Laboratory Plasmas Research Articles

Magnetoacoustic waves in spin-1/2 dense quantum degenerate plasma: nonlinear dynamics and dissipative effects

Abstract Within the confines of a two-fluid quantum magnetohydrodynamic model, the investigation of magnetoacoustic shock and solitary waves is conducted in an electron-ion magnetoplasma that considers electrons of spin 1/2. When the plasma system is nonlinearly investigated using the reductive perturbation approach, the Korteweg de Vries-Burgers (KdVB) equation is produced. Sagdeev’s potential is created, revealing the presence of solitary solutions. However, when dissipative terms are included, intriguing physical solutions can be obtained. The KdVB equation is further investigated using the phase plane theory of a planar dynamical system to demonstrate the existence of periodic and solitary wave solutions. Predicting several classes of traveling wave solutions is advantageous due to various phase orbits, which manifest as soliton-shock waves, and oscillatory shock waves. The presence of a magnetic field, the density of electrons and ions, and the kinematic viscosity significantly alter the properties of magnetoacoustic solitary and shock waves. Additionally, electric fields have been identified. The outcomes obtained here can be applied to studying the nature of magnetoacoustic waves that are observed in compact astrophysical environments, where the influence of quantum spin phenomena remains significant, and also in controlled laboratory plasma experiments.

Phase and Morphology of Water-ice Grains Formed in a Cryogenic Laboratory Plasma

Grains of ice are formed spontaneously when water vapor is injected into a weakly ionized laboratory plasma in which the background gas has been cooled to cryogenic temperatures comparable to those of deep space. These ice grains are levitated indefinitely within the plasma so that their time evolution can be observed under free-floating conditions. Using microscope imaging, ice grains are shown to have a spindle-like fractal structure and grow over time. Both crystalline and amorphous phases of ice are observed using Fourier transform infrared spectroscopy. A mix of crystalline and amorphous grains coexists under certain thermal conditions, and a linear mixing model is used on the ice absorption band surrounding 3.2 μm to examine the ice phase composition and its temporal stability. The extinction spectrum is also affected by inelastic scattering as grains grow, and characteristic grain radii are obtained from Mie scattering theory and compared to size measurements from direct imaging. Observations are used to compare possible ice nucleation mechanisms, and it is concluded that nucleation is likely catalyzed by ions, as ice does not nucleate in the absence of plasma and impurities are not detected. Ice grain properties and infrared extinction spectra show similarity to observations of some astrophysical ices observed in protoplanetary disks, implying that the fractal morphology of the ice and observed processes of homogeneous ice nucleation could occur as well in such astrophysical environments with weakly ionized conditions.

Influence of the shape of the anode assembly inner channel on plasma flow velocity

   This article considers how the shape of the inner channel in the anode assembly affects plasma flow velocity in a plasma torch. Three different shapes of the anode assembly were analyzed, all with a conical confusor part of 50 mm in length: with a diameter transition from 12 to 6 mm, from 12 to 8 mm, and from 12 to 10 mm. A computer experiment was performed using the finite element method and then validated by the subsequent full-scale experiment on a laboratory plasma unit. The obtained results were verified. The verification outcomes showed a satisfactory convergence and were consistent with the published data. A review of the existing plasma unit designs for powder production, application of functional coatings, and surface modification was carried out. The software packages implementing the finite element method to solve these problems were examined. The study yielded practical recommendations for consumers and developers of plasma equipment and identified the shapes of the anode assembly enabling both supersonic and subsonic plasma flow regimes.

Ion flow and dust charging at the sheath boundary in dusty plasma with an electron-emitting surface: applications to laboratory and lunar dusty plasmas

In laboratory and space plasmas, the emission of electrons from the surface significantly affects the characteristics of the plasma sheath that forms at that surface, which is crucial to understanding the overall plasma-wall interaction mechanism. In this work, the collisional fluid model is used for laboratory dusty plasma, whereas the collisionless model is used for lunar dusty plasma. We have extended the Bohm sheath criterion for the formation of the stable plasma sheath due to electron emission from the surface, loss of ion flux, and the gas pressure of the collisional laboratory dusty plasmas. It is found that ion flow at the sheath boundary is considerably influenced by the concentration of electron emission, the ion loss term, and gas pressure. The evolution of the dust charge explicitly determines the magnitude of the ion flow at the sheath boundary. The plasma parameters adopted in the present case are reliable in laboratory and space dusty plasmas, especially the dusty plasma environment on the lunar surface. The lunar surface and dust grains on the Moon become electrically charged as a result of the interaction between solar wind plasma and photoemission electrons emitted from the lunar surface. In addition, the lunar plasma sheath characteristics, dust-charging process, and stable dust levitation in the sheath region have been studied.

Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas

Abstract Broadening of hydrogenic spectral lines is an important tool in spectroscopic diagnostics of various laboratory and astrophysical plasmas. We review recent analytical advances in three areas. First, we review the analytical solution for the splitting of hydrogenic lines under the combination of a circularly polarized electromagnetic wave with a strong magnetic field. Practical applications of this solution relate to the spectroscopic diagnostic of the electron cyclotron waves and to the relativistic laser–plasma interactions. Second, we review analytical results concerning the Stark–Zeeman broadening of the Lyman-alpha (Ly-alpha) line in plasmas. These results allow for the Stark width of the Ly-alpha π-component to be used for the experimental determination of the ion density or of the root-mean-square field of a low-frequency electrostatic plasma turbulence in the situation where the Zeeman effect dominates over the Stark effects. Third, we review recent analytical advances in the area of the intra-Stark spectroscopy: three different new methods, based on the emergent phenomenon of the Langmuir-wave-caused structures (“L-dips”) in the line profiles, for measuring super-strong magnetic fields of the GigaGauss range developing during relativistic laser–plasma interactions. We also review the rich physics behind the L-dips phenomenon – because there was a confusion in the literature in this regard.

449 Does incorporation of plasma biomarkers to the Lung Injury Prediction Score improve the predictive value for development of acute respiratory distress syndrome?

OBJECTIVES/GOALS: To determine if incorporating specific laboratory values and plasma biomarkers (club cell secretory protein (CC16), matrix metalloproteinase 3 (MMP3), interleukin 8 (IL-8), protein C) to the Lung Injury Prediction (LIP) Score improves the predictive value for development of acute respiratory distress syndrome (ARDS) in ICU patients. METHODS/STUDY POPULATION: Adult patients admitted to the ICU on supplemental oxygen over baseline requirement with a LIP Score ≥6 will be included. Patients admitted to the ICU >24 hours, end-stage renal disease, decompensated heart failure, or <100 µL plasma available will be excluded. Whole blood will be collected from the core lab, centrifuged, and plasma will be stored at -80°C. Protein biomarkers will be measured using enzyme-linked immunosorbent assay. Baseline characteristics, laboratory values, ventilator parameters, and clinical outcomes will be collected from the medical record. ARDS will be defined by the Berlin criteria. Machine learning methods will be used to identify the model with the highest predictive accuracy. Area under the receiver operating characteristic curve of each model will be compared to the LIP Score. RESULTS/ANTICIPATED RESULTS: Research is in progress. Plasma samples and clinical data have been collected for 148 of the 160 samples required to achieve power. Biomarker analysis will take place after sample collection is complete. We anticipate a machine learning model incorporating laboratory values and one or more plasma biomarkers into the LIP Score will outperform the baseline LIP Score for prediction of ARDS development. DISCUSSION/SIGNIFICANCE: Delayed diagnosis and intervention contribute to poor ARDS outcomes. Current predictive models for ARDS have low accuracy and enriching these models with plasma biomarkers may increase their predictive value. Development of accurate models may facilitate earlier ARDS diagnosis and intervention as well as enrichment strategies for ARDS trials.

Landau damping effects on dust ion-acoustic solitary waves in a nonthermal pair-ion plasma

