Collisionless Electron Heating Research Articles

Discovery of Year-scale Time Variability from Thermal X-Ray Emission in Tycho’s Supernova Remnant

Mechanisms of particle heating are crucial to understanding the shock physics in supernova remnants (SNRs). However, there has been little information on time variabilities of thermalized particles so far. Here, we present a discovery of a gradually brightening thermal X-ray emission found in the Chandra data of Tycho’s SNR obtained during 2000–2015. The emission exhibits a knot-like feature (Knot1) with a diameter of ≃0.04 pc located in the northwestern limb, where we also find localized Hα filaments in an optical image taken with the Hubble Space Telescope in 2008. The model with the solar abundance reproduces the spectra of Knot1, suggesting that Knot1 originates from the interstellar medium; this is the first detection of thermal X-ray emission from swept-up gas found in Tycho’s SNR. Our spectral analysis indicates that the electron temperature of Knot1 has increased from ∼0.30 to ∼0.69 keV within the period between 2000 and 2015. These results lead us to ascribe the time-variable emission to a small dense clump recently heated by the forward shock at the location of Knot1. The electron-to-proton temperature ratio immediately downstream of the shock (β 0 ≡ T e /T p ) is constrained to be m e /m p ≤ β 0 ≤ 0.15 to reproduce the data, indicating the collisionless electron heating with efficiency is consistent with previous Hα observations of Tycho and other SNRs with high shock velocities.

Conductivity effects during the transition from collisionless to collisional regimes in cylindrical inductively coupled plasmas

A numerical model is developed to study the conductivity effects during the transition from collisionless to collisional regimes in cylindrical inductively coupled argon plasmas at pressures of 0.1–20 Pa. The model consists of electron kinetics module, electromagnetics module, and global model module. It allows for self-consistent description of non-local electron kinetics and collisionless electron heating in terms of the conductivity of homogeneous hot plasma. Simulation results for non-local conductivity case are compared with predictions for the assumption of local conductivity case. Electron densities and effective electron temperatures under non-local and local conductivities show obvious differences at relatively low pressures. As increasing pressure, the results under the two cases of conductivities tend to converge, which indicates the transition from collisionless to collisional regimes. At relatively low pressures the local negative power absorption is predicted by non-local conductivity case but not captured by local conductivity case. The two-dimensional (2D) profiles of electron current density and electric field are coincident for local conductivity case in the pressure range of interest, but it roughly holds true for non-local conductivity case at very high pressure. In addition, an effective conductivity with consideration of non-collisional stochastic heating effect is introduced. The effective conductivity almost reproduces the electron density and effective electron temperature for the non-local conductivity case, but does not capture the non-local relation between electron current and electric field as well as the local negative power absorption that is observed for non-local conductivity case at low pressures.

Landau damping of electrons with bouncing motion in a radio-frequency plasma* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFE0300406) and the National Natural Science Foundation of China (Grant Nos. 11975272, 12075276, 11805133, 11705236, and 11375234).

One-dimensional particle simulations have been conducted to study the interaction between a radio-frequency electrostatic wave and electrons with bouncing motion. It is shown that bounce resonance heating can occur at the first few harmonics of the bounce frequency (nω b,n = 1,2,3,…). In the parameter regimes in which bounce resonance overlaps with Landau resonance, the higher harmonic bounce resonance may accelerate electrons at the velocity much lower than the wave phase velocity to Landau resonance region, enhancing Landau damping of the wave. Meanwhile, Landau resonance can increase the number of electrons in the lower harmonic bounce resonance region. Thus electrons can be efficiently heated. The result might be applicable for collisionless electron heating in low-temperature plasma discharges.

Influence of the excitation frequency on the RF power transfer efficiency of low pressure hydrogen ICPs

