[StuartBenjamin]

Motivation: eliminate discontinuities in the density gradient, and thus bootstrap current -> bad for stability calculations

fast_particles_profiles! caps the fast-ion density at max_fast_frac × the thermal density with a hard min. Where the cap engages over part of the radius, the thermal density gets a slope break at each edge of that region, and the bootstrap current (∝ dp/dψ) jumps there.

A new keyword fast_density_knee (also on intrinsic_sources!) makes the cap soft: the density is unchanged below knee × the limit and saturates smoothly towards the limit above it. The default, 1.0, is today's hard clamp. FUSE sets it from act.ActorSources.fast_density_knee (ProjectTorreyPines/FUSE.jl#1203).

Derivation. With L the limit, x = n_fast / L and knee k < 1, the capped density is n_fast for x ≤ k and L·[k + (1 − k)·tanh((x − k)/(1 − k))] for x > k.

• At x = k it equals k·L = n_fast (continuous), and its slope d/dn_fast = sech²(0) = 1 matches the unchanged branch (no slope break).
• It rises monotonically and tends to L as x → ∞, so it never exceeds the limit.
• k ≥ 1 gives min(n_fast, L), the existing clamp.

Diff: master...StuartBenjamin:IMAS.jl:fast_ion_soft_cap

🤖 Generated with Claude Code

[nanshi1177]

Looks good. The tanh knee keeps the slope continuous at knee·limit and saturates at the limit, so a partially engaged cap no longer leaves a kink in the thermal density (and a jump in the bootstrap current). knee ≥ 1 keeps today's hard clamp.

While reviewing this I found a related issue in the same function. It's not introduced here, and I'll fix it in a separate PR once this one is merged, to avoid conflicts.

density_thermal is reset to the total ion density once, before the loop over sources. But at the end of each source, density_thermal is reduced by the fast density added so far. So for the second and later sources, limit = max_fast_frac .* cion.density_thermal is computed from the already-reduced thermal density, not from the total.