The Landau damping effects on the nonlinear propagation of dust ion-acoustic solitary waves (DIASWs) are studied in an electron-free unmagnetized collisionless dusty pair-ion plasma. The two species of nonthermal ions (positive and negative) are described by the kinetic Vlasov equations, whereas the massive charged dust grains form only the background plasma. Using the multi-scale reductive perturbation technique generalized for the applications to the Vlasov equation, we derive a modified Korteweg–de Vries (KdV) equation that governs the evolution of DIASWs with the effects of linear resonance, in particular, linear Landau damping. The properties of the phase velocity and the Landau damping rate of DIASWs are studied with the effects of positive and negative-ion nonthermality parameters ( α p , α n ), the ratios of the positive to negative ion masses (m) and temperatures (T) as well as the dust to negative-ion number density ratio (δ). It is found that, depend on the degree of positive to negative ion mass ratios (m), both of damped and growing oscillations occur in a collisionless dusty pair-ion plasma due to the resonance phenomena between the wave and the nonthermal particles of the system. The properties of the decay rates of the amplitude of the KdV soliton with a small effect of Landau damping are also studied with the above system of parameters. The results may be useful for understanding the localization of solitary pulses and associated resonance damping and/or growing oscillations of the wave in laboratory and space plasmas, in which the number density of free electrons is much smaller than that of ions and highly charged heavy, micron seized dust grains.

Research of turbulent transport due to dissipative trapped electron mode in tokamak plasmas

The purpose of this article is to study turbulent transport for laboratory plasmas in toroidal devices by gyrokinetic analyses. Linear analysis is performed to clarify the dominant mode for tokamak plasmas. The dissipative trapped electron mode (d-TEM) and the ion temperature gradient (ITG) mode are predicted using the Sugama collision model operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)]. Nonlinear gyrokinetic analysis is used to quantify turbulent transport. The nonlinear simulation results show the levels of particle and energy transport, where the d-TEM and ITG mode are unstable. The effect of zonal flows is studied by the linear and nonlinear simulation results. The results of the analysis are compared when two types of model collision operator, which are the Sugama and Lenard–Bernstein [Phys. Rev. 112, 1456 (1958)] collision model operators, are used. In this study, the simulation results using the Sugama collision operator show a stronger effect of the zonal flows on the turbulent transport than those using the Lenard–Bernstein collision operator, as predicted by the linear simulation result such as the zonal flow decay time.

Observation of turbulence-induced reduced electrostatic particle flux in the presence of QL whistlers in large laboratory plasma

The electrostatic particle flux is measured in the presence of obliquely propagating quasi-longitudinal (QL) whistler turbulence (ωci<ωLH≈ω<ωce) in the large-volume plasma device (LVPD). The QL whistler is observed with frequency band between 40 and 100 kHz, and the characteristic wave numbers k∥≪k⊥ are excited by the reflected energetic electrons via loss cone (localised mirror type magnetic geometry) formation in the presence of a transverse magnetic field [BEEF(x̂)] of electron energy filter and axial magnetic field of LVPD [Bo(ẑ)]. The effect of mirror strength on radial particle flux is explored by changing the BEEF as this variation changes the excited QL-whistler turbulence. We observed that the increase in QL-whistler turbulence level, the radial particle transport, i.e., the radial particle flux subsides, is accompanied by particle flux direction reversal from radially inward to outward.

Crater Structure Behind Reconnection Front

AbstractMagnetic reconnection is the physical process that converts the energy from the fields to the plasmas in space, astrophysical and laboratory plasmas. The Reconnection front (RF) is the structure generated in the reconnection outflow region and participates in the energy release budget. Here, we first report a novel crater structure of magnetic field behind the RF, which is well supported by both the in‐situ observations from the Magnetospheric Multiscale mission and kinetic particle‐in‐cell simulations. The theoretical explanations from the simulations suggests that the formation of the crater structure is possibly due to that high‐speed outflow electron jet from inner electron diffusion region constantly strikes the RF. From another perspective, the crater structure is the continuous impact of the electron jet. Our results can establish a new understanding of the RF and energy conversion during magnetic reconnection.

Segregation of chemical elements in the volume of powder particles during it's treatment as a method for the production of structurally graded powder materials

The paper deals with the examples of the use of microsegregation of chemical elements in powder particles of the Inconel 718 heat-resistant alloy for synthesizing on it's basis the “core-shell” type composite metal-ceramic particles in the inductively coupled plasma. A laboratory plasma treatment plant having a quartz plasmatron with a power of 40 kW and a frequency of 5.2 MHz was used. The spheroidization and degassing of the starting material were performed. It was established that, as the powder moved in the plasma flow, the explosive degassing of its particles, with the internal gas pores, took place first, and then the powder melted and spheroidized. It was shown that during the plasma treatment of the Inconel 718 powder in the presence of oxygen, microsegregation of the chemical elements contained in this alloy took place, with the formation of “core-shell” type composite metal-ceramic particles. The metal core consists predominantly of nickel, while the composition of the ceramic shell includes chromium and iron oxides, as well as spinels of the NiCr2O4 and NiFe2O4 types. By varying the oxygen concentration in the plasma, the shell thickness and the core diameter of the composite particle can be changed. The method makes it possible to synthesize metal-ceramic composite powders of the “core-shell” type for additive manufacturing.

