vmec_jax.integrals¶

Angle and radial integrals.

This module computes simple derived quantities from geometric outputs, notably the volume profile from the Jacobian sqrtg.

Conventions¶

The geometry kernel in vmec_jax.geom computes sqrtg as the Jacobian for coordinates (s, theta, phi_phys), where phi_phys is the physical toroidal angle.

Most of vmec_jax works on one field period using the VMEC internal coordinate zeta in [0, 2π), related by:

phi_phys = zeta / NFP

Therefore, when integrating over the stored zeta grid, include the factor dphi = dzeta / NFP.

VMEC wout convention note¶

VMEC stores several 3D fields in wout_*.nc on the radial half mesh and with angles (theta, zeta) over one field period. In VMEC’s internal bookkeeping, many 1D radial integrals are computed using a simple rectangle rule:

V = Σ_{js=2..ns} (dV/ds)(js) * hs

This differs from a trapezoidal rule and matters at low radial resolution. For regression tests against wout, use the helpers in this module that implement the same conventions.

Functions

`cumrect_s_halfmesh`(y, s)	Cumulative rectangle-rule integral for half-mesh data.
`cumtrapz_s`(y, s)	Cumulative trapezoidal integral in s with V(0)=0.
`dvds_from_sqrtg`(sqrtg, theta, zeta, nfp)	Compute dV/ds from `sqrtg` by integrating over angles.
`dvds_from_sqrtg_zeta`(sqrtg, theta, zeta, *)	Compute dV/ds by integrating over (theta, zeta).
`volume_from_sqrtg`(sqrtg, s, theta, zeta, nfp)	Convenience wrapper: compute (dvds, V) from sqrtg.
`volume_from_sqrtg_vmec`(sqrtg, s, theta, zeta, *)	Compute (dvds, V) using VMEC-like (wout) conventions.