Theory of Plasma Instabilities
... Currently, several possibilities for the coherent excitation of electromagnetic radiation are being considered in space plasma (see, e.g., [6,7]). All of these mechanisms assume the presence of a "population inversion" due to the suitable slope of a distribution function. ...
... There are traditional theoretical approaches [6,7] explaining the excitation and amplification of long wave pulses by electron flows in the presence of a slope of the charged particle distribution function at a velocity corresponding to the Cherenkov-type electron wave resonance. If the slope of the distribution function is absent, then in traditional models (describing various problems of plasma physics and the physics of electron masers), in which the effective length of the interaction of an electron with a wave is unlimited (as in, for example, problems for finding the instability growth rate in a linear approximation), such a flow of charged particles is usually considered to be an inert media. ...
... in the case of the zero slippage factor ε (i.e., when V gr = V φ ). At the beginning of the interaction process, when u(τ = 0) = δ, all particles are far from the wave pulse (|θ| L), and therefore, we should put a → 0 and P → 0 in Equation (6). Thus, in the adiabatic approximation, trajectories of electrons H = const are described by the following formula: ...
In this study, kinetic interaction at the Cherenkov resonance between an electromagnetic wave pulse and a flow of electrons possessing a wide velocity spread at the scale of the characteristic range of the resonant electron wave interaction is considered. Due to the absence of a distribution function slope in the range of velocities corresponding to the electron wave’s resonance, an electron’s flow is a nearly stable media from the point of view of its interaction with a long enough wave pulse. In this paper, we explain our findings on the process of electron interaction with potential relief where the wave pulse is so short that the characteristic scale of the wave amplitude’s inhomogeneity and the profile of the potential relief is comparable to the wavelength. We show that if an appropriate slippage between the phase and group velocities of the wave is provided, then the reflection process of particles from “fast” and “slow” close-to-resonance velocity fractions becomes non-symmetrical. This can provide a mechanism of amplification of short intensive wave pulses with electron flows with very large velocity spreads.
The compact experimental setup ``Solar Wind'' (IAP RAS) is designed for modeling plasma processes in a magnetic arch of the coronal solar loop type. Arc discharges at the bases of the arch create plasma with a significantly increased ionic temperature along the magnetic force line. Optical images show that the plasma rope is stratified into two belts along the upper and lower vaults of the arch or as a near-wall cylindrical layer. The system stratifies when the longitudinal ionic pressure at the top of the loop is 2 times the magnetic pressure. The indicated pressure ratio coincides with the threshold value for the development of the fire-hose instability of the Alfven wave in a plasma with temperature anisotropy. We propose a variant of the growing torsional Alfven oscillation as a mechanism for the formation of a cylindrical layer along the plasma tube wall.
This is the first report of the harmonic structure of upper hybrid waves (UHWs). Using a one-dimensional electromagnetic particle-in-cell simulation, it is demonstrated that the harmonic structure of UHWs can be generated by energetic electrons through non-linear wave-wave coupling, similar to that of lower hybrid waves by energetic ions. After the saturation of UHWs, furthermore, it is found that electron cyclotron waves (ECWs) gradually grow due to the injection of energetic electrons. The involvement of ECWs in non-linear wave-wave coupling can make the harmonic structure of UHWs more complex.
Plasma turbulence is studied via direct numerical simulations in a two-dimensional spatial geometry. Using a hybrid Vlasov-Maxwell model, we investigate the possibility of a velocity-space cascade. A novel theory of space plasma turbulence has been recently proposed by Servidio {\it et al.} [PRL, {\bf 119}, 205101 (2017)], supported by a three-dimensional Hermite decomposition applied to spacecraft measurements, showing that velocity space fluctuations of the ion velocity distribution follow a broad-band, power-law Hermite spectrum P(m), where m is the Hermite index. We numerically explore these mechanisms in a more magnetized regime. We find that (1) the plasma reveals spectral anisotropy in velocity space, due to the presence of an external magnetic field (analogous to spatial anisotropy of fluid and plasma turbulence); (2) the distribution of energy follows the prediction , proposed in the above theoretical-observational work; and (3) the velocity-space activity is intermittent in space, being enhanced close to coherent structures such as the reconnecting current sheets produced by turbulence. These results may be relevant to the nonlinear dynamics weakly-collisional plasma in a wide variety of circumstances.
