Resonant Interaction Of Electrons Research Articles

Phase space dynamics of unmagnetized plasmas: Collisionless and collisional regimes

Eulerian electrostatic kinetic simulations of unmagnetized plasmas (kinetic electrons and motionless protons) with high-frequency equilibrium perturbations have been employed to investigate the phase space free energy transfer across spatial and velocity scales, associated with the resonant interaction of electrons with the self-induced electric field. Numerical runs cover a wide range of collisionless and weakly collisional plasma regimes. An analysis technique based on the Fourier–Hermite transform of the particle distribution function allows to point out how kinetic processes trigger the free energy cascade, which is instead inhibited at finer scales when collisions are turned on. Numerical results are presented and discussed for the cases of linear wave Landau damping, nonlinear electron trapping, and bump-on-tail and two-stream instabilities. A more realistic situation of turbulent Langmuir fluctuations is also discussed in detail. Fourier–Hermite transform shows a free energy spread, highly conditioned by collisions, which involves velocity scales more quickly than the spatial scales, even when nonlinear effects are dominant. This results in anisotropic spectra whose slopes are compatible with theoretical expectations. Finally, an exact conservation law has been derived, which describes the time evolution of the free energy of the system, taking into account the collisional dissipation.

Ducted Chorus Waves Cause Sub‐Relativistic and Relativistic Electron Microbursts

AbstractDuring magnetospheric storms, radiation belt electrons are produced and then removed by collisions with the lower atmosphere on varying timescales. An efficient loss process is microbursts, strong, transient precipitation of electrons over a wide energy range, from tens of keV to sub‐relativistic and relativistic energies (100s keV and above). However, the detailed generation mechanism of microbursts, especially over sub‐relativistic and relativistic energies, remains unknown. Here, we show that these energetic electron microbursts may be caused by ducted whistler‐mode lower‐band chorus waves. Using observations of equatorial chorus waves nearby low‐altitude precipitation as well as data‐driven simulations, we demonstrate that the observed microbursts are the result of resonant interaction of electrons with ducted chorus waves rather than nonducted ones. Revealing the physical mechanism behind the microbursts advances our understanding of radiation belt dynamics and its impact on the lower atmosphere and space weather.

Nonlinear particle trapping by coherent waves in thermal and nonthermal plasmas

We perform a test particle simulation to study the resonant interaction of electrons with a stationary electrostatic wave. In the simulation, we use a new method to generate nonthermal particle distributions efficiently. This method utilizes inverse cumulative distribution function, and compared with the existing methods in the literature, found to have a negligible deviation from the analytical form of the distribution, particularly in the tail side, where nonthermal particles are situated. The simulation revealed that the trapped particle density varies highly with the width (≈10%–60%) and amplitude (≈13%–19%) of the wave potential. The particle trapping is found to be more efficient in nonthermal plasmas than thermal plasma. It implies that particle transport through waves could be more effective in nonthermal plasmas than thermal plasmas. In addition, the simulation sheds light on the particle trapping time and its relation to the characteristics of the wave potential. Overall, the present study will be helpful to understand the particle trapping by the coherent waves, which are frequently seen in space and astrophysical plasmas.

Regimes of Resonant Interactions of Electrons with Auroral Kilometric Radiation

We analyze the resonant interaction of energetic electrons with auroral kilometric radiation (AKR). Possible regimes of such an interaction are studied on the basis of a numerical solution of the particle motion equations in a given field of a quasi-monochromatic AKR wave packet. It is shown that for realistic wave amplitudes 0.2–0.4 V/m, the interaction can be highly nonlinear. As a result of nonlinear interaction, both a substantial (approximately twofold) acceleration of particles and a decrease in their energy (by about 20–50%) are possible. With realistic plasma and wave packet parameters, electrons with initial energies of the order of 10 keV are accelerated, and for electrons with initial energies of several tens of keV, the interaction leads to a decrease in energy.

