# STELLOPT

State-of-the-art stellarator optimization code

# VMEC2PIES

The VMEC2PIES code creates a PIES input file from VMEC input.

### Theory

The VMEC2PIES code allows a PIES run to be conducted from an VMEC input or wout file. This is achieved by calculating a set of nested surfaces for PIES to use as a background coordinate system and placing a magnetic field on that grid. It's most basic output is a pies input file with INPUT, PLTFLG, and EXLSTA namelists. It also outputs the R, Z, B\^S, B\^U, B\^Z, and mode selection matrix in the input file. The pressure and current profiles are output as a series of splines over the VMEC flux coordinates. The code can be initialize from VMEC INDATA namelist or a VMEC wout file. It can 'extend' the VMEC boundary by extrapolating new surfaces in real space. It can also create a PIES coil_data file from a coils file and the EXTCUR array (found in INDATA namelist or wout file). The fixed or free boundary flag in the INDATA namelist or wout file can be overridden for the pies input.

If the user supplies a VMEC input file with INDATA namelist coordinates will be constructed from the RBC/ZBS arrays and the magnetic axis location specification. Pressure and current profiles are extracted from the input file as well. The magnetic field is then calculated by the following relation: math B\^u = \chi'/\sqrt(g)
B\^v = \Phi'/\sqrt(g)
\Phi' = d\Phi/ds = 1*\Phi\left(s=1\right)/2\pi
\chi' = d\chi/ds = \iota(s) * \Phi'(s) math This is the same initial guess VMEC utilizes for it's fields.

If the user supplies a VMEC wout file, coordinates are generated by splining over the VMEC surfaces in real space. Fields are calculated in a similar manner. External surfaces (if requested) are extrapolated in real space. The fields in this external region are either calculated or simply assumed to be the same as found on the VMEC boundary. For a free boundary VMEC run, the vacuum field is calculated from the mgrid file refrenced in the wout file. The plasma response is then calculated by a virtual casing principle.

The pressure and current profile (in both cases) will be represented as a set of spline coefficients over the VMEC coordinate grid (normalized toroidal flux). If the total enclosed toroidal flux is zero the initial scaling factor for PIES (betai) will be set to zero to guarantee the total current is zero (IOTE will be chosen to be 0 and ADJST to 0). Otherwise BETAI and IOTE are chosen to match CURTOR for the current profile supplied.

A coils file (see MAKEGRID) may also be supplied and the EXTCUR array from the VMEC file (input or wout) will be utilized to generate the coil_data file for PIES.

### Compilation

The VMEC2PIES code has been incorporated in the VMEC/STELLOPT makefile system. The code makes use of the EZSpline libraries (\@http://w3.pppl.gov/ntcc/PSPLINE/) and LIBSTEL libraries.

### Input Data Format

The VMEC2PIES code is run from the command line taking the VMEC input file or wout file as it's first argument

XVMEC2PIES <VMEC FILE> -n <NTOR> -m <MPOL> -k <SURFS> -extsurfs <EXTERNAL SURFACES> -c <COILS FILE> -fixed -free -noverb -help


|| Argument || Default || Description || || -n || VMEC_FILE || Maximum selected toroidal mode number || || -m || VMEC_FILE || Maximum selected poloidal mode number || || -k || VMEC_FILE || Maximum number of surfaces || || -extsurfs || 0 || Number of PIES surfaces outside the VMEC domain || || -c || NONE</span> || Makegrid style coils file (used to produce PIES coil_data file, in conjunction with currents in VMEC File) || || -fixed || || Overrides the free boundary VMEC flag and forces a fixed boundary PIES run || || -free || || Overrides the fixed boundary VMEC flag and forces a free boundary PIES run || || -noverb || || Suppresses screen output || In it's simplest invokation the code requires a VMEC input or wout file.

### Execution

The VMEC2PIES code is executed from the command line

> ~/bin/xvmec2pies wout_test.nc -k 99
-----PIES File Parameters-----
extsurfs:  0
k:  99
-----VMEC File Parameters-----
file: test
m:  11   nu:  45
n:   0   nv:   1
mnmax:   12  nuv:   45   nuvp:    45
nfp:   1
ns: 385
lfreeb:   F
iota: [ 0.107, 1.346]
torflux_edge: -3.661
Total Current: 1401793.713
-----PIES File Parameters-----
file: test.in
k:  99 lpinch:  99
m:  22    mda:  22
n:   0    nda:   2
nfp:   1
freeb:   0
rmaj:  1.264
betai: 0.11763476915967E+01
iote: -.28035874579610E+00
freeb:   0


### Output Data Format

The code produces a PIES input file with the INDATA, PLTFLG, EXLSTA namelists, background coordinates, magnetic fields, mode selection matrix, pressure, and current splines (see PIES).

### Visualization

Interested users should see the INIT.rat subroutine in PIES for interpretation of the quantities in the PIES input file.

NCSX Example