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PLASMA ASTROPHYSICS 123 clouds collapse and form stars once a sufficient amount of their magnetic flux has been removed. This picture has been confirmed and extended by extensive theoretical calculations, including static models of magnetized, self- gravitating clouds; dynamical models of gravitational collapse; and both analytical and numerical calculations of ion-neutral drift. PROBLEMS IN PLASMA ASTROPHYSICS The panel has not attempted to make an exhaustive list of problems in plasma astrophysics, but instead has chosen a few problems that arise in a broad variety of physical environments, illustrating how plasma physics touches almost every part of astrophysics. Some of these problems are in the realm of space plasma physics as well. Dense Stellar Plasmas The mass density and temperature at the center of the Sun, which is an ordinary, low-mass star, are predicted to be about 100 g/cm3and 2 Ã 107 K, respectively. The energy produced by nuclear reactions diffuses outward as radiative energy, with most of the opacity due to bound-free transitions in elements heavier than helium. At these temperatures and densities, atoms are significantly perturbed by their nearest neighbors. Recent attempts to take these many-body effects into account when calculating the opacity and equation of state of dense stellar material have produced strikingly different results from earlier calculations, which has injected substantial uncertainty into models of solar-type stars and their evolution. This problem is at the intersection of plasma physics, statistical mechanics, and atomic physics. Thermal Conduction in Plasmas Observations suggest sharp temperature interfaces between the solar corona and lower atmosphere and at the boundaries of interstellar clouds. These interfaces are sharp in the sense that the inferred temperature scale height is comparable to the electron mean free path. The transport of heat becomes strongly nonlocal, and the electron distribution function becomes non- Maxwellian. Attempts to solve this problem have ranged from the application of theories of saturated heat flux regulated by ion-acoustic instabilities to attempts at full kinetic theory solutions of the Boltzmann equation. Structure of Collisionless Shocks Astrophysical shock waves are produced by energetic, impulsive events ranging from solar and stellar flares to sequential supernova explosions in asso