Simulations of Electron Flux Oscillations as Observed by MagEIS in Response to Broadband ULF Waves

AbstractCoherent electron flux oscillations of hundreds of keV are often observed by the Van Allen Probes in the magnetosphere during quiet times in association with ultralow frequency (ULF) waves. They are observed in the form of periodic flux fluctuations, with a drift frequency that is energy dependent, but are not associated with drift echoes following storm‐ or substorm‐related energetic particle injections. Instead, they are associated with the resonant interaction of electrons with ULF waves and are an indication of ongoing electron radial diffusion. To investigate details of such flux oscillations, particle‐tracing simulations are conducted under the effect of realistic, broadband ULF electric and consistent magnetic fluctuations. Virtual detectors are simulated along spacecraft orbits and the results are compared to measurements. Through a parametric study, it is found that the width of electron energy channels is a critical parameter affecting the observed amplitude of flux oscillations, with narrower energy channel widths enabling the observation of higher‐amplitude flux oscillations; this potentially explains why such features were not observed regularly before the Van Allen Probes era, as previous spacecraft generally had lower energy resolution, which only enabled the observation of large‐amplitude drift echoes following a storm or substorm. Results are confirmed using the Magnetic Electron Ion Spectrometer (MagEIS) ultrahigh energy resolution data. Energy width effects are quantified through a parametric simulation study that matches flux oscillation observations during a period that is characterized by extremely quiet conditions, where the Van Allen Probes observed flux oscillations over multiple days.

SUPPRESSION OF ELECTRON THERMAL CONDUCTION IN THE HIGH β INTRACLUSTER MEDIUM OF GALAXY CLUSTERS

ABSTRACT Understanding the thermodynamic state of the hot intracluster medium (ICM) in a galaxy cluster requires knowledge of the plasma transport processes, especially thermal conduction. The basic physics of thermal conduction in plasmas with ICM-like conditions has yet to be elucidated, however. We use particle-in-cell simulations and analytic models to explore the dynamics of an ICM-like plasma (with small gyroradius, large mean free path, and strongly sub-dominant magnetic pressure) driven by the diffusive heat flux associated with thermal conduction. Linear theory reveals that whistler waves are driven unstable by electron heat flux, even when the heat flux is weak. The resonant interaction of electrons with these waves then plays a critical role in scattering electrons and suppressing the heat flux. In a 1D model where only whistler modes that are parallel to the magnetic field are captured, the only resonant electrons are moving in the opposite direction to the heat flux, and the electron heat flux suppression is small. In 2D or more, oblique whistler modes also resonate with electrons moving in the direction of the heat flux. The overlap of resonances leads to effective symmetrization of the electron distribution function and a strong suppression of heat flux. The results suggest that thermal conduction in the ICM might be strongly suppressed, possibly to negligible levels.

Kinetic Models for Whistler Wave Scattering of Electrons in the Solar Corona and Wind

Kinetic models are necessary to describe the physical processes associated with non-Maxwellian velocity distribution functions (VDFs) of electrons or ions in the solar corona and wind. It is shown that pitch-angle scattering of electrons in the solar wind needs to be considered in kinetic solar wind models. Coulomb collisions are not efficient enough to provide this scattering, but resonant interaction with whistler waves is. A solar wind model for undisturbed fast wind is presented, and the influence of scattering on flare electron propagation is investigated. Furthermore, it is found that resonant interaction of electrons with whistler waves is capable of producing suprathermal tails of electron distributions even under quiet conditions without flare activity.

Resonance interaction of electrons with a slow transverse wave in a weakly inhomogeneous plasma

Excitation of a circularly polarized slow wave by external sources and its subsequent propagation in a weakly inhomogeneous plasma with a positive density gradient are described in terms of the adiabatic approach. It is shown that the wave dispersion is mainly determined by the ratio between the contributions of trapped and nonresonant untrapped electrons to the total wave current. The relationship between the wave amplitude and its phase velocity and the limiting phase velocity above which the wave is strongly damped are found using the energy balance equation and the dispersion relation.

On the theory of the resonant interaction of electrons with a high-frequency electric field in one-dimensional two-barrier nanostructures with symmetric barriers of finite height and width

The theory of the interaction of electrons with a high-frequency electric field in one-dimensional two-barrier nanostructures with symmetric barriers of finite height and widths was developed. An exact solution to the Schrodinger equation was found for electrons in this nanostructure in the absence of high-frequency electric field. An analytical expression for the direct current I0 induced in this structure by an incident electron flux with energy e differing slightly from the resonant level energy er(|e − er| er, the current Ic is negative in the entire frequency range, which suggests the possibility of ac electric field amplification and generation in the two-barrier resonant-tunneling structure with the barriers of finite height and width. Within the applicability of the theory (ℏω << er), the frequency at which amplification and generation of the ac electric field are possible reaches ω ≳ 1013s−1; the power transferred by electrons to the field is ∼1 W/cm2.

