Flux density distribution and energy balance equation for cascade particles in solids

Kashlev, Yu. A.

doi:10.1007/bf02551036

Cited by 4 publications

(8 citation statements)

References 8 publications

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“…If the oscillations in the x direction are considered, then there is one diffusion function D(p x ) corresponding to α = β = x. We calculated kinetic functions (10) and (11) for this simplified geometry in [4]. Substituting the functions found in [4] in Eq.…”

Section: Thermodynamic Parameters Of the Channeled-particle Subsystemmentioning

confidence: 99%

“…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 .…”

Section: Thermodynamic Parameters Of the Channeled-particle Subsystemmentioning

confidence: 99%

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Dependence of equilibrium properties of channeled particles on the transverse quasitemperature

Kashlev

2006

Theor Math Phys

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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 .

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Section: Thermodynamic Parameters Of the Channeled-particle Subsystemmentioning

confidence: 99%

Section: Thermodynamic Parameters Of the Channeled-particle Subsystemmentioning

confidence: 99%

Dependence of equilibrium properties of channeled particles on the transverse quasitemperature

Kashlev

2006

Theor Math Phys

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“…We can therefore exclude the evolution of particle number fluctuations from consideration and keep only (14). The same arguments and the same approximation are used in many problems of the theory of nonequilibrium processes (cascade processes [5], [12] and chemical reactions [15]). …”

Section: The Eigenvalue Of the Relaxation Matrix And The Quasitemperamentioning

confidence: 99%

“…In this case, the optical oscillation model makes a small contribution to the kinetic coefficients [8]; therefore, only the interaction of PAs with acoustic phonons is to be taken into account. In the domain of a small transfer of the momentum q, the transport coefficient in balance equation (5) can be written in the form [5] L (ph)…”

Section: Phonon Scattering Of Pas In a Dielectricmentioning

confidence: 99%

“…We note that when passing from the expression for PAs in a dielectric to the expression for PAs in a metal, we should replace N with the density of conductivity electrons. In a stationary quasiequilibrium state, the growth rate of the internal energy can be represented in an unfolded form if we use the expression [5] 1…”

Section: Entropy Thermodynamic Parameters Of the Pa Subsystem And Tmentioning

confidence: 99%

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Nonequilibrium statistical thermodynamics of positronium atoms moving in solids

Kashlev

2005

Theor Math Phys

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We calculate the quasitemperature of positronium atoms moving in a solid in the framework of nonequilibrium statistical thermodynamics. We represent the quasitemperature in the form of the renormalized temperature of the thermostat. The renormalization results from taking the positronium formation rate, the kinetic effects of interaction, and the dynamical effects of collisions into account. We obtain an expression for the thermalization time of positronium atoms.

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Kashlev

2001

Theoretical and Mathematical Physics

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Flux density distribution and energy balance equation for cascade particles in solids

Cited by 4 publications

References 8 publications

Dependence of equilibrium properties of channeled particles on the transverse quasitemperature

Dependence of equilibrium properties of channeled particles on the transverse quasitemperature

Nonequilibrium statistical thermodynamics of positronium atoms moving in solids

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