Fundamentals of Plasma Physics
230 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma Consider an electrostatic wave with potential φ ...
8.1 Uniform plasma 231 it is seen that Eq.(8.8) is identical to the left hand side of Eq.(8.6). Equation (8.6) can thus be rewri ...
232 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma Since the kinetic energymv^2 / 2 of the unpertur ...
8.1 Uniform plasma 233 whereτ=t′−t.Certain Bessel function relations are now of use. The first of these is the integral represen ...
234 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma Using this identity, substitution of Eq.(8.24) i ...
8.2 Analysis of the warm plasma electrostatic dispersion relation 235 tion Eq.(5.51) derived in Chapter 4 to the situation of a ...
236 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma where the subscriptσhas been omitted from theαnt ...
8.3 Bernstein waves 237 (a) (b) 1 2 3 4 c p^2 c^2 p^2 c^2 vgr 0 vgr 0 uh c 1 2 3 4 c Figure 8.1: Electro ...
238 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma The small and largeλlimits of this expression ar ...
8.4 Warm, magnetized, electrostatic dispersion with small, but finitek‖ 239 8.4 Warm, magnetized, electrostatic dispersion with ...
240 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma namely k⊥^2 = S± √ S^2 + 4ǫthk^2 ‖P 2 ǫth . (8.5 ...
8.5 Analysis of linear mode conversion 241 8.5 Analysis of linear mode conversion 8.5.1 Airy equation The procedure for analyzin ...
242 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma and xy = a ∫ Ce p^3 / 3 ( d dp epx ) dp = a [ ep ...
8.5 Analysis of linear mode conversion 243 To see this, it should first be recalled that the theory of complex variables shows t ...
244 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma so the saddle points (denoted by subscripts) are ...
8.5 Analysis of linear mode conversion 245 Providingxis not too close to zero,the two saddle points determined by the±signs are ...
246 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma where it is assumed thatǫthis approximately cons ...
8.5 Analysis of linear mode conversion 247 whereAis a constant. The inverse transform is φ(ξ) =A ∫ C ef(p)dp (8.84) where f(p) = ...
248 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma for largepas f(p) ≃ p^3 3 +pξ−lnp = p ( p^2 3 +ξ ...
8.6 Drift waves 249 Choice of contour path: Forξ < 0 and assumingμ > 0 the saddle points giving solutions that vanish whe ...
«
8
9
10
11
12
13
14
15
16
17
»
Free download pdf