MHD Alfvén Wave Propagation
Magnetized plasma, dispersion relation, plasma beta, wave modes
Plasma Parameters
B₀ (background field)
1.0
Density ρ
1.0
Sound speed c_s
0.80
Propagation angle θ
0°
Alfvén
Fast MS
Slow MS
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v_A (Alfvén):
—
β = c_s²/v_A²:
—
Phase speed v_ph:
—
Mode:
Alfvén
Alfvén (1942):
v_A = B₀/√(μ₀ρ)
MHD dispersion for angle θ to B:
• Alfvén: ω = k·v_A cosθ
• Fast/Slow magnetosonic: ω/k = ½[(v_A²+c_s²) ± √((v_A²+c_s²)²-4v_A²c_s²cos²θ)]^(1/2)
β < 1:
magnetically dominated
β > 1:
thermally dominated