Profiling examples: long-time particle equilibria for Vlasov and GuidingCenter (cylinder/torus without hole)

[spossann]

Stacked on #761 (particle-pole, which is stacked on #759). It retargets once those are merged.

Summary

New profiling examples for the particle-tracing models Vlasov and GuidingCenter. They are long-time equilibrium tests with binning plots in position and velocity space, and the propagator algorithms are compared through variants.

The layout is the same as for the existing cases (#759):

• one params file plus one submit script per model and geometry;
• the variant is chosen with --variant;
• rank counts 1, 2, 4, …, 256;
• post-processing writes .png/.npy files to sim_<id>/results.

Cases

• Vlasov/cuboid_strong_scaling
  • Setup: Maxwellian3D with constant moments (n=1, u=0, vth=1) in a periodic cube (Cuboid, side 2π) with a uniform B along z (HomogenSlab). This is an exact equilibrium.
  • Binning: η1, (η1, η2), v1, v3 and (v1, v2), compared with the initial and the exact profiles.
  • Variants: push_vxb analytic/implicit; push_eta forward Euler/Heun2/Heun3/RK4; Strang splitting; Sobol loading.
• GuidingCenter/polar_cylinder_strong_scaling
  • Geometry: straight cylinder without hole (IGAPolarCylinder, C1 polar splines) with ScrewPinch (Lz = 2πR0, pressure offset p0 so that vth > 0 at the edge).
  • Initial condition: GyroMaxwellian2D with n(r) and vth(r) = √(p/n) from the equilibrium. It is an exact equilibrium, because the GC drifts keep r constant. Markers move through the axis.
  • Binning: η1, (η1, η2), v∥, μ and (η1, v∥). The radial profile is also compared with the exact one, n/|B0|.
• GuidingCenter/polar_torus_strong_scaling
  • Geometry: full torus without hole (IGAPolarTorus, polar splines) with AdhocTorus.
  • Initial condition: CanonicalMaxwellian2D with n and vth as functions of ψc (an exact equilibrium). The density vanishes at the edge, where markers on orbits that leave the plasma are removed.
  • Control: a GyroMaxwellian2D with the same profiles in the flux label of the position. It is not an equilibrium in a torus.
• GuidingCenter variants: discrete gradient 1st order (fixed point, Newton), 2nd order, explicit RK4 and Heun3. The torus adds GyroMaxwellian controls.
  • Default grid: 16×48×48, decomposed only in η2/η3, so 1–256 processes work. ppc 25, dt 0.2, T = 100.
• profiling/examples/particle_diagnostics.py: shared post-processing.
  • Binning plots at the first and last time (2D slices also as difference maps).
  • Relative L2 deviation from t=0 and from the exact profile over time.
  • Relative drift of kinetic_energy/en_tot; scalars that start at 0, such as lost markers, are plotted as absolute values.

Notes

• No hole at r = 0: a Simulation needs polar splines whenever the domain has a pole, and polar splines need a spline mapping. So the cases use IGAPolarCylinder/IGAPolarTorus. HollowCylinder/HollowTorus with a1=0 cannot be used.
• Why not CircularTokamak for the cylinder: it is a toroidal field (B_φ ∝ 1/R, circular flux surfaces around R = R0), and its ψ is not force-balanced: Δ*ψ ≠ 0 with constant p and g. Adding a pressure p(ψ) cannot balance it. The force-balanced ScrewPinch is used instead.
• Discrete-gradient GC pushers near the axis: they are less accurate there. They only get the axis map from Particles on domains with a pole (markers through the axis, polar splines in particle propagators) #761, not the regular ξ update.
• Marker loss on several processes: with disc loading, the first test runs lost markers on several processes. That is fixed in Particles on domains with a pole (markers through the axis, polar splines in particle propagators) #761 (disc loading under MPI).

Checks

• Tiny smoke runs (2 and 4 processes) of all cases complete and write the results.
• On the cylinder with 4 processes (discrete gradient and explicit), the radial profile changes by about 1e-6 per step, no marker is lost and en_tot is constant.
• Vlasov: kinetic_energy is constant and the v3 distribution is unchanged to 1e-16.
• The flags of all 19 variants are accepted by the params files.
• Two separate review agents checked the examples. Their findings are fixed:
  • the decomposition at 128/256 processes;
  • the marker loss under MPI (in Particles on domains with a pole (markers through the axis, polar splines in particle propagators) #761);
  • the plot of scalars that start at zero;
  • the edge losses in the torus;
  • the exact radial profile;
  • the B0 used for loading.

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