The Electron Relaxation to Stationary States in Collision Dominated Plasmas in Molecular Gases

The temporal collision dominated relaxation of electrons to new stationary states, starting from initial stationary states and due to jump-like changes of the electric field, was studied in the plasmas of the molecular gases N₂ and CO. Numerical solving of the time dependent Boltzmann equation for the electrons yields the temporal evolution of their energy distribution function and of resulting macroscopic quantities. The varying relaxation due to different values of the field strength in the final stationary state has been investigated considering the molecules of the plasma only as vibrationally non-excited and, in another case, including the additional impact of collisions with vibrationally excited molecules. The results obtained are discussed and, in particular, the relaxation times found for the transitions to the new stationary states are analysed on the basis of the energy transfer effectiveness by the collision processes. An approximative microphysical basis for the understanding of the main features of the relaxation in such complex molecular gas plasmas could be obtained.     

Die Relaxation der Geschwindigkeitsverteilungsfunktion der Elektronen im homogenen elektrischen Feld mit elastischen und anregenden Stößen. II. Das Verhalten des Elektronenensembles bei aperiodischer Feldänderung zwischen zwei stationären Zuständen

Recently the relaxation of the electron component was investigated under field-free conditions after sudden switch-off the electric field and otherwise after sudden changing the electric field to a new value of field strength. To continue these papers we consider now the relaxation process of the electron ensemble in the presence of a monotonous time variable electric field. The investigations are based on a computation of time change in the isotropic part of the velocity distribution function of the electrons and of the macroscopic parameters determined by the distribution function. The start-ing-point is the non-stationary Boltzmann equation with stationary initial states taking into consideration elastic and exciting collisions. Besides the representation of the received numerical results a physical interpretation is obtained for the duration of the whole relaxation process, for its initial stage as well as for the momentary stage of the relaxation by introduction of normalized characteristic time quantities. Further characterizing conditions are found related to the relaxation after quasi-jumplike change of the electric field and in the case of quasistationary field alteration respectively. With the introduced characteristic time quantities statements about the degree of realization of one of this limiting cases are possible for any given monotonous field. The investigations are per-formed in a low ionized non-thermal neon plasma.     

Die Relaxation der Geschwindigkeitsverteilungsfunktion der Elektronen im homogenen Feld mit elastischen und anregenden Stößen. III. Die Einstellung des periodischen Verhaltens der Elektronen-komponente im elektrischen Feld großen Modulationsgrades

To continue the kinetic investigations concerning the periodic behaviour of the electron component of a low ionized Ne-plasma of a glow discharge column in a periodic electric field [4] with high degree of modulation in this paper the adjustment of the isotropic distribution function of the electrons and by the latter determined macroscopic quantities are calculated and discussed. Starting with the non-stationary Boltzmann equation the adjustment process is considered using different direct components of the field but nearly constant degree of modulation. In the whole range from a nearly momentary adjustment to an adjustment in the high frequency limit of only small modulated distribution function we obtained results concerning the adjustment behaviour and its characteristic times by variation of the cycle time of the electric field starting from the different stationary states. At the other hand the influence of the different degrees of modulation on the adjustment process and its characteristic times was investigated and interpreted. For this interpretation the spectrum of adjustment times of stationary states corresponding to all momentary values of the periodic electric field strength in one cycle plays a dominant role. From the investigations follows that the adjustment times of periodic states can alter their values by some orders of magnitudes in dependence on the parameters of the electric field.     

Die Relaxation der Isotropverteilung und makroskopischer Kenngrößen der Elektronen im abklingenden feldfreien Neon-Plasma

Relaxation of Distribution Function and Macroscopic Parameters of Electrons in Temporal Decaying Neon Plasma without Field Heating We investigate the field-free collision-dominated relaxation in the afterglow of a weak ionized plasma in the first period of temporal decay which is determined especially by the quick alterations in the electron component because of the small inertia of electrons. Therefore the evolution in time of the electron distribution and hence the macroscopic coefficients determined thereby are calculated in dependence on the action of elastic and exciting collisions between electrons and neutral atoms. On the basis of these results we have found characteristic times controlling the relaxation process which depend especially on the action of the different kinds of collisions. Thus it is possible to get a good microscopic understanding of the field free collision dominated relaxation of the electron component.     

