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Free Expansion Validation

Reference

Andersen, S. A., Jensen, V. O., Nielsen, P., & D'Angelo, N. (1969). Continuous supersonic plasma wind tunnel. Physics of Fluids, 12(3), 557–560.

Physics

A collisionless plasma expanding freely through a magnetic aperture develops a characteristic velocity distribution in the exhaust plume. This case validates that the PIC solver correctly reproduces:

  1. Ion velocity distribution (Maxwellian → drifting beam)
  2. Plume divergence angle at the Mach 1 surface
  3. Density falloff with distance: \(n \propto r^{-2}\) in the far field

Configuration

from helicon.validate.cases.free_expansion import FreeExpansionCase
case = FreeExpansionCase()
config = case.get_config()

Key parameters:

Parameter Value
\(n_0\) \(10^{18}\) m⁻³
\(T_i\) 10 eV
\(T_e\) 10 eV
\(B_{throat}\) 0.1 T
Grid 256 × 128

Acceptance Criteria

  • RMS error in ion velocity distribution < 5%
  • Plume half-angle within ±2° of experimental value (28°)
  • Density profile slope within 10% of \(r^{-2}\)

Running

helicon validate --case free_expansion

from helicon.validate.runner import run_validation
result = run_validation("free_expansion", dry_run=True)
print(result.summary)

Results

See docs/validation_results/free_expansion/ for field plots and comparison figures after running helicon validate --case free_expansion.