Collisionless shocks are ubiquitous in space and astrophysical plasmas, and they are essential dynamical features of these systems. Lacking Coulomb collisions, these shocks are mediated by the anomalous dissipation provided by nonlinear plasma instabilities. By numerically resolving the structure of a steady-state, ion gyro- viscous shock, we show that ion gyroviscosity, alone, can produce weak (M < 1.1, where M is the sonic Mach number) shocks in a collisionless, magnetized plasma. We emphasize that this effect does not require an appeal to plasma microturbulence. Moreover, while most collisionless systems may be unsuitable to support purely gyroviscous shocks, we argue that gyro-viscous heating may be an overlooked mechanism, generally; and it may be a key driver within magnetohydrodynamic shocks at large. Representative examples include the plasma environments produced on the plasma liner experiment and the magnetized liner inertial fusion platforms.
First of a kind 6D-Vlasov computer simulations of high frequency ion Bernstein wave turbulence for parameters relevant to the tokamak edge show transport comparable to sub-Larmor-frequency gyrokinetic turbulence. The customary restriction of magnetized plasma turbulence studies to the gyrokinetic approximation may not be based on physics but only on a practical constraint due to computational cost. Deciphering turbulent transport is crucial since edge turbulence significantly influences the confinement properties of magnetically confined plasmas. Despite the high computational costs, performing 6D kinetic simulations is essential for understanding the limitations of our current models.
Published by the American Physical Society 2024
In the limit of sufficiently fast rotation, rotating mirror traps are known to be stable against the loss-cone modes associated with conventional (non-rotating) mirrors. This paper calculates how quickly a mirror configuration must rotate in order for several of these modes to be stabilized (in particular, the high-frequency convective loss cone, drift cyclotron loss cone and Dory–Guest–Harris modes). Commonalities in the stabilization conditions for these modes then motivate a modified formulation of the Gardner free energy and diffusively accessible free energy to be used for systems in which the important modes have wavevectors that are orthogonal or nearly orthogonal to the magnetic field, as well as a modification to include the effects of a loss region in phase space.
The frequency spectra of the Trivelpiece–Gould modes of a waveguide partially filled with non-neutral plasma are determined numerically by solving the dispersion equation. The modes having azimuthal number are considered. The results are presented for the entire acceptable range of electron densities, magnetic field strengths, for different values of the charge neutralization coefficient. The Cherenkov resonance condition of an ion with a diocotron mode having a finite value of the longitudinal wave vector was studied. The characteristics of resonant low-frequency electron–ion instability caused by relative azimuth motion of electrons and ions in crossed fields and by the anisotropy of the distribution function of ions are discussed. Ions are created by ionization of residual gas in the plasma volume. Due to the anisotropy, instability occurs not only in the vicinity of the resonance, but also outside it. For typical values of plasma parameters in experiments, estimations of the frequency growth rate are given. A conclusion is drawn that this instability can be the cause of the low-frequency oscillations observed in linear devices with non-neutral plasma produced in an electron beam channel.
A theoretical investigation is carried out for nonlinear electrostatic Kelvin-Helmholtz (K-H) shock waves a in magnetized electron-positron-ion viscous plasma in the presence of transport equations and non-Maxwellian particles by following the generalized (r, q) distribution function. The propagation of electrostatic K-H modes are studied both in the presence of trapped and free electrons. The nonlinear analysis with inclusion of plasma transport properties (magnetic viscosity and heat conduction) lead to nonlinear electrostatic K-H mode in the form of shock like waves by solving the modified Burgers' equation. The electrostatic K-H shocks are investigated numerically with effect of different plasma parameters such as shear velocity and non-Maxwellian distributed particles. It is observed that the striking features (viz., amplitude and width of dissipative shock through the solution of Burgers' equation) of the K-H mode are significantly modified by the effects of non-thermality of electrons and positrons both at shoulder and tails along with shear velocity due to viscosity. The relevancy of our work to the observations in space (viz., cometary comae and earth's ionosphere), astrophysical (viz., pulsars) and laboratory (viz., solid-high intense laser plasma interaction experiments) plasmas is highlighted.
The problem of the correct asymptotic construction of the radial structure of linearly unstable ion-sound electrostatic eigenmodes is studied. The eigenvalue problem with boundary conditions of the first and second kind (electrodynamic and hydrodynamic types) for the oscillations that propagate in a uniform cylindrical column of magnetized plasma along an axial homogeneous magnetic field is formulated. A method for constructing a discrete spectrum of small-scale unstable oscillations of the system based on the basic principles of geometric optics is proposed. The main idea of the method is an explicit idea of the type of boundary conditions - the conductivity and absorbing properties of the wall bounding the plasma cylinder. A dispersion relation for unstable small-scale modes destabilized due to the effects of differential rotation is derived from the Eikonal equation. For the correct construction instability growth rates spectra an universal recipe for the selection of radial wave numbers of small-scale eigenmodes in accordance with any of the types of boundary conditions is proposed.
