In general, the computation of locally defined or singular quantities will be more efficient with non-uniform fast transforms. In particular, I am referring to the type 2 nonuniform fast transform, which evaluates spectral coefficients at non-uniformly spaced points.

Although a fixed grid with nodes uniformly spaced throughout the plasma is fine for optimizing continuous functions defined throughout the volume, it is of course not well-suited for locally defined quantities such as bounce integrals. There are two hurdles with computing these quantities efficiently:

1. Require computation along field lines.
   • fourier bounce #1119 should cover this, improving upon Bounce averaging #854.
2. They are defined by singular integrals.
   • This requires evaluating the function at points concentrated near the singularity. For flux surface average of bounce integrals in particular, there are infinitely many integrals to be done, so regardless of the efficiency of the quadrature, there will be many function evaluations. Hence, linearithmic performance of fast non-uniform transform is desired over the quadratic performance of MMTs.

We should pick a JAX compatible NFFT package and write drop in replacements for the currently used MMTs. We can check the $\epsilon$ errors of these external NFFT libraries by comparing to those utilities on the tests in that PR.

Here are some candidates:

1. https://github.com/jakevdp/nfft
2. https://github.com/flatironinstitute/jax-finufft