Dynamics of Langmuir and ion-sound waves in type III solar radio sources

Abstract

The evolution of Langmuir and ion-sound waves in type III sourcesis investigated, incorporating linear growth, linear damping, andnonlinear electrostatic decay. Improved estimates are obtained forthe wavenumber range of growing waves and the nonlinear couplingcoefficient for the decay process. The resulting prediction for theelectrostatic decay threshold is consistent with the observed high-fieldcutoff in the Langmuir field distribution. It is shown that the conditionsin the solar wind do not allow a steady state to be attained; rather,bursty linear and nonlinear interactions take place, consistent withthe highly inhomogeneous and impulsive waves actually observed. Nonlineargrowth is found to be fast enough to saturate the growth of the parentLangmuir waves in the available interaction time. The resulting levelsof product Langmuir and ion-sound waves are estimated theoreticallyand shown to be consistent with in situ ISEE 3 observations of typeIll events at 1 AU. Nonlinear interactions slave the growth and decayof product sound waves to that of the product Langmuir waves. Theresulting probability distribution of ion-sound field strengths ispredicted to have a flat tail extending to a high-field cutoff. Thisprediction is consistent with statistics derived here from ISEE 3observations. Agreement is also found between the frequencies ofthe observed waves and predictions for the product S waves. The competingprocesses of nonlinear wave collapse and quasilinear relaxation arediscussed, and it is concluded that neither is responsible for thesaturation of Langmuir growth. When wave and beam inhomogeneitiesare accounted for, arguments from quasi-linear relaxation yield anupper bound on the Langmuir fields that is too high to be relevant.Nor are the criteria for direct wave collapse of the beam-drivenwaves met, consistent with earlier simulation results that implythat this process is not responsible for saturation of the beam instability.Indeed, even if the highest observed Langmuir fields are assumedto be part of a long-wavelength ''condensate'' produced via electrostaticdecay, they still fall short of the relevant requirements for wavecollapse. The most stringent requirement for collapse is that collapsingwave packets not be disrupted by ambient density fluctuations inthe solar wind. Fields of several mV m-1 extending over several hundredkm would be needed to satisfy this requirement; at 1 AU such fieldsare rare at best.