Thermal stability is a crucial issue for the dielectric barrier discharge (DBD) plasma deicing. However, the ice blocks tend to invoke strong nonlinear heating processes, finalized with the devastating instability events, e.g., the arcing and sparking. In this paper, it is proposed that the periodic field enhancing microscale structures with nanowires could be used to reduce the thermal damage risk. The printing circuit board (PCB) based low profile DBD samples of sawtooth configuration with ZnO nanowires (SN) are prepared, and the controlled groups are the parallel-electrode configurations (P), the parallel-electrode configurations with nanowires (PN), and the sawtooth configurations without nanowires (S). It is found that: (1) The thermal stability is strongly correlated with the locally enhanced streamers, namely, the LE-streamers, due to the ice blocks. (2) The ZnO nanowires are shown to play dominant but opposite roles in the LE-streamer dynamics for the PN and SN electrode configurations, i.e., the enhancement of the streamer channel in the former, but the attenuation in the latter. (3) Uniform pattern of co-existence of the multi-LE-streamers only exists in the SN configurations. (4) The heating behavior of such a pattern is shown to be self-modulated. It heats the fastest at lower voltages but demonstrates the best thermal stability at the higher voltages when the LE-streamers in all the other three groups are ready to evolve into devastating arcs or sparks. To interpret the underlying physical mechanism, it is argued that the nonlinear effects during deicing could be effectively compressed by the decentralization of the plasma heating energy into more structure-based field enhancement sites constructed by the nano-micro electrodes. Such an illustration has been supported by further analyzing the spatial-temporal evolution of the temperature field during deicing, where linearity and uniformity are correlated to play the dominant roles in thermal stabilization. Thus, a statistical factor, ST, is suggested as an index to evaluate and predict the thermal stability of a deicing DBD plasma heat source, which is 23.9% for the SN configurations, the least compared to all the controlled groups.
Any partial notch equation, even more so a nonlinear one, including the Korteweg de Vries (KdV) equation, requires certain methodological approaches in order to find its solutions. Since, in solving specific physical problems, it is necessary to take into account the presence of a real environment, the actual point here is to take into account the dissipative term in the KdV equation, and which should be written in general form for any problem, which is the main purpose of this Letter. When solving the KdV equation, we obtain a solution in the form of a soliton, which, as is known, has the form of an inverse function on the square of the hyperbolic cosine. Therefore, when solving a problem taking into account dissipation, we need to take into account its general solutions and introduce a temporary dependence into it using the method of the inverse problem, which is done in this work. The KdV equation obtained in general form, taking into account atten-uation, can be used, for example, when solving problems of studying magnetoplasmic waves. However, the main result of the paper is the possibility of studying any dissipative phenomena in which the soliton takes part.
Magnetohydrodynamics of the Sun is a completely new up-to-date rewrite from scratch of the 1982 book Solar Magnetohydrodynamics, taking account of enormous advances in understanding since that date. It describes the subtle and complex interaction between the Sun's plasma atmosphere and its magnetic field, which is responsible for many fascinating dynamic phenomena. Chapters cover the generation of the Sun's magnetic field by dynamo action, magnetoconvection and the nature of photospheric flux tubes such as sunspots, the heating of the outer atmosphere by waves or reconnection, the structure of prominences, the nature of eruptive instability and magnetic reconnection in solar flares and coronal mass ejections, and the acceleration of the solar wind by reconnection or wave-turbulence. It is essential reading for graduate students and researchers in solar physics and related fields of astronomy, plasma physics and fluid dynamics. Problem sets and other resources are available at www.cambridge.org/9780521854719.
Plain Language Summary
Subauroral arcs radically different from usual aurora occur inside subauroral flows (SAID) with depleted density and high electron temperature. Their interpretation requires specific local distributions of electrons and vibrationally excited neutrals. In Picket Fence at ∼130–140 km, the electron distribution function (EDF) is enhanced at energies <18.75 eV. The ionospheric feedback instability within SAID generates small‐scale field‐aligned currents and electric fields nonlinearly increasing with the SAID and depletion magnitude. Via the EDF, these fields control the power going to the excitation of neutrals (the energy balance). Because the EDF deviates from a Maxwellian, we use a rigorous solution of the Boltzmann kinetic equation with the modeled fields. The resulting energy balance at ∼130–140 km corresponds to the EDF and excited neutral species required for Picket Fence. The theory predictions qualitatively agree with the STEVE features above 200 km. Besides, inside SAID with deep depletions the EDF contains many ionizing electrons at ∼170–200 km. Additional ionization changes the initial density profile and the instability development will likely be saturated when the generated fields in the whole altitude range reduce below the ionization threshold. In other words, subauroral arcs might have the transient phase with typical aurora‐like emissions that fade out afterward.