The influence of the excitation frequency on the RF power transfer of inductively heated hydrogen plasmas is investigated in the pressure range between 0.3 and 10 Pa. The experiments are conducted at a cylindrical ICP at frequencies in the range between 1 and 4 MHz and RF powers up to 1 kW. By applying a subtractive method which quantifies the transmission losses within the plasma coil and the RF network, the RF power transfer efficiency is determined. The key plasma parameters of the discharges are measured via optical emission spectroscopy and a double probe. By increasing the frequency from 1 to 4 MHz at a moderate RF power of 520 W, a significant enhancement of the RF power transfer efficiency is observed. It is most prominent at the presently considered low and high pressure limits and allows to reach high efficiencies of up to 95% at pressures between 3 and 5 Pa. While the AC loss resistance of the coil and the RF circuit only displays a relatively weak variation with the applied frequency due to the skin effect, the observed increase of the power transfer efficiency at higher frequencies is dominated by a considerable enhancement of the plasma equivalent resistance. This increased capability of the plasma to absorb the provided power is discussed against the background of collisional and collisionless heating of electrons. Thereby it is demonstrated that the observed behaviour can most likely be attributed to a decreasing difference between the angular excitation frequency and the effective electron collision frequencies. If the RF power is increased however, the RF power transfer efficiency increases globally while frequency induced differences tend to get less pronounced, as the plasma is generally capable of absorbing most of the provided power due to an increasing electron density.

Inductively coupled array (INCA) discharge

Recently a novel concept for collisionless electron heating and plasma generation at low pressures was theoretically proposed (Czarnetzki and Tarnev 2014, Phys. Plasmas 21 123508). It is based on periodically structured vortex fields, which produce certain electron resonances in velocity space. A more detailed investigation of the underlying theory is presented in a companion paper (Czarnetzki 2018, Plasma Sources Sci. Technol. 27 105011). Here, a new concept is experimentally realized for the first time by the inductively coupled array (INCA) discharge. The periodic vortex fields are produced by an array of small planar coils. It is shown that the array can be scaled up to arbitrary dimensions while keeping its electrical characteristics. Stable operation at pressures around and below 1 Pa is demonstrated. The power coupling efficiency is characterized, and an increase in the efficiency is observed with decreasing pressure. The spatial homogeneity of the discharge is investigated, and the behavior of the plasma parameters with power and pressure are presented. Linear scaling of the plasma density with power and pressure, typical for conventional inductive discharges, is observed. Most notably, the plasma potential and the corresponding mean ion energy show clear evidence of the presence of superenergetic electrons, attributed to stochastic heating. In the stochastic heating mode, the electron distribution function becomes approximately Maxwellian, but with increasing pressure it turns to the characteristic local distribution function known from classical inductive discharges. Large-area processing or thrusters are possible applications for this new plasma source.

Analysis of the high-energy electron population in surface-wave plasma columns in presence of collisionless resonant absorption

In surface-wave plasmas, the energy can be transferred to the plasma electrons through both ohmic (collisional) and collisionless heating mechanisms. At very low pressure, when the electron–neutral collision frequency is much lower than the wave frequency (collisionless regime), a resonance is excited close to the tube walls where the electron plasma frequency in the radially-inhomogeneous plasma column reaches the wave frequency. In such conditions, the sharp rise of the component of the surface-wave electric field perpendicular to the tube axis can induce transit-time heating. At the resonant point, the long-wavelength electromagnetic surface wave can also be converted into short-wavelength electrostatic Langmuir waves that propagate down the density gradient. In this work, spatially-resolved trace-rare-gases optical emission spectroscopy combined with collisional-radiative modeling is used to analyze the electron energy distribution function (EEDF) and wave–particle interactions in low-pressure argon plasma columns sustained by an electromagnetic surface wave at 600 MHz (over-dense plasma). The EEDF is found to depart from a Maxwellian with the presence of a high-energy tail. The relative population of high-energy electrons increases with the axial distance towards the end of the plasma column where the electron density decreases and the resonance point becomes closer to the discharge axis. Over the range of experimental conditions examined, the high-energy tail increases with the characteristic length of the plasma density gradient at the resonance point; a feature that can be linked to collisionless electron heating by Landau damping of Langmuir waves.

Probing suprathermal electrons by trace rare gases optical emission spectroscopy in low pressure dipolar microwave plasmas excited at the electron cyclotron resonance