Low-threshold terahertz Si:As laser

The optical threshold of terahertz intracenter arsenic-doped silicon lasers has been reduced by two orders of magnitude by applying a compressive force to the laser crystal. The Si:As lasers were optically excited with radiation from a CO2 laser operating at a wavelength of 10.59μm. The lowest threshold intensity of 8kW∕cm2 was realized at about 3×108Pa stress applied along the [001] crystal axis. The uniaxial stress breaks the resonant interaction of electrons bound to donors with intervalley f phonons. This changes the upper laser state from 2p± to 2p0, lowers the laser threshold, and increases the output power.

Theory of the ICR heating of a plasma column: Methodological note

A set of wave equations is derived that describes electromagnetic waves at frequencies on the order of the ion gyrofrequency in a plasma column with an arbitrary electron temperature. This set takes into account, in particular, the resonant interaction of electrons with waves in the transit-time magnetic pumping regime. The effect of the amplification of the electromagnetic fields of current-carrying antennas by the plasma is analyzed. The evolution of the fields with an increase of plasma density from a zero value (vacuum) is considered. The main parameters are determined for minority ion cyclotron resonance heating in the planned EPSILON system.

Rapid acceleration of electrons in the magnetosphere by fast‐mode MHD waves

During major magnetic storms, enhanced fluxes of relativistic electrons in the inner magnetosphere have been observed to correlate with ULF waves. The enhancements can take place over a period of several hours. In order to account for such a rapid generation of relativistic electrons, we examine the mechanism of transit‐time acceleration of electrons by low‐frequency fast‐mode MHD waves, here the assumed form of ULF waves. Transit‐time damping refers to the resonant interaction of electrons with the compressive magnetic field component of the fast‐mode waves via the zero cyclotron harmonic. In terms of quasi‐linear theory, a kinetic equation for the electron distribution function is formulated incorporating a momentum diffusion coefficient representing transit‐time resonant interaction between electrons and a continuous broadband spectrum of oblique fast‐mode waves. Pitch angle scattering is assumed to be sufficiently rapid to maintain an isotropic electron distribution function. It is further assumed that there is a substorm‐produced population of electrons with energies of the order of 100 keV. Calculations of the acceleration timescales in the model show that fast‐mode waves in the Pc4 to Pc5 frequency range, with typically observed wave amplitudes (ΔB = 10–20 nT), can accelerate the seed electrons to energies of order MeV in a period of a few hours. It is therefore concluded that the mechanism examined in this paper, namely, transit‐time acceleration of electrons by fast‐mode MHD waves, may account for the rapid enhancements in relativistic electron fluxes in the inner magnetosphere that are associated with major storms.

Alternating space charge and ambiguity of quantum states in double-barrier structures

Summation of a series of perturbation theory was used to obtain a solution to the time-dependent self-consistent Schrodinger and Poisson equations describing the resonance interaction of electrons that tunnel through asymmetric double-barrier structures with a high-frequency electric field. In the case where electrons are uniformly distributed in energy within the width of the quasi-level, the solution is obtained analytically; if the beam is monoenergetic, solution of the equation is reduced to finding the roots of a fifth-degree algebraic polynomial. It is shown that, in a number of cases, the influence of alternating space charge gives rise to an effect that is quite new for the systems under consideration: several different wave functions may correspond to the same amplitude of the high-frequency voltage applied to the structure; consequently, the values obtained for the high-frequency conductivity and the coefficients of transmission and reflection can differ by several times. As a result, instability of the current flow and hysteresis of the current-voltage characteristics can be observed in these structures. Furthermore, the dependence of the coefficients of transmission and reflection of the electrons and high-frequency conductivity on the voltage amplitude are combinations of the N-and S-shaped characteristics for uniform distribution of electrons and are looplike in the case of a monoenergetic beam.

Application restrictions for two-level models of the resonance interaction of electrons with an alternating electric field in two-barrier structures

We analyze the applicability of different variants of the two-level approximation in the problem of electron transitions in a two-barrier structure with current pumping in a resonant electric field of finite amplitude. We show that the solution obtained by a direct iteration of the perturbation method of the first order in the field amplitude can be essentially continued outside the convergency domain of the iteration procedure. On the other hand, the two-level approximation becomes invalid at field amplitudes much smaller than commonly assumed ones because of the influence of side satellites, the nonresonant components of the wave function.