For the Vlasov equation with a self-consistent field, a connection is established between the dispersion relation and the Schur algebraic complement of the generator of the corresponding dynamical system. An estimate of the instability index is obtained in terms of the Hankel transform of the background distribution of electrons, the sign of which is determined using the saddle point method.
Magnetic measurements during dc helicity injection tokamak startup indicate Alfvénic turbulence in the injected current streams mediates magnetic relaxation and results in macroscopic plasma current drive. Localization of such activity to the injected current streams, a bias voltage dependence to its onset, and higher-order spectral analysis indicate super-Alfvénic electrons excite instabilities that drive the observed turbulence. Measured fluctuation helicity is consistent with an α-dynamo electromotive force driving net current comparable to the macroscopic equilibrium current density. These results imply new constraints for scaling local helicity injection to larger devices.
The growing demand for nano-sized and efficient semiconductors leading to a technological revolution in quantum technology has unleashed into the development of new types of compound semiconductors of nano-scale. However, the physical phenomena limiting their efficiency requires more study into the charge transportation phenomena. The study of instabilities like drift instability and modulation instability of the waves excited in a semiconductor plasma due to various force field configurations with the inclusion of quantum effects has gained recent attention, as the solid-state plasma in a semiconductor satisfies the condition for quantum plasma. The different types of instabilities, its mechanism, and effect in a semiconductor quantum plasma, have been studied in detail and presented in this article. Most of the works that has been carried out to study the instabilities have used the quantum hydrodynamic (QHD) model. The important quantum effects that are highlighted in most of the work includes the Bohm potential, exchange potential, and Fermi degenerate pressure in the nano-sized quantum semiconductors. This review work may be relevant to all who wants to have an insight on various instabilities in semiconductor quantum plasma.
The first part of the contributed chapter discuss the overview of electric propulsion technology and its requirement in different space missions. The technical terms specific impulse and thrust are explained with their relation to exhaust velocity. The shortcoming of the Hall thrusters and its erosion problems of the channel walls are also conveyed. The second part of the chapter discuss the various waves and electromagnetic instabilities propagating in a Hall thruster magnetized plasma. The dispersion relation for the azimuthal growing waves is derived analytically with the help of magnetohydrodynamics theory. It is depicted that the growth rate of the instability increases with magnetic field, electron drift velocity and collisional frequency, whereas it is decreases with the initial drift of the ions.
Ionospheric irregularities can adversely affect the performance of Global Navigation Satellite System (GNSS). However, this opens the possibility of using GNSS as an effective ionospheric remote sensing tool. Despite ionospheric monitoring has been undertaken for decades, these irregularities in multiple spatial and temporal scales are still not fully understood. This paper reviews Virginia Tech’s recent studies on multi-scale ionospheric irregularities using ground-based and space-based GNSS observations. First, the relevant background of ionospheric irregularities and their impact on GNSS signals is reviewed. Next, three topics of ground-based observations of ionospheric irregularities for which GNSS and other ground-based techniques are used simultaneously are reviewed. Both passive and active measurements in high-latitude regions are covered. Modelling and observations in mid-latitude regions are considered as well. Emphasis is placed on the increased capability of assessing the multi-scale nature of ionospheric irregularities using other traditional techniques (e.g., radar, magnetometer, high frequency receivers) as well as GNSS observations (e.g., Total-Electron-Content or TEC, scintillation). Besides ground-based observations, recent advances in GNSS space-based ionospheric measurements are briefly reviewed. Finally, a new space-based ionospheric observation technique using GNSS-based spacecraft formation flying and a differential TEC method is demonstrated using the newly developed Virginia Tech Formation Flying Testbed (VTFFTB). Based on multi-constellation multi-band GNSS, the VTFFTB has been developed into a hardware-in-the-loop simulation testbed with external high-fidelity global ionospheric model(s) for 3-satellite formation flying, which can potentially be used for new multi-scale ionospheric measurement mission design.
We study kink oscillations of a straight magnetic tube in the presence of siphon flows. The tube consists of a core and a transitional or boundary layer. The flow velocity is parallel to the tube axis, has constant magnitude, and confined in the tube core. The plasma density is constant in the tube core and it monotonically decreases in the transitional layer to its value in the surrounding plasma. We use the expression for the decrement/increment previously obtained by Ruderman and Petrukhin ( Astron. Astrophys. 631 , A31, 2019) to study the damping and resonant instability of kink oscillations. We show that, depending on the magnitude of siphon-velocity, resonant absorption can cause either the damping of kink oscillations or their enhancement. There are two threshold velocities: When the flow velocity is below the first threshold velocity, kink oscillations damp. When the flow velocity is above the second threshold velocity, the kink oscillation amplitudes grow. Finally, when the flow velocity is between the two threshold velocities, the oscillation amplitudes do not change. We apply the theoretical result to kink oscillations of prominence threads. We show that, for particular values of thread parameters, resonant instability can excite these kink oscillations.
