Hot Electron Distribution Function Research Articles

Hot-tail electrons’ impact on assimilation and injection penetration of D2 shattered pellet injections

The assimilation and the penetration of injected materials play significant roles in the mitigation efficiency of shattered pellet injection (SPI) as a disruption mitigation system (DMS), hence an accurate description of the fragment ablation rate is desirable. Current mainstream 3D MHD codes modelling SPIs mostly assume instantaneous thermalization between the previously hot ambient electrons and the newly released cold electrons. This could result in underestimation of the ablation rate if the hot electron thermalization time is comparable or even longer than the fragment flying time across flux tubes, putting the validity of these 3D SPI simulations into question. To resolve this doubt, we hereby investigate the thermalization dynamics and the overall hot-electron impact. The finite-time collisional thermalization of hot-tail electrons in a rapidly cooling plasma, as well as the so-called ‘self-limiting’ effect are considered. The former effect tends to deplete the colder population within a hot-tail species, while the latter is found to preferentially deplete the higher energy population. The combined result is found to cause an almost self-similar decay of the hot electron distribution function, while its shape does not deviate much from that of Maxwellian distribution and the mean energy does not change much during the thermalization process. Based on this observation, axisymmetric JOREK D2 SPI simulations were carried out with additional hot-tail contribution to evaluate their overall impact onto the injection assimilation and penetration. It is found that the hot-tail effect indeed causes enhanced assimilation and shallower penetration, although the overall effect depends on the exact injection configuration, with the slow injection showing negligible hot-tail effect while the fast single non-shattered pellet case shows drastic hot-tail ablation enhancement. For ITER-like SPI parameters, there is no significant deviation in the total assimilation, but some deviation in the injection penetration is observed for the fast injection velocity cases.

The Generation of Saturn's Aurora at Lower Latitudes by Electrostatic Waves

AbstractIn the present paper we have modeled diffuse auroral emissions, which have been observed at lower latitudes as compared to the main auroral arc at Saturn. It is generally accepted that these emissions are generated by precipitation of hot population of magnetospheric electrons on the closed field lines. We have considered the pitch angle diffusion by electrostatic electron cyclotron harmonic waves as the mechanism to diffuse trapped electrons into the atmospheric loss cone. Electrons are thereby precipitated into the atmosphere and excite the neutral atmospheric constituents producing auroral emissions. Calculation of ultraviolet emission intensities has been performed at two L‐shells 5.35 and 7.0. Observed hot electron distribution functions and observed electrostatic electron cyclotron harmonic wave characteristics have been used in the study. Intensities of Lyman‐alpha emission from excitation of atomic H and Lyman‐alpha produced from dissociative excitation of H2 have been calculated, obtaining the values 20.1 R (1.8 R) and 1.6 kR (0.29 kR), respectively, for both L‐shells 7.0 (5.35).Further, intensities of Lyman and Werner bands of H2 are also calculated. These have the values 7.50 kR (1.43 kR) and 7.52 kR (1.49 kR), respectively, for L‐shells 7.0 (5.35). It is observed that the volume excitation rates of these four excitations peak at an altitude of about 2,000 km. From the range‐energy relation in H2 gas it is estimated that the electrons producing these excitations should have energies less than about 250 eV.

Hot electrons in metal films at low temperatures (Review)

This review discusses research completed as a result of the author's cooperation with the Department of Igor Mikhailovich Dimitrenko, from 1975 to 1992. Based on kinetic equations for electron and phonon distribution functions, we theoretically considered hot electrons at low temperatures in metal films deposited on dielectric substrates with high thermal conductivity. We present a brief analysis of the major results related to hot electrons in superconducting films, the problem of heat removal from a sample, the form of a hot electron distribution function when thermalization criterion is not satisfied, the size effect in heat transfer from metal films, the tunneling of hot electrons, as well as the generalization of these results for metals with arbitrary dispersion of electrons and phonons in terms of Eliashberg spectral functions.

