Stochastic Electron Heating Research Articles

Simulations of ionospheric turbulence produced by HF heating near the upper hybrid layer

AbstractHeating of the ionosphere by high‐frequency (HF), ordinary (O) mode electromagnetic waves can excite magnetic field‐aligned density striations, associated with upper and lower hybrid turbulence and electron heating. We have used Vlasov simulations in one spatial and two velocity dimensions to study the induced turbulence in the presence of striations when the O‐mode pump is mode converted to large‐amplitude upper hybrid oscillations trapped in a striation. Parametric processes give rise to upper and lower hybrid turbulence, as well as to large amplitude, short wavelength electron Bernstein waves. The latter excite stochastic electron heating when their amplitudes exceed a threshold for stochasticity, leading to a rapid increase of the electron temperature by several thousands of kelvin. The results have relevance for high‐latitude heating experiments.

On stochastic heating of electrons by intense laser radiation in the presence of electrostatic potential well

A simple model developed by Paradkar et al. [Phys. Plasmas 19, 060703 (2012)] for the study of synergistic effects of electrostatic potential well and laser radiation is extended for the case where electric field of the well is accelerating electrons moving in the direction of the laser field propagation. It was found that in these cases, the rate of stochastic heating of energetic electrons remains virtually the same as in Paradkar et al. [Phys. Plasmas 19, 060703 (2012)], where electric field in electrostatic potential was slowing down electrons moving in the direction of the laser field propagation. However, the heating of electrons with relatively low energy can be sensitive to the orientation of the electrostatic potential well with respect to the direction of the laser radiation propagation.

Investigation of wave emission phenomena in dual frequency capacitive discharges using particle-in-cell simulation

Dual frequency capacitively coupled discharges are widely used during fabrication of modern-day integrated circuits, because of low cost and robust uniformity over broad areas. At low pressure, stochastic or collisionless electron heating is important in such discharges. The stochastic heating occurs adjacent to the sheath edge due to energy transfer from the oscillating high voltage electron sheath to electrons. The present research discusses evidence of wave emission from the sheath in such discharges, with a frequency near the electron plasma frequency. These waves are damped very promptly as they propagate away from the sheath towards the bulk plasma, by Landau damping or some related mechanism. In this work, the occurrence of strong wave phenomena during the expanding and collapsing phase of the low frequency sheath has been investigated. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. The characteristics of waves in the dual-frequency case are entirely different from the single-frequency case studied in earlier works. The existence of a field reversal phenomenon, occurring several times within a lower frequency period in the proximity of the sheath is also reported. Electron trapping near to the field reversal regions also occurs many times during a lower frequency period. The emission of waves is associated with these field reversal regions. It is observed that the field reversal and electron trapping effects appear under conditions typical of many recent experiments, and are consequently of much greater practical interest than similar effects in single frequency discharges, which occur only under extreme conditions that are not usually realized in experiments.

Stochastic electron acceleration in plasma waves driven by a high-power subpicosecond laser pulse

The mechanism of stochastic electron acceleration and heating by a picosecond laser pulse in underdense plasma is studied using particle-in-cell simulations and theoretical models. The formation of wide electron energy spectra in the simultaneously acting laser and plasma fields is analyzed. It is shown that electron scattering by turbulent plasma fluctuations excited through stimulated forward Raman scattering plays a governing role in the formation of high-energy tails in the electron distribution function.

Coupling of laser energy into hot-electrons in high-contrast relativistic laser-plasma interactions

We use particle-in-cell simulations to explain the mechanisms responsible for the coupling of laser energy into relativistic electrons for the case of sharp interface, solid density metal targets free of pre-plasma. For perfectly flat interfaces, the accelerated electron trajectories are dominated by the standing-wave (SW) field structure formed by interference between incident and reflected pulses. We find that quasi-static magnetic fields that develop near the interface play only a minor role in perturbing the relativistic electron trajectories but can contribute to enhanced absorption. Target surfaces that are structured exhibit enhanced absorption, and the acceleration mechanism deviates from the clean standing-wave acceleration mechanism leading to more stochastic electron heating and larger divergence angles.