The process and applications of a specific type of gaseous discharge—beam–plasma discharge (BPD)—are reviewed. A brief survey of the BPD theory is presented. The basic features of BPD in active geophysical experiments with injection of electron beams into Earth’s ionosphere are discussed. Studies of the physics of BPD have revealed the effects successively applied in plasma technology for processing nanoelectronic materials and structures.
A review is given of the current state‐of‐the‐art of experimental studies and the theoretical understanding of meso‐scale and small‐scale structure of the subauroral geospace, connecting ionospheric structures to plasma wave processes in the turbulent plasmasphere boundary layer (TPBL). Free energy for plasma waves comes from diamagnetic electron and ion currents in the entry layer near the plasma sheet boundary and near the TPBL inner boundary, respectively, and anisotropic distributions of energetic ions inside the TPBL and interior to the inner boundary. Collisionless heating of the plasmaspheric particles gives downward heat and suprathermal electron fluxes sufficient to provide the F‐region electron temperature greater than 6000 K. This leads to the formation of specific density troughs in the ionospheric regions in the absence of strong electric fields and upward plasma flows. Small‐scale MHD wave structures (SAPSWS) and irregular density troughs emerge on the duskside, coincident with the substorm current wedge development. Numerical simulations show that the ionospheric feedback instability significantly contributes to the SAPSWS formation. Antiparallel temperature and density gradients inside the subauroral troughs lead to the temperature gradient instability. The latter and the gradient‐drift instability lead to enhanced decameter‐scale irregularities responsible for subauroral HF radar backscatter.
Observation of low- and high-frequency backward waves in the nonlinear regime of the Buneman instability is reported. Intense low-frequency backward waves propagating in the direction opposite to the electron drift (with respect to the ion population) of ions and electrons are found. The excitation of these waves is explained based on the linear theory for the stability of the electron velocity distribution function that is modified by nonlinear effects. In the nonlinear regime, the electron distribution exhibits a wide plateau formed by electron hole trapping and extends into the negative velocity region. It is shown that within the linear approach, the backward waves correspond to the weakly unstable or marginally stable modes generated by the large population of particles with negative velocities.
Whistlers that originate from lightning strokes are among the prevalent wave phenomena in the magnetosphere, which makes their interactions with magnetospheric plasma particles of particular importance. We develop a theory that takes into account the main features of this interaction, namely, the space‐time boundedness of wave packets representing magnetospherically reflected whistlers, and the variation of frequency, wave normal vector, and amplitude inside wave packets. We take into account the inhomogeneity of the ambient plasma and the geomagnetic field, as well as relativistic effects in particle dynamics. A particular emphasis is placed on energy exchange between resonant particles as an intrinsic component part of wave‐particle interaction in plasma.
Plasma in the earth’s magnetosphere is subjected to compression during geomagnetically active periods and relaxation in subsequent quiet times. Repeated compression and relaxation is the origin of much of the plasma dynamics and intermittency in the near-earth environment. An observable manifestation of compression is the thinning of the plasma sheet resulting in magnetic reconnection when the solar wind mass, energy, and momentum floods into the magnetosphere culminating in the spectacular auroral display. This phenomenon is rich in physics at all scale sizes, which are causally interconnected. This poses a formidable challenge in accurately modeling the physics. The large-scale processes are fluid-like and are reasonably well captured in the global magnetohydrodynamic (MHD) models, but those in the smaller scales responsible for dissipation and relaxation that feed back to the larger scale dynamics are often in the kinetic regime. The self-consistent generation of the small-scale processes and their feedback to the global plasma dynamics remains to be fully explored. Plasma compression can lead to the generation of electromagnetic fields that distort the particle orbits and introduce new features beyond the purview of the MHD framework, such as ambipolar electric fields, unequal plasma drifts and currents among species, strong spatial and velocity gradients in gyroscale layers separating plasmas of different characteristics, etc. These boundary layers are regions of intense activity characterized by emissions that are measurable. We study the behavior of such compressed plasmas and discuss the relaxation mechanisms to understand their measurable signatures as well as their feedback to influence the global scale plasma evolution.