Relaxation of the Electron Distribution Function

This paper discusses an analytical technique for calculating the relaxation in time of the electron distribution function f in an environment in which no perturbing forces act on the electrons. For t = 0, f may have any arbitrary form presumed to be caused by perturbing forces which were not zero during t < 0. The technique then allows calculation of the relaxation of f in time for the following types of electron collisions: a) elastic collisions with cold neutrons, b) excitation collisions in which the threshold energy for an elastic excitation collision is small compared to the electron energy, c) ionizing collisions when the energy lost by the electron is small compared to its energy, and d) any combination of the above. In this paper the method is described and simple examples are presented to illustrate the physics of relaxation for the collisional categories listed above. It is pointed out that a number of important problems can be solved by this technique primarily in the area of nuclear EMP: the forrnative lag time problem and the calculation of thermalization time. In addition, the details of the afterglow of extinguished discharges in the monotomic gases can be determined.     

Die Berücksichtigung der Ionisation durch Elektronenstoß in der Elektronenkinetik des schwachionisierten anisothermen Plasmas III. Das instationäre Verhalten bei großer impulsförmiger Feldstörung

The Influence of Ionization by Electron Collisions on the Electron Kinetics of the Low Ionized Anisothermal Plasmas The time behaviour of the electron component was calculated during the additional application of a single pulse to the electric field in the plasma. The investigations were performed for the weakly ionized Ne-plasma as a typical example taking into account supplementarily the direct ionization due to electron collisions and an electron loss term with a constant life time besides elastic and exciting collisions. Using the instationary Boltzmann equation we determined the time behaviour of the essential macroscopic quantities. Besides the caluclation of the marked temporal development of such quantities as the electron concentration, the electron collision frequencies for excitation and ionization and the different energy transfer rates especially the relaxation of the electron component was analysed after switch on and switch off the additional rectangular pulse.     

Precession spin relaxation mechanism caused by frequent electron-electron collisions

It is shown that the D’yakonov-Perel’ spin relaxation mechanism in a two-dimensional electron gas is controlled not only by the electron-momentum relaxation that accounts for the electron mobility but also by the electron-electron collisions. The kinetic equation describing the mixing of electron spin in the k space was solved, and the spin relaxation time τ_s caused by frequent electron-electron collisions was determined. The time τ _s was calculated for a nondegenerate electron gas both with and without allowance for the exchange interaction.     

High Energy Unequal-nuclei Collisions and Relaxation Time in Fokker Plank Equation

In this paper,the time evolution of high energy heavy ion collisions is described by Fokker-Planck Equation.The rapidity distribution of the final state particles is analysed with this model for ¹⁶O and ³²S particles beams of 200AGeV.The relaxation time for various systems are determined.Results comparable to the usual empirical data are obtained.     

On the Kinetics of the Active Zone of the Stationary SF6 Beam Discharge Plasma

The paper deals with the impact of intensive electron attachment on the kinetics of the electrons in the active zone of the stationary band-like beam discharge plasma in SF₆ which is an alternative useful plasma medium for “dry etching”. The energy distribution of the electrons in this plasma was obtained by numerically solving the Boltzmann equation which includes apart from elastic collisions, different exciting collision processes, attachment in electron collisions, direct ionization, the ambipolar loss of electrons, Coulomb interaction between electrons and of electrons with ions and the power input to the electrons by the turbulent electric field. In particular, due to the needed fulfilment of the consistent electron particle balance, for an extended region of the turbulence energy density in this plasma a large impact on the electron kinetics of the intensive electron attachment, which is the prevailing electron loss process, was found enforcing independent of the turbulence energy density always a large power input to the electrons, smooth and only slowly decreasing energy distributions even in the energy region of direct ionization.     

