Warm Electron Research Articles

Anticathode effect on electron kinetics in electron beam generated E×B plasma

Abstract Electron beam (e-beam) generated plasmas with applied crossed electric and magnetic (E×B) fields are promising for low damage processing of materials with applications to microelectronics and quantum information systems. In cylindrical e-beam E×B plasmas, radial confinement of electrons and ions is achieved by an axial magnetic field and radial electric field, respectively. To control the axial confinement of electrons, such e-beam generated plasma sources may incorporate a conducting boundary known as an anticathode, which is placed on the axially opposite side of the plasma from the cathode. In this work, it is shown that varying the anticathode voltage bias can control the degree to which the anticathode collects or repels incident electrons, allowing control of warm electron (electron energies in 10-30 eV range) and beam electron population confinement. It is suggested that the effect of the anticathode bias on the formation of these distinct electron populations is also associated with the transition between weak turbulence and strong Langmuir turbulence.

Oblique instability of quasi-parallel whistler waves in the presence of cold and warm electron populations

Whistler waves propagating nearly parallel to the ambient magnetic field experience a nonlinear instability due to transverse currents when the background plasma has a population of sufficiently low energy electrons. Intriguingly, this nonlinear process may generate oblique electrostatic waves, including whistlers near the resonance cone with properties resembling oblique chorus waves in the Earth’s magnetosphere. Focusing on the generation of oblique whistlers, earlier analysis of the instability is extended here to the case where low-energy background plasma consists of both a “cold” population with energy of a few eV and a “warm” electron component with energy of the order of 100 eV. This is motivated by spacecraft observations in the Earth’s magnetosphere where oblique chorus waves were shown to interact resonantly with the warm electrons. The main new results are: 1) the instability producing oblique electrostatic waves is sensitive to the shape of the electron distribution at low energies. In the whistler range of frequencies, two distinct peaks in the growth rate are typically present for the model considered: a peak associated with the warm electron population at relatively low wavenumbers and a peak associated with the cold electron population at relatively high wavenumbers; 2) overall, the instability producing oblique whistler waves near the resonance cone persists (with a reduced growth rate) even in the cases where the temperature of the cold population is relatively high, including cases where cold population is absent and only the warm population is included; 3) particle-in-cell simulations show that the instability leads to heating of the background plasma and formation of characteristic plateau and beam features in the parallel electron distribution function in the range of energies resonant with the instability. The plateau/beam features have been previously detected in spacecraft observations of oblique chorus waves. However, they have been attributed to external sources and have been proposed to be the mechanism generating oblique chorus. In the present scenario, the causality link is reversed and the instability generating oblique whistler waves is shown to be a possible mechanism for formation of the plateau and beam features.

Microscopic structure of electromagnetic whistler wave damping by kinetic mechanisms in hot magnetized Vlasov plasmas

Electromagnetic transverse perturbations propagating parallel to the external magnetic field in a warm electron plasma, specifically the warm electron whistler-mode waves, are simulated in Maxwellian as well as κ distributed (with energetic tail) electrons. The Vlasov-Maxwell phase-space continuum simulations are applied to the stable and unstable (i.e. isotropic and anisotropic) VDFs. The variation of real frequency from both numerical solution of dispersion relation and simulations show limited sensitivity to electron temperature in low wave-number regime as compared to high wave number regime, however the opposite holds for the imaginary frequency or the decay rate. The analytically predicted reduction in the decay rate of the whistler-mode with increasing electron temperature is recovered by the Vlasov-Maxwell simulations. The phase-space portraits of the these cases show that after the linear damping phase of the evolution, the particles are trapped in the wave magnetic field leading to the wave amplitudes oscillating about a mean value which follow the theoretical analysis. Palmadesso and Schmidt (1971) Physics of Fluids 14, 1411.

