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Physics 777 Plasma Physics and Magnetohydrodynamics (MHD)

This lecture discusses simple waves, nonlinear waves, solitons, discontinuities, shock waves, and strong turbulence in plasma. It covers the set of MHD equations, entropy simple waves, Alfven simple waves, fast and slow simple waves, Korteweg-de Vries-Burgers equation, solitons, discontinuities and shocks in plasma, evolutionarity of discontinuities, and strong turbulence.

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Physics 777 Plasma Physics and Magnetohydrodynamics (MHD)

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  1. Physics 777Plasma Physics and Magnetohydrodynamics (MHD) Instructor: Gregory Fleishman Lecture 9. Large-Amplitude Waves and Discontinuities 28 October 2008

  2. Plan of the Lecture • Simple Waves • Nonlinear Waves, Solitons • Discontinuities in the Plasma • Shock Waves • Strong Turbulence

  3. Section 1. Simple Waves

  4. Set of MHD equations reads

  5. Section 1.1. Entropy simple waves If If & - arbitrary For other simple waves where

  6. Section 1.2. Alfven simple waves &

  7. Section 1.3. Fast and slow simple waves If for some then for for all Consider simple case

  8. Section 2. Nonlinear Waves, Solitons Korteweg – de Vries – Burgers Equation, which includes nonlinearity, dispersion, and dissipation as additive terms: where Burgers Equation Korteweg – de Vries (KdV) Equation

  9. Section 2.1. Solitons Consider KdV Equation Seek solution

  10. Necessary conditions: Case I For or result in

  11. Rarefaction! Case II Jakobi elliptic function; - Cnoidal wave Chain of solitons

  12. Section 3. Discontinuities and Shocks in the Plasma

  13. Upstream Downstream

  14. Section 4. Evolutionarity of the Discontinuities

  15. Section 5. Strong Turbulence

  16. Upstream Downstream & & &

  17. Section 6. Homework • Complete Progress Reports on the research project. Include Introduction, the work done with plots, and plan for the remaining work. Be ready for brief presentation of the Progress Report.

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