Dynamics of electron beams in plasmas

The characteristic features of the relaxation of the energy and momentum distribution functions of the electrons in a plasma produced by a low-voltage beam discharge in helium are investigated. It is established that, contrary to widely held opinion, the energy of an intense electron beam may relax due to the wave excitation. The critical currents corresponding to a jumplike transition from one relaxation mechanism to another are measured. The density of metastable helium atoms is determined from the comparative analysis of theoretical and experimental results on the structure of the energy spectrum of the electrons of an intense beam. An intense electron beam is found to become more isotropic in the course of its interaction with Langmuir waves in a collisionless plasma. The cross section for quasi-elastic collisions between the electrons and Langmuir plasmons is estimated. The wave nature of the beam-plasma mechanism for the relaxation of the anisotropic electron energy distribution function is demonstrated, and the mechanism itself is shown to come into play when the discharge current exceeds a certain critical level. The experimental threshold criterion for the energy relaxation of an intense monoenergetic beam is obtained for the first time. It is shown that the relaxation occurs in two stages: the isotropization stage, in which the beam energy decreases insignificantly, is followed by the stage in which the beam relaxes to a state with a plateau-like energy distribution function. The threshold criterion for the relaxation of the anisotropic electron energy distribution function is universal in character regardless of the cause of anisotropy.     

CO_2与高振动激发K_2碰撞中的全分辨转动态分布

在K_2+CO_2中,受激发射泵浦得到K_2(E=3 500和4 000cm~(-1))高位振动态,研究了高振动激发K_2与CO_2碰撞产生的CO_2全分辨转动态分布。利用高分辨瞬时激光诱导荧光(LIF)测量了CO_2(0000)J=2~74的转动和平移能量轮廓,利用双高斯函数拟合,分别确定各转动态的产生和倒空线宽,从而得到碰撞产生的Doppler展宽、平移温度和平移能。对于K_2不同的激发能E,能量转移的机制是相似的,为振动-转动/平移弛豫机制。但碰撞出现部分的平移温度均超出池温,而碰撞倒空部分的平移温度均略低于池温,平移能随E的增加而增大,E增加14%,平移能增加40%。CO_2(0000)转动态分布的半对数描绘给出了双指数分布,对于K_2E=3 500cm~(-1),低J态分布T_a=(523±60)K,高J态分布T_b=(1 890±210)K。Ta接近池温,说明低J态为近弹性碰撞,属单量子弛豫过程,而高J态为非弹性碰撞,属多量子驰豫过程。对于K_2E=4 000cm~(-1)同样有双指数行为,低J分布T_a=(620±65)K,高J分布T_b=(2 240±250)K。高振动态K_2(E)与CO_2碰撞,E=4 000cm~(-1)比E=3 500cm~(-1)的Ta和Tb均约高19%,说明转动分布对于K_2不同能量是敏感的,但弹性和非弹性分支比是基本相同的,弱碰撞约占82%,强碰撞约占18%。     

Electron-electron spin-flip scattering and spin relaxation in III–V and II–VI semiconductors

Spin relaxation time of conduction electrons resulting from electron-electron spin-flip collisions has been investigated in III–V and II–VI semiconductors with InSb-like energy band structure. Analytical expression has been obtained for non-degenerate electron gas. The proposed mechanism can be dominent in the experimental conditions of electron spin resonance in InSb at higher temperatures.     

Relaxation of bound electrons in elastic collisions with infinitely heavy particles

The recombination relaxation of bound electrons in collisions with infinitely rigid, infinitely heavy spheres is considered. The relaxation mechanism is due to a change in the electron scattering from the spheres. The distribution functions of bound electrons and the recombination time due to that mechanism are obtained. The characteristics of the relaxation are the same as for the Thompson recombination mechanism (caused by energy transfer from the electron to a third particle) to within replacement of the mass of the third particle by the ion mass.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 48–53, April, 1996.     

Stoßbestimmte Relaxation des Elektronenensembles im Plasma bei zusätzlicher Aufheizung durch ein elektrisches Feld I. Die charakteristischen Zeiten für den Übergang in stationäre Zustände

Collision Dominated Relaxation of the Electron Ensemble in a Plasma with Additional Heating by an Electric Field. I. Characteristic Times for the Transition to Stationary States Starting from time dependent Boltzmann equation for electrons the time development of the isotropic part of the distribution function and of macroscopic quantities as mean energy, mobility, excitation frequency and energy transfer quotients during transition between two stationary states are determined. The computation is referred to weak ionized neon plasmas which are typical for low pressure and for medium pressure discharges. As a result of this investigations we get informations about the characteristic relaxation times which are different in order of magnitude, and about their dependence of the processes of energy transfer. The energy transfer quotients which determine the energy loss by different collision processes in consideration are found to be suitable quantities to characterize the relaxation times.     