A model for the source of microwave main giant pulses (GPs) from the Crab pulsar is proposed and partly investigated. Pulse excitation takes place in a relativistic pair plasma with a strong magnetic field through the beam pulse amplifier (BPA) mechanism, in which short noise pulses of a certain type are amplified by energetic electrons at the Cherenkov resonance, even without strong anisotropy in the distribution function. The wave gain is shown to be as high as with an instability of hydrodynamic type, and wave escaping from the excitation region into the pulsar magnetosphere may not involve significant attenuation. The basic parameters of the source which explains the observed characteristics of the GP electromagnetic bursts have been analysed and are consistent with accepted ideas about physical conditions in the pulsar magnetosphere. The BPA mechanism explains the important properties of the GPs, such as the extremely short pulse duration (extreme nanoshots), the extremely high brightness temperature of the radiation source, the formation of radiation in a wide frequency range, and the possibility of radiation reaching the periphery of the pulsar magnetosphere.
Although the physics of the “sheath”, a thin layer of plasma just in front of the material surface, has been studied for more than 100 years, the peculiarities of fusion devices, such as strong magnetic field, a shallow angle at which the magnetic field lines intersect the material surface, and inhomogeneity of the plasma parameters, bring some new and important features in this topic, which are discussed in this chapter.
We present a statistical analysis of more than 2,400 electrostatic solitary waves interpreted as electron holes (EH) measured aboard at least three Magnetospheric Multiscale (MMS) spacecraft in the Earth's magnetotail. The velocities of EHs are estimated using the multispacecraft interferometry. The EH velocities in the plasma rest frame are in the range from just a few km/s, which is much smaller than ion thermal velocity VTi, up to 20,000 km/s, which is comparable to electron thermal velocity VTe. We argue that fast EHs with velocities larger than about 0.1VTe are produced by bump‐on‐tail instabilities, while slow EHs with velocities below about 0.05VTe can be produced by warm bistream and, probably, Buneman‐type instabilities. We show that typically fast and slow EHs do not coexist, indicating that the instabilities producing EHs of different types operate independently. We have identified a gap in the distribution of EH velocities between VTi and 2VTi, which is considered to be the evidence for self‐acceleration (Zhou & Hutchinson, 2018) or ion Landau damping of EHs. Parallel spatial scales and amplitudes of EHs are typically between λD and 10 λD and between 10⁻³ Te and 0.1 Te, respectively. We show that electrostatic potential amplitudes of EHs are below the threshold of the transverse instability and highly likely restricted by the nonlinear saturation criterion of electron streaming instabilities seeding electron hole formation: eΦ0≲meϖ2d||2, where ϖ = min(γ, 1.5 ωce), where γ is the increment of instabilities seeding EH formation, while ωce is electron cyclotron frequency. The implications of the presented results are discussed.
Recent simulations showed that the whistler heat flux instability, which presumably produces the most of quasi-parallel coherent whistler waves in the solar wind, is not efficient in regulating the electron heat conduction. In addition, recent spacecraft measurements indicated that some fraction of coherent whistler waves in the solar wind may propagate anti-parallel to the electron heat flux, being produced due to a perpendicular temperature anisotropy of suprathermal electrons. We present the analysis of properties of parallel and anti-parallel whistler waves unstable at electron heat fluxes and temperature anisotropies of suprathermal electrons typical of the pristine solar wind. Assuming the electron population consisting of counterstreaming dense thermal core and tenuous suprathermal halo populations, we perform a linear stability analysis to demonstrate that anti-parallel whistler waves are expected to have smaller frequencies, wave numbers, and growth rates compared to parallel whistler waves. The stability analysis is performed over a wide range of parameters of core and halo electron populations. Using the quasi-linear scaling relation, we show that anti-parallel whistler waves saturate at amplitudes of one order of magnitude smaller than parallel whistler waves, which is about 10 − 3 B 0 in the pristine solar wind. The analysis shows that the presence of anti-parallel whistler waves in the pristine solar wind is more likely to be obscured by turbulent magnetic field fluctuations because of lower frequencies and smaller amplitudes compared to parallel whistler waves. The presented results will also be valuable for numerical simulations of the electron heat flux regulation in the solar wind.
Electron beams in two-dimensional systems can provide a useful tool to study energy-momentum relaxation of electrons and to generate microwave radiation stemming from plasma-beam instabilities. Naturally, these two applications cannot coexist: if instability exists, it strongly distorts the distribution function of beam electrons; if scattering is strong, it typically suppresses plasma instabilities. Here, we study the role of inevitable electron-electron (e−e) collisions on possible plasma beam instabilities in graphene and show that scattering effects are far less trivial. We find that an unstable plasma mode associated with beam bunching is stabilized already by weak e−e collisions. Quite surprisingly, further enhancement of e−e collisions results in loss compensation and self-excitation of an ordinary graphene plasmon mode. Such instability is interpreted as viscous transfer of momentum from an electron beam to two-dimensional plasmons. Its growth rate reaches its maximum at hydrodynamic-to-ballistic crossover, when plasmon wavelength and electron mean free path are of the same order of magnitude.
