Electromagnetic radiation from positive-energy bound electrons in the Coulomb field of a nucleus at rest in a strong uniform magnetic field

A classical analysis is presented of the electromagnetic radiation emitted by positive-energy electrons performing bound motion in the Coulomb field of a nucleus at rest in a strong uniform magnetic field. Bounded trajectories exist and span a wide range of velocity directions near the nucleus (compared to free trajectories with similar energies) when the electron Larmor radius is smaller than the distance at which the electron-nucleus Coulomb interaction energy is equal to the mechanical energy of an electron. The required conditions occur in magnetic white dwarf photospheres and have been achieved in experiments on production of antihydrogen. Under these conditions, the radiant power per unit volume emitted by positive-energy bound electrons is much higher than the analogous characteristic of bremsstrahlung (in particular, in thermal equilibrium) at frequencies that are below the electron cyclotron frequency but higher than the inverse transit time through the interaction region in a close collision in the absence of a magnetic field. The quantum energy discreteness of positive-energy bound states restricts the radiation from an ensemble of bound electrons (e.g., in thermal equilibrium) to nonoverlapping spectral lines, while continuum radiative transfer is dominated by linearly polarized bremsstrahlung.     

Nonresonant photocreation of electron-positron pair on a nucleus in the field of a pulsed light wave

The nonresonant Coulomb photocreation of electron-positron pair on a nucleus in the field of a pulsed light wave is theoretically investigated. The approximation is examined when pulsewidth is considerably greater than the characteristic time of wave oscillations. The interaction of an electron and a positron with a Coulomb potential of a nucleus is considered in the first order of perturbation theory (the Born approximation). An analytic expression for the nonresonant differential cross section was obtained for the range of moderately strong fields in the case relativistic and nonrelativistic energies. It is shown, that the nonresonant cross section of Coulomb photocreation of nonrelativistic pair in the field of a pulsed light wave is two times larger than the cross section of Coulomb photocreation in the absence of an external field.     

The short distance behaviour of the anomalous magnetic moment of the electron

The effective anomalous magnetic moment of the electron vanishes at short distances because the electrodynamic form factor F₂(q²) vanishes for |q²| → ∞. The effective potential due to the interaction between the anomalous magnetic moment and the Coulomb field of a nucleus only diverges logarithmically at short distances, and not, as might naively be expected, quadratically. There are no other bound states of an electron in a Coulomb field than the well-known atomic states. In particular, there is no room for high mass resonances emulating the ψ as suggested by Barut and Kraus.     

Smearing of the two-dimensional Kohn anomaly in a nonquantizing magnetic field: implications for interaction effects

Thermodynamic and transport characteristics of a clean two-dimensional interacting electron gas are shown to be sensitive to the weak perpendicular magnetic field even at temperatures much higher than the cyclotron energy, when the quantum oscillations are completely washed out. We demonstrate this sensitivity for two interaction-related characteristics: electron lifetime and the tunnel density of states. The origin of the sensitivity is traced to the field-induced smearing of the Kohn anomaly; this smearing is the result of curving of the semiclassical electron trajectories in magnetic field.     

Scattering of low-energy electrons by positive ions in a magnetic field. II. Resonances,transition probabilities,and transport frequencies

We analyze quantum-mechanically electron-ion collisions in a magnetic field at a low temperature, for which the electron's thermal energy is less than the energy gap between two Landau levels and the electron's Larmor radius is less than the characteristic impact parameter of close collisions without the magnetic field. To calculate transition probabilities, we use the analytical procedure proposed in the first part of our paper. We calculate the energy and lifetime of the resonant (autoionization) states of an electron embedded in the Coulomb electric field of an ion and in a uniform magnetic field. The obtained values coincide in order of magnitude with the known exact numerical values. We find that the electron backward scattering probability irregularly (chaotically) depends on the particle energy and the magnetic field. We propose analytical approximations for the collision transport frequencies, one of which describes the electron braking along the magnetic field and another, equalizing of the temperatures corresponding to the electron motion along and across the magnetic field. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 8, pp. 682–699, August 2008.     

Energy of a bound polaron in a magnetic field in asymmetric polar semiconductor heterostructures

In this paper, a new modified Hamiltonian of a polaron bound to a donor impurity in asymmetric step quantum wells (QWs) in the presence of an arbitrary magnetic field is given, in which the coupling of an electron with confined bulk-like LO phonons, half-space LO phonons and interface phonon modes is included. Especially, the interaction of the impurity with all possible optical-phonon modes is also considered. The ionization energy of a bound polaron in a magnetic field for asymmetric step QWs are studied by using a modified Lee-Low-Pines (LLP) variational method. The effects of the finite electronic confinement potential and the subband nonparabolicity are also considered. The relative importance of the donor impurity located at the well and the step is analyzed. Our results show the interaction between the impurity and the phonon field in screening the Coulomb interaction has a significant influence on the binding energy of bound polaron. The influence of subband non-parabolicity is appreciable on the bound polaron effects for the narrow well. The binding energy of bound polaron given in this paper are excellent agreement with the experimental measurement.     

