Stochastic Electron Heating Research Articles

Generation of energetic electrons by an electron cyclotron wave through stochastic heating in a spherical tokamak

This study presents novel findings on stochastic electron heating via a random electron cyclotron wave (ECW) in a spherical tokamak. Hard x ray measurements demonstrate the time evolution of hard x ray counts at different energy bands, consistent with predictions from the stochastic heating model. The ECW heating rate shows a positive correlation with applied power, confirming the effectiveness of stochastic heating. Remarkably, the ECW-driven plasma current remains insensitive to ECW incidence angle, consistent with model predictions. The observed stochastic heating of electrons offers potential for exploring innovative non-inductive current drive modes in spherical tokamaks. This research contributes to the understanding of plasma behaviour and motivates the development of new models for non-inductive current drive in fusion devices.

Stochastic heating of free electrons in multiple electromagnetic waves: A simple physical analysis.

It is established that charged particles crossing the interference field of two colliding electromagnetic (EM) waves can behave chaotically, leading to a stochastic heating of the particle distribution. A fine understanding of the stochastic heating process is crucial to the optimization of many physical applications requiring a high EM energy deposition to these charged particles. Predicting key stochastic heating features (particle distribution, chaos threshold) is usually achieved using a heavy Hamiltonian formalism required to model particle dynamics in chaotic regimes. Here, we explore an alternative and more intuitive path, which makes it possible to reduce the equationsof motion of particles to rather simple and well-known physical systems such as Kapitza and gravity pendulums. Starting from these simple systems, we first show how to estimate chaos thresholds by deriving a model of the stretching and folding dynamics of the pendulum bob in phase space. Based on this first model, we then derive a random walk model for particle dynamics above the chaos threshold, which can predict major features of stochastic heating for any EM polarization and angle θ_{i}.

Electron heating mechanisms at quasi-perpendicular shocks – revisited with magnetospheric multiscale measurements

ABSTRACTWe demonstrate that measurements obtained from NASA’s magnetospheric multiscale (MMS) mission support quasi-adiabatic electron heating in quasi-perpendicular shocks with temperature Te⊥ ∝ B1 + α, where B is the magnetic field strength and α represents departure from adiabaticity. Adiabatic heating (α = 0) results from the conservation of magnetic moment on spatially increasing magnetic field inside the shock ramp. Negative α < 0 is observed in most situations, where perpendicular energy gain from adiabatic heating is redistributed by interactions with waves to the parallel direction leading to a lower isotropic temperature increase. Positive α is observed when the stochastic heating of electrons is activated by the E × B wave acceleration mechanism by electrostatic waves leading to a higher temperature increase. By using test-particle simulations in a realistic shock model we have elucidated the process of stochastic wave acceleration. We have also shown the equivalence of adiabatic heating and acceleration by gradient B drift at shocks with low Mach numbers and demonstrated that the cross-shock potential does not contribute to the electron heating. Signatures of quasi-adiabatic heating and/or stochastic heating of electrons are observed in all shocks analysed with measurements by the MMS.

Nonlinear degradation of O-X-B mode conversion in MAST Upgrade

Spherical tokamaks like the MAST Upgrade device are often operated in an overdense regime. As a consequence, conventional electron cyclotron resonance heating (ECRH) and current drive (ECCD) are typically not possible. MAST Upgrade is planned to investigate a mode coupling scheme known as O-X-B at high power, which may allow gyrotrons to heat and drive current in overdense plasmas by coupling electromagnetic waves to electrostatic electron Bernstein waves (EBWs) at the upper hybrid (UH) layer. However at the gyrotron beam intensities planned for MAST Upgrade, several nonlinear effects may degrade the linear mode coupling into EBWs. Using particle-in-cell simulations, parametric decay instabilities (PDIs) and stochastic electron heating (SEH) are investigated in the region near the UH layer. It is found that nonlinear effect could have a substantial impact on the O-X-B scheme in MAST Upgrade at high gyrotron intensities.

