Nonlinear Theory of Anomalous Resistivity for Buneman Instability

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。这个项目结合了理论和数值研究的机制之一，可能启动磁重联在地磁亚暴。其一般机理是等离子体不稳定性引起的等离子体电阻率的增强。有效电阻率称为“异常电阻率”。磁重联是当代空间等离子体物理学的重要研究课题之一。尽管它是许多天体物理、空间和磁层过程的核心，但仍有许多与这一基本过程相关的问题尚未被理解。其中包括冻结在流状态的发生过程和破坏机理。人们普遍认为，由小尺度动态等离子体不稳定性引起的异常电阻率是导致磁流体动力学（MHD）冻结磁通状态发生重联的关键因素之一。在与无碰撞重联相关的许多可能的等离子体不稳定性中，该项目将重点研究法利-布曼（FB）不稳定性（也称为双流不稳定性）。文献中异常电阻率的理论计算一直局限于拟线性形式。然而，最近的数值模拟表明，由FB不稳定引起的数值表异常电阻率可能比理论预测高几个数量级。这表明需要非线性理论。本项目发展了一种自洽的FB不稳定异常电阻率非线性理论。由于FB不稳定是一种反应性不稳定，所以传统的教科书理论不适用于它。该项目将基于非线性理论进行定量分析，并将理论结果与数值模拟结果进行比较。鉴于异常电阻率现象对磁层和日地物理、天体物理甚至实验室等离子体物理中的各种问题的重要性，其研究将产生深远的影响。从基础等离子体物理学的角度出发，该研究将为等离子体不稳定性的非线性阶段分析开辟一条新的途径。现代等离子体物理学的早期先驱们提出的等离子体运动论只适用于弱不稳定的动力学不稳定。在等离子体中，动力学不稳定性只是问题的一小部分。更普遍的反应性不稳定性在许多情况下都很重要，而且更为普遍。对于这一类重要的不稳定性，目前还没有理论来分析它们的完全非线性行为。尽管本研究的直接目的是研究Farley-Buneman不稳定性的非线性阶段，但其潜在的非线性理论将适用于任何反应性不稳定性。

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.