Vlasov Theory

  • Hannu E. J. Koskinen
Part of the Springer Praxis Books book series (PRAXIS)


The cold plasma approximation of Chap. 4 was based on the assumption that the phase velocities of the waves are much larger than the thermal velocities of the particle populations. This is essentially the same as approximating the particle distribution functions by delta functions, although taking the limit may be tricky and not necessarily mathematically rigorous. The approximation is evidently not valid at resonances and many aspects of wave–particle interactions are lost. In this chapter we introduce the thermal (or kinetic) effects starting from the Vlasov equation
$${\frac{{\partial f_{\alpha}}}{\partial t}}+{{\bf v}}\cdot{\frac{\partial f_{\alpha}}{\partial {\bf r}}}+{\frac{q_{\alpha}}{m_{\alpha}}({\bf E}+{\bf v}\times{\bf B})}\cdot{\frac{\partial f_{\alpha}}{\partial {\bf v}}}=0.$$


Dispersion Equation Vlasov Equation Langmuir Wave Whistler Mode Ballistic Term 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hannu E. J. Koskinen
    • 1
  1. 1.University of Helsinki and Finnish Meteorological InstituteHelsinkiFinland

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