Reactivity of the Ethenium Cation (C2H5+) with Ethyne (C2H2): A Combined Experimental and Theoretical Study.

The gas-phase reaction between the ethyl cation (C2H5+) and ethyne (C2H2) is re-investigated by measuring absolute reactive cross sections (CSs) and branching ratios (BRs) as a function of collision energy, in the thermal and hyperthermal energy range, via tandem-guided ion beam mass spectrometry under single collision conditions. Dissociative photoionization of C2H5Br using tuneable VUV radiation in the range 10.5-14.0 eV is employed to generate C2H5+, which has also allowed us to explore the impact of increasing (vibrational) excitation on the reactivity. Reactivity experiments are complemented by theoretical calculations, at the G4 level of theory, of the relative energies and structures of the most relevant stationary points on the reactive potential energy hypersurface (PES) and by mass-analyzed ion kinetic energy (MIKE) spectrometry experiments to probe the metastable decomposition from the [C4H7]+ PES and elucidate the underlying reaction mechanisms. Two main product channels have been identified at a centre-of-mass collision energy of ∼0.1 eV: (a) C3H3++CH4, with BR = 0.76±0.05 and (b) C4H5++H2, with BR = 0.22±0.02. A third channel giving C2H3+ in association with C2H4 is shown to emerge at both high internal excitation of C2H5+ and high collision energies. From CS measurements, energy-dependent total rate constants in the range 4.3×10-11-5.2×10-10 cm3·molecule-1·s-1 have been obtained. Theoretical calculations indicate that both channels stem from a common covalently bound intermediate, CH3CH2CHCH+, from which barrierless and exothermic pathways exist for the production of both cyclic c-C3H3+ and linear H2CCCH+ isomers of the main product channel. For the minor C4H5+ product, two isomers are energetically accessible: the three-member cyclic isomer c-C3H2(CH3)+ and the higher energy linear structure CH2CHCCH2+, but their formation requires multiple isomerization steps and passages via transition states lying only 0.11 eV below the reagents' energy, thus explaining the smaller BR. Results have implications for the modeling of hydrocarbon chemistry in the interstellar medium and the atmospheres of planets and satellites as well as in laboratory plasmas (e.g., plasma-enhanced chemical vapor deposition of carbon nanotubes and diamond-like carbon films).

Local dynamic responses of magnetic reconnection to three-dimensional perturbations in a laboratory plasma

The dynamic responses of magnetic reconnection to localized three-dimensional (3D) magnetic field perturbations imposed by a pair of figure-8-shaped coils are investigated in the Magnetic Reconnection Experiment (MRX) device. Both the magnetic field geometry and current sheet profiles are altered by external perturbations. For the case when the inductive electric field associated with these perturbations aligns with the preexisting reconnection electric field, O-type magnetic structures appear within an elongated current sheet. When these magnetic structures are ejected downstream at the speed close to the ion outflow velocity, the inductive electric field is enhanced considerably. Despite that the imposed perturbation amplitude is larger than 30% of the original reconnecting magnetic field, the overall reconnection process remains robust without current sheet disruptions. This technique to form O-type magnetic structures can serve as an additional experimental knob for future systematic laboratory investigations of 3D magnetic reconnection and related instabilities without disrupting two-dimensional current sheet.

