VMECTools

vmec2pest

Transforms a VMEC equilibrium into PEST coordinates. The magnetic equilibrium is specified in the PEST coordinate system $\mathbf{B} = \nabla x^1 \times \nabla x^2$ where $x^1 = \psi_\text{toroidal}/\psi_\text{LCFS}$ is the normalized toroidal flux and $x^2 = \alpha = \theta -\iota \zeta$ is the magnetic field line label parameterized by the straight-field-line coordinates $\theta$ and $\zeta$. For the PEST system, $\zeta$ is chosen to be the geometric toroidal angle.

Building

Building vmec2pest requires the following packages

• Fortran compiler with Fortran 2008 support
• NetCDF libraries
• An optimized BLAS/LAPACK installation (such as OpenBLAS)

The NETCDF_F_INC_DIR, NETCDF_F_LIB_DIR, NETCDF_C_INC_DIR, NETCDF_C_LIB_DIR and BLAS_LIB_DIR directories need to be set to the appropriate path. To make vmec2pest, in the top-level directory, execute

make v2p

which will then build the mini_libstell library if not built and the vmec2pest executable.

Usage

Copy the template input file from the input/ directory to the top-level directory. The following lines in the input file need to be set.

geomdir = 'absolute/path/to/VMEC/wout.nc/file'
surfaces = 0.1, 0.2, ... Array of surfaces on which to compute the transformation
n_field_lines = # of field lines on which to compute the transformation
n_parallel_pts = # of points in the parallel direction on which to compute the transformation
n_field_periods = 1.0  ! The maximum angle will be x3_center + pi*n_field_periods/nfp, where nfp is the number of field periods of the device
x2_center = 0.0   ! Center of the domiain in the bi-normal coordinate (alpha)
x3_center = 0.0   ! Center of the domain in the field line following coordinate
x3_coord = 'zeta'  ! Choice of the field line following coordinate (can be 'theta' or 'zeta')
output_files = 'pest'   ! Choose which files to write (pest, gene, surf), default: pest
surface_quantities = 'bmag' ! Optional: Choose different quantities to write as a function of cylindrical R, Z and phi 

vmec2pest produces by default a pest file for each specified surface. The file contains the metric coefficients, magnetic field strength, Jacobian, curavature drift components and parallel derivative of B as a function of field line label and field-line-following coordinate.

To execute, in the top-level directory, simply run

./vmec2pest

If the outdir directory is not specified in vmec2pest.inp, the files will be written to the top-level directory.

List of quantities computed by vmec2pest

Here $x^1 = \sqrt{s_0}$, $x^2 = \theta - \iota \zeta$, $x^3 = \zeta$

• g11: $\nabla x^1 \cdot \nabla x^1$
• g12: $\nabla x^1 \cdot \nabla x^2$
• g22: $\nabla x^2 \cdot \nabla x^2$
• g13: $\nabla x^1 \cdot \nabla x^3$
• g23: $\nabla x^2 \cdot \nabla x^3$
• g33: $\nabla x^3 \cdot \nabla x^3$
• bmag: magnitude of $B$
• jac: absolute value of $\sqrt{g}=1/(\nabla x^1 \times \nabla x^2 \cdot \nabla x^3)$
• curv_drift_x1: $\frac{\mathbf{B}\times \nabla B}{B^3}\cdot \nabla x^1$
• curv_drift_x2: $\frac{\mathbf{B}\times \nabla B}{B^3}\cdot \nabla x^2$
• d_B_d_x3: $\frac{\partial B}{\partial x^3}$