feat(vfp2d): couple ion hydro and kinetic-electron pressure

[joglekara]

Summary

• add the Gate 0a standalone 2D ideal-ion MUSCL-HLLC finite-volume backbone
• close Gate 0b with quantitative Riemann, translating-vortex, Sedov, and magnetic-divergence benchmarks
• add Gate 1 ion-frame electron operators for bulk transport, deformation, frame acceleration, and local finite-mass exchange
• add the Gate 2a/2b ion-kinetic split with finite-mass remapping, full kinetic electron-pressure feedback, and sparse high-harmonic deformation operators
• close the nonlinear coupled-energy gate under timestep and spatial/radial refinement
• add a field-solver hierarchy: physical explicit Maxwell, slowed explicit Ampere, OSHUN-style implicit current response, and kinetic Ohm

Field-solver hierarchy

• maxwell remains the physical fully explicit Vlasov-Maxwell mode.
• ampere uses a configurable relative_permittivity >= 1 to divide the complete Ampere residual. This slows the light and plasma frequencies by sqrt(relative_permittivity) without changing the steady target J = c^2 curl(B). Its saved electric-field energy uses the corresponding permittivity weight.
• oshun-implicit advances Faraday explicitly, constructs the local discrete 3x3 kinetic response dJ_i/dE_j, and directly solves for the electric field that makes the updated distribution satisfy J = c^2 curl(B). It updates the full harmonic distribution through the Vlasov force operator rather than projecting f1.
• kinetic-ohm remains the long-timescale algebraic closure used by the moving-ion path.

The OSHUN-style mode is an implicit kinetic-current response, not a fully implicit Maxwell solve. It and the slowed-Ampere mode are currently stationary-ion capabilities; moving-ion coupling remains restricted to kinetic Ohm. The implicit mode is also intentionally rejected under spatial sharding until a distributed response solve is validated.

Saved outputs now include the Ampere target current, pointwise residual, residual Linf history, magnetic field energy, solver mode, and relative permittivity. Explicit modes additionally save electric and total electromagnetic field energy.

Nonlinear energy gate

The coupled map is now the symmetric composition

1. ion hydro half-step;
2. coupled pressure/exchange half-step;
3. full kinetic-electron step at midpoint ion kinematics;
4. coupled pressure/exchange half-step; and
5. ion hydro half-step.

The kinetic-Ohm Ampere projection changes only f1, but in a moving ion frame that changes lab-frame electron energy by u_i . Delta p_e. Runs now accumulate that projection work explicitly and save both total_energy and accounted_total_energy = total_energy - current_projection_energy. A direct unit test compares the ledger to the independently measured lab-frame energy jump.

The nonlinear periodic benchmark evolves nonuniform electron density and temperature, accelerates the ions through the full f0 + f2 electron pressure, and generates magnetic field. Its declared accounted-energy tolerance is 3.1e-9:

• the tolerance is met for dt = 2e-3, 1e-3, 5e-4;
• ion-velocity and magnetic observables converge above order 1.8 in time;
• the energy defect decreases by more than 8x from nv = 24 to nv = 96; and
• the energy defect decreases by more than 8x from nx = 6 to nx = 12.

Gate 0b benchmarks

• Sod and pressure-ratio 1e5 strong-shock tubes are compared with an exact Euler Riemann solution on both coordinate axes; normalized L1 tolerances are 3.5% and 12%, respectively.
• A translating isentropic vortex converges above order 1.7 from 24x24 to 48x48.
• A Cartesian Sedov blast preserves total energy to roundoff, stays positive and transpose-symmetric, and keeps fourfold kinetic-shell anisotropy below 5%.
• A divergence-free magnetic field remains divergence-free through 24 nontrivial Faraday updates to 2e-12 absolute tolerance.

Physics demonstrated

• exact frozen-ion regression to the kinetic-Ohm solver when u_i = 0
• analytic ideal bulk magnetic advection with no magnetic-divergence source
• finite-mass velocity-frame translation preserving electron density and lab-frame momentum/energy to roundoff
• symmetric momentum, temperature, and electron-pressure exchange preserving coupled lab-frame invariants
• scalar f0 plus traceless f2 electron pressure and equal-and-opposite pressure work
• classical local-Maxwellian Biermann generation with spectral convergence
• Epperlein-Haines Z* response recovering the analytic Spitzer-Harm T^(5/2) heat-flux coefficient
• Galilean, compression, shear/f2, rigid-rotation, and accelerating-frame checks
• exact slowed-Ampere residual scaling with unchanged Faraday response
• direct OSHUN response-tensor agreement, nonprojective harmonic evolution, explicit Faraday update, and machine-precision quasineutral Ampere enforcement

Explicit boundary

This remains a draft and is not ready for production parameter scans. Moving-ion production is still periodic, nonrelativistic, unsharded, kinetic-Ohm, and quasineutral. ElectronIonExchange remains a weak-drift moment model rather than a full finite-mass Landau operator. Nonperiodic coupled boundaries and production-scale validation remain future gates.

Verification

• uv run pytest -q tests/test_vfp2d -- 72 passed
• GitHub Actions test-vfp2d -- 72 passed
• focused field-solver/operator and configuration tests -- 6 passed
• uvx ruff check on all touched solver and test files -- passed
• uvx ruff format --check on all touched solver and test files -- passed
• git diff --check -- passed

The earlier repository-wide non-slow run was interrupted after 7 passing tests because the existing test_reuse_config_dict path remained in urllib3 network retry for four minutes. The complete relevant VFP2D suite is green.