:), allocatable	hsu
	Upper metric tensor. e^s . e^u.

real(dp), dimension(:,:), allocatable	hsv
	Upper metric tensor. e^s . e^v.

real(dp), dimension(:,:), allocatable	huu
	Upper metric tensor. e^u . e^u.

real(dp), dimension(:,:), allocatable	huv
	Upper metric tensor. e^u . e^v.

real(dp), dimension(:,:), allocatable	hvv
	Upper metric tensor. e^v . e^v.

real(dp), dimension(:,:), allocatable	gssf
	Lower metric tensor full grid. e_s . e_s.

real(dp), dimension(:,:), allocatable	gsuf
	Lower metric tensor full grid. e_s . e_u.

real(dp), dimension(:,:), allocatable	gsvf
	Lower metric tensor full grid. e_s . e_v.

real(dp), dimension(:,:), allocatable	guuf
	Lower metric tensor full grid. e_u . e_u.

real(dp), dimension(:,:), allocatable	guvf
	Lower metric tensor full grid. e_u . e_v.

real(dp), dimension(:,:), allocatable	gvvf
	Lower metric tensor full grid. e_v . e_v.

real(dp)	rmax
	Maximum of the grid R inside the last closed flux surface.

real(dp)	rmin
	Minimum of the grid R inside the last closed flux surface.

real(dp)	zmax
	Maximum of the grid Z inside the last closed flux surface.

real(dp)	zmin
	Minimum of the grid Z inside the last closed flux surface.

real(dp)	skston
	Start timer.

real(dp)	skstoff
	Stop timer.

Detailed Description

Module for reading in VMEC input and computing metric elements on the SIESTA (sqrt-flux) radial grid. Computes and stores the real-space metric elements, Jacobian based on square root of fluc splined vmec coordinate system.

Function/Subroutine Documentation

◆ check_metrics()

subroutine metrics::check_metrics

@ brief Test to check that we computed the upper metric elements correctly.

Check that the metric elements conform to the following relation to machine precission.

hij*gjk = delta_ik (1)

Note the repeated index implys a sum.

◆ cleanup_metric_elements()

subroutine metrics::cleanup_metric_elements

Deallocate memory containing metric elements on the half mesh.

Also deallocates the grid variables.

Note: sqrtg is deallocated in init_bcovar and stored in jacob variable

◆ full_mesh_metrics()

subroutine metrics::full_mesh_metrics

Gets the full grid metric elements.

This subroutine gets the lower metric elements on the full mesh. Preserves positive definiteness of metric tensor.

◆ half_mesh_metrics()

subroutine metrics::half_mesh_metrics	(	real(dp), dimension(nuv,ns_i), intent(in)	r1_i,
		real(dp), dimension(nuv,ns_i), intent(in)	ru_i,
		real(dp), dimension(nuv,ns_i), intent(in)	rv_i,
		real(dp), dimension(nuv,ns_i), intent(in)	z1_i,
		real(dp), dimension(nuv,ns_i), intent(in)	zu_i,
		real(dp), dimension(nuv,ns_i), intent(in)	zv_i
	)

Compute the metric elements on the half mesh.

Parameters

[in]	r1_i	R on the full mesh.
[in]	ru_i	dRdu on the full mesh.
[in]	rv_i	dRdv on the full mesh.
[in]	z1_i	Z on the full mesh.
[in]	zu_i	dZdu on the full mesh.
[in]	zv_i	dZdv on the full mesh.

◆ init_metric_elements()

subroutine metrics::init_metric_elements

Initialize the metric elements.

Loads values on to the SIESTA meshes. This involves splining and interpolating the VMEC quantities from the VMEC radial grid to the SIESTA radial grid.

◆ loadgrid()

subroutine metrics::loadgrid ( integer, intent(out) istat )

Load the R, Z and lambda arrays from VMEC.

R, Z and Lambda are recast onto the SIESTA grid.

Parameters

[out] istat Error status.

◆ rz_to_ijsp()

subroutine metrics::rz_to_ijsp	(	real(dp), dimension(:,:,:), intent(in)	rmn,
		real(dp), dimension(:,:,:), intent(in)	zmn,
		logical, intent(in)	lasym
	)

Transform from fourier R Z to real space qauntities.

Computes R, Z, dr/du, dr/dv, dz/du and dz/dv from the fourier representation.

Parameters

[in]	rmn	Radial fourier amplitudes.
[in]	zmn	Vertical fourier amplitudes.
[in]	lasym	A symmetric flag.