In microwave plasmas with the presence of a magnetic field, fast electrons could result from collisionless energy absorption under electron cyclotron resonance (ECR) conditions. In this case, electrons are trapped between the two poles of the magnetic field and rotate at the cyclotron frequency ωce. When crossing a zone where the cyclotron frequency equals the microwave frequency (ωce=ω), electrons see a steady electric field in their reference frame and are constantly accelerated by the right handed polarized (RHP) wave. When the plasma density reaches the so-called critical density nc at which ωpe2=ω2±ωωce, where ωpe is the plasma electron frequency, the left handed polarized (LHP) electromagnetic wave can excite electrostatic waves that can produce collisionless electron heating and fast electron generation by Landau damping. In this study, a combination of the Langmuir probe and trace rare gas optical emission spectroscopy (TRG-OES) is used to analyze the electron energy probability function (EEPF) in microwave (2.45 GHz) low-pressure argon plasmas excited at ECR in a dipolar magnetic field. While both TRG-OES and Langmuir probe measurements agree on the effective electron temperature (TeAll) from 1.6 to 50 mTorr, TRG-OES, which is more sensitive to high energy electrons, shows that the EEPF is the sum of two Maxwellian populations: one described by TeAll and a high energy tail characterized by a temperature TeTail. Spatially resolved-TRG-OES measurements show that the high-energy tail (TeTail) in the EEPF is spatially localized near the magnet, while the effective electron temperature (TeAll) stays constant. The ratio between the high energy tail and the effective temperatures is found to increase with the absorbed microwave power and decrease with increasing pressure. The former phenomenon is ascribed to a rise in ECR heating due to a stronger RHP wave electric field and to an enhanced absorption of the LHP waves. On the other hand, the decrease in the ratio is attributed to a smaller magnetic confinement of the electrons (increase in the collision frequency), which lessens ECR heating and to a decrease in the LHP field intensity at the resonant position, which impedes the conversion into electrostatic waves.

Comprehensive understanding of chamber conditioning effects on plasma characteristics in an advanced capacitively coupled plasma etcher

An advanced capacitively coupled plasma etcher with two frequencies and additional direct current is characterized with complementary sensors. Due to the restrictive boundary conditions of the manufacturing environment, which the authors had to take into account, applicable plasma sensors are limited. Thus, the plasma parameters depending on the center, wall, sheath, and cathode regions are extracted separately based on the tool parameters, optical emission spectroscopy, and self-excited electron spectroscopy. One main target of this investigation is a cross verification of complementary sensor data and a deeper understanding. Due to the complex chamber setup, the authors use a chemically simple system of an Ar plasma with a blank Si wafer as the substrate. It is found that the removal of SiO2 and sputtering Si from the cathode and wafer changes the chamber condition and thus causes changes in the plasma characteristics. The established plasma process model comprises a change in secondary electron emission caused by changing the surface condition and a subsequent change in collisionless electron heating, in particular, in the case of applied low frequency power. Current electron heating models and conditioning models are used for cross verification of the plasma process model. It indicates that both chemical and electrical aspects to chamber conditioning should be considered in multiple frequency driven plasma etchers. The results presented in this paper are expected to contribute to the understanding of the interaction of the chamber conditioning effects and plasma parameters in advanced plasma etchers for sub-20 nm devices.

Electron heating mode transition induced by mixing radio frequency and ultrahigh frequency dual frequency powers in capacitive discharges

Electron heating mode transitions induced by mixing the low- and high-frequency power in dual-frequency nitrogen discharges at 400 mTorr pressure are presented. As the low-frequency (13.56 MHz) power decreases and high-frequency (320 MHz) power increases for the fixed power of 200 W, there is a transition of electron energy distribution function (EEDF) from Druyvesteyn to bi-Maxwellian type characterized by a distinguished warm electron population. It is shown that this EEDF evolution is attributed to the transition from collisional to collisionless stochastic heating of the low-energy electrons.

Revealing Collisionless Heating of Electrons at the Supernova Remnant Shock Wave with X-Ray Spectroscopy of Non-Equilibrium Plasmas(Research)

Revealing Collisionless Heating of Electrons at the Supernova Remnant Shock Wave with X-Ray Spectroscopy of Non-Equilibrium Plasmas(Research)

Radial acceleration of ions by a laser pulse in a plasma channel

The approximate analytic solution of the Cauchy problem is constructed for a system of kinetic equations of an electron–ion plasma that describe the acceleration of ions and the collisionless heating of electrons caused by the radial ponderomotive force of a laser beam that propagates in the transparent plasma of a gas or other low-density target. Under conditions where the Debye radius, rDe, of the electrons is considerably smaller than the characteristic localization scale, L, of the laser beam along the radius, e = rDe/L ≪ 1, this solution is found by a group transformation that is specified by the operator of approximate renormalization-group symmetries over small parameters, \(\varepsilon {\kern 1pt} and{\kern 1pt} \mu {\kern 1pt} = {\kern 1pt} \sqrt {Zm/M} \), of the initial distribution functions of particles. For an axially symmetric geometry of the laser beam, the temporal and spatial dependences of the distribution functions of particles are obtained and their integral characteristics, such as the density, mean velocity, temperature, and energy spectrum, are found. The formation of a cylindrical density cusp and the localized heating of electrons at the laser-channel boundary are analytically described.

