Self-Similar Theory of Electron Thermal Conduction in a Weakly Collisional Plasma

太阳风是一种热粒子流，主要是电子和离子，以每小时数百万英里的速度从太阳流出。随着太阳风的膨胀，预计它会变冷。然而，在离太阳很远的地方，太阳风并不像人们从简单的热力学定律中预期的那样冷。目前还不清楚是什么加热了太阳风，因为加热通常需要粒子之间频繁的碰撞，而太阳风几乎没有碰撞。类似的问题也出现在其他天体物理和实验室系统中。这个项目将开发一种有效的方法来描述无碰撞等离子体中的加热和热传导。它将利用一种特殊的对称性，即自相似性，这是在膨胀的自然和实验室等离子体中经常观察到的。这一研究项目的成果还将有助于改进空间天气模拟的技术水平，在空间天气模拟中，太阳风的准确表示对于正确传播太阳活动对地球磁层的影响非常重要。电子热传导问题是理解自然和实验室等离子体中能量传输的核心问题。它的一般解析解是未知的，除了Spitzer-Harm情况，当电子的平均自由程明显短于温度梯度的尺度时。许多天然等离子体，如太阳日冕和太阳风，星系团内介质，是弱碰撞的，不满足上述条件。将开发一种新的方法，它考虑到这样一个事实，即在这样的系统中，诸如温度、密度和磁场的物理参数经常随着距离热源的距离的幂而下降。这使得人们能够找到全动力学方程的自相似解，并以非微扰的方式构造电子分布函数。

The solar wind is a flow of hot particles, mostly electrons and ions, streaming from the Sun with the speed of millions of miles per hour. As the solar wind expands, it is expected to cool. However, at large distances from the Sun, the solar wind turns out to be not as cold as one would expect from the simple laws of thermodynamics. It is currently not well understood what heats the solar wind, since heating generally requires frequent collisions between the particles and the solar wind is nearly collisionless. A similar problem arises in other astrophysical and laboratory systems. This project will develop an efficient method for describing heating and heat conduction in collisionless plasmas. It will utilize a special symmetry, self-similarity, often observed in expanding natural and laboratory plasmas. The outcomes of this research project will also be instrumental to improving the state of the art in space weather modeling, where accurate representations of the solar wind are important for correctly propagating the impacts of the solar activity on the Earth's magnetosphere. The problem of electron heat conduction is central for understanding energy transport in natural and laboratory plasmas. Its general analytical solution is unknown, except for the Spitzer-Harm case when the electron mean free path is significantly shorter than the scale of a temperature gradient. Many natural plasmas, e.g., solar corona and solar wind, intracluster medium, are weakly collisional, where the above condition is not satisfied. A novel approach will be developed, which takes into account the fact that the physical parameters such as temperature, density, and magnetic field in such systems often decline as powers of the distance from the heat source. This allows one to find self-similar solutions of the full kinetic equation, and to construct the electron distribution function in a non-perturbative fashion.