◆ set_grid_sizes()

subroutine metrics::set_grid_sizes	(	integer, intent(in)	mpol_in,
		integer, intent(in)	ntor_in,
		integer, intent(in)	nfp_in,
		integer, dimension(-ntor_in:ntor_in), intent(in)	tor_modes
	)

Set grid sizes.

The real space grid is determined from the number of toroidal and poloidal modes.

Parameters

[in]	mpol_in	Number of SIESTA poloidal modes.
[in]	ntor_in	Number of SIESTA toroidal modes.
[in]	nfp_in	Number of field periods.
[in]	tor_modes	Toroidal mode numbers.

◆ surfavg()

subroutine metrics::surfavg	(	real(dp), dimension(nsmin:nsmax), intent(out)	average,
		real(dp), dimension(nu_i,nv_i,nsmin:nsmax), intent(in)	q3d,
		integer, intent(in)	nsmin,
		integer, intent(in)	nsmax
	)

Surface average a quantity.

Parameters

[out]	average	Surface average
[in]	q3d	3D quantity is real space.
[in]	nsmin	Minimum radial index.
[in]	nsmax	Maximum radial index.

◆ tolowerf()

subroutine metrics::tolowerf	(	real(dp), dimension(nuv,ns), intent(in)	xsupsij,
		real(dp), dimension(nuv,ns), intent(in)	xsupuij,
		real(dp), dimension(nuv,ns), intent(in)	xsupvij
	)

Converts to covariant component full grid.

Computes covariant (lower) from contravariant (upper) magnetic field components on the full mesh.

xsubsij = gssf*xsupsij + gsuf*xsupuij + gsvf*xsupvij xsubuij = gsuf*xsupsij + guuf*xsupuij + guvf*xsupvij xsubvij = gsvf*xsupsij + guvf*xsupuij + gvvf*xsupvij

Parameters

[in]	xsupsij	Contravariant s component.
[in]	xsupuij	Contravariant u component.
[in]	xsupvij	Contravariant v component.
[out]	xsubsij	Covariant s component.
[out]	xsubuij	Covariant u component.
[out]	xsubvij	Covariant v component.
[in]	nsmin	Min radial index.
[in]	nsmax	Max radial index.

◆ tolowerh()

subroutine metrics::tolowerh	(	real(dp), dimension(nuv,nsmin:nsmax), intent(in)	xsupsij,
		real(dp), dimension(nuv,nsmin:nsmax), intent(in)	xsupuij,
		real(dp), dimension(nuv,nsmin:nsmax), intent(in)	xsupvij
	)

Converts to covariant component half grid.

Computes covariant (lower) from contravariant (upper) magnetic field components on the half mesh.

xsubsij = gss*xsupsij + gsu*xsupuij + gsv*xsupvij xsubuij = gsu*xsupsij + guu*xsupuij + guv*xsupvij xsubvij = gsv*xsupsij + guv*xsupuij + gvv*xsupvij

Parameters

[in]	xsupsij	Contravariant s component.
[in]	xsupuij	Contravariant u component.
[in]	xsupvij	Contravariant v component.
[out]	xsubsij	Covariant s component.
[out]	xsubuij	Covariant u component.
[out]	xsubvij	Covariant v component.
[in]	nsmin	Min radial index.
[in]	nsmax	Max radial index.

◆ toupper()

subroutine metrics::toupper	(	real(dp), dimension(nuv,nsmin:nsmax), intent(in)	xsubsij,
		real(dp), dimension(nuv,nsmin:nsmax), intent(in)	xsubuij,
		real(dp), dimension(nuv,nsmin:nsmax), intent(in)	xsubvij
	)

Converts to contravariant component full grid.

Computes contravariant (upper) from covariant (lower) components on the full mesh.

xsupsij = hss*xsubsij + hsu*xsupuij + hsv*xsubvij xsupuij = hsu*xsubsij + huu*xsupuij + huv*xsubvij xsupvij = hsv*xsubsij + huv*xsupuij + hvv*xsubvij

Parameters

[in]	xsubsij	Covariant s component.
[in]	xsubuij	Covariant u component.
[in]	xsubvij	Covariant v component.
[out]	xsupsij	Contravariant s component.
[out]	xsupuij	Contravariant u component.
[out]	xsupvij	Contravariant v component.
[in]	nsmin	Min radial index.
[in]	nsmax	Max radial index.

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ check_metrics()

◆ cleanup_metric_elements()

◆ full_mesh_metrics()

◆ half_mesh_metrics()

◆ init_metric_elements()

◆ loadgrid()

◆ rz_to_ijsp()

◆ set_grid_sizes()

◆ surfavg()

◆ tolowerf()

◆ tolowerh()

◆ toupper()