Modeling the effect of stochastic heating and surface chemistry in a pure CF4 inductively coupled plasma

The physics and chemistry of inductively coupled plasma generated in pure tetrafluoromethane are analyzed using a self-consistent two-dimensional plasma fluid model coupled with Maxwell's equations. The model also takes into account the stochastic electron heating typical for low-pressure inductive discharges. We show that this effect is important for the explanation of experimentally measured plasma parameters. We also analyze the influence of several model parameters on the plasma. These parameters include the mechanism of surface reactions, the sticking coefficient of fluorine atoms at the walls, the uncertainty in the electron impact dissociation reactions, and the background gas pressure.

Enhanced ion acceleration using the high-energy petawatt PETAL laser

The high-energy petawatt PETAL laser system was commissioned at CEA’s Laser Mégajoule facility during the 2017–2018 period. This paper reports in detail on the first experimental results obtained at PETAL on energetic particle and photon generation from solid foil targets, with special emphasis on proton acceleration. Despite a moderately relativistic (<1019 W/cm2) laser intensity, proton energies as high as 51 MeV have been measured significantly above those expected from preliminary numerical simulations using idealized interaction conditions. Multidimensional hydrodynamic and kinetic simulations, taking into account the actual laser parameters, show the importance of the energetic electron production in the extended low-density preplasma created by the laser pedestal. This hot-electron generation occurs through two main pathways: (i) stimulated backscattering of the incoming laser light, triggering stochastic electron heating in the resulting counterpropagating laser beams; (ii) laser filamentation, leading to local intensifications of the laser field and plasma channeling, both of which tend to boost the electron acceleration. Moreover, owing to the large (∼100 μm) waist and picosecond duration of the PETAL beam, the hot electrons can sustain a high electrostatic field at the target rear side for an extended period, thus enabling efficient target normal sheath acceleration of the rear-side protons. The particle distributions predicted by our numerical simulations are consistent with the measurements.

Enhanced laser-driven proton acceleration via improved fast electron heating in a controlled pre-plasma

The interaction of ultraintense laser pulses with solids is largely affected by the plasma gradient at the vacuum–solid interface, which modifies the absorption and ultimately, controls the energy distribution function of heated electrons. A micrometer scale-length plasma has been predicted to yield a significant enhancement of the energy and weight of the fast electron population and to play a major role in laser-driven proton acceleration with thin foils. We report on recent experimental results on proton acceleration from laser interaction with foil targets at ultra-relativistic intensities. We show a threefold increase of the proton cut-off energy when a micrometer scale-length pre-plasma is introduced by irradiation with a low energy femtosecond pre-pulse. Our realistic numerical simulations agree with the observed gain of the proton cut-off energy and confirm the role of stochastic heating of fast electrons in the enhancement of the accelerating sheath field.

Stochastic heating of electrons due to Raman backscatter radiations in interaction of intense laser pulse with nitrogen atoms

In this paper, simulation study of electron stochastic heating arising from the Raman backscatter radiations during the interaction of the laser pulse with the nitrogen atoms is presented by use of a massively parallel particle-in-cell code. For this purpose, the self-consistent evolutions of the laser pulse via the time–space Fourier transforms of transvers vector potential are investigated at the different times of propagation. It is shown that since the ionization has effect on the emission of the Raman backscattered radiation; it noticeably contributes on the stochastic heating threshold of the electrons. According to our results, it has been found that, when there is the long rise time laser pulse (here 100 fs), the Raman backscattered radiations are seeded by a strong initial noise at the earlier times. Therefore, by considering the ionization, the necessary condition for chaos threshold is met sooner, which, in turn, causes the electron stochastic heating start quickly compared to the case the laser pulse is propagated in the pre-plasma. As a result, in agreement with chaotic nature of the motion, the electrons gain more energy through the stochastic mechanism in the field-ionized plasma.

