Effect Of Electron-electron Collisions Research Articles

Effect of electron-electron collisions on entrance potential drop in high-mobility 2DEG channels

Usually, the evidence of viscous hydrodynamic transport of frequently colliding conduction electrons is considered to be the “Gurzhi effect,” which requires the scattering of electrons on the channel walls with momentum loss. However, we demonstrate that expansion of Sharvin’s potential drop directly related to frequent electron-electron collisions can be detected even in channels with ideally smooth walls in a two-dimensional degenerate electron gas (2DEG). In theory, this effect could be experimental evidence of the predicted earlier difference between the relaxation times of the antisymmetric and symmetric momentum distributions attributed to the Pauli principle and topological limitations in 2DEG.

Investigation of the skin effect in plasmas with the use of a two-parameter kinetic equation

An analytic solution taking into account the effect of electron-electron collisions has been obtained for the problem on the skin effect in a nondegenerate electron plasma. The impedance was analyzed in relation to a parameter b, which describes the ratio of the frequency of electron-electron collisions to the total frequency of electron scattering. For b→0 the results obtained become the classical ones for weakly ionized plasma.

On quantum effects in the theory of conductivity of fully ionized quasiclassical plasma

A study is made of the static conductivity of a fully ionized plasma in a parameter range where the effect of electron-electron collisions can be ignored. It is shown that a convergent expression for the static conductivity of a fully ionized, weakly nonideal plasma in the range of large wave vectors can be obtained from a quantum statistical description of correlation functions, without using an artificial truncation procedure.

Influence of damping on proton energy loss in plasmas of all degeneracies

The purpose of the present paper is to describe the effects of electron-electron collisions on the stopping power of plasmas of any degeneracy. Plasma targets are considered fully ionized so electronic stopping is only due to the free electrons. We focus our analysis on plasmas which electronic density is around solid values n(e) approximately = 10(23) cm(-3) and which temperature is around T approximately = 10 eV ; these plasmas are in the limit of weakly coupled plasmas. This type of plasma has not been studied extensively though it is very important for inertial confinement fusion. The electronic stopping is obtained from an exact quantum mechanical evaluation, which takes into account the degeneracy of the target plasma, and later it is compared with common classical and degenerate approximations. Differences are around 30% in some cases which can produce bigger mistakes in further energy deposition and projectile range studies. Then we consider electron-electron collisions in the exact quantum mechanical electronic stopping calculation. Now the maximum stopping occurs at velocities smaller than for the calculations without considering collisions for all kinds of plasmas analyzed. The energy loss enhances for velocities smaller than the velocity at maximum while decreases for higher velocities. Latter effects are magnified with increasing collision frequency. Differences with the same results for the case of not taking into account collisions are around 20% in the analyzed cases.

Proton stopping in plasmas considering e−–e− collisions

The purpose of the present paper is to describe the effects of electron-electron collisions on proton electronic stopping in plasmas of any degeneracy. Plasma targets are considered fully ionized so electronic stopping is only due to the free electrons. The stopping due to free electrons is obtained from an exact quantum mechanical evaluation in the random phase approximation, which takes into account the degeneracy of the target plasma. The result is compared with common classical and degenerate approximations. Differences are around 30% in some cases which can produce bigger mistakes in further energy deposition and projectile range studies. We focus our analysis on plasmas in the limit of weakly coupled plasmas then electron-electron collisions have to be considered. Differences with the same results without taking into account collisions are more than 50%.

Effect of electron-electron interaction on spin relaxation of charge carriers in semiconductors

An analysis of spin dynamics is presented for semiconductor systems without inversion symmetry that exhibit spin splitting. It is shown that electron-electron interaction reduces the rate of the Dyakonov-Perel (precession) mechanism of spin relaxation both via spin mixing in the momentum space and via the Hartree-Fock exchange interaction in spin-polarized electron gas. The change in the Hartree-Fock contribution with increasing nonequilibrium spin polarization is analyzed. Theoretical predictions are compared with experimental results on spin dynamics in GaAs/AlGaAs-based quantum-well structures. The effect of electron-electron collisions is examined not only for two-dimensional electron gas in a quantum well, but also for electron gas in a bulk semiconductor and a quantum wire.