Analytic model of the energy distribution function for highly energetic electrons in magnetron plasmas

This paper analyzes a situation which is common for magnetized technical plasmas such as dc magnetron discharges and high power impulse magnetron sputtering (HiPIMS) systems, where secondary electrons enter the plasma after being accelerated in the cathode fall and encounter a nearly uniform bulk. An analytic calculation of the distribution function of hot electrons is presented; these are described as an initially monoenergetic beam that slows down by Coulomb collisions with a Maxwellian distribution of bulk (cold) electrons, and by inelastic collisions with neutrals. Although this analytical solution is based on a steady-state assumption, a comparison of the characteristic time-scales suggests that it may be applicable to a variety of practical time-dependent discharges, and it may be used to introduce kinetic effects into models based on the hypothesis of Maxwellian electrons. The results are verified for parameters appropriate to HiPIMS discharges, by means of time-dependent and fully kinetic numerical calculations.

Concerning mechanisms for the zebra pattern formation in the solar radio emission

The nature of the zebra patterns in continuous type-IV solar radio bursts is discussed. The most comprehensively developed models of such patterns involve mechanisms based on the double plasma resonance and plasma wave-whistler interaction. Over the last five years, there have appeared a dozen papers concerning the refinement of the mechanism based on the double plasma resonance, because, in its initial formulation, this mechanism failed to describe many features of the zebra pattern. It is shown that the improved model of this mechanism with a power-law distribution function of hot electrons within the loss cone is inapplicable to the coronal plasma. In recent papers, the formation of the zebra pattern in the course of electromagnetic wave propagation through the solar corona was considered. In the present paper, all these models are estimated comparatively. An analysis of recent theories shows that any types of zebra patterns can form in the course of radio wave propagation in the corona, provided that there are plasma inhomogeneities of different scales on the wave path. The superfine structure of zebra stripes in the form of millisecond spikes with a strict period of ∼30 ms can be attributed to the generation of continuous radio emission in the radio source itself, assuming that plasma inhomogeneities are formed by a finite-amplitude wave with the same period.

X-ray polarization spectroscopy to study energy transport in ultra-high intensity laser produced plasmas

X-ray polarization spectroscopy was studied to derive directly the velocity distribution function (VDF) of hot electrons propagating in plasma created with a high intensity laser pulse. Polarization measurement was made at around 1018 W/cm2 using a laser pulse (∼10 J in ∼1 ps) from Alisé facility at CEA/CESTA. Chlorinated triple-layer targets were irradiated, and C1 Heα line was observed with an x-ray polarization spectrometer. Polarization degrees were measured as a function of the target overcoat thickness. It is found that the polarization is weakly negative for thin coating, but becomes positive, and finally zero for thick coating. This result is consistent with predictions made with a time-dependent atomic kinetics code developed to gain an insight into the generation of polarized C1 Heα radiation. The de-polarization on the surface is attributed to excessive bulk electron temperature and that in the deep region to elastic-scattering processes by the isotropic bulk electrons in dense region.

Stopping power and range of energetic electrons in dense plasmas of fast-ignition fusion targets

Current theoretical predictions of the stopping range of fast electrons in the dense cores of fast-ignition fusion targets differ by about a factor of 2. Inconsistencies in the previous derivations are discussed and correct values of the stopping power, scattering coefficients, and ranges of fast electrons are obtained. Such more-accurate results can be used in theoretical studies of the ignition conditions and particles-in-cell and Monte Carlo simulations of the collisional electron transport in the plasma of fast-ignition targets. Convenient approximate relations for the stopping range and angular moments of the hot-electron distribution function are also obtained.

Monte Carlo simulation of hot electron effects in compensated GaN semiconductor at moderate electric fields

The electron distribution function and transport characteristics of hot electrons in GaN semiconductor are calculated by the Monte Carlo method. We studied the electron transport at temperatures of 10, 77, and 300 K under low and moderate electric fields. We found that, at low temperatures and low electric fields (a few hundreds of V/cm), the second ohmic region is to be observed on the I-V characteristic. In this case, the mean energy is very slowly dependent on the field. The streaming effect can occur in bulk GaN with low electron concentration (<10 16 cm -3 ) at low temperatures and electric particularly GaN, differ from other semiconductor А III В V compounds well studied at the present moment. The nitrides have specific material characteristics: the large optical phonon energy eLO , the large energy splitting between the Γ-minimum and the lowest satellite valleys in the conduction band ∆e , and strong electron-polar- optical-phonon coupling (characterized by the Frohlich constant α). For GaN, these quantities are equal to eLO ≈ 0.092 eV, ∆e ≈ 1.4 - 1.8 eV (3), and α = 0.41, respectively. These material properties allow one to assume the existence of new electron phenomena at a moderate electric field which are hardly to be observable in other known polar semiconductors such as GaAs. The one of such effects is the streaming regime induced by optical phonon emission. In this regime, the electron motion is quasiperiodic in the energy space with alternating quasiballistic acceleration and emission of a polar optical phonon. The streaming regime can be realized at low lattice temperatures (10 - 77 K) and low electron concentrations (10 14

