Electron Heating Model Research Articles

Minute-cadence observations of the LAMOST fields with the TMTS – III. Statistical study of the flare stars from the first two years

ABSTRACTTsinghua University-Ma Huateng Telescopes for Survey (TMTS) aims to detect fast-evolving transients in the Universe, which has led to the discovery of thousands of short-period variables and eclipsing binaries since 2020. In this paper, we present the observed properties of 125 flare stars identified by TMTS within the first two years, with an attempt to constrain their eruption physics. As expected, most of these flares were recorded in late-type red stars with GBP − GRP >2.0 mag; however, the flares associated with bluer stars tend to be on average more energetic and have broader profiles. The peak flux (Fpeak) of the flare is found to depend strongly on the equivalent duration (ED) of the energy release, i.e. Fpeak∝ED0.72 ± 0.04, which is consistent with results derived from the Kepler and Evryscope samples. This relation is likely to be related to the magnetic loop emission, while, for the more popular non-thermal electron heating model, a specific time evolution may be required to generate this relation. We notice that flares produced by hotter stars have a flatter Fpeak - ED relation compared to that from cooler stars. This is related to the statistical discrepancy in light-curve shape of flare events with different colours. In spectra from LAMOST, we find that flare stars have apparently stronger H α emission than inactive stars, especially at the low-temperature end, suggesting that chromospheric activity plays an important role in producing flares. On the other hand, the subclass with frequent flares is found to show H α emission of similar strength in its spectra to that recorded with only a single flare but similar effective temperature, implying that chromospheric activity may not be the only trigger for eruptions.

Kinetic Simulation of Nonrelativistic Perpendicular Shocks of Young Supernova Remnants. IV. Electron Heating

Abstract High-Mach-number collisionless shocks are found in planetary systems and supernova remnants (SNRs). Electrons are heated at these shocks to temperatures well above the Rankine–Hugoniot prediction. However, the processes responsible for causing the electron heating are still not well understood. We use a set of large-scale particle-in-cell simulations of nonrelativistic shocks in the high-Mach-number regime to clarify the electron heating processes. The physical behavior of these shocks is defined by ion reflection at the shock ramp. Further interactions between the reflected ions and the upstream plasma excites electrostatic Buneman and two-stream ion–ion Weibel instabilities. Electrons are heated via shock surfing acceleration, the shock potential, magnetic reconnection, stochastic Fermi scattering, and shock compression. The main contributor is the shock potential. The magnetic field lines become tangled due to the Weibel instability, which allows for parallel electron heating by the shock potential. The constrained model of electron heating predicts an ion-to-electron temperature ratio within observed values at SNR shocks and in Saturn’s bow shock.

Global model for pulsed inductively coupled plasma sources: Effect of edge-to-center density ratio and electron heating

The volume-averaged global plasma model has been widely used to analyze the characteristics of plasma, although the spatial variation of plasma parameters cannot be obtained from it. It has also been used to obtain temporal plasma parameters for pulsed plasma sources. In this work, we analyzed the effect of an edge-to-center density ratio (h factor) and an electron heating model on the plasma parameters in pulsed plasma simulations using the global model for Ar discharges. In most previous pulse simulations using the global model, the h factor has been applied to pulse conditions in the same way it has been applied to radio frequency, and the power absorbed by the electrons was assumed to be equal to the applied power. However, in this work, we considered a time-varying h factor and determined the absorbed power using an analytical electron heating model, solving the spatially averaged transport equations in a self-consistent manner. We found that a decreased h factor increases the plasma density and consequently changes the time dependence of the electron temperature. In addition, the overshoot of the electron temperature is limited at the beginning of the pulse power-on in the self-consistent electron heating model. Our results are of great relevance with respect to the analysis of plasma parameters.

Effect of low frequency power on the electron energy distribution function in argon inductively coupled plasmas

In plasma processing and application, the electron energy distribution function (EEDF) is of fundamental interest because the ion and radical densities related to physical and chemical reactions on the substrate are predominantly governed by the EEDF or electron temperature. In this paper, the effect of low frequency power on the EEDF is investigated when 2 MHz power is added to the plasma originally driven at 13.56 MHz. In a 13.56 MHz operation, the EEDF shows a Maxwellian-like distribution, and as the RF power increases, the electron density increases and the electron temperature decreases. However, when a small amount of 2 MHz power is applied to the 13.56 MHz discharge, the electron density slightly increases and the electron temperature significantly increases. In dual-frequency operation, EEDFs have a low slope of low-energy region and evolve into a Druyvesteyn-like distribution. It turns out that the dual-frequency operation can significantly change the electron temperature. This is consistent with the results calculated using the analytical electron heating model, and the relevant heating mechanism is also presented.

