vmecpp.qs module

Quasisymmetry objectives built only from the public geometry API.

The metric is the one SIMSOPT’s QuasisymmetryRatioResidual implements: for quasisymmetry the ratio (B x grad B . grad psi) / (B . grad B) is constant on a flux surface, so

f = sum_j w_j < [ (1/B^3) ( (N - iota M) B x grad B . grad psi

  • (M G + N I) B . grad B ) ]^2 >

with < . > the flux-surface average, G and I the poloidal and toroidal current profiles, and (M, N) the desired helicity. Discretized on a uniform (theta, phi) grid over one field period this is a sum of squares,

R = sqrt( w_j nfp dtheta dphi / V’ * sqrt(g) ) / B^3

  • ( (N - iota M) B x grad B . grad psi - (M G + N I) B . grad B ),

which is what quasisymmetry_residuals returns.

Everything is computed from the product-basis geometry contract in JAX. The flux-surface measure sqrt(g) matters: dropping it changes the objective, and its derivative is one of the two errors that only show up end to end.

vmecpp.qs.magnetic_field_strength(geometry, coordinates)

Return |B| reconstructed from R, Z, lambda, and fluxes.

Parameters:

  • geometry (Geometry)

  • coordinates (Array)

Return type:

Array

vmecpp.qs.quasisymmetry_residuals(geometry, surfaces=(0.5,), *, helicity_m=1, helicity_n=0, weights=None, ntheta=63, nphi=64)

Return the flat vector of quasisymmetry residuals R.

helicity_n = 0 is quasi-axisymmetry. The residuals are normalized so that the sum of their squares is the objective f; this matches SIMSOPT’s QuasisymmetryRatioResidual.residuals() term by term.

Parameters:
Return type:

Array

vmecpp.qs.quasisymmetry_total(geometry, *args, **kwargs)

Return the scalar quasisymmetry error f, the sum of squared residuals.

Parameters:

geometry (Geometry)

Return type:

Array