Electron Thermal Velocity Research Articles

Unstable entropy mode in a current-carrying turbulent plasma and double layer formation

In this manuscript, we developed an analytical model for double layer and unstable entropy formation in current-carrying turbulent plasma. In the presence of a strong axial current, ion acoustic turbulence can give rise to enhanced anomalous resistivity and inhibited thermal conductivity. This state of uniform turbulence is, however, shown to be unstable to a purely growing axial perturbation when v02υ/ve2>k2χ, where v0,ve,υ,and χ are the electron drift velocity, thermal velocity, collision frequency, and thermal conductivity, respectively. The temperature perturbation enhances the local resistivity of electrons and raises their heating rate, further enhancing the temperature perturbation. When this tendency overpowers the opposing effect of thermal conduction, the instability grows. The nonlinear state of this instability has been analyzed and its possible relevance to the experimental results with double layer formation in a long plasma column has been discussed.

Toroidal Alfvén mode instability driven by plasma current in low-density Ohmic plasmas of the spherical tori

Due to intrinsically low magnetic fields, at low density the drift speed of the current-carrying electrons in spherical tokamaks can exceed fraction of the Alfvén speed sufficient for the excitation of the Alfvén gap modes. A particular case of the toroidal mode, observed during minor disruptions in Ohmic shots on SUNIST [Liu et al., Phys. Plasmas 23, 120706 (2016)], is considered in the present communication. Due to the negligible effect of the electron pressure gradient, the growth rate scales linearly with the drift speed, with slope inversely proportional to electron thermal velocity. In the absence of continuum damping, the threshold value of the drift speed for TAE excitation is independent of electron temperature.

Dual polarization for efficient III-nitride-based deep ultraviolet micro-LEDs

The deep ultraviolet (DUV) micro-light emitting diode (μLED) has serious electron leakage and low hole injection efficiency. Meanwhile, with the decrease in the size of the LED chip, the plasma-assisted dry etching process will cause damage to the side wall of the mesa, which will form a carrier leakage channel and produce non-radiative recombination. All of these will reduce the photoelectric performance of μLED. To this end, this study introduces polarized bulk charges into the hole supply layer (p-HSL) and the electron supply layer (n-ESL) respectively (dual-polarized structure) of the DUV μLED at an emission wavelength of 279 nm to enhance the binding of carriers and increase the injection efficiency of carriers. This is because the polarization-induced bulk charge can shield the polarized sheet charge on the interface and reduce the polarization electric field. The reduced polarization electric field in p-HSL can increase the effective barrier height of the conduction band in the p-type region and reduce the effective barrier height of the valence band. The decrease in the polarized electric field of n-HSL can reduce the thermal velocity of electrons, thereby enhancing the electron injection efficiency, reducing the Shockley–Read–Hall (SRH) recombination, and increasing the effective barrier height of the valence band. The study results indicate that the electron concentration and hole concentration of a μLED with dual polarization were increased by 77.93% and 93.6%, respectively. The optical power and maximum external quantum efficiency of μLED reached 31.04 W/cm2 and 2.91% respectively, and the efficiency droop is only 2.06% at 120 A/cm2. These results provide a new approach to solving the problem of insufficient carrier injection and SRH recombination in high-performance DUV μLEDs.

