Loading a MHD Equilibrium

One of the inputs to Raytrax is a MagneticConfiguration, which is a grid in cylindrical coordinates holding the values of the magnetic field \(\vec{B}\), the effective minor radius \(\rho\), and some other geometric quantities. Raytrax can compute this configuration from a magnetohydrodynamic (MHD) equilibrium.

At present, Raytrax supports loading equilibria from the VMEC++ code, which is a modern implementation of the widely used VMEC code for computing stellarator equilibria.

Using VMEC++

To instantiate a magnetic configuration from a VMEC++ equilibrium, you need a vmecpp.VmecWOut object, which can be either obtained by running VMEC++ on an input file, or by loading an existing equilibrium file in NetCDF "wout" format (created with VMEC++ or the original VMEC).

Example for loading an existing wout file:

import vmecpp

vmec_wout = vmecpp.VmecWOut.from_wout_file("w7x.nc")

Alternatively, you can run VMEC++ on an input file yourself:

import vmecpp

vmec_input = vmecpp.VmecInput.from_file("input.w7x")
vmec_output = vmecpp.run(vmec_input)
vmec_wout = vmec_output.wout

For more options and details, see the VMEC++ documentation.

Once you have the VmecWOut object, you can create a MagneticConfiguration from it:

mag_conf = raytrax.MagneticConfiguration.from_vmec_wout(vmec_wout)

Tuning grid resolution

The import involves two grids: an intermediate curvilinear grid in VMEC flux coordinates \((\rho, \theta, \phi)\) on which the Fourier series are evaluated, and the final cylindrical grid \((R, \phi, Z)\) on which the ray tracer operates. Both are controlled via VmecGridResolution:

grid = raytrax.VmecGridResolution(
    cylindrical=raytrax.CylindricalGridResolution(
        n_r=60,    # R points on the output cylindrical grid
        n_z=70,    # Z points on the output cylindrical grid
        n_phi=64,  # toroidal planes on the output cylindrical grid
        n_rho_profile=200,  # points for the 1-D dV/dρ profile
    ),
    n_rho=50,    # radial flux surfaces on the intermediate VMEC grid
    n_theta=60,  # poloidal points on the intermediate VMEC grid
)
mag_conf = raytrax.MagneticConfiguration.from_vmec_wout(vmec_wout, grid=grid)

The defaults (n_r=45, n_z=55, n_phi=50, n_rho=40, n_theta=45) are adequate for most stellarator geometries. Increasing them improves accuracy at the cost of memory and import time, which scales roughly as \(n_r \cdot n_\phi \cdot n_z\).