Experimental investigation on the spatial distribution of floating potential at the wafer-level in inductively coupled oxygen plasma

The spatial distribution of floating potential for charging distribution at the wafer-level is measured by using a wafer-type probe array, and the experiment is performed in an inductively coupled oxygen plasma. At low pressures, the floating potential distribution exhibits a convex shape. As the pressure increases, the profile gradually evolves into a concave shape, indicating more negative charge at the center, which is unusual for electropositive plasmas. A similar evolution is observed for positive ion flux under the same discharge conditions. It is noteworthy that the charging distribution at the wafer position in process plasmas at high pressures can be reversed due to negative ions compared to that in electropositive plasmas. In addition, the correlation between the floating potential and electronegativity is also presented. In order to investigate the effect of negative ions on floating potential distribution, a 2D fluid simulation with an electron-heating model is conducted, and the experimental results are in good agreement with those from the 2D fluid simulation.

Theoretical Model for Negative Differential Conductance in 2D Semiconductor Monolayers

A simple theoretical model of electron heating in a system with two valleys is applied for the first time to describe 2D semiconductor monolayers of the MoS2 and WS2 types. The model is demonstrated to describe sufficiently well the available experimental data on the negative differential conductance effect in a WS2 monolayer. It confirms a possibility to fabricate Gunn diodes of a new generation based on the structures concerned. Such diodes are capable of generating frequencies of an order of 10 GHz and higher, which makes them attractive for many practical applications.

Slab magnetised non-relativistic low-beta electron–positron plasmas: collisionless heating, linear waves and reconnecting instabilities

The properties of a non-relativistic magnetised low-beta electron–positron plasma in slab geometry are investigated. The two species are taken to be drift kinetic while we retain Larmor radius effects in quasi-neutrality, and inertia in Ohm’s law. A linear analysis shows that, for small magnetic perturbations, Alfvénic perturbations travel at the electron Alfvén speed, which is based on the electron mass. We discuss the role of the displacement current when Larmor-scale and Debye-scale effects are both retained. We predict the existence of a kinetic electron Alfvén wave which connects to the K-modes of Mishchenko et al. (J. Plasma Phys., 2017 (submitted)) in the electrostatic limit. It is found that linear drift waves are not supported by the system if the two species have the same temperature. Tearing modes can be driven unstable by equilibrium current density gradients. Also in this case, the characteristic time is based on the electron Alfvén speed. Nonlinear hybrid fluid-kinetic equations are also derived. It is shown that each species is described, to leading order, by the kinetic reduced electron heating model (KREHM) kinetic equation of Zocco & Schekochihin (Phys. Plasmas, vol. 18, 2011, 102309). The model is extended to retain first-order Larmor radius effects. It supports collisionless dispersive waves, which can greatly impact nonlinear magnetic reconnection. Diamagnetic effects enter the nonlinear equations via the first-order magnetic compressibility. A minimal nonlinear model for two-dimensional low-frequency isothermal pair plasmas is derived.

Axial heating and temperature of RF-excited non-neutral plasmas in Penning-Malmberg traps

Electro-magnetostatic traps have been used for decades to provide long-term storage of charged particle samples or non-neutral plasmas. The dynamics and equilibrium states of these ideally simple systems can be strongly diverted from the usual working conditions (i.e. single-species, quiescent samples) in the presence of oppositely charged particles or external electric field perturbations. Both these conditions occur when the plasma is generated by means of a radio-frequency (RF) excitation continuously applied on a trap electrode. The application of RF drives of some volts over periods larger than typical collisional time scales leads to residual-gas ionization and to the accumulation of an electron plasma, a process that has previously been exploited as an alternative to thermionic or photoemission electron sources. The analysis of the axial energy distribution shows a deviation of the continuously excited final state from maxwellianity dependent on the radial position and the subsequent relaxation to equilibrium after the interruption of the drive. Systematic measurements also indicate the high sensitivity to the residual gas pressure of both the total confined charge and of the attainable densities and plasma profiles. The results are compared to the information obtained from a very simple one-dimensional electron heating model and show the validity of its most basic features together with its shortcomings.