The fundamental idea of Laser Wakefield Acceleration (LWFA) is reviewed. An ultrafast intense laser pulse drives coherent wakefields of relativistic amplitude with the high phase velocity robustly supported by the plasma. The structures of wakes and sheaths in plasma are contrasted. While the large amplitude of wakefields involves collective resonant oscillations of the eigenmode of the entire plasma electrons, the wake phase velocity ~ c and ultrafastness of the laser pulse introduce the wake stability and rigidity. When the phase velocity gets smaller, wakefields turn into sheaths. When we deploy laser ion acceleration or high density LWFA in which the phase velocity of plasma excitation is low, we encounter the sheath dynamics. A large number of world-wide experiments show a rapid progress of this concept realization toward both the high energy accelerator prospect and broad applications. The strong interest in this has driven novel laser technologies, including the Chirped Pulse Amplification, the Thin Film Compression (TFC), the Coherent Amplification Network, and the Relativistic Compression (RC). These in turn have created a conglomerate of novel science and technology with LWFA to form a new genre of high field science with many parameters of merit in this field increasing exponentially lately. Applications such as ion acceleration, X-ray free electron laser, electron and ion cancer therapy are discussed. A new avenue of LWFA using nanomaterials is also emerging, adopting X-ray laser using the above TFC and RC. Meanwhile, we find evidence that the Mother Nature spontaneously created wakefields that accelerate electrons and ions to very high energies.
The prebreakup arc at the inner edge of the auroral boundary is intensified upon arrival of an auroral streamer—the ionospheric signature of the earthbound mesoscale plasma flows (MPF). Yet the cause of electron precipitation enhancement only in this region remains unclear. We suggest that the intensified precipitation comes from the turbulent plasmasphere boundary layer (TPBL) that forms due to short circuiting of MPFs over the presubstorm plasmapause and overlaps with the plasma sheet (PS) inner boundary. Resonance interaction of the PS electrons with intense low‐frequency plasma waves leads to enhanced precipitation from this narrow region. Indeed, the DMSP spacecraft observations near the substorm onset show intensified electron fluxes in a narrow region near the auroral boundary, which maps into the TPBL. The same pattern observed in conjunction with postonset auroral streamers points to the common mechanism, which is the short‐circuiting process. Therefore, we suggest that the enhanced precipitation into the prebreakup arc is causally related to the MPFs' short circuiting over the plasmapause.
A plasma with an anisotropic velocity distribution of particles in a magnetic field is considered. It is shown that the Weibel instability arises in the reference frame rotating together with the particles, for example, ions. When considered in the immobile reference frame, this instability is known as the Alfvén cyclotron instability.
The stationary phase method is applied to investigate the asymptotic behavior at infinity of the Hankel transform of order zero.
High-frequency collective modes in plasma with strongly anisotropic velocity distribution of photoelectrons formed by multiphoton or above-threshold ionization of gas atoms are studied. In the case of multiphoton ionization, along with the usual electromagnetic wave, there are two additional modes. In the region of large wavelengths, the higher-frequency mode is similar to the electron Langmuir wave. Its group velocity is mainly determined by the average photoelectron velocity, and Cherenkov damping is due to small velocity dispersion of photoelectron distribution. In the region of short waves, but with a small Cherenkov damping, the group and phase velocities of this wave are close to the average electron velocity. The second mode, which has lower frequency, in the region of wavelengths smaller than the ratio of average electron velocity to the plasma frequency, corresponds to quasi-potential wave. Its dispersion law is close to the linear one. In contrast, in the region of large wavelengths, this mode corresponds to aperiodic instability, the maximum growth rate of which is comparable to the plasma frequency. The distribution of photoelectrons formed during above-threshold ionization is characterized by the large number of energy peaks, which is accompanied by increasing in the number of collective modes. In particular, in plasma with photoelectron distribution which has two energy peaks, in addition to the electromagnetic mode four extra modes are possible. In the shortwave region, all four modes correspond to the waves that are damped due to Cherenkov interaction with photoelectrons. Two of these modes in the region of relatively long wavelengths are unstable. One of these unstable modes corresponds to quasi-potential wave whose amplitude aperiodically increases with time. The reason for the instabilities is the presence of counter streams of photoelectrons.