Eigenmodes and growth rates of relativistic current filamentation instability in a collisional plasma

I theoretically found eigenmodes and growth rates of relativistic current filamentation instability in collisional regimes, deriving a generalized dispersion relation from self-consistent beam-Maxwell equations. For symmetrically counterstreaming, fully relativistic electron currents, the collisional coupling between electrons and ions creates the unstable modes of growing oscillation and wave, which stand out for long-wavelength perturbations. In the stronger collisional regime, the growing oscillatory mode tends to be dominant for all wavelengths. In the collisionless limit, those modes vanish, while maintaining another purely growing mode that exactly coincides with a standard relativistic Weibel mode. It is also shown that the effects of electron-electron collisions and thermal spread lower the growth rate of the relativistic Weibel instability. The present mechanisms of filamentation dynamics are essential for transport of homogeneous electron beam produced by the interaction of high power laser pulses with plasma.

Effects of electron-electron collisions on the characteristics of DC and microwave discharges in argon at low pressures

The authors present a systematic investigation of the effects caused by electron-electron collisions on the electron kinetics in Ar under the action of DC and microwave fields. The analysis is based on solutions to the homogeneous electron Boltzmann equation using the effective field approximation, i.e. assuming that the electron energy distribution function is time independent. The calculated electron transport parameters and ionization coefficient are used together with a generalized charged particle balance equation to derive the characteristics for the maintenance field and the mean absorbed power per electron for steady-state DC and microwave discharges in Ar. Results are provided for the cases of (i) single-step ionization; (ii) multi-step ionization, via the metastable and the resonance levels of Ar.

Effect of electron-electron collisions on properties of hot electrons

We calculate analytically the electron distribution, electron temperature and electric current of a non degenerate electron gas in a large electric field including finite electron-electron collisions. We demonstrate that these quantities vary very slightly with the electron-electron collision time: this establishes for the first time the validity of the results obtained from the famous but unjustified displaced Maxwellian distribution function.

Effects of electron-electron collisions with small energy transfers on quantum localisation

The effect of electron-electron collisions with small energy transfers on the quantum electron localisation has been studied. It is shown that in one and two dimensions such collisions determine the temperature dependence of the conductivity. In three dimensions the contribution of processes with small energy transfers is less than that of the usual electron-electron collisions, in which the energy transfer is of the order of the temperature T. The criterion for the quasiparticle description of electrons in metals in different dimensions is discussed. It is shown that for d>or=2 this description is valid, while for d=1 it is not correct. The effect of noise in the external circuit on quantum corrections to the conductivity is studied.

Effects of electron-electron interactions on the electron distribution function of a plasma in the presence of an external electric field

The electron distribution function, the electron temperature and some transport parameters (electrical conductivity and energy flow coefficient) are obtained starting from the nonlinear Boltzmann equation for a plasma under the action of an external electric field. The Fokker-Planck approximation is used for electron-electron and electron-ion interactions. The effects of electron-electron collisions are studied for different values of collision frequencies and electric field.

Electron Landau damping and electron collisions

The effect of electron-electron collisions on the Landau damping of a single wave in a magnetized or unmagnetized plasma is calculated using a model Fokker–Planck operator. The resulting form of Landau damping could play a role in the saturation of some parametric and trapped-particle instabilities.

Effect of electron-electron collisions on stimulated multiphoton bremsstrahlung of a highly ionized plasma in an intense electromagnetic field

The usual formulas for stimulated bremsstrahlung and inverse bremsstrahlung are modified to take into account the effect of electron-electron collisions in highly ionized plasmas. We consider only limiting cases in which the collision time is much larger or much smaller than the period of oscillation of the intense electromagnetic field.

Warm electrons in polar semiconductors

A method based on an interactive solution of the Boltzmann equation is presented for the calculation of the warm electron coefficient beta in polar semiconductors. The effect of electron-electron collisions is incorporated by using a Maxwellian energy distribution function for the carriers. With the aid of the method the warm-electron coefficients in InAs, InSb, InP and Hg0.8Cd0.2Te are computed taking account of all the relevant scattering mechanisms. The effects of band nonparabolicity, p-function admixture and electron screening are included in the calculations. The sensitivity of beta on the choice of the scattering parameters is studied and the available experimental data are analysed in the light of the calculated values. Agreement between theory and experiment is found to be satisfactory in the case of InAs only.

