Basic Plasma Physics Principles

Basic Plasma Physics Principles Gordon Emslie Oklahoma State University Outline Single particle orbits; drifts Magnetic mirroring MHD Equations Force-free fields Resistive Diffusion The Vlasov equation; plasma waves Single particle orbits E and B fields are prescribed; particles are “test particles” Single particle orbits F = q (E + v × B) Set E = 0 (for now) F = q v × B Since F ⊥ v, no energy gain (F.v = 0) Particles orbit field line mv²/r = qvB r = mv/qB (gyroradius) ω = v/r = qB/m (gyrofrequency) Motion in a Uniform Magnetic Field Is this an electron or an ion? Drifts F = q (E + v × B) Now let E ≠ 0. Relativistic transformation of E and B fields: E' = γ(E + (v/c) × B) B' = γ(B –(v/c) × E) E'² – B'² = E² – B² If E < B (so that E² – B² < 0), transform to frame in which E = 0: v = c (E × B)/B² In this frame, we get simple gyromotion So, in ‘lab’ frame, we get gyro motion, plus a drift, at speed vD = c (E × B)/B² E × B drift Drifts Exercise: What if E > B? Drifts: vD = c (E × B)/B² E is “equivalent electric field” Examples: (1) E is actual electric field: vD = c (E × B)/ B² (independent of sign of q) (2) Pressure gradient: qE = -∇p: vD = -c∇p × B/qB² (dependent on sign of q) (3) Gravitational field: mg = qE: vD = (mc/q) g × B/B² (dependent on m and sign of q) Puzzle: in absence of magnetic field, particles subject to g accelerate at the same rate and in the same direction; particles subject to E accelerate in opposite directions at a rate which depends on their mass. Why is the exact opposite true when a B is present?