By Rudolf A. Treumann
This e-book builds at the fluid and kinetic conception of equilibria and waves awarded in a significant other textbook, simple house Plasma Physics (by a similar authors), yet may also function a stand-alone textual content. It extends the sector coated there into the area of plasma instability and nonlinear idea. The booklet offers a consultant choice of the numerous attainable macro- and microinstabilities in an area plasma, from the Rayleigh-Taylor and Kelvin-Helmholtz to electrostatic and electromagnetic kinetic instabilities. Their quasilinear stabilization and nonlinear evolution and their program to house physics difficulties are taken care of. The chapters on nonlinear concept contain nonlinear waves, susceptible turbulence and robust turbulence, all offered from the point of view in their relevance to house plasma physics. specific issues contain auroral particle acceleration, soliton formation and caviton cave in, anomalous shipping, and the idea of collisionless shocks.
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54). Inserting all this into Eq. 57) This expression depends only weakly on the electron current speed above threshold. The dominating number in the argument of the logarithm is the Debye number, ND = nλ3D . Its logarithm is typically of the order of 15–30. Hence, in terms of the electron plasma frequency the self-disruption time of the current due to Buneman instability in an electron-proton plasma takes about 200 electron plasma periods or about 10 Buneman oscillations. 03 ωpe . 4. 4. Ion Beam Instability As for a last introductory example we discuss an instability generated by two counterstreaming plasma flows, the electrostatic streaming instability or counterstreaming ion beam instability.
Vb v 28 vthe< Dispersion Relation Let us assume ideal conditions though usually the narrow transition layer may contain some kind of viscous interaction. Then the electric field is given by E = −v × B. 41) B0 Plasma Vacuum v0 x B0 2 −v0 Fig. 5. Two configurations leading to Kelvin-Helmholtz instability. 2 44 3. 42) µ0 mi n0 d δx/dt2 = −µ0 ∇δp − δB × (∇ × B0 ) − B0 × (∇ × δB) 2 The induction law in the above version has been integrated with respect to time t. 43) Eliminating δB from the second Eq. 44) ∂t2 √ We have introduced here the Alfv´en velocity, vA = B0 / µ0 mi n0 , defined by the background parameters.
Advanced space plasma physics by Rudolf A. Treumann
Dispersion Relation Let us assume ideal conditions though usually the narrow transition layer may contain some kind of viscous interaction. Then the electric field is given by E = −v × B. 41) B0 Plasma Vacuum v0 x B0 2 −v0 Fig. 5. Two configurations leading to Kelvin-Helmholtz instability. 2 44 3. 42) µ0 mi n0 d δx/dt2 = −µ0 ∇δp − δB × (∇ × B0 ) − B0 × (∇ × δB) 2 The induction law in the above version has been integrated with respect to time t. 43) Eliminating δB from the second Eq. 44) ∂t2 √ We have introduced here the Alfv´en velocity, vA = B0 / µ0 mi n0 , defined by the background parameters.