Hot electron distribution function for the Boltzmann equation with analytic bands

The shape of the electron energy distribution (EED) is of paramount importance in order to predict disruptive phenomena in semiconductor devices. Monte Carlo simulations with parabolic bands prove that the EED tail is maxwellian [1], [2], and several analytic euristic models have been introduced for modeling the EED in the bulk case [3], [4]. Starting form the Bolzmann transport equation in the bulk case, with quasi parabolic band, scattering with impurities, acoustic and optical phonons, we prove analytically that its EED, for large values of the energy e, is of the following type

Electron acceleration via collisions with ions in plasma under the action of a relativistically strong laser field

Electron-ion collisions in plasma in a strong electromagnetic field are considered in the ultrarelativistic limit (in which the vector potential A is such that a = eA/mc2 ≫ 1). Expressions relating the electron drift coordinates and momentum to those in the laboratory frame are obtained using exact canonical transformations with allowance for adiabatic effects. The appearance of ultrafast particles with a maximum energy proportional to the third power of the laser pulse vector potential is predicted. Expressions for the energy (and number) distribution function of such high-energy (hot) electrons appearing as a result of electron-ion collisions are obtained. These distribution functions obey a power law, which agrees with the results recently obtained by Mangles et al. [1] in experiments with a petawatt laser.

Hot electron velocity distribution in ultra-short laser produced plasma diagnosed with X-ray polarization spectroscopy

Polarization degree of helium-like Cl-Hea line (1s 2 1 s 0 - ls2p 1 P 1 ) from a chrolinated triple-layer target was measured using a 130 fs laser pulse at 10 17 W/cm 2 . The polarization degree was given as a function of overcoat thickness. It was found that the emission from a layer closer to the target surface is polarized parallel to the surface direction whereas emission from a deeper region in perpendicular to the surface. The experimental result was analyzed using a two dimensional (2D) Maxwellian distribution function for hot electrons. Beam-like distribution was found in the depth of plasma.

Study of fast electron transport in hot dense matter using x-ray spectroscopy

Experimental study on energy transport in ultra-high intensity laser plasma was made. X-ray emission from a triple-layer target irradiated at 1019 W cm−2 was observed with x-ray spectrographs, monochromatic imagers and an x-ray polarimeter to provide a temperature profile in the depth of the target, lateral extension of the heated region and the velocity distribution function of hot electrons. For PW plasma, a very shallow region (∼0.5 µm from the target surface) was heated up to 650 eV but the temperature of deeper region (up to 5 µm) was around 100 eV. These depths are much shorter than those expected from the classical penetration of the hot electrons. The localized energy deposition is also found for the plasma generated at 1017 W cm−2, and the degree of polarization of the helium-like Cl–Heα line (1s2 1S0–1s2p 1P1) from the surface region is polarized parallel to the surface direction whereas that from a deeper region is in perpendicular to it. The experimental result is analysed using a two-dimensional Maxwellian distribution function for hot electrons. Beam-like distribution was found in the depth of plasma.

X-ray line polarization spectroscopy to study hot electron transport in ultra-short laser produced plasma

Observation is reported of the polarization of the helium-like Cl–He α line (1s 2 1S 0–1s2p 1P 1), at 2.79 keV emitted from a triple-layer target irradiated with a 130 fs laser pulse. The polarization degree is determined as a function of overcoat thickness of the target. It is found that the emission from a layer closer to the target surface is polarized parallel to the surface direction whereas emission from a deeper region in perpendicular to the surface. The experimental result is analyzed using a two-dimensional (2D) Maxwellian distribution function for hot electrons. Beam-like distribution was found in the depth of plasma.