Stochastic and Quasi-adiabatic Electron Heating in Quasi-parallel Shocks

Abstract Using Magnetospheric Multiscale observations at the Earth’s quasi-parallel bow shock we demonstrate that electrons are heated by two different mechanisms: a quasi-adiabatic heating process during magnetic field compression, characterized by the isotropic temperature relation T / B = ( T 0 / B 0 ) ( B 0 / B ) α with α = 2/3 when the electron heating function ∣ χ e ∣ < 1 , and a stochastic heating process when ∣ χ e ∣ > 1 . Both processes are controlled by the value of the stochastic heating function χ j = m j q j − 1 B − 2 div ( E ⊥ ) for particles with mass m j and charge q j in the electric and magnetic fields E and B . Test-particle simulations are used to show that the stochastic electron heating and acceleration in the studied shock are accomplished by waves at frequencies (0.4–5) f ce (electron gyrofrequency) for bulk heating, and waves f > 5 f ce for acceleration of the tail of the distribution function. Stochastic heating can give rise to flat-top electron distribution functions, frequently observed near shocks. It is also shown that obliquely polarized electric fields of electron cyclotron drift and ion acoustic instabilities scatter the electrons into the parallel direction and keep the isotropy of the electron distribution. The results reported in this paper may be relevant to electron heating and acceleration at interplanetary shocks and other astrophysical shocks.

Stochastic ion and electron heating on drift instabilities at the bow shock

Abstract The analysis of the wave content inside a perpendicular bow shock indicates that heating of ions is related to the lower hybrid drift (LHD) instability, and heating of electrons is related to the electron cyclotron drift (ECD) instability. Both processes represent stochastic acceleration caused by the electric field gradients on the electron gyroradius scales, produced by the two instabilities. Stochastic heating is a single-particle mechanism where large gradients break adiabatic invariants and expose particles to direct acceleration by the direct current and wave fields. The acceleration is controlled by function $\chi = m_iq_i^{-1} B^{-2}$div(E), which represents a general diagnostic tool for processes of energy transfer between electromagnetic fields and particles, and the measure of the local charge non-neutrality. The identification was made with multipoint measurements obtained from the Magnetospheric Multiscale spacecraft. The source for the LHD instability is the diamagnetic drift of ions, and for the ECD instability the source is ExB drift of electrons. The conclusions are supported by laboratory diagnostics of the ECD instability in Hall ion thrusters.

Stochastic electron heating in an interference field of several laser pulses of a picosecond duration

Efficient electron acceleration and heating is demonstrated in a multimode structure created by interference of several laser beams of a relativistic intensity and a picosecond duration near a sharp target boundary. Electron energization proceeds in two steps, with a slow stochastic heating followed by a fast regular acceleration in a resonance interaction with one of wave packets. It results in formation of a population of energetic electrons with an exponential distribution in energy characterized by a high effective temperature and a sharp cutoff. Hot electron characteristics depend on the number of crossing laser beams and their respective angles. This process is an example of efficient electron heating in vacuum by electromagnetic fields without participation of electrostatic plasma waves. It might contribute to creation of a superthermal particle population with an effective temperature significantly exceeding the common ponderomotive scaling.

Stochastic electron heating in the laser and quasi-static electric and magnetic fields

The dynamics of relativistic electrons in the intense laser radiation and quasi-static electromagnetic fields both along and across the laser propagating direction are studied in the 3/2 dimensional (3/2D) Hamiltonian framework. It is shown that the unperturbed oscillations of the relativistic electron in these electric fields could exhibit a long tail of the amplitude of harmonics which makes an onset of stochastic electron motion be a primary candidate for electron heating. Chirikov-like mappings which describe the recurrence relations of electron energy and time passing through zero canonical momentum plane are derived, and then, the criteria for instability are obtained. It follows that for both transverse and longitudinal electric fields, there exist upper limits of the stochastic electron energy depending on the laser intensity and electric field strength. These maximum energies could be increased by a weak electric field. However, the maximum energy is reduced for the superluminal phase velocity in both cases. The impacts of the magnetic fields on the electron dynamics are different for these two cases and discussed qualitatively. These analytic results are confirmed by the numerical simulations of solving the 3/2D Hamiltonian equations directly.

The Influence of Secondary Electron Emission and Electron Reflection on a Capacitively Coupled Oxygen Discharge

The one-dimensional object-oriented particle-in-cell Monte Carlo collision code oopd1 is applied to explore the role of secondary electron emission and electron reflection on the properties of the capacitively-coupled oxygen discharge. At low pressure (10 mTorr), drift-ambipolar heating of the electrons dominates within the plasma bulk, while at higher pressure (50 mTorr), stochastic electron heating in the sheath region dominates. Electron reflection has negligible influence on the electron energy probability function and only a slight influence on the electron heating profile and electron density. Including ion-induced secondary electron emission in the discharge model introduces a high energy tail to the electron energy probability function, enhances the electron density, lowers the electronegativity, and increases the effective electron temperature in the plasma bulk.

