Module magnetohydrodynamics 

Functions

advection_time

Advection time: τ_a = L / v.

alfven_speed

Alfvén speed: vₐ = B / √(μ₀ ρ).

bennett_pinch_condition

Bennett pinch condition: checks whether I² ≈ 8π N k_B T / μ₀. Returns true when the plasma is in pressure balance.

fast_magnetosonic_speed

Fast magnetosonic speed (perpendicular propagation): v_fast = √(vₐ² + cₛ²).

grad_shafranov_beta_limit

Rough Troyon-like beta limit: β_max ≈ 1 / aspect_ratio.

hartmann_number

Hartmann number: Ha = B L √(σ / μ_visc). Ratio of electromagnetic to viscous forces in a conducting fluid.

is_frozen_in

Returns true when Rm > 100, indicating the magnetic field is frozen into the plasma.

lundquist_number

Lundquist number: S = vₐ L / η. Ratio of resistive diffusion time to Alfvén transit time.

magnetic_diffusion_time

Magnetic diffusion time: τ_d = L² / η.

magnetic_diffusivity

Magnetic diffusivity: η = 1/(μ₀ σ).

magnetic_pressure

Magnetic pressure: P_B = B² / (2 μ₀).

magnetic_reynolds_number

Magnetic Reynolds number: Rm = μ₀ σ v L. Quantifies the ratio of magnetic advection to diffusion.

magnetosonic_mach

Magnetosonic Mach number: M_ms = v / v_fast.

pinch_pressure_balance

Z-pinch pressure balance. Computes the magnetic pressure from the azimuthal field B_θ = μ₀ I / (2π r).

plasma_beta

Plasma beta: β = 2 μ₀ P / B². Ratio of gas pressure to magnetic pressure.

reconnection_electric_field

Reconnection electric field: E = v_in × B (magnitude).

slow_magnetosonic_speed

Slow magnetosonic speed (perpendicular propagation): v_slow = min(vₐ, cₛ).

sweet_parker_rate

Sweet-Parker reconnection rate: v_in / vₐ = 1 / √S.

total_pressure

Total pressure (gas + magnetic): P_total = P + B² / (2 μ₀).