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Resistive Detachment Validation

Reference

Dimov, G. I., & Taskaev, S. Yu. (2003). Propagation of a plasma stream in a non-uniform magnetic field. In Proceedings of the 30th EPS Conference on Controlled Fusion and Plasma Physics.

Physics

Resistive detachment occurs when electron-ion collisions are frequent enough to break the frozen-in condition. The dimensionless Hall parameter

\[\Omega_e \tau_e = \frac{\omega_{ce}}{\nu_{ei}}\]

governs the transition:

  • \(\Omega_e \tau_e \gg 1\): magnetized electrons, frozen-in, good confinement
  • \(\Omega_e \tau_e \sim 1\): resistive regime, partial slippage
  • \(\Omega_e \tau_e \ll 1\): demagnetized, poor confinement

This case validates that Helicon correctly identifies the transition density where \(\Omega_e \tau_e \approx 1\) and shows the expected detachment behavior.

Configuration

from helicon.validate.cases.resistive_dimov import ResistiveDimovCase
case = ResistiveDimovCase()
config = case.get_config()

Key parameters at the \(\Omega_e \tau_e \approx 1\) threshold:

Parameter Value Notes
\(n_0\) \(10^{21}\) m⁻³ Threshold density
\(B\) 0.05 T Applied field
\(T_e\) 10 eV Electron temperature
\(\Omega_e \tau_e\) ~1 Hall parameter at threshold

Threshold Derivation

At \(B = 0.05\) T, \(T_e = 10\) eV, the electron cyclotron frequency is

\[\omega_{ce} = \frac{eB}{m_e} \approx 8.8 \times 10^9 \text{ rad/s}\]

The Spitzer collision frequency \(\nu_{ei} \propto n T_e^{-3/2}\) equals \(\omega_{ce}\) at \(n \approx 10^{21}\) m⁻³.

Running

helicon validate --case resistive_dimov

Results

See docs/validation_results/dimov/ for Hall parameter profiles and detachment efficiency plots.