Towards ion stopping power experiments with the laser-driven LIGHT beamline

The main emphasis of the Laser Ion Generation, Handling and Transport (LIGHT) beamline at GSI Helmholtzzentrum für Schwerionenforschung GmbH are phase-space manipulations of laser-generated ion beams. In recent years, the LIGHT collaboration has successfully generated and focused intense proton bunches with an energy of 8 MeV and a temporal duration shorter than 1 ns (FWHM). An interesting area of application that exploits the short ion bunch properties of LIGHT is the study of ion-stopping power in plasmas, a key process in inertial confinement fusion for understanding energy deposition in dense plasmas. The most challenging regime is found when the projectile velocity closely approaches the thermal plasma electron velocity ( $v_{i}\approx v_{e,\text {th}}$ ), for which existing theories show high discrepancies. Since conclusive experimental data are scarce in this regime, we plan to conduct experiments on laser-generated plasma probed with ions generated with LIGHT at a higher temporal resolution than previously achievable. The high temporal resolution is important because the parameters of laser-generated plasmas are changing on the nanosecond time scale. To meet this goal, our recent studies have dealt with ions of lower kinetic energies. In 2021, laser accelerated carbon ions were transported with two solenoids and focused temporally with LIGHT's radio frequency cavity. A bunch length of 1.2 ns (FWHM) at an energy of 0.6 MeV u $^{-1}$ was achieved. In 2022, protons with an energy of 0.6 MeV were transported and temporally compressed to a bunch length of 0.8 ns. The proton beam was used to measure the energy loss in a cold foil. Both the ion and proton beams will also be employed for energy loss measurements in a plasma target.

ICE modes with high wave numbers

This work deals with high-k modes of the ion cyclotron emission (ICE)—the modes with frequencies close to ion cyclotron harmonics and wave numbers well exceeding those of fast magnetoacoustic modes (FMM). These modes exist due to finite Larmor radius of the ions. They are responsible for the ICE recently observed in the DIII-D tokamak [N. A. Crocker et al., Nucl. Fusion 62, 026023 (2022)]. The work is aimed at knowing the radial structure of high-k eigenmodes. Its analysis is relied on a comprehensive study carried out by employing a general dispersion equation for traveling waves, which allowed to group modes and determine conditions of their existence. Differential equations for various eigenmodes (standing waves) were obtained and analyzed. In particular, electrostatic modes and electromagnetic modes with various ratios of the longitudinal phase velocity to the electron thermal velocity were considered. A numerical code solving these equations was developed. It is found that high-k modes with sufficiently large poloidal mode numbers are located at the plasma periphery, and their amplitudes in the plasma core are very small. It is concluded that high-k modes are not an exceptional case, although presumably FMMs can explain most ICE experiments. They exist in plasmas with various magnitudes of β, representing different wave branches associated with finite Larmor radius of the ions. The mentioned experiment on DIII-D is discussed.

Role of electron temperature at extremely low density in negative positive ion plasma

It is pointed out that the role of electrons in the dynamics of pair ion and negative positive ion plasmas cannot be neglected even at extremely low density of electrons, i.e., ne0n+0≪mem+ (where nj0 is the background density of jth species and mj is the mass of the particles of the j-species while j = e, +, −) because electron thermal velocity is almost always larger than thermal velocities of ions, i.e., vT± ≪ vTe. An analysis of electrostatic waves in unmagnetized negative positive ion electron (NPIE) and pair ion electron (PIE) plasmas is presented for the case ωpe ≪ ωp+ (where ωpj=(4πnj0e2mj)1/2 is the plasma oscillation frequency corresponding to j-species). The electron dynamics contribute to electrostatic perturbations at ion plasma oscillation time scale at longer wavelengths for λDe2k2<1 where λDe=(Te4πne0)1/2 is the electron Debye length. On the other hand, the electron plasma wave turns into thermal wave when the conditions ωpe ≪ ωp± and 1≪λDe2k2 hold simultaneously and ion acoustic wave approaches the sum of ion plasma oscillation frequencies of positive and negative ions. The only electrostatic normal mode of such a plasma is the ion plasma wave corresponding to longer wavelengths, which also includes the contribution of electrons. The electron thermal wave is separated from plasma oscillations and electron time scale disappears with respect to electrostatic perturbations. Similar situation also occurs in plasmas having negatively charged dust particles. To elaborate these points, the analytical results are applied to the two experiments with NPIE and PIE plasmas.