Viriato: A Fourier–Hermite spectral code for strongly magnetized fluid–kinetic plasma dynamics

We report on the algorithms and numerical methods used in Viriato, a novel fluid–kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model (KREHM) equations (Zocco and Schekochihin, 2011) (which reduce to the standard Reduced-MHD equations in the appropriate limit) and (ii) the kinetic reduced MHD (KRMHD) equations (Schekochihin et al., 2009). Two main applications of these equations are magnetized (Alfvénic) plasma turbulence and magnetic reconnection. Viriato uses operator splitting (Strang or Godunov) to separate the dynamics parallel and perpendicular to the ambient magnetic field (assumed strong). Along the magnetic field, Viriato allows for either a second-order accurate MacCormack method or, for higher accuracy, a spectral-like scheme composed of the combination of a total variation diminishing (TVD) third order Runge–Kutta method for the time derivative with a 7th order upwind scheme for the fluxes. Perpendicular to the field Viriato is pseudo-spectral, and the time integration is performed by means of an iterative predictor–corrector scheme. In addition, a distinctive feature of Viriato is its spectral representation of the parallel velocity-space dependence, achieved by means of a Hermite representation of the perturbed distribution function. A series of linear and nonlinear benchmarks and tests are presented, including a detailed analysis of 2D and 3D Orszag–Tang-type decaying turbulence, both in fluid and kinetic regimes.

Giant Fano factor and bistability in a Corbino disk in the quantum Hall effect breakdown regime

We performed noise measurements for a Corbino disk in the quantum Hall effect breakdown regime. We investigated two Corbino-disk-type devices with different sizes and observed that the Fano factor increases when the length between the contacts doubles. This observation is consistent with the avalanche picture suggested by the bootstrap electron heating model. The temperature dependence of the Fano factor indicates that the avalanche effect becomes more prominent as temperature decreases. Moreover, in the highly nonlinear regime, negative differential resistance and temporal oscillation due to bistability are found. A possible interpretation of this result is that Zener tunneling of electrons between Landau levels occurs.

Time-resolved measurement of single pulse femtosecond laser-induced periodic surface structure formation induced by a pre-fabricated surface groove.

Time-resolved diffraction microscopy technique has been used to observe the formation of laser-induced periodic surface structures (LIPSS) from the interaction of a single femtosecond laser pulse (pump) with a nano-scale groove mechanically formed on a single-crystal Cu substrate. The interaction dynamics (0-1200 ps) was captured by diffracting a time-delayed, frequency-doubled pulse (probe) from nascent LIPSS formation induced by the pump with an infinity-conjugate microscopy setup. The LIPSS ripples are observed to form asynchronously, with the first one forming after 50 ps and others forming sequentially outward from the groove edge at larger time delays. A 1-D analytical model of electron heating including both the laser pulse and surface plasmon polariton excitation at the groove edge predicts ripple period, melt spot diameter, and qualitatively explains the asynchronous time-evolution of LIPSS formation.

ELECTRON HEATING BY THE ION CYCLOTRON INSTABILITY IN COLLISIONLESS ACCRETION FLOWS. I. COMPRESSION-DRIVEN INSTABILITIES AND THE ELECTRON HEATING MECHANISM

In systems accreting well below the Eddington rate, the plasma in the innermost regions of the disk is collisionless and two-temperature, with the ions hotter than the electrons. Yet, whether a collisionless faster-than-Coulomb energy transfer mechanism exists in two-temperature accretion flows is still an open question. We study the physics of electron heating during the growth of ion velocity-space instabilities, by means of multi-dimensional particle-in-cell (PIC) simulations. A large-scale compression - embedded in a novel form of the PIC equations - continuously amplifies the field. This constantly drives a pressure anisotropy P_perp > P_parallel, due to the adiabatic invariance of the particle magnetic moments. We find that, for ion plasma beta values beta_i ~ 5-30 appropriate for the midplane of low-luminosity accretion flows, mirror modes dominate if the electron-to-proton temperature ratio is > 0.2, whereas if it is < 0.2 the ion cyclotron instability triggers the growth of strong Alfven-like waves, that pitch-angle scatter the ions to maintain marginal stability. We develop an analytical model of electron heating during the growth of the ion cyclotron instability, which we validate with PIC simulations. We find that for cold electrons (beta_e < m_e/m_i), the electron energy gain is controlled by the magnitude of the E-cross-B velocity induced by the ion cyclotron waves. This term is independent of the initial electron temperature, so it provides a solid energy floor even for electrons starting with extremely low temperatures. On the other hand, the electron energy gain for beta_e > m_e/m_i - governed by the conservation of the magnetic moment in the growing fields of the instability - is proportional to the initial electron temperature. Our results have implications for two-temperature accretion flows as well as the solar wind and intracluster plasmas. [abridged]

