Nonlinear Theory of Anomalous Resistivity for Buneman Instability

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This project combines a theoretical and numerical study of one of the mechanisms that may initiate magnetic reconnection in a geomagnetic substorm. The general mechanism is an enhancement in the electrical resistivity of the plasma brought on by a plasma instability. The effective electrical resistivity is referred to as "anomalous resistivity." Magnetic reconnection is one of the most important research topics in contemporary space plasma physics. Although it is at the core of many astrophysical, space, and magnetospheric processes, there are still many issues associated with this fundamental process that have yet to be understood. The onset process and the mechanism which breaks the frozen-in-flux condition are among them. It is widely recognized that the anomalous resistivity that arises from small-scale kinetic plasma instabilities is one of the crucial factors that can lead to the onset of reconnection by breaking the magnetohydrodynamics (MHD) frozen-in-flux condition. Of the many possible plasma instabilities relevant for collisionless reconnection, this project will focus on the Farley-Buneman (FB) instability (also known as the two-stream instability). Theoretical computation of anomalous resistivity in the literature has been limited to quasilinear formalism. However, recent numerical simulations show that numerically tabulated anomalous resistivity from FB instability can be orders of magnitude higher than the theoretical prediction. This shows that nonlinear theory is called for. This project develops a self-consistent nonlinear theory of anomalous resistivity for the FB instability. The customary text book theory is inapplicable for the FB instability since it is a reactive instability. The project will perform a quantitative analysis based upon the nonlinear theory, and compare the theoretical results with results from numerical simulations. In view of the importance of anomalous resistivity phenomena for a variety of problems in magnetospheric and solar-terrestrial physics, astrophysics, and even laboratory plasma physics, the research will have far-reaching consequences. From the perspective of fundamental plasma physics, the research will lead to a new way of analyzing nonlinear stages of plasma instabilities. The plasma kinetic theory developed by the early pioneers of modern plasma physics is valid only for weakly unstable kinetic instabilities. In plasmas, kinetic instabilities form only a small subset of problems. More general reactive instabilities are important for many situations, and are far more prevalent. For this important class of instabilities, there is currently no theory to analyze their fully nonlinear behavior. Even though the immediate goal of this research is to investigate only the nonlinear phase of the Farley-Buneman instability, the underlying nonlinear theory will be valid for any reactive instability.