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The collision of two expanding plasma clouds is investigated, emphasizing instabilities and electron energization in the plasma mixing layer. This work is not only directly relevant to laboratory experiments with explosively created laser or z-pinch plasmas but may also elucidate naturally occurring plasma collisions in astrophysical or space physics contexts. In the previous publications [Malkov and Sotnikov, Phys. Plasmas 25, 102108 (2018) and Sotnikov et al., Phys. Plasmas 27, 122113 (2020)], we have studied, analytically and numerically, the flow emerging from interpenetrating coronas launched by two parallel wires vaporized in a vacuum chamber. The main foci of the studies have been on the general flow pattern and lower-hybrid and thin-shell instabilities that under certain conditions develop in the collision layer. The present paper centers around the initial phase of the interpenetration of the two plasmas. Two-stream ion–ion instability, efficient electron heating, and stochastic acceleration dominate plasma mixing at this phase. Both the adiabatic (reversible) electron heating and stochastic (irreversible) acceleration and heating mechanisms, powered by unstably driven electric fields, are considered. The irreversibility results from a combination of electron runaway acceleration in the wave electric fields and pitch-angle scattering on ions and neutrals. [ABSTRACT FROM AUTHOR]

The collision of two expanding plasma flows is investigated with an emphasis on the mixing flow. The study adheres to laboratory experiments where two Ohmically exploding parallel wires launch hot plasma coronas toward each other. The interpenetration and mixing of the coronas is followed by the collision and mixing of the slowly moving phases of the melted wires. In a recent publication [M. A. Malkov and V. I. Sotnikov, Phys. Plasmas 25(10), 102108 (2018)], a stationary flow that emerges from interpenetrating coronas and plasma microinstabilities in the mixing region had been studied analytically. In this present work, using two-dimensional numerical simulations, we investigate the time evolution of the flow, compare its patterns resulting from collisions of the rarefied coronas and dense wire material, and examine the macroscopic stability of the flow. The stability of the mixing layer with respect to the so-called thin-shell instability is specifically addressed. [ABSTRACT FROM AUTHOR]

Methods for inferring the electron distribution function (EDF) from a probe current–voltage trace are reviewed for moderate-collisional plasma. The explicit accounting of particle collisions, modeling sheath depletion, and electron refilling processes are rarely performed when analyzing probe measurements, yet they are critical for regime validity, EDF-profile accuracy, and space potential quantification precision. The advantages, limitations, and utilization of large-area wall probes in moderate-collisional plasma, capable of highly resolved indications of energetic electrons in plasma, are outlined. [ABSTRACT FROM AUTHOR]

Microscopic instability and the macroscopic flow pattern resulting from colliding plasmas are studied analytically in support of laboratory experiments. The plasma flows are assumed to stream radially from two separate centers. In a quasi-planar (2D) geometry, they may arise from an Ohmic explosion of two parallel wires, but similar configurations emerge from other outflows, e.g., colliding winds in binary star systems. One objective of this paper is to characterize the flow instabilities developing near the flow stagnation line. An exact solution for the Buneman-type dispersion equation is obtained without conventional simplifications. The unstable wave characteristics are key to anomalous resistivity that determines the reconnection rate of opposite magnetic fields transported with each flow toward the stagnation zone. The second objective of this paper is to calculate the stream function of the plasma shocked upon collision. We addressed this task by mapping the flow region to a hodograph plane and solving a Dirichlet problem for the stream function. By providing the instability growth rate, responsible for anomalous transport coefficients, and the overall flow configuration, these studies lay the ground for the next step. From there, we will examine the field reconnection scenarios and emerging mesoscopic structures, such as radial striata observed in the experiments. [ABSTRACT FROM AUTHOR]