Stochastic theory of nonlinear rate processes with multiple stationary states. II. Relaxation time from a metastable state

We have developed a methodology for obtaining a Fokker-Planck equation for nonlinear systems with multiple stationary states that yields the correct system size dependence, i.e., exponential growth with system size of the relaxation time from a metastable state. We show that this relaxation time depends strongly on the barrier heightU(x) between the metastable and stable states of the system. For a Fokker-Planck (FP) equation to yield the correct result for the relaxation time from a metastable state, it is therefore essential that the free energy functionU(x) of the FP equation not only correctly locate the extrema of U(x), but also have the correct magnitudeU at these extrema. This is accomplished by so choosing the coefficients of the FP equation that its stationary solution is identical to that of the master equation that defines the nonlinear system.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

The Ulam problem and the ionization of Rydberg atoms by microwave radiation

We study the Ulam problem for long times (several million collisions) by numerical methods. We show that in the diffusion regime, which is valid for moderate times, this problem is mathematically equivalent to the problem of the diffusive ionization of atomic Rydberg states by microwave radiation. It is concluded that the diffusion regime sets in only for a very small number of initial conditions (field phases). It is theorized that the analogy between the two problems can be extrapolated to times longer than the diffusion time. We show in the Ulam problem that after the diffusional buildup of energy has finished, the quasistationary regime does not continue indefinitely: after several million particle-wall collisions the energy rapidly drops to zero. On the basis of this extrapolation we examine the possibility that an electron which has reached the continuous spectrum will not fly off to infinity (ionization), but will return to bound Rydberg states of the atoms (if the field acts for a sufficiently long time). This can make the diffusive ionization probability much lower than the value given by the known estimates. Zh. éksp. Teor. Fiz. 114, 37–45 (July 1998)     

Metal particle polarization

The effect of electron collisions with lattice atoms in metals on metal particle polarization in an ac electric field was analyzed. It was shown that, in contrast to collisionless (free) electron gas, an increase in the negative electronic permittivity with decreasing electric field frequency in relaxation metal particles is limited by the conductivity relaxation time. It was shown that the plasma frequency appears in relaxation metal only if the dielectric relaxation time is less than the free path time in metal.     

Gasaufheizung und Energiebilanz einer stationären hochfrequenten Ringentladung in Edelgasen

Gasheating and Energy Balance of a Stationary High Frequency Ring Discharge in Rare Gases The energy balance of an inductively coupled high frequency (28,5 Mhz) discharge in a cylindrical vessel (11,2 cm diam.) in Ne, Ar, Kr, Xe at pressures between 0,1 and 10 Torr and at power inputs between 10 and 1000 W is investigated. The heat power transferred to the neutral gas in the stationary discharge is determined from the time behaviour of the neutral gas pressure in the afterglow period. The power measurements are completed by probe measurements of the electron density and energy distribution function. The measured electron energy distribution functions are maxwellian with a slight deficit electrons in the energy range of inelastic collisions. The electron temperatures show a rather low radial space dependence which can be explained on the basis of the local energy, balance by thermal conduction in the electron gas. The measured gas heating power is within the experimental error (factor 2) in agreement with calculations from the measured electron temperature and density under the assumption that the gas is heated by elastic electron-atom-collision only. A discussion of the energy balance for the total discharge indicates volume recombination losses of the ions which increase the density of the excited atoms and hence the energy losses by stepwise exitations.     

Electronic properties of cleaved CdTe(110) surfaces

Photoemission yield spectroscopy measurements were performed on a set of n- and p-doped CdTe single crystals. The surfaces were obtained by cleavage in ultrahigh vacuum and characterized by low energy electron diffraction and Auger electron spectroscopy. On clean and properly cleaved surfaces, no band bending was found, neither on n- nor on p-type samples, showing the absence of intrinsic surface states in the gap. The ionization energy is found at 5.80±0.05 eV. Oxygen adsorption removes defect-induced surface states on the valence band side of the gap and develops a band bending on n-type samples which indicates the presence of acceptor surface states in the gap down to 0.70 eV below the conduction band edge. The ionization energy remains constant.