Revisiting the Vashishta-Singwi dielectric scheme for the warm dense uniform electron fluid

The finite temperature version of the Vashishta-Singwi (VS) dielectric scheme for the paramagnetic warm dense uniform electron fluid is revisited correcting for an earlier thermodynamic derivative error. The VS scheme handles quantum mechanical effects at the level of the random phase approximation and treats correlations via the density expansion of a generalized Singwi-Tosi-Land-Sjölander (STLS) closure that inserts a parameter determined by enforcing the compressibility sum rule. Systematic comparison with quasiexact results, based on quantum Monte Carlo simulations, reveals a structural superiority of the VS scheme towards strong coupling and a thermodynamic superiority of the STLS scheme courtesy of a favorable cancellation of errors. Guidelines are provided for the construction of dielectric schemes that are expected to be more accurate but computationally costly. Published by the American Physical Society 2024

Ab Initio Path Integral Monte Carlo Simulations of the Uniform Electron Gas on Large Length Scales.

The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, materials science, and related disciplines. At finite temperatures, the gold standard is given by ab initio path integral Monte Carlo (PIMC) simulations, which do not require any empirical input but exhibit an exponential increase in the required computation time for Fermionic systems with an increase in system size N. Very recently, computing Fermionic properties without this bottleneck based on PIMC simulations of fictitious identical particles has been suggested. In our work, we use this technique to perform very large (N ≤ 1000) PIMC simulations of the warm dense electron gas and demonstrate that it is capable of providing a highly accurate description of the investigated properties, i.e., the static structure factor, the static density response function, and the local field correction, over the entire range of length scales.

Interaction of inhomogeneous warm electron beam with collisional cold plasma

The linear interaction of a warm non-homogeneous electron beam (EB) with a non-homogeneous, unmagnetized, collisional cold plasma is investigated. The inhomogeneity and warmness of beam which leads to electric field amplification have no effect on the dielectric of the unmagnetized plasma. The study revealed that the dielectric constant remains unaffected by the warmness of the beam whereas the amplification of the electric field is affected by the warmness of the beam.

Potential for electron acoustic mode in the coma of a weakly outgassing comet

This study aims to explore the electron acoustic (EA) mode in the vicinity of comet 67P/Churyumov–Gerasimenko, considering the existence of multiple electron species. In Region I, where all three suprathermal, warm and cold electron populations present and in Region II, where only warm and cold electrons present there is a chance to observe the EA mode for the plasma parameters measured at the comet. At smaller wave number (k), hotter electrons whereas at larger k, the cold electrons cause damping of the mode, and the mode only propagates at intermediate wave lengths. In these regions, it is determined that the mode observation enhances with the streaming speeds of hotter species, and it could be observed even for , which is not possible at lower or in the absence of drift speeds. In Region III, both warm and suprathermal electrons significantly damp the mode and hence, it is non-observable for the reported plasma parameters, and the mode could be only observable for the temperature ratio and surprisingly, the most favorable density for the observation is . Here, and stand for suprathermal and warm electron temperatures, respectively.

(Digital Presentation) Temporal Evolution of Kinetic Energy in Two Different Plasma Systems

During the last few decades, simulation has emerged as a powerful new tool. Numerous branches of science and engineering have been revolutionized by computer simulations. Through the use of particle-in-cell simulation systems comprising many species, including electrons, ions, neutrals, molecules, dust particles, etc., are studied by the plasma research community. The current work attempts to investigate the kinetic energy behavior in two various electrostatic plasma systems using a 1D PIC simulation. Two homogeneous and non-collisional systems are considered. In the first system, just cold electrons are present. Along with cold electrons, the second system also contains electrons with a thermal velocity of 0.4 ωpe/K . In other words, the second system includes two kinds of electrons (cold and warm electrons). The same initial perturbation is applied to both systems at t=0 s. Ions are assumed to be infinitely massive and only serve as a neutralizing background for electrons.Diagrams of I, II, and III represent the kinetic energy of cold electrons, kinetic energy of electrons with a thermal velocity of 0.4 ωpe/K, and the total kinetic energy, respectively. It is worth noting that kinetic energy of cold electrons is equal to total kinetic energy in the first system. From the comparison of Figs. 1(a) and (b), it can be understood that when there is a cold type of electron in the system, the particles receive energy from the wave, but in a system that contains two types of cold and warms electrons, only warm electrons will receive energy from the wave and the kinetic energy of these warm particles increases. In contrast to Fig. 1(a), cold electrons give energy to the system. Additionally, in both cases, the total kinetic energy increases and as time goes on, the system approximates to stability and fluctuations decline. This result indicates that not only all the initial energy is not absorbed by the environment, but also a portion of it will remain in the medium. Figure 1

