Balance equation and the quasitemperature of channeled particles in equilibrium

Abstract

Using the methods of nonequilibrium statistical thermodynamics, we obtain the equation for the transverse energy and momentum balance for fast atomic particles moving in the planar channeling regime. Based on the solution of this equation, we obtain an expression for the transverse quasitemperature in the quasiequilibrium in terms of the basic parameters of the theory. We show that the equilibrium quasitemperature of channeled particles is established because of particle diffusion in the space of transverse energies (subsystem "heating"), the dissipative process ("cooling"), and the anharmonic effects of particle oscillations between the channel walls (the redistribution of energies over the oscillatory degrees of freedom is the internal thermalization of the subsystem). According to the estimates for particles with an energy of the order of 1 MeV, the quasitemperature values are in the characteristic temperature range for a low-temperature plasma.1. The concept of quasitemperature as the modulus of the equilibrium distribution of an isolated subsystem of particles (quasiparticles, spins) is successfully used in the case of systems far from complete thermodynamic equilibrium. We list several characteristic examples of the application of this concept:• quasitemperature in the presence of interactions between particles (quasiparticles, spins);• quasitemperature in the case of weak interactions between some (translational, internal) degrees of freedom when the corresponding relaxation processes are independent;• quasitemperature in the presence of interactions of particles with a heat bath and of an additional energy exchange between the internal degrees of freedom of the subsystem.The first case is typical for the subsystem of nuclear spins isolated from the lattice when spins pass to the internal quasiequilibrium because of the spin-spin interaction. In this case, the probability that the subsystem is in a given energy state is described by the Boltzmann distribution [1]. The second case is realized in a plasma [2], [3] when the modulus of the distribution over all degrees of freedom except the translational one is the effective electron temperature. More precisely, the distribution of heavy particles (ions, neutral particles) over the translational degrees of freedom is determined by the temperature of the heavy plasma component, while the modulus of the distribution over all the other degrees of freedom is the electron temperature. The third case is directly related to "hot" atoms moving in crystalline solids, including high-energy channeled particles (CPs) [4], [5]. The planar channeling effect can be considered from the standpoint of nonequilibrium statistical thermodynamics because the CPs constitute an independent thermodynamic subsystem.