Fundamentals of Plasma Physics
170 Chapter 5. Streaming instabilities and the Landau problem also energy in coherent particle motion - to be discussed in Chapt ...
5.2 The Landau problem 171 On applying the Taylor expansion technique discussed in conjunction with Eqs.(5.82) and (5.83) we fin ...
172 Chapter 5. Streaming instabilities and the Landau problem 5.3 The Penrose criterion The analysis so far showed that electros ...
5.3 The Penrose criterion 173 Q-plane origin and ending at this same origin as shown by the various possible mappings sketched i ...
174 Chapter 5. Streaming instabilities and the Landau problem to an instability. However, curves of the form sketched in Figs.5. ...
5.4 Assignments 175 These contributions are weighted according to how far they are fromvminby the factor (v−vmin)−^2. The Penros ...
176 Chapter 5. Streaming instabilities and the Landau problem the dummy variable of integrationkby−kso thatdk→−dkand the±∞limits ...
5.4 Assignments 177 appropriate subset of these parameters. Suppose a cylindrical mercury plasma with Te=1− 2 eV,Ti=0. 1 eV, dia ...
6 Cold plasma waves in a magnetized plasma Chapter 4 showed that finite temperature is responsible for the lowest order dispersi ...
6.2 Dielectric tensor 179 One might expect that a procedure analogous to the previous derivation of electrostatic susceptibiliti ...
180 Chapter 6. Cold plasma waves in a magnetized plasma The tilde ̃denotes a small-amplitude oscillatory quantity with space-tim ...
6.2 Dielectric tensor 181 and the elements of the dielectric tensor are S=1− ∑ σ=i,e ω^2 pσ ω^2 −ω^2 cσ , D= ∑ σ=i,e ωcσ ω ω^2 p ...
182 Chapter 6. Cold plasma waves in a magnetized plasma where, for clarity, the tildes have been dropped. It is now useful to in ...
6.2 Dielectric tensor 183 What does all this algebra mean? Equation (6.25) states that forθ=0the dispersion re- lation has two d ...
184 Chapter 6. Cold plasma waves in a magnetized plasma 1 c 2 vA^2 n^2 L n^2 R 1 ci |ce| n 2 Figure 6.1: Propagation pa ...
6.2 Dielectric tensor 185 the electric field in the plane orthogonal toˆzhas the form E⊥ = Re{E⊥(ˆx+iˆy)exp(ikzz−iωt)} = |E⊥|{ˆx ...
186 Chapter 6. Cold plasma waves in a magnetized plasma and again two distinct modes appear. The first mode has as its eigenvect ...
6.2 Dielectric tensor 187 BecauseD=0the determinant factors into two modes, one where ( S−n^2 ) Ey=0 (6.43) and the other where ...
188 Chapter 6. Cold plasma waves in a magnetized plasma 6.2.6 Wave normal surfaces The information contained in a dispersion rel ...
6.2 Dielectric tensor 189 ce^2 ^2 pe^2 pi^2 ^2 Figure 6.2: CMA diagram. It is actually unnecessary to plot this very lar ...
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