This paper presents a theory for the collapse of the edge zonal shear layer, as observed at the density limit at low β. This paper investigates the scaling of the transport and mean profiles with the adiabaticity parameter α, with special emphasizes on fluxes relevant to zonal flow (ZF) generation. We show that the adiabaticity parameter characterizes the strength of production of zonal flows and so determines the state of turbulence. A 1D reduced model that self-consistently describes the spatiotemporal evolution of the mean density n ¯ , the azimuthal flow v ¯ y , and the turbulent potential enstrophy ε = ⟨ ( n ̃ − ∇ 2 ϕ ̃ ) 2 / 2 ⟩ —related to fluctuation intensity—is presented. Quasi-linear analysis determines how the particle flux Γn and vorticity flux Π = − χ y ∇ 2 v y + Π r e s scale with α, in both hydrodynamic and adiabatic regimes. As the plasma response passes from adiabatic (α > 1) to hydrodynamic (α < 1), the particle flux Γn is enhanced and the turbulent viscosity χy increases. However, the residual flux Πres—which drives the flow—drops with α. As a result, the mean vorticity gradient ∇ 2 v ¯ y = Π r e s / χ y —representative of the strength of the shear—also drops. The shear layer then collapses and turbulence is enhanced. The collapse is due to a decrease in ZF production, not an increase in damping. A physical picture for the onset of collapse is presented. The findings of this paper are used to motivate an explanation of the phenomenology of low β density limit evolution. A change from adiabatic ( α = k z 2 v t h 2 / ( | ω | ν e i ) > 1 ) to hydrodynamic (α < 1) electron dynamics is associated with the density limit. [ABSTRACT FROM AUTHOR]

An analytic solution describing an ion-acoustic collisionless shock, self-consistently with the evolution of shock-reflected ions, is obtained. The solution extends the classic soliton solution beyond a critical Mach number, where the soliton ceases to exist because of the upstream ion reflection. The reflection transforms the soliton into a shock with a trailing wave and a foot populated by the reflected ions. The solution relates parameters of the entire shock structure, such as the maximum and minimum of the potential in the trailing wave, the height of the foot, as well as the shock Mach number, to the number of reflected ions. This relation is resolvable for any given distribution of the upstream ions. In this paper, we have resolved it for a simple "box" distribution. Two separate models of electron interaction with the shock are considered. The first model corresponds to the standard Boltzmannian electron distribution in which case the critical shock Mach number only insignificantly increases from M ≈ 1.6 (no ion reflection) to M ≈ 1.8 (substantial reflection). The second model corresponds to adiabatically trapped electrons. They produce a stronger increase, from M ≈ 3.1 to M ≈ 4.5. The shock foot that is supported by the reflected ions also accelerates them somewhat further. A self-similar foot expansion into the upstream medium is described analytically. [ABSTRACT FROM AUTHOR]

Recent efforts in cosmic ray (CR) confinement and transport theory are discussed. Three problems are addressed as being crucial for understanding the present day observations and their possible telltale signs of the CR origin. The first problem concerns CR behavior right after their release from a source, such as a supernova remnant. At this phase, the CRs are confined near the source by self-emitted Alfven waves. The second is the problem of diffusive propagation of CRs through the turbulent interstellar medium. This is a seemingly straightforward and long-resolved problem, but it remains controversial and reveals paradoxes. A resolution based on the Chapman-Enskog asymptotic CR transport analysis, that also includes magnetic focusing, is suggested. The third problem is about a puzzling sharp (~10°) anisotropies in the CR arrival directions that might bear on important clues of their transport between the source and observer. The overarching goal is to improve our understanding of all aspects of the CR's source escape and ensuing propagation through the galaxy to the level at which their sources can be identified observationally. [ABSTRACT FROM AUTHOR]

The links between the microscopic dynamics and macroscopic threshold physics of the L → H transition are elucidated. Emphasis is placed on understanding the physics of power threshold scalings, and especially on understanding the minimum in the power threshold as a function of density Pthr (n). By extending a numerical 1D model to evolve both electron and ion temperatures, including collisional coupling, we find that the decrease in Pthr (n) along the low-density branch is due to the combination of an increase in collisional electron-to-ion energy transfer and an increase in the heating fraction coupled to the ions. Both processes strengthen the edge diamagnetic electric field needed to lock in the mean electric field shear for the L→H transition. The increase in Pthr (n) along the high-density branch is due to the increase with ion collisionality of damping of turbulence-driven shear flows. Turbulence driven shear flows are needed to trigger the transition by extracting energy from the turbulence. Thus, we identify the critical transition physics components of the separatrix ion heat flux and the zonal flow excitation. The model reveals a power threshold minimum in density scans as a crossover between the threshold decrease supported by an increase in heat fraction received by ions (directly or indirectly, from electrons) and a threshold increase, supported by the rise in shear flow damping. The electron/ion heating mix emerges as important to the transition, in that it, together with electron-ion coupling, regulates the edge diamagnetic electric field shear. The importance of possible collisionless electron-ion heat transfer processes is explained. [ABSTRACT FROM AUTHOR]