Electron cooling and finite potential drop in a magnetized plasma expansion

The steady, collisionless, slender flow of a magnetized plasma into a surrounding vacuum is considered. The ion component is modeled as mono-energetic, while electrons are assumed Maxwellian upstream. The magnetic field has a convergent-divergent geometry, and attention is restricted to its paraxial region, so that 2D and drift effects are ignored. By using the conservation of energy and magnetic moment of particles and the quasi-neutrality condition, the ambipolar electric field and the distribution functions of both species are calculated self-consistently, paying attention to the existence of effective potential barriers associated to magnetic mirroring. The solution is used to find the total potential drop for a set of upstream conditions, plus the axial evolution of various moments of interest (density, temperatures, and heat fluxes). The results illuminate the behavior of magnetic nozzles, plasma jets, and other configurations of interest, showing, in particular, in the divergent plasma the collisionless cooling of electrons, and the generation of collisionless electron heat fluxes.

Collisionless electron heating in periodic arrays of inductively coupled plasmas

A novel mechanism of collisionless heating in large planar arrays of small inductive coils operated at radio frequencies is presented. In contrast to the well-known case of non-local heating related to the transversal conductivity, when the electrons move perpendicular to the planar coil, we investigate the problem of electrons moving in a plane parallel to the coils. Two types of periodic structures are studied. Resonance velocities where heating is efficient are calculated analytically by solving the Vlasov equation. Certain scaling parameters are identified. The concept is further investigated by a single particle simulation based on the ergodic principle and combined with a Monte Carlo code allowing for collisions with Argon atoms. Resonances, energy exchange, and distribution functions are obtained. The analytical results are confirmed by the numerical simulation. Pressure and electric field dependences are studied. Stochastic heating is found to be most efficient when the electron mean free path exceeds the size of a single coil cell. Then the mean energy increases approximately exponentially with the electric field amplitude.

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.

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.

ALFVÉN WAVE SOLAR MODEL (AWSoM): CORONAL HEATING

We present a new version of the Alfven Wave Solar Model (AWSoM), a global model from the upper chromosphere to the corona and the heliosphere. The coronal heating and solar wind acceleration are addressed with low-frequency Alfven wave turbulence. The injection of Alfven wave energy at the inner boundary is such that the Poynting flux is proportional to the magnetic field strength. The three-dimensional magnetic field topology is simulated using data from photospheric magnetic field measurements. This model does not impose open-closed magnetic field boundaries; those develop self-consistently. The physics includes: (1) The model employs three different temperatures, namely the isotropic electron temperature and the parallel and perpendicular ion temperatures. The firehose, mirror, and ion-cyclotron instabilities due to the developing ion temperature anisotropy are accounted for. (2) The Alfven waves are partially reflected by the Alfven speed gradient and the vorticity along the field lines. The resulting counter-propagating waves are responsible for the nonlinear turbulent cascade. The balanced turbulence due to uncorrelated waves near the apex of the closed field lines and the resulting elevated temperatures are addressed. (3) To apportion the wave dissipation to the three temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating. (4) We have incorporated the collisional and collisionless electron heat conduction. We compare the simulated multi-wavelength EUV images of CR2107 with the observations from STEREO/EUVI and SDO/AIA instruments. We demonstrate that the reflection due to strong magnetic fields in proximity of active regions intensifies the dissipation and observable emission sufficiently.