DOI:https://doi.org/10.1103/PhysRevLett.123.219402
It is shown that the turbulent flow of acoustic waves propagating outward from the inner edge of the disk causes the accretion of the matter onto the center. The exponential amplification of waves takes place in the resonance region, . Here is the frequency of the acoustic wave, n is its azimuthal wave number, is the angular frequency of rotation of the disk. The effect is similar to the inverse Landau damping in a collisionless plasma. Energy comes from the energy of rotation of the disk. That leads to decrease of the disk angular momentum and to accretion of the matter. The value of the accretion rate dM/dt is . Here is the speed of sound of the disk gas, is the Keplerian rotation velocity, is the surface density of the disk, W is total power of the acoustic turbulence, , is the spectral power of turbulence. The presented picture of accretion is consistent with the observed variations of X-ray and optical radiation from objects whose activity is associated with accretion of gas onto them.
These lecture notes were presented by Allan N. Kaufman in his graduate plasma theory course and a follow-on special topics course (Physics 242A, B, C and Physics 250 at the University of California Berkeley). The notes follow the order of the lectures. The equations and derivations are as Kaufman presented, but the text is a reconstruction of Kaufman’s discussion and commentary. The notes were transcribed by Bruce I. Cohen in 1971 and 1972, and word processed, edited and illustrations added by Cohen in 2017 and 2018. The series of lectures is divided into four major parts: (i) collisionless Vlasov plasmas (linear theory of waves and instabilities with and without an applied magnetic field, Vlasov–Poisson and Vlasov–Maxwell systems, Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) eikonal theory of wave propagation); (ii) nonlinear Vlasov plasmas and miscellaneous topics (the plasma dispersion function, singular solutions of the Vlasov–Poisson system, pulse-response solutions for initial-value problems, Gardner’s stability theorem, gyroresonant effects, nonlinear waves, particle trapping in waves, quasilinear theory, nonlinear three-wave interactions); (iii) plasma collisional and discreteness phenomena (test-particle theory of dynamic friction and wave emission, classical resistivity, extension of test-particle theory to many-particle phenomena and the derivation of the Boltzmann and Lenard–Balescu equations, the Fokker–Planck collision operator, a general scattering theory, nonlinear Landau damping, radiation transport and Dupree’s theory of clumps); (iv) non-uniform plasmas (adiabatic invariance, guiding-centre drifts, hydromagnetic theory, introduction to drift-wave stability theory).
This chapter looks at some application of the general formalism for the linear mode analysis to characterize some properties of stable and unstable linear modes in Vlasov plasmas. It describes the relation between polarization, phase and group velocities, refractive index, cut‐off and resonant conditions of electromagnetic waves propagating in a plasma. A case more general than a single plane wave, which is of physical interest for its relevance to a variety of phenomena, is that of a wave packet. If the terminology about waves propagating in a plasma is varied and has undergone some changes over the years, it is nevertheless quite precise and well‐established in comparison with the terminology encountered when dealing with instabilities. The chapter discusses some general features and classification criteria of linear instabilities. It considers an alternative interpretation proposed to explain the physical mechanism behind collisionless damping in plasmas and some related, open issues.
This chapter discusses some general properties of the Vlasov plasma as a medium in which electrostatic and electromagnetic waves can be excited, propagate and/or become unstable. It aims to revise some key elements of the formalism which is normally used to study them. In discussing the response of the plasma to small electromagnetic perturbations, the chapter analyzes the notion of polarization charge and the meaning which should be attributed to the “dielectric function” and to conductivity and resistivity in plasmas. It considers the small amplitude limit, which makes it possible to establish linear relations between the involved fields. The chapter also discusses the general formalism developed to treat the full Vlasov–Maxwell system. The complexity related to the solution of the dispersion relation and identification of the different branches that can propagate in a collisionless Vlasov plasma can be eased by the use of reduced models, which yield polynomial approximations of the dispersion equations.
We use the one-dimensional TRISTAN-MP particle-in-cell code to model the nonlinear evolution of the whistler heat flux instability (WHFI) that was proposed by Gary et al. and Gary & Li to regulate the electron heat flux in the solar wind and astrophysical plasmas. The simulations are initialized with electron velocity distribution functions typical for the solar wind. We perform a set of simulations at various initial values of the electron heat flux and β e. The simulations show that parallel whistler waves produced by the WHFI saturate at amplitudes consistent with the spacecraft measurements. The simulations also reproduce the correlations of the saturated whistler wave amplitude with the electron heat flux and β e revealed in the spacecraft measurements. The major result is that parallel whistler waves produced by the WHFI do not significantly suppress the electron heat flux. The presented simulations indicate that coherent parallel whistler waves observed in the solar wind are unlikely to regulate the heat flux of solar wind electrons.
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