Non-thermal Tomonaga-Luttinger liquid eventually emerging from hot electrons in the quantum Hall regime

Dynamics of integrable systems, such as Tomonaga-Luttinger (TL) liquids, is deterministic, and the absence of stochastic thermalization processes provides unique characteristics, such as long-lived non-thermal metastable states with many conserved quantities. Here, we show such non-thermal states can emerge even when the TL liquid is excited with extremely high-energy hot electrons in chiral quantum-Hall edge channels. This demonstrates the robustness of the integrable model against the excitation energy. Crossover from the single-particle hot electrons to the many-body TL liquid is investigated by using on-chip detectors with a quantum point contact and a quantum dot. The charge dynamics can be understood with a single-particle picture only for hot electrons. The resulting electron-hole plasma in the TL liquid shows a non-thermal metastable state, in which warm and cold electrons coexist without further thermalization. The multi-temperature constituents are attractive for transporting information with conserved quantities along the channels.

Probe experiment on basic plasma parameter investigation in a quasi-gasdynamic ion source GISMO

Plasma parameters in a 28 GHz gasdynamic continuous electron cyclotron resonance discharge (ECR) with a high volumetric energy input were investigated with a Langmuir probe. The knowledge of the dependencies of plasma density and temperature on external parameters is useful for tuning the ECR source to the desired mode of operation. The design features of the plasma chamber and the configuration of the magnetic field made it possible to use the approximation a non-magnetized flat probe to calculate the temperature and electron density at various gas pressures and power of the heating microwave. A movable tungsten probe was used, allowing for studying plasma parameters along the magnetic field at various distances from the plasma electrode. At high powers, the electron density in the plug turned out to be close to the cutoff density (about 10 13 cm − 3). A fraction of warm ( > 30 eV) electrons, appearing at high powers, was found, which explains the formation of a pure proton beam in a number of experiments at the same facility. The abrupt increase in the temperature of the warm fraction with power was also found, which makes it of great interest to perform experiments on a multi-charged ions production in heavy gases.

Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons.

We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within the Kohn-Sham density functional theory for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of the warm dense matter. Generated by laser-induced compression and heating in the laboratory, the warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing with the exact quantum Monte Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used, compared with the previously reported results for the PBE, PBEsol, local-density approximation, and AM05 functionals; B3LYP, on the other hand, does not perform well for the considered system. Additionally, the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are more accurate for the density response properties than SCAN in the regime of partial degeneracy.

On the Chemical Potential of Many-Body Perturbation Theory in Extended Systems.

Finite-temperature many-body perturbation theory in the grand-canonical ensemble is fundamental to numerous methods for computing electronic properties at nonzero temperature, such as finite-temperature coupled-cluster. In most applications it is the average number of electrons that is known rather than the chemical potential. Expensive correlation calculations must be repeated iteratively in search for the interacting chemical potential that yields the desired average number of electrons. In extended systems with mobile charges the situation is particular, however. Long-ranged electrostatic forces drive the charges such that the average ratio of negative and positive charges is one for any finite chemical potential. All properties per electron are expected to be virtually independent of the chemical potential, as they are in an electric wire at different voltage potentials. This work shows that per electron, the exchange-correlation free energy and the exchange-correlation grand potential indeed agree in the infinite-size limit. Thus, only one expensive correlation calculation suffices for each system size, sparing the search for the interacting chemical potential. This work also demonstrates the importance of regularizing the Coulomb interaction such that each electron on average interacts only with as many electrons as there are electrons in the simulation, avoiding interactions with periodic images. Numerical calculations of the warm uniform electron gas have been conducted with the Spencer-Alavi regularization employing the finite-temperature Hartree approximation for the self-consistent field and linearized finite-temperature direct-ring coupled-cluster doubles for treating correlation.

Two-phonon scattering in nonpolar semiconductors: A first-principles study of warm electron transport in Si

The ab-initio theory of charge transport in semiconductors typically employs the lowest-order perturbation theory in which electrons interact with one phonon (1ph). This theory is accepted to be adequate to explain the low-field mobility of non-polar semiconductors but has not been tested extensively beyond the low-field regime. Here, we report first-principles calculations of the electric field-dependence of the electron mobility of Si as described by the warm electron coefficient, $\beta$. Although the 1ph theory overestimates the low-field mobility by only around 20%, it overestimates $\beta$ by over a factor of two over a range of temperatures and crystallographic axes. We show that the discrepancy in $\beta$ is reconciled by inclusion of on-shell iterated 2-phonon (2ph) scattering processes, indicating that scattering from higher-order electron-phonon interactions is non-negligible even in non-polar semiconductors. Further, a ~20% underestimate of the low-field mobility with 2ph scattering suggests that non-trivial cancellations may occur in the perturbative expansion of the electron-phonon interaction.