Electron energy distribution function and dense-gas ionization in the presence of a strong field

The mechanism for dense-gas ionization is analyzed in the case when the deceleration of electrons by gas can be neglected in the equation of motion of a single electron. An expression for the electron energy distribution function in the presence of a strong field is derived. The characteristic width of the distribution corresponds to the energy acquired by the electron at a length determined by the inverse Townsend coefficient. The electron energy distributions are calculated for various distances form the cathode. It is demonstrated that the distribution becomes independent of the coordinate at a distance from the cathode that is significantly greater than the inverse Townsend coefficient. In this case, the distribution coincides with the distribution obtained with analytical calculations. The absence of the coordinate dependence is realized even in the presence of an extremely strong field when, in accordance with the commonly accepted point of view, the majority of electrons are runaway electrons.     

Inelastic electron collisions with Rydberg atoms

The standard classical method of computer simulation is used for evaluation of the inelastic cross section in electron collisions with a highly excited (Rydberg) atom. In the course of collision, the incident and bound electrons move along classical trajectories in the Coulomb field of the nucleus, and the scattering parameters are averaged over many initial conditions. The reduced ionization cross section of a Rydberg atom by electron impact approximately corresponds to that of atoms in the ground states with valence s-electrons and coincides with the results of the previous Monte Carlo calculations. The cross section of an atom transition between Rydberg atom states as a result of electron impact is used for finding the stepwise ionization rate constant of atoms in collisions with electrons or the rate constant of three-body electron-ion recombination in a dense ionized gas because these processes are determined by kinetics of highly excited atom states. Surprisingly, the low-temperature limit of electron temperatures is realized when the electron thermal energy is lower than the atom ionization potential by about three orders of magnitude, as follows from the kinetics of excited atom states. The article is published in the original.     

Stability of negatively charged ions moving in a magnetic field.

In a magnetic field the center of mass (c.m.) motion of an atom or molecule couples to the electronic motion. It is demonstrated that this coupling dramatically influences the properties of negative ions. Neglecting c.m. effects the external field gives rise to a series of infinitely many bound states of the ion. Center of mass effects terminate this series and turn bound states into short-lived resonance states. Whether bound states exist at all, their number and properties as well as the lifetimes of the resonance states depend on the neutral system to which an electron is attached, and on the magnetic field.     

Enhanced electron trapping by a static longitudinal magnetic field in laser wakefield acceleration

An externally applied longitudinal magnetic field was found to enhance the particle trapping in the laser wakefield acceleration. When a static magnetic field of a few tens of tesla is applied in parallel with the propagation direction of a driving laser pulse, it is shown from two-dimensional particle-in-cell simulations that total charge of the trapped beam and its maximum energy increase. The analysis of electron trajectories strongly suggests that the enhanced trapping originates from the suppression of the transverse motion by the magnetic field. The enhanced trapping by the magnetic field was observed consistently for various values of the plasma density, the amplitude of the laser pulse and pulse spot size.     

Edge excitons in a 2D topological insulator in a magnetic field

Exciton edge states and the microwave edge exciton absorption of a 2D topological insulator subject to the in-plane magnetic field are studied. The magnetic field forms a narrow gap in electron edge states that allows the existence of edge exciton. The exciton binding energy is found to be much smaller than the energy of a 1D Coulomb state. Phototransitions exist on the exciton states with even numbers, while odd exciton states are dark.     

Resonant electron-positron pair photoproduction on a nucleus in a pulsed light field

The resonant photoproduction of an electron-positron pair on a nucleus in the field of a pulsed light wave is studied theoretically. The approximation where the electromagnetic pulse duration is much longer than the characteristic time of wave oscillations is considered. The interaction of the electron and positron with the Coulomb potential of the nucleus is considered in the Born approximation. An analytical expression for the resonant differential cross section is derived for the range of moderately strong external fields. This cross section contains a resonant peak whose height and width are determined by the external pulsed wave characteristics. The resonant cross section for pair photoproduction on a nucleus in a pulsed laser field can exceed the corresponding cross section for pair photoproduction on a nucleus in the absence of an external field by an order of magnitude.     

Ionization of atoms in strong low-frequency electromagnetic field

The ionization of atoms in a low-frequency linearly polarized electromagnetic field (the photon energy is much lower than the ionization potential of an atom) is considered under new conditions, in which the Coulomb interaction of an electron with the atomic core in the final state of the continuum cannot be considered in perturbation theory in the interaction of the electron with the electromagnetic field. The field is assumed to be much weaker that the atomic field. In these conditions, the classical motion of the electron in the final state of the continuum becomes chaotic (so-called dynamic chaos). Using the well-known Chirikov method of averaging over chaotic variations of the phase of motion, the problem can be reduced to non-linear diffusion on the energy scale. We calculate the classical electron energy in the final state, which is averaged over fast chaotic oscillations and takes into account both the Coulomb field and the electromagnetic field. This energy is used to calculate the probability of ionization from the ground state of the atom to a lower-lying state in the continuum using the Landau-Dykhne approximation (to exponential accuracy). This ionization probability noticeably depends on the field frequency. Upon a decrease in frequency, a transition to the well-known tunnel ionization limit with a probability independent of the field frequency is considered.     

