Fundamentals of Plasma Physics
130 Chapter 4. Elementary plasma waves For self-consistency, it is necessary to havec^2 s>> κTi 0 /mi;if this were not tru ...
4.3 Low frequency magnetized plasma: Alfvén waves 131 In the limit of no plasma so thatω^2 p→ 0 ,Eq.(4.43) reduces to the standa ...
132 Chapter 4. Elementary plasma waves an inductive character (i.e.,∇×E= 0 ). Faraday’s law∇×E=−∂B/∂tshows that if the electric ...
4.3 Low frequency magnetized plasma: Alfvén waves 133 The fields and gradient operator can be written as E 1 = E⊥ 1 B 1 = B⊥ 1 + ...
134 Chapter 4. Elementary plasma waves 4.3.3 Fast mode (mode whereBz 1 =0) In this case only thezcomponent of Faraday’s law is ...
4.3 Low frequency magnetized plasma: Alfvén waves 135 direction of propagation of compressional Alfven wave compressed field lin ...
136 Chapter 4. Elementary plasma waves while the linearized continuity equation ∂ρ 1 ∂t +ρ∇·U 1 =0 (4.70) together with the equa ...
4.3 Low frequency magnetized plasma: Alfvén waves 137 Equations (4.78) and (4.81) constitute two coupled equations in the variab ...
138 Chapter 4. Elementary plasma waves 4.3.8 Limitations of the MHD model The MHD model ignores parallel electron dynamics and s ...
4.4 Two-fluid model of Alfvén modes 139 The ratio of electron thermal velocity to Alfvén velocity is also ofinterest and is v^2 ...
140 Chapter 4. Elementary plasma waves the boxed terms (this mode is called theEzmode since it has finiteEz) and the other disti ...
4.4 Two-fluid model of Alfvén modes 141 when the perpendicular current, i.e.,J 1 ⊥= ∑ nqσuσ⊥ 1 is considered, the electron and i ...
142 Chapter 4. Elementary plasma waves Combining Eqs.(4.103) and (4.101) and then integrating in time gives n 1 n = Bz 1 B (4.10 ...
4.4 Two-fluid model of Alfvén modes 143 4.4.1 Two-fluid slow (shear) modes As discussed above these modes haveBz 1 =0,E⊥ 1 =−∇φ ...
144 Chapter 4. Elementary plasma waves which gives the ion acoustic waveω^2 =k^2 zκTe/midiscussed in Sec.4.2.1. This shows that ...
4.4 Two-fluid model of Alfvén modes 145 which is called the inertial Alfvén wave (IAW). Ifk⊥^2 c^2 /ω^2 peis not too large, then ...
146 Chapter 4. Elementary plasma waves thenk⊥must be in theydirection while in cylindrical geometry, this means that ifuσ⊥ 1 is ...
4.5 Assignments 147 4.4.3 Differences between the two-fluid and MHD descriptions The two-fluid description shows that the slow m ...
148 Chapter 4. Elementary plasma waves an oscillating electric field ̃E⊥where⊥means in the direction perpendicular toz.ˆ What is ...
5 Streaming instabilities and the Landau problem 5.1 Streaming instabilities The electrostatic dispersion relation for a zero-te ...
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