The proof of cosmic ray (CR) origin in supernova remnants (SNR) must hinge on full consistency of the CR acceleration theory with the observations; direct proof is impossible because of the orbit stochasticity of CR particles. Recent observations of a number of galactic SNR strongly support the SNR-CR connection in general and the Fermi mechanism of CR acceleration, in particular. However, many SNR expand into weakly ionized dense gases, and so a significant revision of the mechanism is required to fit the data. We argue that strong ion-neutral collisions in the remnant surrounding lead to the steepening of the energy spectrum of accelerated particles by exactly one power. The spectral break is caused by a partial evanescence of Alfven waves that confine particles to the accelerator. The gamma-ray spectrum generated in collisions of the accelerated protons with the ambient gas is also calculated. Using the recent Fermi spacecraft observation of the SNR W44 as an example, we demonstrate that the parent proton spectrum is a classical test particle power law ∝E-2, steepening to E-3 at Ebr≈7 GeV. [ABSTRACT FROM AUTHOR]

A simple one-field L-H transition model is studied in detail, analytically and numerically. The dynamical system consists of three equations coupling the drift wave turbulence level, zonal flow speed, and the pressure gradient. The fourth component, i.e., the mean shear velocity, is slaved to the pressure gradient. Bursting behavior, characteristic for predator-prey models of the drift wave - zonal flow interaction, is recovered near the transition to the quiescent H-mode (QH) and occurs as strongly nonlinear relaxation oscillations. The latter, in turn, arise as a result of Hopf bifurcation (limit cycle) of an intermediate fixed point (between the L- and H-modes). The system is shown to remain at the QH-mode fixed point even after the heating rate is decreased below the bifurcation point (i.e., hysteresis, subcritical bifurcation), but the basin of attraction of the QH-mode shrinks rapidly with decreasing power. This suggests that the hysteresis in the H-L transition may be less than that expected from S-curve models. Nevertheless, it is demonstrated that by shaping the heating rate temporal profile, one can reduce the average power required for the transition to the QH-mode. [ABSTRACT FROM AUTHOR]

The two-field (pressure/density) model for the L→H transition is extended and analyzed qualitatively. In its original form the model is ambiguous as to the location of the transition within the range of bistability of particle and thermal fluxes. Here, the model is regularized by including (i) hyperdiffusion, (ii) time dependence, and (iii) curvature of the pressure profile. The regularizations (i)–(ii) agree and indicate that the Maxwell rule for the forward and back transition applies, as opposed to the maximum flux forward and minimum flux backward transition rules (which yields hysteresis) as suggested previously. Regarding (i)–(ii), simple models suggest that for a pressure gradient driven electric field shear bifurcation, the basic scale of the pedestal is inexorably tied to the particle fueling depth, which normally is the neutral penetration depth. There is no hysteresis predicted by the local model of transport suppression. However, the effect of pressure profile curvature (iii) changes these results substantially. When it dominates, the curvature effect reduces the transition threshold to the lower end of the range of heating power, which falls within the phase coexistence region for both forward and back transitions. This softens the transition threshold requirements. In this limit, the model with pressure curvature also predicts transitions which occur in regimes of flat density and driven exclusively by the temperature gradient. This allows the pedestal to extend beyond the fueling depth, and also allows some decoupling of density and pressure profiles. In a parameter range where the pressure curvature is less important the transition occurs somewhere between the above two limits. [ABSTRACT FROM AUTHOR]