非均匀磁场约束条件下的电子束空气等离子体特性

为了揭示大气环境电子束等离子体的性质,基于蒙特卡罗程序包Geant4建立了一个包含电离、激发以及轫致辐射等物理过程的计算模型,用于模拟非均匀磁场约束条件下高能强流稳态电子束的输运特性、以及大气环境等离子体的性质。结果表明:非均匀磁场可以有效控制电子束在空气中的输运轨迹,显著降低电子束的发散;随着电子束在空气中行程的增加,电子束能谱开始展宽并向低能区移动;输运装置出口能量损失比电子束射程末端高2个量级,且随着电子束输运距离的增加,等离子体密度降低;等离子体密度的高低与电子束能量直接相关。     

Effect of the anode-current magnetic field on the motion of electrons in a triode with a virtual cathode

The effect of the anode-current magnetic field on the electron motion in a triode with a virtual cathode is considered. It is shown that the anode-current magnetic field influences the oscillation period and trajectories of electrons. The condition of self-isolation of the electron beam is investigated as a function of the diode parameter. It is shown that the displacement of the beam electrons under the action of the anode-current magnetic field leads to a decrease in the electron phase modulation and an increase in the spread in the electron oscillation amplitude; as a result, the generation efficiency of microwave radiation decreases.     

大回旋半径电子枪渐变线圈磁场的设计及优化

对大回旋半径电子枪的渐变线圈磁场进行了设计,采用3个线圈实现所需要的渐变磁场分布,增加了线圈磁场系统的调节能力,理论和计算机仿真的磁场分布结果符合得很好。将实现的渐变磁场分布同给定的静电场分布相结合,通过求解带电粒子的运动方程得到了粒子轨迹,在此基础上建立大回旋半径电子枪的3维粒子仿真模型,在给定静电场分布条件下分析了3个线圈安匝数对电子束参数的影响,完成了工作电压为40 kV、工作电流为1 A的大回旋半径电子枪的参数优化,得到了横纵速度比为1.4～2.5,纵向速度离散小于8%(横纵速度比为1.9时)的大回旋半径电子束。     

A Similar Change in the Kinetic-Energy Components of Longitudinal Continuous Motion of Magnetized Electrons within the Landau Levels and Determination of the Characteristics of a Degenerate System

Account is taken of a similar change in the kinetic-energy components of a longitudinal electron motion along the magnetic field within each Landau energy level. The maximum electron energy is found as well as the kinetic energy of a transverse electron motion in the magnetic field. The electron concentrations are determined depending on the magnetic-field strength, whose intrinsic magnetic moments are directed along and opposite the field. The magnetic-field strengths for which a certain number of Landau quantum levels is realized in an electron degenerate system of a specified concentration are also found.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 18–22, March, 2005.     

磁场对量子阱中弱耦合束缚极化子性质的影响

采用线性组合算符及幺正变换方法研究了磁场对量子阱中弱耦合束缚极化子的性质的影响。导出了量子阱中束缚极化子的基态能量与振动频率、库仑束缚势、磁场和阱宽之间的变化关系。同时也讨论了振动频率与库仑束缚势、磁场之间的变化关系。通过数值计算结果表明:量子阱中束缚极化子的基态能量因振动频率、库仑束缚势、磁场和阱宽的不同而不同,它随振动频率和磁场的增加而增大,随库仑束缚势和阱宽的增大而减小。量子阱中束缚磁极化子的基态能量与振动频率无关,随库仑束缚势和阱宽的增大而减小,随磁场的增大而增大。     

An exciton in a quantum well in the presence of crossed electric and magnetic fields

An analytical approach to the problem of the Wannier–Mott exciton in a semiconductor quantum well (QW) in the presence of external magnetic and electric fields is developed. The magnetic field is taken to lie in the heteroplanes while the electric field is directed perpendicular to the heteroplanes. Explicit dependencies of the energy levels and wave-functions of the exciton on the magnitudes of the fields for a wide range of the width of the QW are obtained. For the narrow QW, the results are valid for arbitrary electron and hole effective masses. In the case of intermediate and wide QWs, the adiabatic approximation implying the extreme difference of the electron and hole masses is used. In the intermediate QW, the states of the relative motion are the standard Coulomb states affected by the external fields while the states of the centre of mass are the size-quantized states in the QW. We focus particularly on the delocalized states caused by the external electric field and the motion of the excitons centre of mass in the magnetic field. These states are localized far away from the Coulomb centre. A strong influence of the boundaries of the wide QW on the delocalized exciton states is found to occur. Estimates of the expected values are made using typical parameters associated with GaAs QW.