Large interference-induced increase in the intensity of quantum transitions in triple-barrier structures

A solution of the nonstationary Schrodinger equation describing the resonance interaction of electrons with a weak rf field is found for asymmetric triple-barrier resonance-tunneling structures with thin, high barriers, and an expression is obtained for the active weak-signal conductivity of such structures. It is found that in a number of cases the probability of quantum resonance transitions from an upper to a lower level can increase sharply when the lower levels are shifted relative to one another.

A self-consistent analytical model for non-collisional heating

Non-collisional heating is an important phenomenon in low-pressure inductively coupled plasmas. In this paper, a self-consistent analytical model for non-collisional heating is developed which shows that non-collisional heating is a warm-electron effect that relies on a resonant interaction of electrons with the electromagnetic wave. Electrons with velocities comparable to the effective wave phase speed resonantly interact with the wave and gain net energy from it. Collisions randomize this directed energy thereby leading to electron heating. Non-collisional heating becomes more efficient if a larger proportion of electrons participate in the resonant interaction process. This can occur due to an increase in the electron temperature or decrease in the effective wave phase speed. Collisions destroy the essential phase correlation between the electrons and the wave, making the non-collisional heating process less efficient.

Resonant interaction of electrons with an rf electric field in asymmetric double-barrier structures

Analytical expressions for the electron wave functions, the low-signal, high-frequency conductance, and the widths of the energy levels (minibands) in a asymmetric double-barrier structure with thin barriers are obtained under conditions of coherent electron tunneling strictly along the centers of the energy levels and with the electron energies deviating from exact resonance. It is shown that an electron transmittance equal to 1 and a substantial increase in the integrated (taking into account the energy distribution of the electrons incident on the structure) rf conductance of the structure can be obtained by choosing the appropriate arrangement of the minibands of the structure relative to the conduction band bottom of the semiconductor materials to the left and right of the structure.

Dependence of the resonant conductivity of symmetric double-barrier structures on the amplitude of rf field

An analytical expression for the rf amplitude dependence of the conductivity in a symmetric double-barrier resonance-tunneling structure with high, thin barriers under conditions of collisionless electron transport is found on the basis of the solution of a nonstationary Schrodinger equation describing the resonance interaction of electrons with the rf field. It is shown that under the action of a rf field with frequency ω and amplitude approximately corresponding to triple the width of the resonance level, up to half of the electrons passing through this level can be transferred, emitting or absorbing a quantum of energy ℏω, into a neighboring level.

Resonant interaction of electrons with a high frequency electric field in two-barrier structures

The frequency dependences of the small-signal dynamic conductivity of symmetric and nonsymmetric two-barrier heterostructures are calculated in a one-electron approximation. Special attention is focused on the case of electron tunnelling through the upper minibands. In the approximation of high-barrier power (width), an analytic expression is obtained for the dynamic conductivity of a two-barrier resonance-tunnel structure that agrees with a rigorous calculation. It is shown that (a) the dynamic conductivity increases as the fourth power of the barrier width, (b) quantum transitions with an even change in the level number are forbidden, and (c) the dynamic conductivity is inversely proportional to the cube of the frequency if the separation between the levels varies with frequency in a way such that the resonance condition is always satisfied. The maximum possible intensity of the radiating transitions of twobarrier heterostructures are calculated as a function of the quantum numbers of the working levels under conditions such that the supply current density and the characteristic time for breakup of the coherence by phonon scattering are constant. It is shown that the intensity increases significantly if, for example, the fourth level of the structure, rather than the ground state, is used as the working level.

Anomalous suppression of the probability of resonance interaction of electrons with an rf field in asymmetric double-barrier structures on account of plasma oscillations

An analytical self-consistent solution of the nonstationary Schrodinger and Poisson equations describing the resonance interaction of electrons with a radio-frequency (rf) field has been found for asymmetric resonance-tunneling structures with high, thin barriers. It is shown that plasma oscillations limit the probability of transitions between neighboring levels and suppress anomalously strongly transitions in which the level number changes by more than 1 (by tens and hundreds of times compared with transitions between neighboring levels).