Nonlinear Plasma Waves at the Earth's Bow Shock

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It is intended to carry out several theoretical and observational studies related to nonlinear MHD waves and Langmuir waves in the region of space upstream to the Earth's bowshock. It is planned to compare the large amplitude MHD waves, and in particular their steepened appearance, to the solutions of nonlinear wave equations such as the Derivative Nonlinear Schrondinger Equation (DNLS). Efforts will be made to append terms to the DNLS which describe important physical effects such as resonant particle interactions, realistic particle distribution functions, oblique propagation, and two and three dimensionality. An extensive investigation, currently in progress, of the various linear and nonlinear wave processes which are important in the upstream MHD waves will be completed. Twenty periods of upstream wave activity have been identified, the data acquired, and power spectra and cross correlation functions calculated. New work will address the extent to which pondermotive nonlinearities, the parametric decay instability, and three dimensional wave effects can be discerned in the data. In the study of Langmuir waves, work will concentrate on further numerical and analytic studies of the saturated phase of the beam instability using computer simulations in part. The goal of these studies will be to better understand such phenomena as wave backscattering, generation of low frequency waves, and the long time evolution of the beam-driven waves.