STELLOPT
The STELLOPT code is designed to optimize 3D MHD equilibria for a set of target physics parameters encompassing stellarator design and 3D equilibrium reconstruction. It is currently interfaced to the VMEC 3D equilibrium solver.
STELLOPT is currently hosted on the Princeton University’s GitHub repository.
Table of Contents
Theory
The STELLOPT code can be thought of as a multi-dimensional non-linear curve fitting algorithm. The curve to which a fit is sought is parameterized by a set of target parameters which themselves may be MHD equilibrium quantities (beta, aspect ratio, etc.) or non-linear functions of the equilibrium itself (stability, particle transport, etc). The function used to fit these targets is the MHD equilibrium itself. Here the input parameters to the equilibrium serve as a set of coefficients parameterizing our non-linear fit function. The quality of fit is determined by the Chi-squared metric $$ \chi_i^2=\frac{\left(f_i^{target}-f_i^{equilbria}\right)^2 }{\sigma_i^2} .$$ The sigma here represents the tolerance of the target value. The goal of the code is to minimize the total chi-squared value. STELLOPT natively provides a few optimization algorithms: a modified Levenberg-Marquardt algorithm, genetic algorithm, and differential evolution. Over 30 more optimization algorithms are available if you build STELLOPT with the MANGO library, discussed in more detail here.
The user specifies which equilibrium input values to vary independently of the targets. Targets (Chisq values) are turned on by setting the SIGMA_VAR variables less than 1E30 in the input namelist. The X vector is determined by logical flags being set to True in the input namelist. It should be noted that in addition to the VMEC equilibrium inputs, X vector variables exist for electron density, electron temperature, ion temperature, electrostatic scalar potential, ion effective charge, and three dimensional coil splines. The following list outlines the currently available targets:
| Target | Dimension | Description |
|---|---|---|
| ASPECT | Single | Equilibrium Aspect Ratio |
| BETA | Single | Equilibrium Total Plasma Beta |
| BETATOR | Single | Equilibrium Toroidal Plasma Beta |
| BETAPOL | Single | Equilibrium Poloidal Plasma Beta |
| CURTOR | Single | Equilibrium Total Toroidal Current |
| PHIEDGE | Single | Equilibrium Total Enclosed Toroidal Flux |
| R0 | Single | Equilibrium Radial Magnetic Axis Position (phi=0) |
| Z0 | Single | Equilibrium Radial Magnetic Axis Position (phi=0,non-stellarator symmetric) |
| B0 | Single | Equilibrium Magnetic Field on axis (phi=0) |
| RBTOR | Single | Equilibrium R-B_toroidal |
| WP | Single | Equilibrium Stored Energy |
| VOLUME | Single | Equilibrium Volume |
| CURVVATURE | Single | Equilibrium Boundary Curvature |
| CURVVATURE_P2 | Single | Equilibrium Boundary Curvature (P2) |
| KAPPA | Single | Equilibrium Boundary Ellipticity |
| KAPPA_BOX | Single | Equilibrium Boundary Ellipticity (bounding box) |
| KAPPA_AVG | Single | Equilibrium Boundary Ellipticity (average) |
| LGRADB | Single | L.grad(B) coil distance metric |
| EXTCUR | Vector | Vacuum Field Currents |
| NE_LINE | Vector | Array of line integrated electron density measurements |
| TE_LINE | Vector | Array of line integrated electron temperature measurements |
| TI_LINE | Vector | Array of line integrated ion temperature measurements |
| ZEFF_LINE | Vector | Array of line integrated Zeff measurements |
| VISBREM_LINE | Vector | Array of visual Bremsstrahlung measurements |
| XICS_BRIGHT | Vector | Array of XICS brightness measurements |
| XICS_TI | Vector | Array of XICS Ti measurements |
| XICS_W3 | Vector | Array of XICS W3 measurements |
| XICS_V | Vector | Array of XICS V measurements |
| SXR | Vector | Array of soft X-ray measurements |
| FARADAY | Vector | Array of Faraday Rotation measurements |
| MSE | Vector | Array of MSE measurements (R,PHI,Z) |
| PRESS | Vector | Array of pressure profile measurements (R,PHI,Z or S) |
| NE | Vector | Array of electron density measurements (R,PHI, Z or S) |
| TE | Vector | Array of electron temperature measurements (R, PHI, Z or S) |
| TI | Vector | Array of ion temperature measurements (R, PHI, Z or S) |
| VPHI | Vector | Array of toroidal rotation measurements (R, PHI, Z or S) |
| IOTA | Vector | Array of rotational transform measurements (R, PHI, Z or S) |
| VACIOTA | Vector | Array of vacuum transform -S12/S11 (R, PHI, Z or S) |
| JDOTB | Vector | Array of <j.B> -S12/S11 (S) |
| MAGWELL | Vector | Array of Magnetic Well/Hill (+/-) (S) |
| JCURV | Vector | Array of average toroidal current density (S) |
| GAMMA_C | Vector | Array of Gamma_C Fast Ion Confinement proxy (S) |
| TXPORT | Vector | Array of Turbulent transport proxies (S) |
| HELICITY | Vector | Array of magnetic field spectrum proxy (S) |
| QUASIISO | Vector | Array of magnetic quasi-isodynamic spectrum proxy (S) |
| BPROBE | Vector | Array of B-Field measurements calculated by DIAGNO |
| FLUXLOOP | Vector | Array of Flux Loop measurements calculated by DIAGNO |
| ROGOWSKI | Vector | Array of Rogowski Coil measurements calculated by DIAGNO |
| VESSEL | Matrix | Limiting points in space |
| SEPARATRIX | Matrix | Desired edge points in space |
| BALLOON | Vector | Array of radial locations for ballooning stability calculation by COBRAVMEC |
| BOOTSTRAP | Vector | Array of radial locations for bootstrap calculation by BOOTSJ |