Equivalence of the hard-wall and kinetic-fluid models of collisionless electron heating in capacitively coupled discharges

By re-evaluating the hard-wall collisionless electron heating model from first principles, we show that despite previous criticisms (Gozadinos et al 2001 Phys. Rev. Lett. 87 135004), this model can in general be made consistent with the requirement of radio frequency (rf) current continuity at the sheath edge, while still producing a net heating effect. In addition, we demonstrate that the hard-wall and kinetic-fluid heating models stem from the same basic physical mechanism, and are in many ways the same theory; they differ only in the spatial region where electron heating is assumed to occur, and the way in which the effective electron distribution function is determined. Fundamentally, both models predict that collisionless heating occurs because of a non-isothermal compression and expansion of the plasma electrons by an oscillating rf sheath.

Transition dynamics in the electrical breakdown of the quantum Hall effect

We investigate the dynamic properties of the breakdown of integer quantum Hall states (QHSs). The critical field of QHS breakdown that occurs at a filling factor of $\ensuremath{\nu}\ensuremath{\sim}2$ is found to depend on the scan rate of the applied Hall field ${E}_{H}$ and to fluctuate stochastically; in contrast, a smooth breakdown is observed at $\ensuremath{\nu}\ensuremath{\sim}4$. The histogram of the critical values of ${E}_{H}$ can be used to derive the escape and relaxation time, ranging from a few seconds to 10 $\ensuremath{\mu}$s between the low-dissipation QHS and the dissipation state. The increase of the escape rate between the low-dissipative QHS and the dissipative state is accompanied by a decrease of the relaxation rate and vice versa, indicating the bistable nature of the breakdown phenomena. The observed results agree well with the calculated results based on the basis of the bootstrap electron heating model. We conclude that the dynamic behaviors of QHS breakdown are governed by the transition probability that resides in the thermal bistable regime between the QHS and the dissipation states.

SAMI2‐PE: A model of the ionosphere including multistream interhemispheric photoelectron transport

In order to improve model comparisons with recently improved incoherent scatter radar measurements at the Jicamarca Radio Observatory we have added photoelectron transport and energy redistribution to the two dimensional SAMI2 ionospheric model. The photoelectron model uses multiple pitch angle bins, includes effects associated with curved magnetic field lines, and uses an energy degradation procedure which conserves energy on coarse, non‐uniformly spaced energy grids. The photoelectron model generates secondary electron production rates and thermal electron heating rates which are then passed to the fluid equations in SAMI2. We then compare electron and ion temperatures and electron densities of this modified SAMI2 model with measurements of these parameters over a range of altitudes from 90 km to 1650 km (L = 1.26) over a 24 hour period. The new electron heating model is a significant improvement over the semi‐empirical model used in SAMI2. The electron temperatures above the F‐peak from the modified model qualitatively reproduce the shape of the measurements as functions of time and altitude and quantitatively agree with the measurements to within ∼30% or better during the entire day, including during the rapid temperature increase at dawn.

Adiabatic electron heating in the magnetotail current sheet: Cluster observations and analytical models