Impact of external magnetic field on temperature anisotropy driven Weibel instability in a magnetized plasma

In this paper, we investigate the impact of an external magnetic field on the Weibel instability driven by temperature anisotropy in a magnetized plasma. The study provides the influence of electron temperature anisotropy, considering both cold as well as warm ions. We derive expressions for the growth rate Γ (s−1) in each case to quantify the effect of some specific parameters on the instability. For example, the growth rate is plotted against the magnetic field for three distinct cases: considering only electrons, including cold ions, and incorporating warm ions. It is observed that the growth rate decreases as the applied magnetic field increases. Furthermore, the addition of both cold and warm ions to the plasma significantly influences the observed effects. It can be explained as follows: in the presence of cold ions, the growth rate is decreased with an increase in the wave number kz (cm−1). In addition, a decrease in the growth rate is observed with an increasing wave number in the case of warm ions. Therefore, it can be seen that the Weibel instability, propelled by thermal anisotropy, holds significant implications owing to its prevalence in both astrophysical and laboratory plasmas. The findings presented here are expected to contribute to the advancements in magnetic field generation and particle acceleration in various astrophysical phenomena, including gamma-ray bursts, relativistic collisionless shock fronts, radio supernovae, and pulsar winds.

The first plasma in a newly constructed linear device for plasma turbulence research

Parameters of the first plasma in a newly built middle-size multi-functional linear plasma device named LEAD (Linear Experimental Advanced Device) were presented. The LEAD device is built to serve as a multi-purpose laboratory plasma experiment platform for various topics, including plasma turbulence, plasma-material interaction, and other fundamental plasma physics. This device is also useful for testing new diagnostic systems. It will be complementary to the HL-2A/HL-3 tokamaks in Southwestern Institute of Physics. The plasma was generated by a large-area helicon plasma source with a multi-ring antenna driven by a 13.56 MHz, 5 kW radio frequency (RF) power source. Argon plasma parameters were measured by a Langmuir probe in different external parameters including RF power, axial magnetic field, and neutral pressure. The threshold power for helicon mode transition is empirically confirmed to be 180 W. Steady-state argon plasma with a density of higher than 1019 m-3 was generated when RF power reached 3 kW. Plasma parameters are crucially influenced by the axial magnetic field. With a weak magnetic field, the radial density profile is Gaussian-like. However, with a stronger magnetic field, shear and reversion of azimuthal rotation velocity reversion appear, resulting in a hollow-shaped density profile. When further increasing the magnetic field, plasma density decreases. Steady-state plasma discharges were achieved under a wide range of argon neutral pressure from 0.1 Pa to over 10 Pa. With increasing neutral pressure, plasma density increases to its maximum at 2.5 Pa and then drops, while electron temperature drops monotonically.

Final results of the first phase of the PROTO-SPHERA experiment: obtainment of the full current stable screw pinch and first evidences of the jet + torus combined plasma configuration

In astrophysics, the boundary conditions for plasma phenomena are provided by nature and the astronomer faces the problem of understanding them from a variety of observations [Hester J J et al 1996 Astrophys. J. 456 225], on the other hand, in laboratory plasma experiments the electromagnetic boundary conditions become a major problem in the set-up of the machine that produces the plasma, an issue that has to be investigated step by step and to be modified and adapted with great patience, in particular in the case of an innovative plasma confinement experiment. The PROTO-SPHERA machine [Alladio F et al 2006 Nucl. Fusion 46 S613] is a magnetic confinement experiment, that emulates in the laboratory the jet + torus plasma configurations often observed in astrophysics: an inner magnetized jet of plasma centered on the (approximate) axis of symmetry and surrounded by a magnetized plasma torus orthogonal to this jet. The PROTO-SPHERA plasma is simply connected, i.e., no metal current conducting rod is linked to the plasma torus, while instead it is the inner magnetized plasma jet (in the following always called the plasma centerpost) that is linked to the torus. It is mandatory that no spurious plasma current path modifies the optimal shape of the plasma centerpost. Moreover, as the plasma torus is produced and sustained, in absence of any applied inductive electric field, by the inner plasma centerpost through magnetic reconnections [Taylor J B and Turner M F 1989 Nucl. Fusion 29 219], it is required as well that spurious current paths do not surround the torus on its outboard, in order not to lower the efficiency of the magnetic reconnections that maintain the plasma torus at the expense of the plasma centerpost. Boundary conditions have been corrected, up to the point that the first sustainment in steady state has been achieved for the combined plasma.