Impact of Magnetic Focusing on the Transport of Energetic Electrons in the Solar Corona

Observations of Type III radio bursts discovered that electron beams with power-law energy spectra are commonly produced during solar flares. The locations of these electron beams are ~ 300 Mm above the particle acceleration region of the photosphere, and the velocities range from 3 to 10 times the local background electron thermal velocity. However, the mechanism that can commonly produce electron beams during the propagation of energetic electrons with power-law energy spectra in the corona remains unclear. In this paper, using kinetic transport theory, we find for the first time that the magnetic focusing effect governs the formation of electron beams over the observational desired distance in the corona. The magnetic focusing effect can sharply increase the bulk velocity of energetic electrons to the observed electron beam velocity within 0.4 solar radii (300 Mm) as they escape from the acceleration region and propagate upward along magnetic field lines. In more rapidly decreasing magnetic fields, energetic electrons with a harder power-law energy spectrum can generate a higher bulk velocity, producing type III radio bursts at a location much closer to the acceleration region. During propagation, the spectral index of the energetic electrons is unchanged.

Electron Bernstein wave aided Hermite cosh-Gaussian laser beam absorption in collisional plasma

In this paper, we theoretically study the electron Bernstein wave aided Hermite-Cosh-Gaussian laser beam absorption in collisional plasma with a static magnetic field. This laser beam may have the potential to couple the pre-existing electron Bernstein wave with the coupled wave frequency and wave number where and are the electron Bernstein wave and laser beam frequencies, respectively, and and are the electron Bernstein wave and laser beam wave numbers, respectively. The plasma electron oscillatory velocities associated with the coupled wave mode produce the linear and nonlinear current density. An expression for the nonlinear absorption coefficient of an electron Bernstein wave aided Hermite cosh-Gaussian laser beam is analytically derived and more concisely discussed via different relative graphs. The graphical results promise that the absorption coefficient is strongly dependent on Hermite mode index m, beam decentered parameter d associated with the cosh term, laser beam width, laser beam frequency, electron Bernstein wave frequency, electron cyclotron frequency, electron thermal velocity and collisional frequency. Nonlinear coupling, collision phenomena and laser beam decentered parameter (very sensitive parameter) play an important role in absorption processes. The association of a very small electron Bernstein wave frequency with the laser beam causes too much of an increase in the absorption coefficient compared to only the laser beam. This efficient nonlinear absorption process may be applicable to plasma electron heating and the harmonic generation process.

Interplay between electron and ion plasma waves

We report the observation of the interplay between the first kind of high-frequency electron-dominated plasma waves (EPWs) and the second kind of low-frequency ion-dominated plasma waves (IPWs) in a DC glow discharge plasma experiment. On application of positive DC voltage on a probe immersed in plasma when the drift velocity of the electrons (vd) ≈1.3× the thermal velocity of electrons (vte), it gives rise to an instability resulting in the formation of double layers (DL). Under DL conditions, the anode sheath extends deep into plasma. The DL represents a nonequilibrium plasma condition that is known for the instabilities and excitation of plasma waves. In this experiment, the effect of the monotonic increase of plasma density fluctuations (δn≈0.01%) on the evolution of DL has been studied. The interplay between EPWs and IPWs is observed in the course of this investigation. The overall plasma response on density fluctuations is recorded as floating potential fluctuations (FPFs) which vary with an increase of δn. The FPFs exhibit order-chaos-order transition with the evolution of DLs. Further analysis of the fluctuations using the wavelet method gives a spectrum in both the time and frequency domains simultaneously. Wavelet spectra reveal that the nonlinear evolution of FPFs is a consequence of the interplay between EPWs and IPWs due to the trapping and detrapping of electrons in the extended anode sheath region. These results explain that the ordered oscillation corresponds to dominant EPWs and the chaotic fluctuations are due to the coexistence of EPWs and IPWs. This new understanding may assist to study the complex plasma behaviour observed in laboratories as well as space plasmas.

