Book contents
- Frontmatter
- Contents
- Preface
- 1 Basic concepts
- 2 The Vlasov, two-fluid, and MHD models of plasma dynamics
- 3 Motion of a single plasma particle
- 4 Elementary plasma waves
- 5 Streaming instabilities and the Landau problem
- 6 Cold plasma waves in a magnetized plasma
- 7 Waves in inhomogeneous plasmas and wave-energy relations
- 8 Vlasov theory of warm electrostatic waves in a magnetized plasma
- 9 MHD equilibria
- 10 Stability of static MHD equilibria
- 11 Magnetic helicity interpreted and Woltjer–Taylor relaxation
- 12 Magnetic reconnection
- 13 Fokker–Planck theory of collisions
- 14 Wave–particle nonlinearities
- 15 Wave–wave nonlinearities
- 16 Non-neutral plasmas
- 17 Dusty plasmas
- Appendices
- Bibliography and suggested reading
- References
- Index
15 - Wave–wave nonlinearities
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Basic concepts
- 2 The Vlasov, two-fluid, and MHD models of plasma dynamics
- 3 Motion of a single plasma particle
- 4 Elementary plasma waves
- 5 Streaming instabilities and the Landau problem
- 6 Cold plasma waves in a magnetized plasma
- 7 Waves in inhomogeneous plasmas and wave-energy relations
- 8 Vlasov theory of warm electrostatic waves in a magnetized plasma
- 9 MHD equilibria
- 10 Stability of static MHD equilibria
- 11 Magnetic helicity interpreted and Woltjer–Taylor relaxation
- 12 Magnetic reconnection
- 13 Fokker–Planck theory of collisions
- 14 Wave–particle nonlinearities
- 15 Wave–wave nonlinearities
- 16 Non-neutral plasmas
- 17 Dusty plasmas
- Appendices
- Bibliography and suggested reading
- References
- Index
Summary
Introduction
Wave nonlinearity is a vast subject and is not specific to plasma physics because nonlinear wave behavior occurs in virtually any physical medium where waves can propagate. However, because of the enormous variety of plasma waves, there is usually at least one plasma context where any given type of wave nonlinearity is an important issue. Three general types of nonlinear wave behavior will be discussed in this chapter: mode–mode coupling instabilities, self-modulation, and solitons. Before discussing these phenomena in detail, we first present a qualitative overview showing how certain basic wave nonlinearities are manifested.
Mode–mode coupling instabilities
Suppose a linear wave is excited in a plasma by an antenna driven by an appropriately tuned sine wave generator. In particular, suppose the plasma frequency is ωpe/2π = 100 MHz and the sine wave generator is tuned to a frequency well above the plasma frequency, say ω/2π = 500 MHz, so as to cause the antenna to radiate an electromagnetic plasma wave with dispersion relation. This wave propagates through the plasma and is picked up by a distant receiving probe connected to a spectrum analyzer, a device that provides a graphic display of signal amplitude versus frequency. The received signal shows up on the spectrum analyzer display as a sharp peak at 500 MHz, as shown in Fig. 15.1(a).
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- Information
- Fundamentals of Plasma Physics , pp. 491 - 529Publisher: Cambridge University PressPrint publication year: 2006