NEW EVIDENCE FOR EFFICIENT COLLISIONLESS HEATING OF ELECTRONS AT THE REVERSE SHOCK OF A YOUNG SUPERNOVA REMNANT

Although collisionless shocks are ubiquitous in astrophysics, certain key aspects of them are not well understood. In particular, the process known as collisionless electron heating, whereby electrons are rapidly energized at the shock front, is one of the main open issues in shock physics. Here we present the first clear evidence for efficient collisionless electron heating at the reverse shock of Tycho's supernova remnant (SNR), revealed by Fe-K diagnostics using high-quality X-ray data obtained by the Suzaku satellite. We detect K-beta (3p->1s) fluorescence emission from low-ionization Fe ejecta excited by energetic thermal electrons at the reverse shock front, which peaks at a smaller radius than Fe K-alpha (2p->1s) emission dominated by a relatively highly-ionized component. Comparison with our hydrodynamical simulations implies instantaneous electron heating to a temperature 1000 times higher than expected from Coulomb collisions alone. The unique environment of the reverse shock, which is propagating with a high Mach number into rarefied ejecta with a low magnetic field strength, puts strong constraints on the physical mechanism responsible for this heating, and favors a cross-shock potential created by charge deflection at the shock front. Our sensitive observation also reveals that the reverse shock radius of this SNR is about 10% smaller than the previous measurement using the Fe K-alpha morphology from the Chandra observations. Since strong Fe K-beta fluorescence is expected only from low-ionization plasma where Fe ions still have many 3p electrons, this feature is key to diagnosing the plasma state and distribution of the immediate postshock ejecta in a young SNR.

Fast Collisionless Reconnection and Electron Heating in Strongly Magnetized Plasmas

Magnetic reconnection in strongly magnetized (low-beta), weakly collisional plasmas is investigated by using a novel fluid-kinetic model [Zocco and Schekochihin, Phys. Plasmas 18, 102309 (2011)] which retains nonisothermal electron kinetics. It is shown that electron heating via Landau damping (linear phase mixing) is the dominant dissipation mechanism. In time, electron heating occurs after the peak of the reconnection rate; in space, it is concentrated along the separatrices of the magnetic island. For sufficiently large systems, the peak reconnection rate is cE(∥)(max) ≈ 0.2v(A)B(y,0), where v(A) is the Alfvén speed based on the reconnecting field B(y,0). The island saturation width is the same as in magnetohydrodynamics models except for small systems, when it becomes comparable to the kinetic scales.

Simulation study of wave phenomena from the sheath region in single frequency capacitively coupled plasma discharges; field reversals and ion reflection

Capacitively coupled radio-frequency (RF) discharges have great significance for industrial applications. Collisionless electron heating in such discharges is important, and sometimes is the dominant mechanism. This heating is usually understood to originate in a stochastic interaction between electrons and the electric fields. However, other mechanisms may also be important. There is evidence of wave emission with a frequency near the electron plasma frequency, i.e., ωpe, from the sheath region in collisionless capacitive RF discharges. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. These waves are damped in a few centimeters during their propagation from the sheath towards the bulk plasma. The damping occurs because of the Landau damping or some related mechanism. This research work reports that the emission of waves is associated with a field reversal during the expanding phase of the sheath. Trapping of electrons near to this field reversal region is observed. The amplitude of the wave increases with increasing RF current density amplitude J̃0 until some maximum is reached, beyond which the wave diminishes and a new regime appears. In this new regime, the density of the bulk plasma suddenly increases because of ion reflection, which occurs due to the presence of strong field reversal near sheath region. Our calculation shows that these waves are electron plasma waves. These phenomena occur under extreme conditions (i.e., higher J̃0 than in typical experiments) for sinusoidal current waveforms, but similar effects may occur with non-sinusoidal pulsed waveforms for conditions of experimental interest, because the rate of change of current is a relevant parameter. The effect of electron elastic collisions on plasma waves is also investigated.

Investigation on characteristics of argon corona discharge under atmospheric pressure

Spatially two-dimensional and axial-symmetric plasma model is developed to investigate the characteristics of a bar–plate corona discharge of argon gas under atmospheric pressure. An improved nonlocal collision-less electron heat flux is used in the model. Numerical simulation for the process of argon corona discharge under atmospheric pressure are carried out with a separation of 0.2 mm between the bar and plate and the discharge is excited by an external circuit. The results indicate that metastable argon atoms are mainly produced by ground state excitation reaction, the metastable step-wise ionization is the dominated reaction and the highest contribution to electron production during the discharge. In addition, the maximum of electron temperature arises in the cathode sheath due to Joule heating in the high electric field. Elastic collision is the dominant volumetric electron energy loss in atmosphere corona discharge, which is negligible in low pressure glow discharge. The discharge current–voltage characteristic is predicted and shows a good agreement with the results obtained by experiments.