Numerical simulations of energy transfer in counter-streaming plasmas

Collisionless shock formation is investigated with large scale fully electromagnetic two-dimensional Particle-in-Cell numerical simulations. Two plasmas are colliding in the center of mass reference frame at sub-relativistic velocities. Their interaction leads to collisionless stochastic electron heating, ion slowing down and formation of a shock front. We focus here on the initial stage of evolution where electron heating is due to the Weibel-like micro-instability driven by the high-speed ion flow. A two stage process is described in the detailed analysis of our simulation results. Filament generation, followed by turbulent mixing, constitute the dominant mechanism for energy repartition. The global properties are illustrated by examination of single filament evolution in terms of energy/particle density and fields.

Raman scattering of laser radiation in magnetoactive plasma

Raman scattering in a subcritical plasma is simulated numerically for the case where the laser radiation propagates transversely to an external magnetic field. It is shown that, in the linear stage of Raman instability, the magnetic field decreases the instability growth rate for forward scattering and increases it for backward scattering. As the value of the magnetic field increases, the stochastic heating of plasma electrons is enhanced in the region of backscattering.

Stochastic heating by ECR as a novel means of background reduction in the KATRIN spectrometers

The primary objective of the KATRIN experiment is to probe the absolute neutrino mass scale with a sensitivity of 200 meV (90% C.L.) by precision spectroscopy of tritium β-decay. To achieve this, a low background of the order of 10−2 cps in the region of the tritium β-decay endpoint is required. Measurements with an electrostatic retarding spectrometer have revealed that electrons, arising from nuclear decays in the volume of the spectrometer, are stored over long time periods and thereby act as a major source of background exceeding this limit. In this paper we present a novel active background reduction method based on stochastic heating of stored electrons by the well-known process of electron cyclotron resonance (ECR). A successful proof-of-principle of the ECR technique was demonstrated in test measurements at the KATRIN prespectrometer, yielding a large reduction of the background rate. In addition, we have carried out extensive Monte Carlo simulations to reveal the potential of the ECR technique to remove all trapped electrons in a few ms with negligible loss of measurement time in the main spectrometer. This would allow the KATRIN experiment attaining its full physics potential.

Mechanism of heating of pre-formed plasma electrons in relativistic laser-matter interaction

The role of the longitudinal ambipolar electric field, present inside a pre-formed plasma, in electron heating and beam generation is investigated by analyzing single electron motion in the presence of one electromagnetic plane wave and “V” shaped potential well (constant electric field) in a one dimensional slab approximation. It is shown that for the electron confined in an infinite potential well, its motion becomes stochastic when the ratio of normalized laser electric field a0, to normalized longitudinal electric field Ez, exceeds unity, i.e., a0/Ez≳1. For a more realistic potential well of finite depth, present inside the pre-formed plasma, the condition for stochastic heating of electrons gets modified to 1≲a0/Ez≲L, where L is the normalized length of the potential well. The energy of electron beam leaving such a potential well and entering the solid scales ∼a02/Ez, which can exceed the laser ponderomotive energy (∼a0) in the stochastic regime.

Development of a Radiofrequency Plasma Diagnostic System with a Langmuir Probe and Study of a Capacitively Coupled Argon Plasma

A single rf-compensated cylindrical Langmuir probe has been developed in order to characterise a plasma RF discharge. A circuit using radiofrequency filtering and the passive compensation method was employed to minimize the probe curve distortions. The effect of the rfcompensation on the probe measurements was discussed. The latter were performed at power and pressure of 50 W and 510-2–1.2 mbar, respectively. Compensated measurements of the electron energy distribution function (EEDF) and plasma parameters were conducted at powers ranging from 5 to 120 W and pressure of 0.3 mbar. They exhibit a transition between the stochastic electron heating mode operating at low powers and the secondary-electron emission heating mode (γ) operating at high powers. The electronic density increases from 1.5×109 to 3.2×1010 cm-3 while the effective electron temperature decreases from 3.7 to 2.3 eV. The EEDFs were found to be Druyvesteyn-like in the range of 5–80W and then evolve to the Maxwellian beyond 90W.

