Fundamentals of Plasma Physics
110 Chapter 3. Motion of a single plasma particle and thezaxis has been chosen to be in the direction ofB 0 .Equation (3.197) ca ...
3.9 Wave-particle energy transfer 111 speed, andvfas the fast speed (out of traffic jam). It is tempting, but wrong, to say that ...
112 Chapter 3. Motion of a single plasma particle The average velocity for each of these four representative particles will now ...
3.9 Wave-particle energy transfer 113 portion, the forces are the same, but the distances are half as much, so the time to trave ...
114 Chapter 3. Motion of a single plasma particle 3.9.4 Wave-particle energy transfer in a sinusoidal wave The calculation will ...
3.9 Wave-particle energy transfer 115 By defining thebouncefrequency ω^2 b= k^2 qφ 0 m (3.223) and the dimensionless bounce-norm ...
116 Chapter 3. Motion of a single plasma particle which corresponds to considering small amplitude waves sinceα∼ω−b^1 andωb∼ √ φ ...
3.9 Wave-particle energy transfer 117 and so the rate at which energy is transferred from the wave to the particles is dW dt = − ...
118 Chapter 3. Motion of a single plasma particle Using the identities 〈sin(θ 0 +ατ)cos(θ 0 +ατ)〉= 0 〈sinθ 0 cos(θ 0 +ατ)〉=−^12 ...
3.10 Assignments 119 If the distribution function has the Maxwellian formf∼exp(−v^20 / 2 v^2 T)wherevTis the thermal velocity, a ...
120 Chapter 3. Motion of a single plasma particle Show that of all the standard drifts (E×B,∇B, curvature, polarization) only t ...
3.10 Assignments 121 the time for the particle to make one complete bounce between the walls if thenomi- nal distance between wa ...
122 Chapter 3. Motion of a single plasma particle center atz= +L/ 2 .The radiiaandbare chosen so as to intercept the field lines ...
4 Elementary plasma waves 4.1 General method for analyzing small amplitude waves All plasma phenomena can be described by combin ...
124 Chapter 4. Elementary plasma waves so the variables are written as f = f 0 +f 1 g = g 0 +g 1 +g 2 +.... h = h 0 +h 1 +h 2 +. ...
4.2 Two-fluid theory of unmagnetized plasma waves 125 Eq. (4.6) is then mσnσ 0 ∂uσ 1 ∂t =qσnσ 0 E 1 −∇Pσ 1. (4.7) The electric f ...
126 Chapter 4. Elementary plasma waves so Eq. (4.12) becomes mσ ∂^2 nσ 1 ∂t^2 =qσnσ 0 ∇^2 φ 1 +γκTσ 0 ∇^2 nσ 1 (4.16) wherePσ 0 ...
4.2 Two-fluid theory of unmagnetized plasma waves 127 Equation (4.24) shows that ifφ 1 = 0, the quantity1 +χe+χimust vanish. In ...
128 Chapter 4. Elementary plasma waves 1 2 3 /k T 0 /m ≈^1 k^2 D^2 ≈− p^2 ^2 Figure 4.1: Susceptibilityχas a functi ...
4.2 Two-fluid theory of unmagnetized plasma waves 129 standard form for the high-frequency, electrostatic, unmagnetized plasma w ...
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