We consider the electron distribution in current sheets observed by Cluster mission in the Earth magnetotail. We use the statistics of 70 fast (less than 20 minutes) and 12 slow (more than one hour) crossings of horizontal current sheets. We demonstrate that for both types electron temperature decreases with increase of magnetic field ∣Bx∣ away from the current sheet center. We use the approximations Te⊥/Te⊥ max ≈ 1 − αT⊥(Bx/Bext)2 and Te∥/Te∥ max ≈ 1 − αT∥(Bx/Bext)2, where Bext is value of Bx in the lobes. For statistics of thin current sheets (fast crossings) we obtain mean values 〈αT⊥〉 ≈ 〈αT∥〉 ≈ 1. For thick current sheets (slow crossings) we also obtain 〈αT⊥〉 ≈ 〈αT∥〉, but 〈αT⊥〉, 〈αT∥〉 &gt; 1. The electron temperature anisotropy is about Te∥/Te⊥ = 1.1 − 1.2 and vertical profiles Te∥/Te⊥ ≈ const. Observed vertical distributions of Te∥ and Te⊥ are described by the analytical model of electron heating in the course of the earthward convection in thin current sheets with (Bx(z), Bz(x)) and in thick current sheets with (Bx(x, z), Bz(x, z)). We also show that the observed electron temperature anisotropy is provided by the electron population in the energy range between 50 ev and 3 keV. The cold core of electron distribution (&lt;50 eV) is isotropic and the hot tail (&gt;5 keV) has Te∥/Te⊥ ∼ 1 or even Te∥/Te⊥ &lt; 1. We consider electron pressure tensor in observed thin current sheets and demonstrate that electron velocity distribution is gyrotropic with high accuracy.

An improved model of the lightning electromagnetic field interaction with the D‐region ionosphere

We present an improved time‐domain model of the lightning electromagnetic pulse (EMP) interaction with the lower ionosphere. This improved model inherently accounts for the Earth's curvature, includes an arbitrary number of ion species, and uses a convolutional Perfectly Matched Layer (PML) boundary. We apply an improved model of electron heating due to the lightning EMP and electrostatic fields, and we include ionization, attachment, and detachment. In addition to modeling lightning, this model can be used for long‐distance VLF wave propagation in the Earth‐ionosphere waveguide, heating of the lower ionosphere by VLF transmitters, and heating in the F‐region ionosphere by lightning. In this paper we present three initial results of this model. First, we compare results of ionospheric heating and electron density disturbances with and without electron detachment taken into account. We find that detachment is important only for the QE effects on time scales longer than 1 ms. Second, we find a simple explanation for the recently‐reported “elve doublets”, which we find are an effect of the rise and fall times of the lightning waveform. In particular, we find that all elves are doublets, and the rise and fall times of the current pulse control the brightness and separation in time of the two successive halves of the elve. Third, we find a similar simple explanation for “ring” sprites, whole columns appear in a circle symmetric around the discharge axis. We find that ring sprites can be initiated for particular current waveforms, where the QE and EMP fields in the mesosphere produce a maximum reduced field away from the discharge axis.

The dynamics of hot-electron heating in direct-drive-implosion experiments caused by two-plasmon-decay instability

Two-plasmon-decay (TPD) instability is identified as a potential source of target preheat in direct-drive-implosion experiments on OMEGA. A physical model of electron heating is developed that relies on extended Zakharov simulations to predict the nonlinearly saturated Langmuir wave spectrum. Hot electron generation is estimated via a test-particle approach. It is noted that because of the relatively low areal density of the targets during the time of TPD instability, hot-electron recirculation and reheating are potentially important effects. This is modeled by a particular form of boundary conditions on the test particles. Such boundary conditions might prove useful in other kinetic simulations of particle heating where recirculation is a possibility.

A self-consistent global model of solenoidal-type inductively coupled plasma discharges including the effects of radio-frequency bias power

We developed a self-consistent global simulator of solenoidal-type inductively coupled plasma discharges and observed the effect of the radio-frequency (rf) bias power on the plasma density and the electron temperature. We numerically solved a set of spatially averaged fluid equations for charged particles, neutrals, and radicals. Absorbed power by electrons is determined by using an analytic electron heating model including the anomalous skin effect. To analyze the effects of rf bias power on the plasma properties, our model also combines the electron heating and global transport modules with an rf sheath module in a self-consistent manner. The simulation results are compared with numerical results by using the commercial software package cfd-ace + (ESI group) and experimental measurements by using a wave cutoff probe and a single Langmuir probe.

XUV emission from autoionizing hole states induced by intense XUV-FEL at intensities up to 1017 W/cm2

Aluminium targets were irradiated with 92 eV radiation from FLASH Free Electron Laser at DESY at intensities up to 1017 W/cm2 by focussing the beam on target down to a spot size of ∼1 μm by means of a parabolic mirror. High resolution XUV spectroscopy was used to identify aluminium emission from complex hole-states. Simulations carried out with the MARIA code show that the emission characterizes the electron heating in the transition phase solid-atomic. The analysis allows constructing a simple model of electron heating via Auger electrons.