Stochastic heating of electrons by a large-amplitude extraordinary wave in plasma

Stochastic heating of plasma electrons by a large-amplitude electromagnetic wave propagating across a strong external magnetic field is studied theoretically and numerically. An analytic estimate of the threshold wave amplitude at which heating begins is obtained. The dependence of the average electron energy on the magnetic field and plasma density is investigated using particle-in-cell simulations.

Parallel electric field generation by Alfvén wave turbulence

{This work aims to investigate the spectral structure of the parallel electric field generated by strong anisotropic and balanced Alfvenic turbulence in relation with the problem of electron acceleration from the thermal population in solar flare plasma conditions.} {We consider anisotropic Alfvenic fluctuations in the presence of a strong background magnetic field. Exploiting this anisotropy, a set of reduced equations governing non-linear, two-fluid plasma dynamics is derived. The low-$\beta$ limit of this model is used to follow the turbulent cascade of the energy resulting from the non-linear interaction between kinetic Alfven waves, from the large magnetohydrodynamics (MHD) scales with $k_{\perp}\rho_{s}\ll 1$ down to the small "kinetic" scales with $k_{\perp}\rho_{s} \gg 1$, $\rho_{s}$ being the ion sound gyroradius.} {Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of $k_{\perp}$ and $k_{\parallel}$, showing that the electric field develops a component parallel to the magnetic field at large MHD scales.} {The spectrum we derive for the parallel electric field fluctuations can be effectively used to model stochastic resonant acceleration and heating of electrons by Alfven waves in solar flare plasma conditions}

A hybrid, one-dimensional model of capacitively coupled radio-frequency discharges

A one-dimensional, numerical model was developed to aid in the investigation of electron dynamics in the plasma boundary sheath of RF discharges. It incorporates several different modules. A fluid based plasma boundary sheath model and an accompanying equivalent circuit model are first used to calculate the time-dependent electric field due to displacement current and charged particle densities in the sheath. The electric fields calculated in this model are then combined with the Ohmic electric field or the field due to conduction current and joined to a simplified model of the plasma bulk. This combination is then used in a Monte Carlo simulation to calculate the electron energy distribution function. This model includes stochastic and Ohmic heating of electrons. The model reproduces experimentally measured electron energy probability functions over a broad range of pressures.

Numerical Modeling of Electron Beams Accelerated by the Radio Frequency Boundary Sheath

The stochastic heating of electrons by the radio frequency boundary sheath in capacitively coupled plasmas is not completely understood or at least agreed upon by researchers. To aid in understanding this phenomena, a conceptually simple simulation of electron heating is presented. A fluid model is used to calculate the electric fields in the discharge, and a Monte Carlo simulation is used to calculate electron distribution functions. The plots of the density of energetic electrons are presented in this paper. They show electron beams that have been accelerated by the sheath.

Stochastic heating and acceleration of electrons by high intensity lasers in inhomogeneous plasmas

Electron acceleration by sub-picosecond relativistic intense laser pulse propagating in inhomogeneous plasmas has been studied by one-dimensional (1D) particle-in-cell (PIC) simulations. It is found that the effective temperature of electrons scales as (I · τL)1/2, where I is the laser intensity and τL is the laser pulse duration. The high temperature electrons produced in the earlier stage are mainly due to the stochastic acceleration in the colliding laser fields, where the backward propagating fields are produced in part by the Raman backscattering in the underdense plasma region as well as by reflection from the overdense plasma region. The induced electrostatic fields in inhomogeneous plasma can accelerate electrons randomly, which contribute to the increase of the electron temperature at later stage.

