STELLGAP

Stellgap calculates the shear Alfvén gap structure for 3D configurations (stellarators, RFPs, 3D tokamaks)

These codes are used to calculate shear Alfven continua for 3D configurations, both with and without sound wave coupling effects. The associated paper is D. A. Spong, R. Sanchez, A. Weller, “Shear Alfvén continua in stellarators,” Phys. Plasmas 10 (2003) 3217–3224.

Theory

The Alfvén continuum equation for 3D stellarator equilibira in low plasma beta, incompressible limite is written:

\[\mu_0\rho\omega^2\frac{|\nabla\psi|^2}{B^2}E_\psi+\vec{B}\cdot\nabla\left[\frac{|\nabla\psi|^2}{B^2}\left(\vec{B}\cdot\nabla\right)E_\psi\right]=0\]

The STELLGAP code reformulates this equation in terms of a eigenvalue equation which is sovled using the Lapack routine DGGEV routine.

The following table provides a list of Alfvén couplings which are of interest to 3D equilibria.

Abbreviation	Name	$\delta_m$	$\delta_n$
GAE	Global Alfvén eigenmode	0	0
TAE	Toroidal Alfvén eigenmode	±1	0
EAE	Elliptical Alfvén eigenmode	±2	0
NAE	Noncircular Alfvén eigenmode	>2	0
MAE	Mirror Alfvén eigenmode	0	±1, ±2, …
HAE	Helical Alfvén eigenmode	>0	±1, ±2, …

Compilation

The STELLGAP code can be found in the ORNL repository Github:STELLGAP. Once you download the code there are shell scripts for building the code, otherwise you can use the following makefile:

PRECOMP=gcc -traditional-cpp -cpp 
FC=mpif90 -g -fbacktrace -fexternal-blas
BUILD_TYPE = -DSERIAL

LIBSTELL_DIR = $(STELLOPT_PATH)LIBSTELL/Release
LIBSTELL_LIB = ~/bin/libstell.a

FFLAGS= -I${LIBSTELL_DIR} $(shell nf-config --fflags)
LDFLAGS=${LIBSTELL_LIB} $(shell nf-config --flibs) -framework Accelerate 


OBJ=fitpack.o Fourier_lib_convolve.o 

%.o: %.f
	$(PRECOMP) -E -P $(BUILD_TYPE) $^ > temp.f
	$(FC) -c -o $@ temp.f $(FFLAGS)

xmetric: metric_element_create_ver8.46.o
	$(FC) -o $@ $^ $(LDFLAGS)

xstgap: stellgap_ver5.o $(OBJ) 
	$(FC) -o $@ $^ $(LDFLAGS)

xstgap_snd_ver6: stellgap_soundwave_lagrng_ver6.o $(OBJ) 
	$(FC) -o $@ $^ $(LDFLAGS)

xstgap_snd_ver7: stellgap_soundwave_lagrng_ver7.o $(OBJ) 
	$(FC) -o $@ $^ $(LDFLAGS)

clean:
	@rm -rf *.o xmetric xstgap xstgap_snd_ver6 xstgap_snd_ver7 temp.f

Note that the parallel version can be built by changing the line BUILD_TYPE to -DPARALLEL. It is important that whatever compiler was used to build LIBSTELL be used to build STELLGAP.

Input Data Format

The STELLGAP code requires that the VMEC equilibrium be transformed into Boozer Coordinates by the [BOOZ_XFORM] code. The output of that code is then transformed into input files for STELLGAP. There are two files the user must provide (fourier.dat and plasma.dat).

The plasma.dat code contains a Fortran input namelist which defines the density profile for the computation.

&PLASMA_INPUT
! ION MASS in AMU
 ion_to_proton_mass = 2.
! Core Ion Density in m^3
ion_density_0 = 2.5e+20
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!  Ion Profiles
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Ion profile type iota
! ion_profile = 0 ! [iota(rho)/iota(0)]**2
! Ion profile type polynomial
! ion_profile = 1
! nion = 1.0 -2.0 1.0 ! Similar to AM/AI/AC array
! Ion profile type constant
! ion_profile = 2
! Ion profile type two power
 ion_profile = 3 ! [1 - aion*rho**bion]**cion
 aion = 0.99
 bion = 0.50
 cion = 1.00
!!!!!!!!!!!!!!!!!!!!!!!!!!
!! Unused AE3D variables
!!!!!!!!!!!!!!!!!!!!!!!!!!
 jdqz_data = T
 egnout_form = 'asci'
/

The fourier.dat file is a text file containing the grid and spectrum information it has the following format (all quantities are integers).

NFP  NTHETA  NZETA  MODE_FAMILY
NMODES
N ML MU
N ML MU
N ML MU
...

NFP: number of field periods
NTHETA: Number of poloidal grid points (see surface_area_elements)
NZETA: Number of toroidal grid points (see surface_area_elements)
MODE_FAMILY: Toroidal mode number about which the eigenfunctions are built (not utilized by code)
NMODES: Number of toroidal modes used (should be multiple of NFP)
N: Toroidal mode number
ML: Starting Poloidal mode number
MU: Ending Poloidal mode number

The choice of toroidal mode numbers to investigate should follow the mode coupleing paradigm. Specically N=n0+NFP*k and N=n0-NPF*k. For example, and n0=1 modes for an NFP=5 device would be -11,-9,-6,-4,4,6,9,11 where both postive and negative n0 are accounted for.

Execution

To execute the STELLGAP code you must start from a [VMEC] equilibrium, transform the equilibrium to Boozer coordiantes using [BOOZ_XFORM], process the Boozer coordinates with the xmetric routine, generate the fourier.dat and profiles.dat files, and finally run a version of STELLGAP (xstgap, xstgap_snd_ver6, xstgap_snd_ver7).

Run the [VMEC] code to produce a wout file.
Generate the in_booz file for your VMEC for all radial gridpoints in your equilibrium.
Run the xmetric utility to generate input files. This routine takes the boozmn file suffix as input on the command line.
Generate the fourier.dat and profiles.dat files for your run.
Run STELLGAP (xstgap, xstgap_snd_ver6, xstgap_snd_ver7). STELLGAP takes two values command line input (irad and ir_fine_scl)
- irad: should be set to the number of flux surface in original file - 2.
- ir_fine_scl: Number of surfaces in the output should be greater than irad.

Output Data Format

The following files are produced by the code.

XMETRIC
- ae_metric.dat : First line is (nsd-2), izeta, itheta, nznt, then followed by profiles and finally various metric elements.
- cart_coords : X,Y,Z data.
- full_torus_coords : X,Y,Z over entire torus.
- metrics : Metric elements
- surf_area_elements : First line is nfp, izeta, itheta, then zeta, theta, and surface area.
- tae_data_boozer : Each block starts with ks,iotac,phipc,jtorc,jpolc followed by metric information.
- torus_slice_coords : X,Y,Z data.
XSTELGAP
- alfven_spec : rho, alfr, alfi, beta, m, n
- coef_array : rm, rn, f1, f3a, f3b, f3c
- data_post : iopt, mn, if_fine_scale, isym_opt
- ion_profile : rho, n_ion, iota, va
- modes : Table of modes

Visualization

STELLGAP provides two routines post_process.f and post_process_snd.f to aide in plotting values from alfven_spec. These routine process the alfven_spec file defining lam_r = alfr/beta and lam_i = alfi/beta. Then the complex number omega2 = (lam_r,lam_i) is defined. Finally, omega_r is computed as the real part of the square root of omega2.

Tutorials

TBD