Stochastic growth of localized plasma waves

Abstract

Localized bursty plasma waves are detected by spacecraft in many space plasmas. The large spatiotemporal scales involved imply that beam and other instabilities relax to marginal stability and that mean wave energies are low. Stochastic wave growth occurs when ambient fluctuations perturb the system, causing fluctuations about marginal stability. This yields regions where growth is enhanced and others where damping is increased; bursts are associated with enhanced growth and can occur even when the mean growth rate is negative. In stochastic growth, energy loss from the source is suppressed relative to secular growth, preserving it far longer than otherwise possible. Linear stochastic growth can operate at wave levels below thresholds of nonlinear wave-clumping mechanisms such as strong-turbulence modulational instability and is not subject to their coherence and wavelength limits. These mechanisms can be distinguished by statistics of the fields, whose strengths are lognormally distributed if stochastically growing and power-law distributed in strong turbulence. Recent applications of stochastic growth theory (SGT) are described, involving bursty plasma waves and unstable particle distributions in type III solar radio sources, the Earth’s foreshock, magnetosheath, and polar cap regions. It is shown that when combined with wave–wave processes, SGT also accounts for associated radio emissions.

S/WAVES: The Radio and Plasma Wave Investigation on the STEREO Mission

“…Three major coupled questions need to be answered (Cairns and Kaiser 2002;Kellogg 2003): (i) why are the waves bursty, (ii) what is the origin of the localized wave packets that are sometimes observed, and (iii) what are the roles of linear and nonlinear processes in the evolution of Langmuir waves and the production of type II and III radiation? In addition to these major studies, simultaneous high time resolution (≈ 1 µs) TDS data on 3 electric antennas will allow detailed comparison with stochastic growth theory (SGT) (Robinson 1992(Robinson , 1995Robinson et al 1993;Cairns and Robinson 1999;Robinson and Cairns 2001), together with frequency-domain and correlation analyses of nonlinear product waves (Bale et al 1998), and investigation of the reflection and linear mode conversion of Langmuir waves by density irregularities (Hinkel-Lipsker et al 1992;Bale et al 1998;Yin et al 1999;Willes and Cairns 2001). In addition, localized Langmuir wavepackets will be compared with the predictions of strong turbulence "wave collapse" (Robinson 1997).…”

Statistics of auroral Langmuir waves

“…SGT involves waves driven by a linear instability and subject to damping and scattering that vary with position and time in an inhomogeneous medium (Robinson, 1992(Robinson, , 1995Robinson et al, 1993;Robinson and Cairns, 2001;Cairns and Menietti, 2001). Wave-particle interactions then lead to the system evolving to a state near marginal stability in which the wave gain G= dt = ln(E/E 0 ) is a stochastic random variable.…”

Waveform and envelope field statistics for waves with stochastically driven amplitudes

“…8,9 Statistical plasma theories such as stochastic growth theory ͑SGT͒, 10,11 nonlinear strong turbulence theory ͑STT͒, 12 and self-organized criticality ͑SOC͒ 13 have successfully described wave fluctuations in various complex systems in laboratory, space, astrophysical, and simulated plasmas. 12,[14][15][16][17] SGT predicts that the probability distribution functions of stochastically driven waves follow lognormal distributions, while STT and SOC predict powerlaw distributions at high fields.…”