Experimental and numerical investigations of electron characteristics in 2 MHz and 13.56 MHz inductively coupled hydrogen plasmas with an expansion region

The electron characteristics are investigated in 2 MHz and 13.56 MHz inductively coupled hydrogen discharges with an expansion region. The influence of the gas pressure and radio-frequency of the power source on the electron energy probability functions (EEPFs), electron density, and electron temperature at high deposition power has been presented. The measured EEPFs in the driver region of the discharge evolve from a three-temperature Maxwellian distribution to a Maxwellian distribution as the pressure increases. Different characteristic frequencies calculated based on the measured plasma parameters show that stochastic heating of electrons dominates at pressures lower than 0.3 Pa and it has to be considered for pressures lower than 1.0 Pa, while Ohmic heating dominates at higher pressure. Furthermore, the EEPFs as a function of the total energy evolve from the identical shape to discrete shapes with axial position and pressure, indicating a transition of electron kinetics from nonlocal to local regimes. This can be explained by the calculated electron energy relaxation length. In order to verify the experimental results, COMSOL Multiphysics is used to calculate the electron density and electron temperature at different pressures and frequencies of power source. The simulated axial distributions of the plasma parameters agree well with the measured results at 5.0 Pa, while the calculated electron density is lower and the calculated electron temperature is higher at 1.0 Pa. In addition, there is no frequency dependence of axial resolved EEPFs, electron density, and electron temperature in high power deposition discharges (1.5 kW).

Enhanced power coupling efficiency in inductive discharges with RF substrate bias driven at consecutive harmonics with adjustable phase

Inductive discharges with radio-frequency (RF) substrate bias are frequently used for various technological applications. We operate such a hybrid discharge with a phase-locked RF substrate bias at twice the frequency of the inductive coupling with fixed but adjustable phase between both RF sources in neon at low pressures of a few Pa. The ion flux to the substrate is found to be a function of this relative phase in the H-mode at constant RF powers as long as some residual capacitive coupling of the planar coil is present. For distinct choices of the phase, Phase Resolved Optical Emission Spectroscopy measurements show that energetic beam electrons generated by the expanding boundary sheaths (i) are well confined, (ii) are accelerated efficiently, and (iii) propagate vertically through the inductive skin layer at the times of maximum azimuthal induced electric field within the fundamental RF period. This enhances the inductive stochastic electron heating, the power coupling efficiency, and finally the ion flux.

Time evolution of the distribution function for stochastically heated relativistic electrons in a laser field of picosecond duration

We report a numerical analysis of the stochastic acceleration of electrons, stipulated by a random change in the phase of the force acting on the electron. The main source of randomness is the random spatial distribution of electromagnetic fields in the focal region of multimode laser radiation. A typical frequency of the random phase change corresponding to the maximum impact of the effect under consideration lies in the range of (0.25 – 0.5)ν (ν is the radiation frequency of a neodymium laser). A wave packet model convenient for calculations taking into account the radiative transitions of the neodymium ion is proposed. The dependence of the average energy of relativistic electrons on the flux density in the range of 1015 – 1018 W cm−2 is calculated. The time dependence of the average electron energy during the laser pulse in the form of approximating formulas is constructed. The typical time for the development of stochastic heating of electrons is determined. It is found that the stochastic acceleration process weakly depends on the laser pulse duration, when the latter exceeds several hundred periods of the electromagnetic wave.