Radiation-driven diffusive transport of fast electrons in solar flares

Fast electron scattering on plasma ions due to stimulated Bremsstrahlung is investigated and modeled. Comparison with Coulomb scattering suggests that stimulated Bremsstrahlung scattering can be dominant in low-density, radiation-driven plasmas, provided that the radiation spectrum has a sufficiently high brightness temperature in the neighborhood of the plasma frequency. While stimulated Bremsstrahlung scattering cannot be easily observed in laboratory plasmas due to their small size, it should operate in large-scale astrophysical plasmas, such as those met in the flaring solar corona. The effect of the solar microwave radiation on fast-electron scattering is evaluated through a parameterized flaring corona model. We find that stimulated Bremsstrahlung greatly enhances the fast-electron scattering frequency in the flare magnetic loop, leading the transport of deka-keV electrons to occur in the diffusion regime, characterized by significant precipitation rates. This prediction is consistent with the interpretation of the above-loop-top hard x-ray and microwave emissions from the X3.1 flare of August 24, 2002. Our analysis indicates that stimulated Bremsstrahlung may play an essential role in the dynamics of fast electrons trapped in solar flare loops.

Advancements in neural network techniques for electric and magnetic field reconstruction: Application to ion radiography

In the realm of high-energy-density laboratory plasma experiments, ion radiography is a vital tool for measuring electromagnetic fields. Leveraging the deflection of injected protons, ion imaging can reveal the intricate patterns of electromagnetic fields within the plasma. However, the complex task of reconstructing electromagnetic fields within the plasma system from ion images presents a formidable challenge. In response, we propose the application of neural network techniques to facilitate electromagnetic field reconstructions. For the training data, we generate corresponding particle data on ion radiography with diverse field profiles in the plasma system, drawing from analytical solutions of charged particle motions and test-particle simulations. With these training data, our expectation is that the developed neural network can assimilate information from ion radiography and accurately predict the corresponding field profiles. In this study, our primary emphasis is on developing these techniques within the context of the simplest setups, specifically uniform (single-layer) or two-layer systems. We begin by examining systems with only electric or magnetic fields and subsequently extend our exploration to systems with combined electromagnetic fields. Our findings demonstrate the viability of employing neural networks for electromagnetic field reconstructions. In all the presented scenarios, the correlation coefficients between the actual and neural network-predicted values consistently reach 0.99. We have also learned that physics concepts can help us understand the weaknesses in neural network performance and identify directions for improvement.

Features of the Dynamic Spectrum of Signals Generated by a Wide-Aperture Electron Beam in a Large-Scale Magnetized Plasma

Electromagnetic signals generated by a wide-aperture electron beam in the laboratory plasma under conditions limitedly modeling the interaction between waves and particles in the near-Earth plasma have been studied at the large-scale Krot device. The spectrum of electromagnetic radiation includes whistler noise, which is presumably due to the current instability, and discrete (narrowband) signals near harmonics of the electron cyclotron and plasma frequencies. It has been shown that narrowband signals with a positive frequency drift that are observed at the injection of the electron beam are caused by nonstationary variations of the plasma density due to an additional ionization of a neutral gas by accelerated electrons. These effects should be taken into account to interpret nonconventional forms of the dynamic spectrum in various laboratory experiments simulating processes in the Earth’s ionosphere and magnetosphere.

Kinetic Alfvén solitary waves in a low-β plasma with regularized kappa-distributed electrons

This study examines the characteristics of small-amplitude kinetic Alfvén waves (KAWs) in a typical magnetoplasma, where both ions and electrons are considered to have a regularized kappa distribution (RKD). The restrictions imposed on the standard Kappa distribution function will be removed by considering the RKD function. The RKD can also be used for kappa areas for spectral index κ < 3/2. We then use the Korteweg–de Vries equation to investigate the KAWs in this model, which we obtained from the reductive perturbation method. It is observed that the equation’s nonlinear and dispersive coefficients are functions of the Kummar functions and the cut-off parameter. It is found that the nonlinear and dispersive coefficients of this equation depend on the Kummar functions and the cut-off parameter. Due to the negativity of the coefficients of the wave equation, only compressive KAWs can exist and propagate in this model. The numerical results demonstrate a positive correlation between the soliton’s profile (amplitude and width) with an increase in the cut-off parameter. Conversely, the superthermality has a negative influence on the soliton profile. The influence of the soliton’s propagation angle on the magnetic field’s direction is investigated. It is found that the solitary wave will not propagate in the ambient when the propagation angle θ becomes 0 or 90. Overall, the results obtained from this research can be used in space and laboratory plasmas with low β that have non-Maxwellian electrons.