The collisionless expansion into a vacuum of a thin plasma foil adiabatically cooling down is studied with a particular emphasis on the evolution of the electron distribution function. It is shown that during the expansion the bulk of the distribution function evolves towards a top-hat distribution. As a result, while the electrons globally lose energy in favor of the ions, the rarefaction wave accelerates until it reaches the center of the foil. The electron temperature becomes strongly inhomogeneous, with a maximum in the center of the foil, a strong dip in the outer part of the foil, and a constancy of the initial temperature in the far corona.
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