Comprehensive Analysis of Copper Plasma: A Laser-Induced Breakdown Spectroscopic Approach

The emergence of diversified applications of laser-induced breakdown spectroscopy in the biomedical field, electronics, space physics, and material processing necessitates a comprehensive understanding of plasma parameters. The present work delineates the structure and evolution of copper plasma under different ambient pressures (0.01 mbar to 100 mbar) along with other plasma parameters. The study reveals the role of ambient pressure in the increase of plasma temperature (Te), electron density (Ne), number of particles in the Debye sphere, plasma frequency, inverse bremsstrahlung absorption coefficient, electron thermal velocity, electron–ion collision frequency and in the decrease of Debye length (λD) and plasma skin depth (PSD). The experimental techniques and the theoretical explanations for the variation of plasma parameters and their applications are also detailed. As the ambient pressure increases, the motion of plasma species becomes restricted, resulting in the increase of Te, calculated using the Boltzmann plot. From the values of λD, PSD, and Ne, it is understood that the copper plasma under investigation is thermally non-relativistic and satisfies McWhirter’s criterion, thus, revealing the local thermodynamic equilibrium condition of plasma. The effects of Debye shielding and stark broadening on the spectral lines are also investigated. Thus, the study helps bring newfangled dimensions to the application of plasma by exploring the possibility of tailoring plasma parameters.

A model of non-Maxwellian electron distribution function for the analysis of ECE data in JET discharges

Recent experiments performed in JET at high level of plasma heating, in preparation of, and during the DT campaign have shown significant discrepancies between electron temperature measurements by Thomson Scattering (TS) and Electron Cyclotron Emission (ECE). In order to perform a systematic analysis of this phenomenon, a simple model of bipolar distortion of the electron distribution function has been developed, allowing analytic calculation of the EC emission and absorption coefficients. Extensive comparisons of the modelled ECE spectra (at both the 2nd and the 3rd harmonic extraordinary mode) with experimental measurements display good agreement when bulk electron distribution distortions around 1-2 times the electron thermal velocity are used and prove useful for a first level of analysis of this effect.

Generating High Efficiency Terahertz Radiation From Relativistic Nano-Bunches in the Interaction of Ultrarelativistic Lasers With Thin Solid Targets

The interaction of femtosecond laser pulses with thin solid targets is one of the most efficient methods to obtain terahertz (THz) radiation. In the specific conditions, the electron of plasma surface distribution became so localized and nano-bunches are formed which causes coherent synchrotron emission (CSE). In this mechanism which occurs when the relativistic laser is obliquely incident on plasma, the plasma electrons gather in a very dense and thin layer of nanometer width. The electrons of nano-bunch can emit intense coherent emissions in different ranges of electromagnetic radiation. In this study, producing high-efficiency THz radiating from relativistic nano-bunches is discussed. The effect of plasma and nano-bunch parameters, the mobility of ions, the initial thermal velocity of electrons, and the speed of electrons are investigated. According to the results, the direct relation between the width of the nano-bunch and the efficiency is seen. The nonlinear relation between the initial thermal velocity of electrons and the THz yield is seen. In the desirable conditions, a high THz yield of up to 37% is obtained from nano-bunches with the initial thermal velocities as 0.3 of light speed.

Direct measurement of ion and electron flux ratio at their respective sheath-edges and absence of the electron Bohm criterion effects

A recent theory suggests that electrons enter electron sheaths at an electron Bohm velocity given by (T e/m e)1/2 instead of the electron thermal velocity as conventionally assumed. To test this theory, the flux density ratio Γe,se/Γi,se of electrons and ions entering their respective sheaths was directly measured via an almost continuous A i/A e area ratio scanning. The measured value agrees with the predictions assuming electrons entering the electron sheaths at their thermal velocity. The predictions associated with the electron Bohm criterion have not been found. If the predictions of such theories are true, the electron or ion presheath density drops will be very different from conventionally expected values.