Two‐Dimensional Vlasov Simulations of Fast Stochastic Electron Heating in Ionospheric Modification Experiments

AbstractIonospheric heating experiments using high‐frequency ordinary (O)‐mode electromagnetic waves have shown the induced formation of magnetic field‐aligned density striations in the ionospheric F region, in association with lower hybrid (LH) and upper hybrid (UH) turbulence. In recent experiments using high‐power transmitters, the creation of new plasma regions and the formation of descending artificial ionospheric layers (DAILs) have been observed. These are attributed to suprathermal electrons ionizing the neutral gas, so that the O‐mode reflection point and associated turbulence is moving to a progressively lower altitude. We present the results of two‐dimensional (2‐D) Vlasov simulations used to study the mode conversion of an O‐mode pump wave to trapped UH waves in a small‐scale density striation of circular cross section. Subsequent multiwave parametric decays lead to UH and LH turbulence and to the excitation of electron Bernstein (EB) waves. Large‐amplitude EB waves result in rapid stochastic electron heating when the wave amplitude exceeds a threshold value. For typical experimental parameters, the electron temperature is observed to rise from 1,500 K to about 8,000 K in a fraction of a millisecond, much faster than Ohmic heating due to collisions which occurs on a timescale of an order of a second. This initial heating could then lead to further acceleration due to Langmuir turbulence near the critical layer. Stochastic electron heating therefore represents an important potential mechanism for the formation of DAILs.

RF power transfer efficiency of inductively coupled low pressure H2 and D2 discharges

The RF power transfer efficiency and the relevant power absorption mechanisms of inductively heated hydrogen and deuterium plasmas are investigated in the low-pressure region between 0.25 and 10 Pa. The discharges are generated in a cylindrical vessel via a helical coil applying a frequency of 1 MHz and delivered RF powers up to 800 W. The power transfer efficiency η is quantified by a subtractive method that relies on the measurement of the delivered RF power and of the RF current through the plasma coil both with and without discharge operation. By means of optical emission spectroscopy and electrical probe measurements, the key plasma parameters are obtained. For both H2 and D2, the relative behavior of the power transfer efficiency is well comparable, which increases with increasing delivered RF power and describes a maximum at pressures between 1 and 3 Pa where more than of the provided power are absorbed by the plasma. The observed relative dependencies of η on the operational parameters are found to be well explained by an analytical approach that considers the power absorption by the plasma via evaluating the RF plasma conductivity based on the measured plasma parameters. At the parameters present, non-collisional stochastic heating of electrons has to be considered for pressures , while collisional heating dominates at higher pressure. Molecular dissociation is found to have a significant influence on the power transfer efficiency of light molecular discharges. The direct comparison of H2 and D2 identifies the higher atomic density in deuterium to cause a systematically increased power transfer efficiency due to an increased ionization rate in the present electron temperature region.

Transition from Coherent to Stochastic electron heating in ultrashort relativistic laser interaction with structured targets

Relativistic laser interaction with micro- and nano-scale surface structures enhances energy transfer to solid targets and yields matter in extreme conditions. We report on the comparative study of laser-target interaction mechanisms with wire-structures of different size, revealing a transition from a coherent particle heating to a stochastic plasma heating regime which occurs when migrating from micro-scale to nano-scale wires. Experiments and kinetic simulations show that large gaps between the wires favour the generation of high-energy electrons via laser acceleration into the channels while gaps smaller than the amplitude of electron quivering in the laser field lead to less energetic electrons and multi-keV plasma generation, in agreement with previously published experiments. Plasma filling of nano-sized gaps due to picosecond pedestal typical of ultrashort pulses strongly affects the interaction with this class of targets reducing the laser penetration depth to approximately one hundred nanometers. The two heating regimes appear potentially suitable for laser-driven ion/electron acceleration schemes and warm dense matter investigation respectively.

Threshold Conditions for Terahertz Laser Discharge in Atmospheric Gases

In this study, we accurately measured the breakdown thresholds in four atmospheric gases using the high-power terahertz radiation of the Novosibirsk free electron laser (NovoFEL). The breakdown intensities of the 130-μm radiation in a form of 74-ps pulses were equal to 1.1–1.4 GW/cm2. These data have been compared with calculations based on a phenomenological criterion for a breakdown and the classical theory of stochastic microwave heating of electrons. Presented are threshold conditions for a quasi-continuous plasma discharge that is maintained by means of a sequence of pulses of the NovoFEL. At a pulse repetition rate of 5.6 MHz, the discharge quenching thresholds are 15–60% lower than the breakdown thresholds depending on the amount of plasma emerging.