Initial Electron Distribution Research Articles

Transient simulation of electron emission from quantum-wire structures.

We model a GaAs quasi-one-dimensional quantum wire in an applied longitudinal field and focus on mechanisms of electron emission leading to real-space transfer from the wire. The Monte Carlo simulation assumes an initial electron distribution in the wire and calculates the time required for electrons to undergo nonequivalent intervalley scattering to three-dimensional states. The model includes multiple subbands, polar optic and acoustic phonons, intervalley scattering, and band-structure nonparabolicity. Results have been obtained for different confinement conditions as well as different temperatures. We find that the required time is a very strong function of the longitudinal field and ranges from 4 ns down to 1 ps for fields in the range of 100 V/cm to 8 kV/cm. The corresponding distances in the wire vary from 130 \ensuremath{\mu}m down to the submicrometer range.

Field impoverishment modes in a diode with an AlxGa1−xAS/GaAs heterojunction: a simulation analysis

We have examined in a previous paper [1] the possibility of the formation of low-field domains as opposed to the traditional high-field domains found in Gunn diodes. Initial electron distributions that may lead to the growth of these domains are now further examined by numerical simulation with the purpose of finding conditions that are easier to meet in practice. We confirm that a significant number of electrons in the upper valleys is a necessary condition. However, it is found that the charge neutrality, uniform distribution in physical space, and direction of the wave number, that were imposed in the previous simulation, are not determinant. A AlxGa1−xAs(n)/GaAs(n) abrupt heterojunction is studied next in the frame of the Boltzmann transport equation. It is predicted that it may be used as an electron launcher into upper valleys for impoverishment field domains, provided the composition makes the ternary compound an indirect band gap semiconductor. When the injection guarantees 50% of the electrons in the satellite valleys at the heterojunction plane, our results show that, at a distance of 0.25 μm from the heterojunction interface, as much as 30% of the total number of electrons remains in the upper valleys. A diode that exhibits the formation of repetitive transit time field impoverishment modes is proposed.

Electron Fermi acceleration in collapsing magnetic traps: Computational and analytical models

We consider the heating and acceleration of electrons trapped on magnetic field lines between approaching magnetic mirrors. Such a collapsing magnetic trap and consequent electron energization can occur whenever a curved (or straight) flux tube drifts into a relatively straight (or curved) perpendicular shock. Our relativistic, three‐dimensional, collisionless test particle simulations show that an initial thermal electron distribution is bulk heated while a few individual electrons are accelerated to many times their original energy before they escape the trap. Upstream field‐aligned beams and downstream pancake distributions perpendicular to the field are predicted. In the appropriate limit the simulation results agree well with a nonrelativistic analytic model of the distribution of escaping electrons which is based on the first adiabatic invariant and energy conservation between collisions with the mirrors. Space science and astrophysical applications are discussed.

Constraints on a hot intergalactic medium from the X-ray and submillimeter backgrounds

If the X-ray background is due to emission from a hot intergalactic medium (IGM), the cosmic microwave background is expected to be distorted as a result of Compton scattering. Recently, an excess in the submillimeter band has been measured by the Nagoya-Berkeley group. It is shown that even if the initial electron distribution function is non-Maxwellian, the reported distortion at 0.3 mm is too small to be consistent with a hot, homogeneous IGM model for the X-ray background. 25 refs.

Nonlinear bound on unstable field energy in relativistic electron beams and plasmas

This paper makes use of Fowler’s method [J. Math Phys. 4, 559 (1963)] to determine the nonlinear thermodynamic bound on field energy in unstable plasmas or electron beams in which the electrons are relativistic. Treating the electrons as the only active plasma component, the nonlinear Vlasov–Maxwell equations and the associated global conservation constraints are used to calculate the lowest upper bound on the field energy [ΔℰF]max that can evolve for the general initial electron distribution function fb 0≡fb(x,p,0). The results are applied to three choices of the initial distribution function fb 0. Two of the distribution functions have an inverted population in momentum p⊥ perpendicular to the magnetic field B0êz, and the third distribution function reduces to a bi-Maxwellian in the nonrelativistic limit. The lowest upper bound on the efficiency of radiation generation, ηmax=[ΔℰF]max/[V−1∫d3x∫ d3p(γ−1)mc2fb 0], is calculated numerically over a wide range of system parameters for varying degrees of initial anisotropy.

Relativistic quantum dynamics and quantum noise in short-wavelength free electron lasers

A novel relativistic quantum theory of the free electron laser is formulated using the Dirac equation. It is shown that the theory has the correct classical limit. It is predicted that for two-stage free electron lasers, quantum noise can be comparable to the classical noise due to the thermal spread of the beam, or the random initial distribution of electrons in phase.