A simple model of the dynamics of Taylor relaxation is derived using symmetry principles alone. No statistical closure approximations are invoked or detailed plasma model properties assumed. Notably, the model predicts several classes of nondiffusive helicity transport phenomena, including traveling nonlinear waves and superdiffusive turbulent pulses. A universal expression for the scaling of the effective magnetic Reynolds number of a system undergoing Taylor relaxation is derived. Some basic properties of intermittency in helicity transport are examined. [ABSTRACT FROM AUTHOR]

The predictions of the extended predator–prey model of the coupled spectral dynamics of drift wave–zonal flow turbulence are presented. The model exhibits three possible types of time-dependent solutions, depending on system parameters, which are: (1) quasiperiodic bursting of the transport and turbulence intensity levels; (2) oscillatory relaxation to a stationary state, and in the collisionless limit; (3) an intensity pulse followed by saturation of zonal flow. These solutions are consistent with the time dependent behavior recently observed in the global gyrokinetic simulations. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A simple criterion that allows one to determine whether or not a given wave spectrum will generate zonal flows, is derived and analyzed. In the context of a coupled drift wave-zonal turbulence, the results are pertinent to the limit of small zonal flow damping, γ[sub d]→0, in which previous analyses found that the turbulence vanishes. However, the practically important issue of the drift wave amplitude threshold for zonal flow excitation was not resolved. In its formal mathematical appearance, the criterion obtained is similar to the well-known Penrose criterion that is used for stability analysis of stellar distributions and particle distributions in plasmas. By contrast, the derived criterion, being applied to wave quanta rather than to particle distribution, shows that even “normal” (wave density decaying with wave number) distributions with an intensity above the threshold should generate zonal flows. This clearly points at the ubiquity of the latter. American Institute of Physics. [ABSTRACT FROM AUTHOR]

One of the main features of astrophysical shocks is their ability to accelerate particles to extremely high energies. The leading acceleration mechanism, the diffusive shock acceleration, is reviewed. It is demonstrated that its efficiency critically depends on the injection of thermal plasma into acceleration which takes place at the subshock of the collisionless shock structure that, in turn, can be significantly smoothed by energetic particles. Furthermore, their inhomogeneous distribution provides free energy for magnetohydrodynamic (MHD) turbulence regulating the subshock strength and injection rate. Moreover, the MHD turbulence confines particles to the shock front controlling their maximum energy and bootstrapping acceleration. Therefore, the study of the MHD turbulence in a compressive plasma flow near a shock is a key to the understanding of the entire process. The calculation of the injection rate became part of the collisionless shock theory. It is argued that the further progress in diffusive shock acceleration theory is impossible without a significant advance in these two areas of plasma physics. [ABSTRACT FROM AUTHOR]

The Cohen–Kulsrud–Burgers equation (CKB) is used to consider the nonlinear evolution of resistive, quasiparallel Alfvén waves subject to a long-wavelength, plane-polarized, monochromatic instability. The instability saturates by nonlinear steepening, which proceeds until the periodic waveform develops an interior scale length comparable to the dissipation length; a fast or an intermediate shock then forms. The result is a periodic train of Alfvén shocks of one or the other type. For propagation strictly parallel to the magnetic field, there will be two shocks per instability wavelength. Numerical integration of the time-dependent CKB equation shows that an initial, small-amplitude growing wave asymptotes to a stable, periodic stationary wave whose analytic solution specifies how the type of shock embedded in the shock train, and the amplitude and speed of the shock train, depend on the strength and phase of the instability. Waveforms observed upstream of the Earth’s bowshock and cometary shocks resemble those calculated here. [ABSTRACT FROM AUTHOR]

Interacting drift wave–zonal flow turbulence is examined at the spectral level of description using an extended “predator–prey” model. Analytic solutions that describe both the linear scaling of transport with ion–ion collisionality as well as the saturation regime are obtained for a simple model of drift wave turbulence. A theory of self-regulation in this system is presented. The possibility of bifurcation to a state with higher turbulence level and transport is demonstrated. This bifurcation is associated with the appearance of a condensate solution at the largest scales. The possible relevance of this phenomenon to the bursting events of turbulence and transport recently observed in gyrokinetic simulations of ITG instability is discussed. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]