Density effect on electronic structure of warm dense matter based on X-ray fluorescence spectroscopy

Warm dense matter (WDM), a kind of transition state of matter between cold condensed matter and high temperature plasma, is one of the main research objects of high energy density physics (HEDP). Compared with the structure of isolated atom, the electron structure of WDM will change significantly because of the influences of density and temperature effect. As WDM is always strongly coupled and partly degenerate, accurate theoretical description is very complicated and the accurate experimental research is also very challenging. In this paper, the density effect on the warm dense matter electron structure based on the X-ray fluorescence spectroscopy is studied. The warm dense titanium with density larger than solid density is produced experimentally based on a specially designed hohlraum. Then, the titanium is pumped to emit fluorescence by using the characteristic line spectrum emitted by the laser irradiating the pump material (Vanadium). The X-ray fluorescence spectra of titanium with different states are diagnosed by changing the delay time between the pump laser and drive laser. The experimental fluorescence spectrum indicates that the difference in energy between <inline-formula><tex-math id="M5">\begin{document}${\mathrm{K}}_{\text{β}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231215_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231215_M5.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ {\mathrm{K}}_{\text{α}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231215_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231215_M6.png"/></alternatives></inline-formula> (<inline-formula><tex-math id="M7">\begin{document}$\Delta E_{{\mathrm{K}}_{\text{β}}\text{-}{\mathrm{K}}_{\text{α}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231215_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231215_M7.png"/></alternatives></inline-formula>) of the compressed titanium (7.2–9.2 g/cm<sup>3</sup>, 1.6–2.4 eV) is about 2 eV smaller than that of cold titanium. Two theoretical methods, i.e. finite-temperature relativistic density functional theory (FTRDFT) and two-step Hartree-Fock-Slater (TSHFS), are used to calculate the fluorescence spectrum of warm dense titanium. The calculated results indicate that the energy difference (<inline-formula><tex-math id="M10">\begin{document}$\Delta E_{{\mathrm{K}}_{\text{β}}\text{-}{\mathrm{K}}_{\text{α}}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231215_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231215_M10.png"/></alternatives></inline-formula>) decreases with the increase of density but changes slowly with the increase of temperature during the calculated state (4.5–13.5 g/cm<sup>3</sup>, 0.03–5 eV). The FTRDFT overestimates the density effect on the line shift, while TSHFS underestimates the density effect. The future work will focus on optimizing the experimental method of X-ray fluorescence spectroscopy, obtaining X-ray fluorescence spectrum of titanium with more states, and then testing the theoretical method for warm dense matter.

Streaming instability of electron-acoustic waves with nonextensive q-distributed electrons

The linear characteristics of electron-acoustic waves and associated kinetic instability are investigated in an unmagnetized electron-ion plasma containing streaming warm (hot) electrons, dynamical cool electrons and static background of the positive ions. The plasma under consideration is modeled by using a non-gyrotropic nonextensive q-distribution function in which the free energy source for wave excitation is provided by the relative directed motion of streaming warm electrons with respect to the cool electrons.In the frame work of kinetic theory, the Vlasov-Poisson equations are solved to derive the expressions for linear dispersion relation and Landau damping rate. The results are analyzed for threshold condition of wave dispersion and instability growth rate in the presence of nonextensive effects. The relevance of study to the observed situations is also described. • The plasma under consideration is modeled by using a non-gyrotropic nonextensive q-distribution function. • In the frame work of kinetic theory, the Vlasov-Poisson equations are solved to derive the expressions for linear dispersion relation and Landau damping rate. • The results are analyzed for threshold condition of wave dispersion and instability growth rate in the presence of nonextensive effects.