Initial electron distributions for free electron lasers generated by injector and accelerator simulations

Early free electron laser (FEL) development was guided by simple performance criteria based on the number of undulator periods, electron beam quality, and current. The beam quality (emittance and energy spread) was used to characterize the initial distribution of axial electron velocities along the undulator axis. While the emittance and energy spread determine the overall width of the distribution, its detailed shape is also important. As new accelerators are designed specifically for FEL applications, it becomes important to obtain distribution shape information from simulations that include the electron gun, accelerator, and beam transport in addition to the usual electron/optical interaction in the undulator.The distribution at the entrance to the undulator can be calculated from numerical simulations of the cathode emission, acceleration, and transport of an electron beam. We have modeled the beam generation, from cathode emission up to the energy of the accelerator injector, using an axisymmetric, cylindrical geometry particle simulation (DPC). This code solves the relativistic force equation with fields obtained from Maxwell's equations in the Darwin model. The DPC calculation is run repeatedly varying parameters such as accelerating stress, electrode configuration, and axial magnetic field profile until a good match is obtained for the accelerator. The beam exiting from the injector can be accelerated and transported using the transfer matrix technique with a simple model for accelerating gaps and magnets. Alternatively, acceleration and transport can be simulated with a particle code that solves for the axisymmetric evolution of a slice of an electron beam including possible emittance growth.The phase space obtained from the accelerator can be evaluated for performance using either the simple FEL integral equation method or the more complete FRED simulation code.

Band-structure effects on the femtosecond energy relaxation of photoexcited electrons in AlxGa1-xAs/GaAs quantum wells.

Results of Monte Carlo simulations of the femtosecond relaxation of electrons in an ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As/GaAs quantum well excited by a 2-eV laser are presented. Mixing of light- and heavy-hole subbands results in an initial photoexcited electron distribution much broader in energy than in bulk GaAs. Comparison with experiments [M. Rosker, F. Wise, and C. L. Tang, Appl. Phys. Lett. 49, 1714 (1986)] shows that the previously unexplained lack of a 160-s relaxation component in the quantum well, observed in bulk GaAs and attributed to polar-optical-phonon (POP) scattering, can be accounted for by this broad distribtuion and is not associated with an absence of POP scattering.

Relativistic quantum dynamics and quantum noise in short-wavelength free-electron lasers.

A novel relativistic quantum theory of the free-electron laser is formulated using the Dirac equation. It is shown that the theory has the correct classical limit. It is predicted that for two-stage free-electron lasers, quantum noise can be comparable to the classical noise due to the thermal spread of the beam or the random initial distribution of electrons in phase.

Absolute radiolytic yields of N 2(C 3Π u) in N 2/rare gas mixtures : Theoretical and experimental determinations

The absolute radiolytic luminescence yield for the emission from the C 3Π u state of N 2 has been determined for pulsed electron beam irradiation of He/N 2 and Ne/N 2 mixtures. The yields—corrected for all quenching processes—are compared to those calculated, by Monte-Carlo methods, from a model based on sub-excitation electron processes. The results confirm that this model and the Platzman initial sub-excitation electron distribution function are fully compatible with the observed results. The yields from experiment and theory are G(N 2, C 3Π u) = 0.079 ± 0.010 and 0.10 ± 0.01, respectively in He/N 2; 0.116 ± 0.037 and 0.094 ± 0.007 in Ne/N 2 mixtures. The G-values for absolute photon yields may be calculated from this data using appropriate kinetic quenching rate constants.

Transient nonequilibrium effects in the attachment of electrons to chlorofluoroethanes

A study of the transient behavior of a nonequilibrium electron swarm in argon together with a small amount of an electron attaching chlorofluoroethane is carried out. The initial electron distribution function is assumed to be a delta function in energy and the subsequent temporal evolution of the distribution function is determined with the two-term solution of the Boltzmann equation. Owing to the small electron mass relative to the other constituents, the Boltzmann equation reduces to a Fokker–Planck equation. Quite generally, the electron attachment process affects the nature of the electron thermalization and vice versa, that is, thermalization and reaction are coupled processes. The experimental determination of attachment rate coefficients involves the assumption that the attachment process has an insignificant effect on the electron distribution function and that the thermalization to a steady state occurs sufficiently quickly so that the attachment kinetics can be described by the steady state electron distribution. In the present paper, the coupling of the thermalization process and the attachment reaction is studied in detail. The time dependence of the electron energy and the attachment rate coefficient are considered for several chloroflouroethanes which exhibit either attachment cooling or attachment heating. A discussion of these steady state effects is presented in connection with similar concepts in hot atom chemistry.

Initial vibrational and rotational yields from subexcitation electrons in molecular hydrogen

As the energy of a single source electron injected into a molecular gas is degraded through collisions, initial products include secondary electrons, ions, and excited molecules. Electrons with kinetic energies less than the minimum required for excitation of the lowest electronic state are given the designation subexcitation electrons. These electrons are still capable of exciting vibrational and rotational states of molecular gases. In this calculation, the initial numbers of vibrational and rotational excitations (yields) produced as the subexcitation electrons undergo further energy degradation are determined for molecular hydrogen. The calculation requires a complete set of cross section data for numerical solution of the Boltzmann equation. The initial energy distribution of electrons is taken to be the subexcitation distribution which was determined previously. The initial yields are tabulated for gas temperatures from 50 K to 1500 K for a source electron with initial energy 10 keV. 26 references.

