Kinetic Balance Equations Research Articles

A Model for Bias Potential Effects on the Effective Langmuir Adsorption–Desorption Processes

We discuss the foundations of a model based on an extension of the Langmuir approximation for the adsorption–desorption phenomena, in which the phenomenological coefficients depend on the bias potential, in addition to their dependence on the adsorption energy. The theoretical analysis focuses on the effect of these effective coefficients on the electrical response of an electrolytic cell to an external electric field, as predicted by the Poisson–Nernst–Planck model. Kinetic balance equations govern the current densities on the electrodes when the adsorption phenomenon occurs in the presence of an electric bias. The influence of the phenomenological parameters entering the model, as well as of the symmetry of the cell on the cyclic voltammetry, is investigated.

Time Dependent Studies on the Energy Gain of D-T Fuel Using Determination of Total Energy Deposited of Deuteron Beam in Hot Spot

In fast (FI) mechanism, a pellet containing the thermonuclear fuel is first compressed by a nanosecond laser pulse, and then irradiated by an intense ignition beam, initiated by a high power picosecond laser pulse, is one of the promising approaches to the realization of the inertial confinement fusion (ICF). If the beam is composed of deuterons, an additional energy is delivered to the target, in which coming from fusion reactions of the beam-target type, directly initiated by particles from the beam .In this article, the D+T fuel is selected and at first step we compute new average reactivity using three parameter cross section formula in terms of temperature at second step we use the obtained results of step one and calculate the total deposited energy of deuteron beam inside the target fuel at available physical conditions, then in third step we write the nonlinear point kinetic balance equation of D+T mixture and solve numerically these nonlinear differential coupled equations versus time .In forth step ,we estimate the power density and energy gain under physical optimum conditions and finally we conclude that maximum energy deposited in the target from D+T and D+D reaction are equal to 19269.39061 keV and 39198.58043 keV, respectively

The influence of interaction between Rydberg atoms and slow electrons on distribution function in the ultracold plasma

Expressions for the cross sections and rate constants of transitions during collisions of Rydberg atoms with electrons whose energy E is lower than the transition energy Eif are proposed. The populations of Rydberg states were calculated using the numerical solution of the set of kinetic balance equations as functions of time in an ultracold plasma based on the obtained transition rate constants. The calculation results are in good agreement with the experiment.

Distribution function and diffusion of electrons in the Rydberg energy space in a nonideal ultracold plasma

The distribution functions and diffusion coefficient of electrons in the Rydberg energy space in an ultracold plasma are obtained as functions of temperature by numerically solving a system of kinetic balance equations. As the initial conditions, the results obtained in previous papers by the molecular dynamics method are used. From calculation of Rydberg electron fluxes, the temperature dependence of the recombination coefficient is obtained, in good agreement with the recombination coefficient calculated previously by the molecular dynamics method.

Nonlinear Nonequilibrium Quasiparticle Relaxation in Josephson Junctions

I solve numerically a full set of nonlinear kinetic balance equations for stacked Josephson junctions, which allows analysis of strongly nonequilibrium phenomena. It is shown that nonlinearity becomes significant already at very small disequilibrium. The following new, nonlinear effects are obtained: (i) At even-gap voltages V = 2nDelta/e (n = 2, 3, ...) nonequilibrium bosonic bands overlap. This leads to enhanced emission of Omega = 2Delta bosons and to the appearance of dips in tunnel conductance. (ii) A new type of radiative solution is found at strong disequilibrium. It is characterized by the fast stimulated relaxation of quasiparticles. A stack in this state behaves as a light emitting diode and directly converts electric power to boson emission, without utilization of the ac-Josephson effect. The phenomenon can be used for realization of a new type of superconducting cascade laser in the THz frequency range.

Mapping of the relativistic kinetic balance equations onto the Klein–Gordon and second-order Dirac equations

In previous work we have shown that the quantum potential can be derived from the classical kinetic equations both for particles with and without spin. Here, we extend these mappings to the relativistic case. The essence of the analysis consists of Fourier transforming the momentum coordinate of the distribution function. This procedure introduces a natural parameter η with units of angular momentum. In the non-relativistic case the ansatz of either separability, or separability and additivity, imposed on the probability distribution function produces mappings onto the Schrödinger equation and the Pauli equation, respectively. The former corresponds to an irrotational flow, the latter to a fluid with non-zero vorticity. In this work we show that the relativistic mappings lead to the Klein–Gordon equation in the irrotational case and to the second-order Dirac equation in the rotational case. These mappings are irreversible; an approximate inverse is the Wigner function. Taken together, these results provide a statistical interpretation of quantum mechanics.

Mapping of the classical kinetic balance equations onto the Pauli equation

Here we find a mapping onto the Pauli equation of the first two balance equations derived from the classical Boltzmann equation. The essence of this mapping, which we previously used to obtain the particular case of the Sturm–Liouville operator known as Schrödinger's equation, consists of applying a Fourier transform to the momentum coordinate of the distribution function. This procedure introduces a natural parameter η with units of angular momentum. The main difference between the two cases is the conditions imposed on the probability distribution function, a difference most clearly understood at the level of the hydrodynamic equations generated in the first steps of the mapping. The case leading to the Sturm–Liouville operator corresponds to an irrotational flow, while here the ansatz leading to the Pauli equation corresponds to a fluid with non-zero vorticity. In the context of fluid dynamics, the magnitude of the angular momentum associated with the vorticity is η/2. To perform the mapping we follow the standard technique common in hydrodynamic problems, namely writing the Lagrangian for the Euler equations with the corresponding constraints expressed in terms of the Clebsch variables.

Mapping of the classical kinetic balance equations onto the Schrödinger equation

Here we find a mapping onto the Sturm–Liouville operator of the first two balance equations derived from Boltzmann's equation. This mapping, which is irreversible and valid only for a subclass of solutions, is achieved by applying a Fourier transform to the momentum coordinate. In light of this irreversibility, it is necessary to develop a set of consistent prescriptions to find the probability of any physical quantity in the p-conjugate space such that it will coincide with the average over the momentum of the true probabilities obtained from the original Boltzmann equation. The one drawback of this prescription is that it is impossible to predict exactly the precise values of the position x and the momentum p at the same time. This uncertainty is limited by the relationship that all conjugate variables in a Fourier transform should obey, namely Δ x Δ p = η/2, where η is a free parameter of the theory. The prescriptions we have found appear to coincide with the postulates of quantum mechanics, when η is set equal to ℏ. This procedure seems to provide a statistical representation of quantum mechanics.

On the mechanism for dose rate dependence of stationary luminescence of F and F+ centres excited by electron beam in α-Al 2O 3

We have examined the kinetic model proposed by Moroño and Hodgson for the dose rate dependence of stationary luminescence of colour centres under electron beam excitation. A set of kinetic balance equations based on their model is formulated and analytic solution is derived in terms of stationary concentrations of electrons and holes under irradiation. The solution shows that the ratio of F + to F luminescence intensities is proportional to the stationary concentration of holes. For high electron beam currents, the effect of saturation of the F centre emission is predicted. Possible mechanisms related to dose rate dependent quenching of the F centre are presented.

Thermo-chemical Modeling of Internal-reforming SOFCS at the IDAHO National Engineering Laboratory

The Idaho National Engineering Laboratory is performing research and development of a cross-flow, internal-reforming SOFC. Part of the effort entails development of a thermo-chemical computer model to execute scoping, design, and performance studies of the INTEL SOFC design. A one-dimensional model is being completed and extensions to two and three-dimensions are planned. Mass, heat, electrochemical, and chemical kinetic balance equations are presented along with preliminary simulation results.