desc.integrals.Bounce2D.integrate

Bounce2D.integrate(integrand, pitch_inv, data=None, names=None, points=None, *, num_well=None, nufft_eps=1e-06, is_fourier=False, low_ram=False, quad=None, check=False, plot=False)Source

Bounce integrate ∫ f(ρ,α,λ,ℓ) dℓ.

Computes the bounce integral ∫ f(ρ,α,λ,ℓ) dℓ for every field line and pitch.

Warning

Make sure to replace √(1−λB) with √|1−λB| or clip the radicand to some value near machine precision when defining integrand to account for imperfect computation of bounce points.

Parameters:

  • integrand (callable or list[callable]) – The composition operator on the set of functions in data that determines f in ∫ f(ρ,α,λ,ℓ) dℓ. It should accept a dictionary which stores the interpolated data and the arguments B and pitch.

  • pitch_inv (jnp.ndarray) – Shape (num ρ, num pitch). 1/λ values to compute the bounce integrals. 1/λ(ρ) is specified by pitch_inv[ρ] where in the latter the labels are interpreted as the indices that correspond to that field line.

  • data (dict[str, jnp.ndarray]) – Shape (num ρ, num ζ, num θ). Real scalar-valued periodic functions in (θ, ζ) ∈ [0, 2π) × [0, 2π/NFP) evaluated on the grid supplied to construct this object. Use the method Bounce2D.reshape to reshape the data into the expected shape.

  • names (str or list[str]) – Names in data to interpolate. Default is all keys in data.

  • points (tuple[jnp.ndarray]) – Shape (num ρ, num α, num pitch, num well). Optional, output of method self.points. Tuple of length two (z1, z2) that stores ζ coordinates of bounce points. The points are ordered and grouped such that the straight line path between z1 and z2 resides in the epigraph of B.

  • num_well (int) – See self.points for the description of this parameter.

  • nufft_eps (float) – Precision requested for interpolation with non-uniform fast Fourier transform (NUFFT). If less than 1e-14 then NUFFT will not be used.

  • is_fourier (bool) – If true, then it is assumed that data holds Fourier transforms as returned by Bounce2D.fourier. Default is false.

  • low_ram (bool) – Whether to use a more memory efficient algorithm. However, this is slower to differentiate with JAX. For best performance, one should only use this option if batching is already being done via Bounce2D.batch with surf_batch_size=1.

  • quad (tuple[jnp.ndarray]) – Optional quadrature points and weights. If given this overrides the quadrature chosen when this object was made.

  • check (bool) – Flag for debugging. Must be false for JAX transformations.

  • plot (bool) – Whether to plot the quantities in the integrand interpolated to the quadrature points of each integral. Ignored if check is false.

Returns:

result (jnp.ndarray or list[jnp.ndarray]) – Shape (num ρ, num α, num pitch, num well). Last axis enumerates the bounce integrals for a given field line and pitch value.