Transient microwave conductivity of electrons in helium

The microwave conductivity of electrons in partially ionized helium gas is studied with the Fokker-Planck equation and characterized by quasi-steady field. The calculated time-dependent conductivity agrees better with the experimental results of Warman and de Haas (J. Chem. Phys. 63 (1975) 2094) than that reported by Koura (J. Chem. Phys. 84 (1986) 6227). For P = 760 Torr, T = 295 K, microwave frequency 8.84 GHz, electric field strength 4.4 V cm −1, and an initial δ-function electron distribution at 0.864 eV, the time for the conductivity to decay to within 10% of the thermal value was calculated to be 54 ns whereas the experimental value is 50 ns.

Monte Carlo Simulation of Electron–Phonon Scattering in the XUV‐Induced Electron Emission of NaCl

AbstractA Monte Carlo simulation of the electron emission induced in NaCl by 60 to 250 eV photons is carried out. The number as well as the initial energy and spatial distribution of conduction electrons, obtained in a previous paper, are used as the input. Electron–phonon scattering events are treated semiclassically. Optical as well as acoustical phonons are taken into account, so that with the increase of electron energy the scattering probability decreases for optical and increases for acoustical phonons. The parameters of the model are adjusted to fit the experimental quantum yield and energy spectra of emitted electrons. It appears that for high‐energy (>2 to 3 eV) electrons the electron–phonon scattering is mainly due to acoustical phonons.

Time-dependent tunnelling and the injection of coherent Zener oscillations

The Zener oscillator, a device based upon time-dependent tunnelling through the potential barrier of an n-i heterojunction under modulated bias, is investigated as a possible source of terahertz electromagnetic radiation. The authors show that coherent Zener oscillations can be injected from an initial thermal distribution of electrons. The electrons trapped in the confines of the tilted band structure oscillate, and the resulting circuit voltage is capable of maintaining the coherence of the oscillations. These oscillations release energy to the external circuit by drifting through the intrinsic semiconductor until collected at a metal contact. Scattered electrons which get out of phase are also eliminated by the same process. The device depends upon the existence of the Wannier ladder. In relation with the Zener oscillator, they report the results on a study of polar scattering by longitudinal optical phonons of localised or accelerated electrons. The degree of localisation of the electrons, or position uncertainty, is found not to affect the lifetime since the thermal broadening of electron Bloch states is smaller than the optical phonon energy. The scattering of Zener oscillations might be reduced in the steady state when the Zener frequency is much larger than the optical phonon frequency, but the turn-on transient remains problematic. An alternative implementation might be realised using a superheterojunction made of the junction of two superlattices. The Zener oscillator is opening up a new class of devices based on coherent electronic processes.

Laser utilizing free electrons moving in transverse gradient fields

Quantum-mechanical equations are derived for the amplitudes of the probabilities of transitions in a free-electron laser when transverse electron oscillations are due to a static potential, which is homogeneous in the direction of motion of the beam, but has a transverse gradient. The resonance frequency of the system is found and the linear gain is derived for the odd harmonics of this frequency. Averaging of the gain is carried out over the initial distribution of electrons in a transverse cross section of the beam. Estimates are obtained of the maximum lasing frequency and of the gain at this frequency.

Theory of Runaway-Current Sustainment by Lower-Hybrid Waves

A mechanism is proposed whereby high-phase-velocity lower-hybrid waves can interact with lower-parallel-velocity electrons through nonlinearly excited plasma waves. Significant steady-state current can be sustained by the rf after the Ohmic field is turned off in a tokamak provided the initial electron distribution is in the runaway regime with density below a critical value.

Theory of Current Drive With Lower Hybrid Waves

A mechanism is proposed whereby high phase velocity lower hybrid waves can interact with lower parallel velocity electrons through non-linearly excited plasma waves. Significant steady-state current can be sustained by the r.f. after the ohmic field is turned off in a tokamak provided the initial electron distribution has a substantial runaway tail.

Rate constant/diffusion coefficient ratio for electron reactions in the radiolysis of supercritical hydrocarbons

The ratio of rate constant for electron reactions to the sum of the electron and hole diffusion coefficients is expressed in terms of the reactivity parameter on the basis of the solution of Smoluchowski equation obtained by Crumb and Baird and by Tachiya. Comparison of this expression with that obtained previously with the use of Nernst–Einstein relationship as to several types of distribution function suggests the Gaussian function is the best representation of the initial distribution of electrons in the radiolysis of supercritical hydrocarbons.

A critical analysis of ionising wave propagation mechanisms in breakdown

The formation and propagation of ionising waves in impulsive overvolted gas discharges for parallel plane electrode geometry is studied. The spatio-temporal evolution of the electronic and ionic densities together with the space-charge distorted field was thoroughly examined for different initial electron distributions. The study elucidates the important role of the electrons present ahead of both the anode and cathode ionising waves and shows particularly how the wavefront profile evolves during its propagation. In all cases, provided that the discharge gap is sufficiently large, the wavefront is transformed into an electron shock wave defined by a shock zone of extremely high electronic density and field gradients. This limits the domain of validity of the gas discharge models that neglect both the thermal diffusion of charge carriers and gas photoionisation of photodetachment.