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

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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.