Fundamentals of Plasma Physics
250 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma direction but are constrained to make Larmor orb ...
8.6 Drift waves 251 cylindrical magnetized plasma typical particle orbit typicalfield line radial density profile z r Figure 8.3 ...
252 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma 8.6.1 Simple two-fluid model of drift waves The ...
8.6 Drift waves 253 Equating the electron and ion perturbed densities, respectively given by Eqs.(8.104) and (8.107), provides t ...
254 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma with the continuity equation gives the perturbed ...
8.6 Drift waves 255 the distance diffused in timetis given byz^2 ∼ 4 D‖t. Equation (8.121) shows that in the limitτ‖→ 0 ,the ele ...
256 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma Since the plasma is quasi-neutral, the normalize ...
8.6 Drift waves 257 which is true provided the ratioνei/ωceis sufficiently small for a given geometric factor ky/k^2 zL. The ima ...
258 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma Γx = 1 2 Re [ − n 0 qe Te ( 1 −i(ω∗−ω)τ‖ )iky|φ ...
8.6 Drift waves 259 and potentialfluctuations resulting in an imaginary term in the dispersion relation.Also, since Vlasov analy ...
260 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma motion. The appropriately normalized lab frame d ...
8.6 Drift waves 261 which causes Eq.(8.140) to become fσ 1 (x,v,t) = − qσ ̃φfσ 0 mσ ∫t −∞ dt′eik·x(t ′)−iωt′ [ 2ik·v v^2 Tσ − 2i ...
262 Chapter 8. Vlasov theory of warm electrostatic waves in a magnetized plasma |uzi|<<|uze|since the parallel equilibriu ...
8.7 Assignments 263 There are many more varieties of drift waves besides the basic versionsdiscussed here. The common feature is ...
9 MHD equilibria 9.1 Why use MHD? Of the three levels of plasma description – Vlasov, two-fluid, and MHD – Vlasov is the most ac ...
9.2 Vacuum magnetic fields 265 9.2 Vacuum magnetic fields The simplest non-trivial magnetic field results when the magnetic fiel ...
266 Chapter 9. MHD equilibria or two directions (theθandzdirections for the cylindrical example here), and exponen- tially growi ...
9.2 Vacuum magnetic fields 267 is in fact the lowest energy field. Thus, the only way to ensure thatBminis indeed the true minim ...
268 Chapter 9. MHD equilibria 9.3 Force-free fields Although the vacuum field is the lowest energy configuration satisfying pres ...
9.4 Magnetic pressure and tension 269 parallel currents attract each other. Conversely, anti-parallel currents repel each other. ...
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