Electrostatic Solitary Waves and Electron-beam Instabilities in the Separatrix Region of Magnetic Reconnection

Using 2D particle-in-cell (PIC) simulations, the generation of electrostatic solitary waves (ESWs) and the associated plasma waves in symmetric magnetic reconnection are studied, and multiple kinds of ESWs with different propagating speeds are identified. Near the current sheet in the outflow region, there are two kinds of ESWs propagating away from the X line: their propagating speeds are about 0.73V Te0 and 1.2V Te0 (where V Te0 is the initial electron thermal velocity), and their generation is associated with the Buneman instability and the electron two-stream instability, respectively. In the separatrix region, there is one kind of ESW propagating toward the X line with a propagating speed of about 1.2 V Te0, which is formed during the nonlinear evolution of the electron two-stream instability. We also run a case with a guide field, and there exist two kinds of ESWs: the ESWs propagating away from the X line can be generated near the separatrices with electron outflow, while the ESWs propagating toward the X line can be generated near the separatrices with electron inflow. The two kinds of ESWs are associated with the electron two-stream instability and the Buneman instability, respectively.

Langmuir probe characterization of spatially confined laser-induced Bismuth plasma

The influence of spatial confinement on the laser induced plasma parameters of Bismuth (Bi) at different laser irradiances ranging from 2.9 GWcm −2 to 6.2 GWcm −2 has been investigated using Langmuir probe technique. The spatial confinement is introduced with the help of metallic blocker placing at different distances of 5 mm, 10 mm and 15 mm from the target. It is observed that electron temperature ( T e ), electron density ( n e ), and electron thermal velocity ( v th,e ) of Bi plasma are significantly influenced by laser irradiance, biasing voltage and blocker distances. In the absence of blocker, maximum values of T e , n e , and v th,e , are 13 eV, 1.6 × 10 17 cm −3 and 2.4 × 10 8 cms −1 respectively, whereas, in the presence of blocker these values are significantly enhanced to 31.6 eV, 2.9 × 10 17 cm −3 and 3.7 × 10 8 cms −1 respectively. This enhancement is attributed to increased collisional frequency of plasma species after compression due to reflection of shock waves from blocker. The analytical evaluated values of work done to compress plume vary from 0.7 mJ to 0.2 mJ, whereas, the variation in plasma pressures is from 0.35 MPa to 1.47 MPa and shock pressures variation comes out to be in the range from 0.32 GPa to 0.56 GPa.

Electromagnetic Weibel instability in spatial anisotropic electron–ion plasmas

The Weibel instability due to temperature anisotropy of electrons and ions in a plasma in the presence of cold and warm ions is reported. Numerical calculations of the normalized growth rate are carried out when the frequency of electromagnetic waves is greater than or less than the thermal velocity of electrons for typical existing plasma parameters. The normalized growth rate increases with an increasing normalized wave number, and after attaining maxima, it decreases due to thermal effects. Therefore, a parabolic plot is obtained for the growth rate. The threshold values of the growth rate depend on the anisotropy parameters. On increasing the value of the temperature anisotropy ratio of either plasma component, the observed growth rate increases. There is a considerable and contrasting effect of the presence of cold and warm ions on the growth rate of the Weibel instability in the plasma. The addition of cold ions stabilizes the instability and reduces the maximum growth rate values, while the addition of warm ions to the plasma increases the instability with a considerable decrease in the domain of instability. Our theoretical investigations of the effect of temperature anisotropy on the growth rate of the Weibel instability are in good agreement with the existing experimental results.

Eliminating finite-grid instabilities in gyrokinetic particle-in-cell simulations

