Fundamentals of Plasma Physics
70 Chapter 3. Motion of a single plasma particle whereα(t)andβ(t)have the same sign. The termHextremumin Eq.(3.39) has been drop ...
3.4 Extension of WKB method to general adiabatic invariant 71 Let the Hamiltonian depend on time via a slowly changing parameter ...
72 Chapter 3. Motion of a single plasma particle From Eq.(3.16) it is seen thatP/mis not, in general, the velocity and so the ve ...
3.5 Drift equations 73 3.5 Drift equations We show in this section that it is possible to deduce intuitive and quite accurate an ...
74 Chapter 3. Motion of a single plasma particle will also decelerate in thex-direction. Moving with negativevymeans the ion is ...
3.5 Drift equations 75 This may be solved to give the average drift velocity vE≡〈v〉= E×B B^2 . (3.57) This steady ‘EcrossB’ drif ...
76 Chapter 3. Motion of a single plasma particle averaging out the gyromotion. As sketched in Fig.3.4, the particle’s positionan ...
3.5 Drift equations 77 fields, the Lorentz equation becomes m d[vgc(t) +vL(t)] dt = q [ E(xgc(t)) + (rL(t)·∇)E ] +q[vgc(t) +vL(t ...
78 Chapter 3. Motion of a single plasma particle while the component perpendicular toBis m [ dv⊥gc(t) dt +v^2 ‖gcB̂·∇B̂ ] = q ...
3.5 Drift equations 79 To simplify the algebra for the averaging, a local Cartesian coordinate system is used with xaxis in the ...
80 Chapter 3. Motion of a single plasma particle ̂ R̂ R B center of curvature Figure 3.5: Local cylindrical coordinate system ...
3.5 Drift equations 81 3.5.3 μconservation We now imagine being in a frame moving with the velocityv⊥gc;in this frame the only p ...
82 Chapter 3. Motion of a single plasma particle (which gives the rate at which the perpendicular electric field does workon the ...
3.5 Drift equations 83 Conservation of magneticflux enclosed by gyro-orbit- Because the magneticfluxΦ enclosed by the gyro-orbi ...
84 Chapter 3. Motion of a single plasma particle particle orbitarea contracts in inverse proportion to the field strength after ...
3.5 Drift equations 85 transverse to the initial direction of the magnetic field, i.e., a field in thexorydirections. In a cylin ...
86 Chapter 3. Motion of a single plasma particle between the coils, andB(s)tends to zero ass→±∞.To focus attention on magnetic t ...
3.5 Drift equations 87 trapped particles – these haveW 0 < μBmaxand bounce back and forth between the mirrors of the magneti ...
88 Chapter 3. Motion of a single plasma particle of adiabatic invariance presented in Sec.3.4.1, the quantity J= ∮ P‖ds= ∮ (mv‖+ ...
3.5 Drift equations 89 distanceLof the mirror-trapped particle slowly decreases. This would typically occur by reducing the axia ...
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