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).