Electron heating by the magnetic field-aligned electron–cyclotron waves in plasmas

It is shown that resonant nonlinear interactions between the magnetic-field aligned right-hand circularly polarized electromagnetic (CPEM) electron–cyclotron waves and electrons can produce electron temperature anisotropy due to the stochastic electron heating by waves in magnetized plasmas. The present result can thus account for the simultaneous presence of CPEM waves and an anisotropic electron temperature distribution in laboratory and space magnetoplasmas.

Laser beam filamentation and stochastic electron heating at upper hybrid layer

This paper presents an investigation of the filamentation (single hot spot) of an ultrahigh-power laser beam in homogeneous plasma. Upper hybrid wave (UHW) coupling in these filaments has been studied. We have discussed two extreme scenarios: (1) The laser beam has ultrahigh power so that relativistic and ponderomotive nonlinearities are operative; and (2) the laser beam power is moderate, therefore only ponderomotive nonlinearity dominates. At ultrahigh laser powers, relativistic and ponderomotive nonlinearities lead to filamentation of the laser beam. In these filamentary regions, the UHW gets coupled to the laser beam, and a large fraction of the pump (laser beam) energy gets transferred to UHW and this excited UHW can accelerate the electrons. In the second case, nonlinear coupling between the laser beam and the upper hybrid wave leads to the localization of the UHW. Electrons interacting with the localized fields of the UHW demonstrate chaotic motion. The simulation result confirms the presence of chaotic fields, and interaction of these fields with electrons leads to velocity space diffusion, which is accompanied by particle heating. Using the Fokker–Planck equation, the heating of electrons has been estimated. The effect of the change of background magnetic field strength on heating has also been discussed.

Stochastic heating and acceleration of electrons by high-intensity lasers in inhomogeneous plasmas

Electron acceleration by a sub-picosecond relativistic intense laser pulse propagating in inhomogeneous plasmas has been studied by particle-in-cell simulations. It is found that the effective temperature of electrons scales as (I·τL)1/2, where I is the laser intensity and τL is the laser pulse duration. The scaling coefficient is relevant to the plasma density scale length. The high-temperature electrons produced in the earlier stage are mainly due to the stochastic acceleration in the colliding laser fields, where the backward propagating fields are produced in part by the Raman backscattering in the underdense plasma region as well as by reflection from the overdense plasma region. The induced electrostatic fields in inhomogeneous plasma can accelerate electrons randomly, which contribute to the increase in the electron temperature at a later stage.

Stochastic heating of electrons in focused multimode laser fields

A direct relativistic electron-acceleration-simulation model with a given electromagnetic field, which is determined by the wave-packet parameters, is considered. The multimode time-spatial structure of a focused Nd-laser beam with stochastic phase disturbances of each spectral components is taken into account as a source of random forces. The electron energies of more than 10 MeV are derived even at moderate flux densities of 1016 W/cm2. The numerical code developed makes it possible to obtain a quantitative energy-distribution function with respect to both the field intensities and the temporal U-shaped laser pulse. An efficient heating of electrons can be triggered in the presence of a counter-propagating wave reflected from the critical plasma area with a varied reflection coefficient. The heating mechanism occurs with a delay with respect to the beginning of a pulse when the laser fields exceed certain threshold amplitudes. A qualitative comparison of the results of simulation with the experimental data is given to justify this mechanism.

Measurement of Large Parallel and Perpendicular Electric Fields on Electron Spatial Scales in the Terrestrial Bow Shock

Large parallel (<or=100 mV/m) and perpendicular (<or=600 mV/m) electric fields were measured in the Earth's bow shock by the vector electric field experiment on the Polar satellite. These are the first reported direct measurements of parallel electric fields in a collisionless shock. These fields exist on spatial scales comparable to or less than the electron skin depth (a few kilometers) and correspond to magnetic-field-aligned potentials of tens of volts and perpendicular potentials up to a kilovolt. The perpendicular fields are amongst the largest ever measured in space, with energy densities of epsilon0E2/nkBTe of the order of 10%. The measured parallel electric field implies that the electrons are demagnetized, which may result in stochastic (rather than coherent) electron heating.