We use methods of nonequilibrium thermodynamics to investigate the quasiequilibrium and kinetic characteristics of channeled particles regarded as a separate thermodynamic subsystem. For the channeled particles, we derive the energy-momentum balance equation in the moving coordinate system and show that the solution of the balance equation provides an expression for the main thermodynamic parameter, the transverse quasitemperature of the channeled-particle subsystem. We study the quasiequilibrium angular distribution of particles after their passage through a thin single crystal, the quasiequilibrium distribution over the particle exit angles under backscattering conditions, and also the rate constant for the nonequilibrium (dechanneling) process at large deviations of the system as a whole from the thermodynamic equilibrium. We discuss a measurement method for the particle beam transverse temperature over the peak height of the angular particle distribution found in the framework of a "shoot-through" experiment.
Thermodynamic parameters of the channeled-particle subsystemAccording to [1], for fast particles incident on a crystal at small angles not exceeding the critical value, the beam of particles moving along the crystallographic planes (axes) splits into two fractions, namely, channeled and chaotic ones. The formation of the two particle fractions occurs at a penetration depth L of the order of the coherence length L coh ∼ 10 4Å [2]. Therefore, as a rule, analytic calculations are based on the property that a quasiequilibrium distribution over the transverse energies is attained in the channeled-particle (CP) subsystem at a depth ∼ L coh . At this depth, the probability amplitudes in the CP density-matrix equation are damped, but the diagonal matrix entries characterizing the occupancy of the transverse-energy levels are preserved. Therefore, a quasiequilibrium statistical operator ρ l [3], [4] and a quasiequilibrium CP distribution can be introduced at a depth ∼ L coh .If the chaotic part of the beam is excluded from consideration for simplicity, then the remaining part of the system should be further divided into two parts, first, the thermostat (i = 1) including the crystal lattice and the electron gas and, second, the light atomic particles (i = 2) moving in the channel regime. It is convenient to take the Hamiltonians P 1i = H i of the two subsystems, the total momenta P 2i = P i , and the numbers of particles P 3i = N i as the coordinates P mi . As is known [1], CP-electron collisions occur most frequently, and we therefore confine ourself to taking only the particle-electron collisions into account. Then the CP Hamiltonian is written in the form P 21 = H 2 = H (2) 0 + H (2) int + H (2) int , where H (2) 0 includes the continuous atomic chain (or plane) potential U a describing the action of the regular lattice on the CP under conditions of correlated collisions [1]. The total Hamiltonian of the system is H = H 1 + H 2 .