Finite-grid (aliasing) instabilities are known to place severe limitations on momentum-conserving particle-in-cell (PIC) methods applied to models including charge separation effects by requiring the resolution of the Debye length. Gyrokinetic models, on the other hand, generally enforce quasi-neutrality thereby removing the Debye length analytically. Recent studies with momentum-conserving PIC applied to gyrokinetic models, however, show that a manifestation of this instability exists in certain physical parameter regimes for arbitrary spatial resolution. In this paper, we show that a simple reformulation of the discrete equations, making use of a co-located discretization of the continuity equation, eliminates this instability for all practical purposes. We perform numerical dispersion analyses for both the original and reformulated schemes, including the effects of finite mean parallel velocity and finite β . We demonstrate that the reformulated scheme is numerically stable for stationary plasmas at any spatial resolution and for plasmas in which the electron mean parallel velocity is smaller than the electron thermal velocity (generally ensured by ambipolarity in plasmas of interest). This reformulation may be particularly useful for codes with complicated meshes, where high-order shape functions or energy-conserving schemes are difficult to implement. The analysis presented here may also be useful for explaining the success of previously considered methods to remove particle instabilities, such as the split-weight scheme. • A detailed numerical analysis for finite-grid instabilities in gyrokinetic particle-in-cell simulations is performed. • A reformulation of the discrete equations is proposed, which eliminates finite-grid instabilities for all practical purposes. • The simplicity of the proposed reformulation may be particularly useful when complicated meshes are involved. • The analysis presented may be useful for understanding the success of certain previously proposed schemes.

The bipolar charge plasma spectrometer (BCPS) based on the 2π-field-of-view double-channel electrostatic analyzer.

In this paper, we propose a bipolar charge plasma spectrometer based on the double-channel electrostatic analyzer for simultaneously measuring thermal ions and electrons with a 2π hemispherical field-of-view. Both ions and electrons within the wide field-of-view enter the spectrometer, pass through the variable geometric factor channel, and are then separated by the double-channel electric fields. Two microchannel plates are accommodated at the exit of the analyzer for ion and electron detection. The main performance of the spectrometer has been obtained from on-ground calibration. With the electrostatic deflectors and the cylindrically symmetric structure, the spectrometer provides simultaneous measurements of thermal ion and electron velocity distributions with a shared field-of-view of 360° (azimuth angle) by 90° (elevation angle) and a broad energy range for both ions and electrons. The ion analyzer constant and the electron analyzer constant are 11.1 and 9.7, respectively. The detecting energy range of 33.3-44.4 keV for ions and 29.1-38.8 keV for electrons can be obtained by using the sweeping electrostatic analyzer voltage range of 3-4000 V. The ion and electron energy resolutions are 9.6% and 6.1%, respectively. The variable geometric factor function provides a large geometric factor adjusting range for both ion and electron measurements by two orders of magnitude, which fulfills the requirements of a large dynamic flux range for simultaneous measurements of space thermal plasma in the solar wind and magnetosphere.

Evolution of electron cyclotron waves in a Hall-type plasma

A theoretical study of high-frequency electron waves in the plasma of a Hall-type discharge with crossed electric and magnetic fields is presented. The analysis of dispersion relations for a homogeneous weakly collisional plasma with the electron velocity distribution function obtained in the relaxation approximation is performed. It is shown that the nonequilibrium character of the electron distribution function can lead to kinetic instability of cyclotron waves. This instability occurs when the thermal velocity of electrons is comparable with the drift velocity in crossed fields. In the quasilinear approximation, a compact form of the diffusion coefficient of the distribution function in the velocity space is obtained, describing unstable modes' evolution and saturation. The analytical solutions are compared with the results of numerical simulation by the particle-in-cell method.

Excitation of electron Bernstein waves by beating of two cosh-Gaussian laser beams in a collisional plasma

In this paper, a theoretical study has been proposed for excitation of electron Bernstein waves in collisional plasma with dc magnetic field by nonlinear interactions of two cosh-Gaussian laser beams. The beat wave with frequency and wave vector , exerts a nonlinear ponderomotive force on electrons. This nonlinear force has the potential to drive the electron Bernstein wave in collisional plasma with dc magnetic field. The convective loss of waves in plasma is also discussed. An analytical formalism is developed for power going into the electron Bernstein wave with respect to total laser power. The variation of normalized potential and power distribution profile as a function of beam direction, normalized beat wave frequency, and normalized collisional frequency is demonstrated to excite Electron Bernstein waves (EBWs) under resonance conditions. The spatial shape of laser beam, optimum laser beam width parameter, decentred parameter, extreme value of electron thermal velocity and cyclotron frequency is proposed for much more excitation. This proposed theory of electron Bernstein wave excitation may be applicable for plasma heating.