Electronic pair alignment and roton feature in the warm dense electron gas

The study of matter under extreme densities and temperatures as they occur, for example, in astrophysical objects and nuclear fusion applications has emerged as one of the most active frontiers in physics, material science, and related disciplines. In this context, a key quantity is given by the dynamic structure factor S(q, ω), which is probed in scattering experiments—the most widely used method of diagnostics at these extreme conditions. In addition to its importance for the study of warm dense matter, the modelling of such dynamic properties of correlated quantum many-body systems constitutes an important theoretical challenge. Here, we report a roton feature in the dynamic structure factor S(q, ω) of the warm dense electron gas, and introduce a microscopic explanation in terms of an electronic pair alignment model. Our results will have direct impact on the interpretation of scattering experiments and may provide insights into the dynamics of a number of correlated quantum many-body systems such as ultracold helium, dipolar supersolids, and bilayer heterostructures.

Nonlinear Langmuir oscillations in an ultrarelativistic degenerate quantum electron-ion plasma

The investigation of the nonlinear Langmuir associations in an ultrarelativistic, fully degenerate quantum plasma, composed of stationary ions and warm electrons is considered. The quantum hydrodynamic model with the equation of state of electrons is used to derive a nonlinear differential equation that describes the chemical potential of electrons. Then, the Runge Kutta method is used to solve this equation numerically. Hence, the profiles of the chemical potential and electron number density are graphically presented. Numerical results show that the Bohm quantum force produces small scale quantum Langmuir oscillations along with the classical oscillations. These findings are helpful in understanding the features of nonlinear Langmuir waves in various astrophysical plasmas such as planetary interiors and compact objects.

Interaction of electron acoustic solitons in auroral region for an electron beam plasma system

The propagation of linear and nonlinear electron acoustic waves (EAWs) in an unmagnetized plasma, comprising dynamical inertial electrons, hot (r, q) distributed electrons, warm electron beam, and immobile ions is studied. The linear dispersion relation is investigated for varying beam velocity. The Korteweg-de Vries (KdV) equation for EAWs is derived in the small amplitude limit. Depending on the beam density, temperature and velocity, we get a critical condition for which the quadratic nonlinearity vanishes from the plasma system. For such a condition, the modified Korteweg de Vries (mKdV) equation, with cubic nonlinearity, is derived, which admits both negative and positive potential solitary structures. It is noted that the spectral indices r and q of the generalized (r, q) distribution, the concentration of the cold, hot and the beam electrons, and the temperature ratios, significantly affect the fundamental properties of the propagation and interaction of electron acoustic solitary waves (EASWs). The types of possible overtaking interaction of two mKdV solitons are investigated. The spatial regime for the two soliton interaction is found to vary in accordance with the variation of single soliton for various plasma parameters. The results of present study may be beneficial to comprehend the interaction between two EASWs in laboratory, space and astrophysical plasmas.

Exchange-correlation effect in the charge response of a warm dense electron gas

The study of warm dense matter, widely existing in nature and laboratories, is challenging due to the interplay of quantum and classical fluctuations. We develop a variational diagrammatic Monte Carlo method and determine the exchange-correlation kernel ${K}_{\mathrm{XC}}(q;T)$ of a warm dense electron gas for a broad range of temperature $T$ and momentum $q$. We observe several interesting physics, including the $T$-dependent evolution of the hump structure and the large-$q$ tail and the emergence of a scaling relation. Particularly, by deriving an analytical form for $q\ensuremath{\rightarrow}\ensuremath{\infty}$, we obtain large-$q$ tails of ${K}_{\mathrm{XC}}$ with high precision. It is shown that the ${K}_{\mathrm{XC}}$ data can be reliably transformed into real space, which can be directly used in density-functional-theory calculations of real warm dense matter.

Spin-resolved density response of the warm dense electron gas

We present extensive ab initio path integral Monte Carlo (PIMC) results for the spin-resolved density response of the uniform electron gas at warm dense matter conditions. This allows us to unambiguously assess the accuracy of previous theoretical approximations, thereby providing valuable insights for the future development of dielectric schemes. From a physical perspective, we observe a nontrivial manifestation of an effective electron-electron attraction that emerges in the spin-offdiagonal static density response function at strong coupling, ${r}_{s}\ensuremath{\gtrsim}5$. All PIMC results are freely available online and can be used to benchmark approximations and simulation schemes.