Fundamentals of Plasma Physics
90 Chapter 3. Motion of a single plasma particle coordinate system(r,θ,z)withzaxis coaxial with the coils, it is seen that in th ...
3.6 Relation of Drift Equations to the Double Adiabatic MHD Equations 91 where we have usedv∇B∼vc∼v^2 ⊥/ωcr∼ωcr^2 L/r.Thus, if t ...
92 Chapter 3. Motion of a single plasma particle Suppose there exists a large number or ensemble of particles with densitynσand ...
3.6 Relation of Drift Equations to the Double Adiabatic MHD Equations 93 the dashed curve), then the two opposing currents do no ...
94 Chapter 3. Motion of a single plasma particle The total magnetic force is Jtotal×B = (JM+J∇B+Jc+JP)×B = −∇× ( P⊥Bˆ ...
3.7 Non-adiabatic motion in symmetric geometry 95 or [ ρ dU dt ] ⊥ = [ Jtotal×B−∇· { P⊥ ←→ I+ ( P⊥−P‖ )ˆ BBˆ }] ⊥ (3.142) which ...
96 Chapter 3. Motion of a single plasma particle Lagrange’s equationP ̇j=−∂L/∂Qjhas no limitations on the rate at which changes ...
3.7 Non-adiabatic motion in symmetric geometry 97 z B r,zis flux linked by this circle Figure 3.12: Azimuthally symmetricflux ...
98 Chapter 3. Motion of a single plasma particle a Poisson-like equation. Since no current loops can exist at infinity, the fiel ...
3.7 Non-adiabatic motion in symmetric geometry 99 In this cylindrical coordinate system the Lagrangian, Eq.(3.12), has the form ...
100 Chapter 3. Motion of a single plasma particle Figure 3.14: Specific example (withzdependence suppressed) showingψ andχrela- ...
3.7 Non-adiabatic motion in symmetric geometry 101 defined by Eq.(3.161). From Eq.(3.157) the angular velocity is θ ̇=^1 mr^2 ( ...
102 Chapter 3. Motion of a single plasma particle Eq.(3.165) can only be satisfied if|Pθ|is not too large, because the right han ...
3.7 Non-adiabatic motion in symmetric geometry 103 Becauseψ(r(t),z(t),t)is theflux measured in the frame of a particle moving wi ...
104 Chapter 3. Motion of a single plasma particle cross the cusp. Such an analysis is possible because two constants of the moti ...
3.7 Non-adiabatic motion in symmetric geometry 105 (a) (b) particle vvz 0 ẑ B adiabatic non-adiabatic adiabatic region solenoi ...
106 Chapter 3. Motion of a single plasma particle particle is confined between the two cusps. Cusps have also been used to trap ...
3.7 Non-adiabatic motion in symmetric geometry 107 should be construed assin[ky(t)−ωt] so that, taking into account the time dep ...
108 Chapter 3. Motion of a single plasma particle i.e., dδv dt = q m [δx·∇E+δv×B]. (3.185) The difference velocity is related to ...
3.8 Motion in small-amplitude oscillatory fields 109 where〈x(t)〉is the particle’s time-averaged position andδx(t)is the instanta ...
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