Estimates of the optical thickness for some processes of unlimited compression of a gas

The unlimited unshocked compression of an ideal gas (the unlimited increase in the density and no shock waves) is considered when the gas is at rest i nside a cylinder, a sphere [1], a tetrahedron [2] and a solid of revolution with a triangular generatrix [3, 4] at the initial instant of time. It is proved that the value of the optical thickness increases without limit and the asymptotic form of its increase for instants of time close to the insta nt when the gas collapses to a point is obtained. Estimates are made of the ratio of the optical thickness to the energy expended in the compression. (C) 2000 Elsevier Science Ltd. All rights reserved.