| NEO | Vector | Array of radial locations for Neoclassical transport calculation by NEO |
| DKES_11 | Vector | Array of surfaces on which to calculate L11 DKES |
| DKES_31 | Vector | Array of surfaces on which to calculate L31 DKES |
| DKES_33 | Vector | Array of surfaces on which to calculate L33 DKES |
| DKES_BOOT | Vector | Array of surfaces on which to calculate DKES Bootstrap proxy DKES |
| DKES_ERDIF | Vector | Array of surfaces on which to calculate L11 Er Spread DKES |
| DKES_ALPHA | Vector | Array of surfaces on which to calculate L11 Er Alpha DKES |
| ORBIT | Vector | Array of radial locations on which to calculate confinement BEAMS3D |
| JSTAR | Vector | Array of radial locations for particle confinement calculation |
| KINK | Single | Equilibrium kink stability as calculated by TERPSICHORE |
| BNORMAL | Single | Total Normal Magnetic field on surface (coil optimization) |
| COIL_BAXIS | Single | Alignment of magnetic field to maganetic axis (coil optimization) |
| COIL_BNMNS | Matrix | Total normal magnetic field spectrum on surface sine (coil optimization) |
| COIL_BNMNC | Matrix | Total normal magnetic field spectrum on surface cosine (coil optimization) |
| COIL_LENGTH | Vector | Array of lengths of coils (coil optimization) |
| COIL_ENERGY | Vector | Array of vacuum energy of coils (coil optimization) |
| COIL_CURVATURE | Single | Mean coil curvatures (coil optimization) |
| COIL_TORSION | Single | Mean coil torsion (coil optimization) |
| COILCOIL_DISTANCE | Single | Minimum coil-coil distance (coil optimization) |
Compilation
Compilation of the STELLOPT suite is discussed on the STELLOPT Compilation Page
Input Data Format
The STELLOPT code takes an input file which contains all the input namelists necessary to run the equilibrium code, STELLOPT, and any additional codes called by the optimizer. The STELLOPT code itself requires an OPTIMUM namelist which contains the runtime parameters for the code, specifies which input variables to vary, any additional profiles, and the target parameters to match.
Execution
The STELLOPT routine is designed to be run on a multi-processor machine or cluster. In general, it should be executed via a call to mpirun (most likely inside a SLURM script). The call should take the form:
mpirun -np $NPROCS /path-to/xstelloptv2 $runid > log.$runid
Here $NPROCS is the number of processors being requested and $runid is
the suffix assigned to the input file. Upon execution STELLOPT will
create a working directory entitled stellopt_$runid where
$runid is the value passed to it from the command line. All work
and final output is preformed in this directory. Optional arguments
which control the code behavior are:
| Argument | Default | Description |
|---|---|---|
| -one_iter | NONE | Overrides the OPTIMUM namelist and conducts a single iteration run. |
| -renorm | NONE | Renormalizes each TARGET group to have a total chi-squared of one. |
| -restart | NONE | Use wout_reset_file.nc in directory to restart VMEC run on first iteration. |
| -noverb | NONE | Suppress screen output. |
| -log | NONE | Send screen output to log file (useful on systems where >& doesn’t work). |
| -autodomain XX | NONE | Automatically calculate bounds as percentage (-autodomain 0.2, produces a +/-20% bound) |
| -tri FILE1 FILE2 | NONE | Use FILE1 and FILE2 to set Min and Max bounds respectively (used in hyperplane mapping mode) |
| -xvec_file FILE1 | NONE | Use FILE1 to initialize population for Differential Evolution and Particle Swarm runs. |
| -help | NONE | Print help message |
Also note that we provide a helper utility xvmec2stel whicn can
generate a template OPTIMUM namelist based on an INDATA namelist.
Output Data Format
The STELLOPT code will produce many files so it is suggested that each run be kept in a separate directory. A stereotypical run looks something like:
Once a run has completed the code will output a stellopt.ext file,
and a input.ext_min file. The _min file contains an
equilibrium input file corresponding to the best fit as found by
STELLOPT. The stellopt. file contains an iteration by iteration
analysis of the fit to the target parameters. The file begins with a
version string (VERSION 2.65). Each iteration is demarked by an
iteration line (ITER XXXX). Each target type is then noted by line
indicating a type, the number of target values, and the number of output
values (TYPE 3 1). Immediately following that line is a line of text
indicating the value in each column.
Additionally, many working files denoted by _optXX are produced by
STELLOPT. These files may be removed once a run has completed. If the
user has elected to keep minimum states as the code iterated, various
files produced by the equilibrium calculation, and other codes will be
kept with an iteration number appended to their name. In this way a step
by step analysis of the optimization may be evaluated. The optimization
routines may themselves create output files.
Visualization
The final output of the STELLOPT routine is a combination of STELLOPT files, VMEC files, and the output files of the physics modules invoked durring the run.
Tutorials
Boundary Representations Explained
Optimization of an NCSX-like configuration
Optimization of Iota using LMDIF
STELLOPT Energetic Particle Optimization
Old STELLCOPT tutorials (depricated)
STELLOPT Coil Optimization COILOPT++ (OLD)
STELLCOPT Tutorial Document (OLD)