X-ray polarization spectroscopy for measurement of anisotropy of hot electrons generated with ultraintense laser pulse

Polarization spectroscopy is a useful diagnostic method to measure directly the anisotropy of hot electron velocity distribution function inside ultrahigh intense laser produced plasmas. Polarization of a Cl–He α line (2.79 keV) from double-layer targets, which consist of polystyrene and chlorinated polystyrene, was observed with a toroidally curved crystal spectrograph. It was found that the line from the target surface is polarized more parallel to the surface, whereas that from a deeper region is more perpendicular to it. The polarization of emitted x rays corresponds to the shape of velocity distribution function of hot electrons. The anisotropic shape of hot electron velocity distribution function depending on depth of a target was clarified for the first time using this diagnostic method.

Hot-electron effect in spin dephasing inn-type GaAs quantum wells

We perform a study of the effect of the high in-plane electric field on spin precession and spin dephasing due to the D'yakonov--Perel' mechanism in $n$-type GaAs (100) quantum wells by constructing and numerically solving kinetic Bloch equations. We self-consistently include all scattering such as electron$∕$phonon,electron $∕$nonmagnetic impurity as well as electron--electron Coulomb scattering in our theory and systematically investigate how the spin precession and spin dephasing are affected by the high electric field under various conditions. The hot-electron distribution functions and spin correlations are calculated rigorously in our theory. It is found that the D'yakonov--Perel' term in the electric field provides a nonvanishing effective magnetic field that alters the period of spin precession. Moreover, spin dephasing is markedly affected by the electric field. The important contribution of the electron--electron scattering to spin dephasing is also discussed.

Characterization of the hot electron distribution function using six moments

The shape of the hot electron distribution function in semiconductor devices is insufficiently described using only the first four moments. We propose using six moments of the distribution function to obtain a more accurate description of hot carrier phenomena. An analytic expression for the symmetric part of the distribution function as a function of the even moments is given which shows good agreement with Monte Carlo data for both the bulk case and inside n+−n−n+ test structures. The influence of the band structure on the parameters of the distribution function is studied and proven to be of importance for an accurate description.

Group-III Nitrides Hot Electron Effects in Moderate Electric Fields

We studied the distribution function and basic characteristics of hot electrons in InN, GaN and AlN under moderate electric fields, and found that in relatively low fields (of the order of kV/cm) the optical phonon emission dominates the electron kinetics. This strongly inelastic process gives rise to a spindle-shaped distribution function and an extended portion of quasi-saturation of the current-voltage characteristics (the streaming-like regime). We prove that this hot electron regime holds for all three nitrides. We suggest that the effects can be detected by the measurement of the I-V characteristics, or the thermopower of hot electrons in the transverse direction.

Group-III Nitrides Hot Electron Effects in Moderate Electric Fields

We studied the distribution function and basic characteristics of hot electrons in InN, GaN and AlN under moderate electric fields, and found that in relatively low fields (of the order of kV/cm) the optical phonon emission dominates the electron kinetics. This strongly inelastic process gives rise to a spindle-shaped distribution function and an extended portion of quasi-saturation of the current–voltage characteristics (the streaming-like regime). We prove that this hot electron regime holds for all three nitrides. We suggest that the effects can be detected by the measurement of the I–V characteristics, or the thermopower of hot electrons in the transverse direction.

Hot-electron distribution functions in a subpicosecond laser interaction with solid targets of varying initial gradient scale lengths.

We have studied the distribution function of the hot electrons produced during the interaction of a 120-fs, 60-mJ, 800-nm wavelength and a p-polarized laser pulse with bilayered Al/Fe targets. The main pulse interacts with a preformed plasma, obtained with a controlled prepulse, whose density gradient scale length has been measured. The electron distribution function is characterized by means of the Kalpha emission of the two materials of the target as a function of the Al-layer thickness. The low-energy region (<50 keV) of the hot-electron distribution function shows no dependency in shape on the gradient scale length, but only a variation in the total number of the generated electrons. The comparison between the experimental results and the particle-in-cell and Monte Carlo calculations of the electron distribution function and the Kalpha emission is gratifying.

Phonons acoustiques chauds dans l'InP a basses temperatures

We present a numerical method of determination of steady state hot-electron and hot-phonon distribution functions. The coupled Boltzmann equations for acoustical phonons and for the electrons, in the Γ and L valleys of III–V semiconductor compounds, are solved. The computation are used for InP at 77 K. We obtain a significant modification of the distribution of hot acoustical phonons.