title: Self-Similar Theory of Thermal Conduction and Application to the Solar Wind.
abstract: We propose a self-similar kinetic theory of thermal conductivity in a magnetized plasma, and discuss its application to the solar wind. We study a collisional kinetic equation in a spatially expanding magnetic flux tube, assuming that the magnetic field strength, the plasma density, and the plasma temperature decline as power laws of distance along the tube. We demonstrate that the electron kinetic equation has a family of scale-invariant solutions for a particular relation among the magnetic-, density-, and temperature-scaling exponents. These solutions describe the heat flux as a function of the temperature Knudsen number γ, which we require to be constant along the flux tube. We observe that self-similarity may be realized in the solar wind; for the Helios data 0.3-1  AU we find that the scaling exponents for density, temperature, and heat flux are close to those dictated by scale invariance. We find steady-state solutions of the self-similar kinetic equation numerically, and show that these solutions accurately reproduce the electron strahl population seen in the solar wind, as well as the measured heat flux.
authors.affiliation: Department of Physics, University of Wisconsin, Wisconsin-Madison 53706, USA.
authors.forename: K
authors.initials: K
authors.lastname: Horaites
authors.affiliation: Department of Physics, University of Wisconsin, Wisconsin-Madison 53706, USA.
authors.forename: S
authors.initials: S
authors.lastname: Boldyrev
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California 92093, USA.
authors.forename: S I
authors.initials: SI
authors.lastname: Krasheninnikov
authors.affiliation: Space Sciences Laboratory, University of California, Berkeley, California 94720, USA.
authors.forename: C
authors.initials: C
authors.lastname: Salem
authors.affiliation: Space Sciences Laboratory, University of California, Berkeley, California 94720, USA.|Department of Physics, University of California, Berkeley, California 94720, USA.
authors.forename: S D
authors.initials: SD
authors.lastname: Bale
authors.affiliation: Space Sciences Laboratory, University of California, Berkeley, California 94720, USA.
authors.forename: M
authors.initials: M
authors.lastname: Pulupa