On test charge potentials in collisional plasmas

The effect of electron-electron collisions on the potential of a slowly moving test charge in a plasma is considered. A new dipole-like term is found.

Anomalous Plasma Resistivity at Low Electric Fields

Experiments have shown the appearance of “nonclassical” resistivity, higher than that predicted by the known transport theory based on electron-ion collisions, in magnetically confined plasmas where the electron gyrofrequency is larger than the Langmuir frequency and the electric field is well below the runaway threshold. A theoretical interpretation of the anomalous resistivity onset is proposed observing that (at long but finite mean free paths) nonresonant modes, associated with the effects of electron-electron collisions, are excited when the electron flow velocity along the magnetic field is roughly larger than the ion sound-wave velocity. The magnitude of anomalous resistivity is then discussed in relation with the nonlinear effects of resulting fluctuations and of related modes with wavelengths shorter than the mean free path. A comparison between several experiments on plasma confined in different stellarator and tokamak configurations is given. The differences in physical regimes that lead to various mechanisms for the appearance of “nonclassical” resistivity and the relationship with anomalous diffusion are pointed out.

Effect of electron-electron collisions on the electrical conductivity of plasmas with trapped particles

Plasmas with electrons trapped in magnetic mirrors have a lower electrical conductivity than plasmas in homogeneous fields. It is shown that like-particle collisions reduce this difference by about twenty per cent. Electron-electron encounters are simulated by the BGK-model, whose validity for this case is discussed.

Electrical Properties ofN-Type Germanium

Measurements of conductivity and Hall effect from 11\ifmmode^\circ\else\textdegree\fi{}K to 300\ifmmode^\circ\else\textdegree\fi{}K on a set of $n$-type germanium samples covering the range from intrinsic to degenerate are reported. The purity and uniformity of the samples and extensiveness of the data permit a more thorough-going comparison with theory than has been possible in previous work.The theory of mobility is reviewed briefly. The treatment of impurity scattering by Brooks and Herring is presented, and their formula for the impurity mobility is used throughout. An analytical formula for obtaining the mobility from lattice and impurity mobilities is included. The effect of electron-electron collisions on the mobility is considered in a qualitative manner.The principal conclusions concerning the mobility are as follows: (1) Over the range 20.4\ifmmode^\circ\else\textdegree\fi{}K to 300\ifmmode^\circ\else\textdegree\fi{}K the lattice mobility varies as ${T}^{\ensuremath{-}1.64}$ rather than the theoretically predicted ${T}^{\ensuremath{-}1.5}$. (2) The impurity mobility increases with temperature less rapidly than the theoretical formula predicts, the exponent of $T$ in the numerator being apparently between 1.0 and 1.5. (3) The Erginsoy formula for neutral impurity scattering appears to fit the experimental data reasonably well for a value of effective mass about one-third the free electron mass. (4) Dislocation scattering is negligible, leading to the conclusion that the density of edge-type dislocations is less than ${10}^{6}$/${\mathrm{cm}}^{2}$.In fitting the concentration data, the parameters involved are activation energy, acceptor concentration, and effective mass. An effective mass in the neighborhood of one-quarter the free electron mass gives the best fit for all samples. The values of acceptor concentration obtained in this way for this effective mass agree well with those calculated from the low-temperature mobility values. The activation energy obtained for the purer samples is 0.0125 ev, in agreement with the value calculated from the hydrogen-like model for one-quarter the free electron mass.The variation of activation energy with concentration does not agree with that observed by Pearson and Bardeen for $p$-type silicon. The effects which have been proposed to explain the variation are: residual potential energy of attraction between free electrons and ionized donors, screening of trapping centers by the free electrons, polarization of neutral centers by free electrons. It is concluded that a combination of the three effects will probably be required to explain the results.The ratio of Hall to drift mobility is shown to agree with the theoretically predicted value within about 10 percent in the range 78\ifmmode^\circ\else\textdegree\fi{}K to 300\ifmmode^\circ\else\textdegree\fi{}K.