Kelvin-Helmholtz instability of a cylindrical plasma flow with an arbitrary temperature

The dispersion relation for Kelvin-Helmholtz magnetohydrodynamic instability of a cylindrical plasma flow in a longitudinal magnetic field is studied with allowance for plasma compressibility. Stability of the system in a wide range of plasma parameters is thoroughly analyzed in the incompressible plasma approximation. Using the results obtained, a diagram of the system stability is constructed in terms of the magnetic field and the ratio between the plasma densities in the flow and the ambient space. It is shown by numerically solving the dispersion relation for the case of a compressible plasma that perturbations with scale lengths on the order of the flow diameter and larger can develop even at a zero temperature. For low ion-sound velocities, c _S ²/U ₀² < 0.25, the growth rate of the axisymmetric mode with m = 0 is much smaller than that of non-axisymmetric modes. It is shown that, in an incompressible plasma, the eigenmodes are damped monotonically with distance from the flow. In plasma with a finite temperature, the character of damping is oscillatory; in this case, the lower the plasma temperature, the larger the distance at which the ambient plasma is perturbed.     

Large-scale perturbations due to a small-scale instability in a finite-conductivity plasma

By considering kink modes in a plasma cylinder in a strong axial magnetic field as an example, it is demonstrated that, because of the finite plasma conductivity (the finite longitudinal plasma permittivity ?_∥), large-scale perturbations can grow with time due to a small-scale instability that develops near a certain magnetic surface.     

Generation of zonal flows and large-scale magnetic fields by drift-Alfvén turbulence

The possibility of generating zonal perturbations by drift-Alfvén turbulence in a plasma with a finite pressure (1>β>m_e/m_i) is investigated. A set of coupled equations is derived that includes the equation for the spectral function of the turbulence and the averaged equations for zonal perturbations. It is shown that, in particular cases, the equation for the spectral function possesses action invariants; i.e., it takes the form of a conservation law for some quantities that are proportional to the spectral function of turbulence. Two types of instability of the zonal perturbations are revealed. The first type of instability generates only a zonal flow. Two regimes of this instability—resonant and hydrodynamic regimes—are examined, and the corresponding instability growth rates are determined. The second type of instability takes place when the resonant interaction of drift-Alfvén waves with electrons is taken into account. Because of this instability, the generation of a zonal magnetic field is inevitably accompanied by the generation of a zonal flow. It is found that the growth rate of the second type of instability is slower than that of the first type.     

A nonlinear single-mode structure in a plasma with anisotropic temperature

An exact solution is derived to the equations of vortex electron anisotropic hydrodynamics for a plasma that is unstable against the Weibel instability driven by the electron temperature anisotropy. This solution describes saturation of the Weibel instability in the single-mode regime with an arbitrary wavelength and corresponds to a standing helical wave of magnetic perturbations in which the amplitude of the generated magnetic field varies periodically over time. The longitudinal and transverse (with respect to the rotating anisotropy axis) plasma temperatures are subject to the same periodic variations. In this case, the maximum magnetic field energy can be on the order of the plasma thermal energy.

     

Raising the efficiency of a plasma opening switch by applying an external magnetic field

The influence of an external magnetic field on the performance of a high-impedance plasma opening switch is studied experimentally. A 1.5-fold increase in the output voltage of a plasma opening switch operating in the erosion mode is achieved by applying an external magnetic field. The magnetic field strength and the parameters of the plasma opening switch at which the maximum output voltage is attained are determined. It is shown experimentally that the predicted dependence of the maximum output voltage on the Marx generator voltage, U _POS [MV]=3.6 (U _MG [MV])^4/7, is confirmed experimentally.     

Steady-state vortex structure in a plasma with a strong magnetic field

A study is made of nonquasineutral vortex structures in a plasma with a magnetic field B _z in which the charges separate on a spatial scale equal to the magnetic Debye radius r _B=B _z/4πen _e. The electric field arising due to charge separation leads to radial expansion of the ions, thereby destroying the initial electron vortex. It is shown that the ion pressure gradient stops ion expansion in a nonquasineutral electron vortex and gives rise to a steady structure with a characteristic scale on the order of r _B. With the electron inertia taken into account in the hydrodynamic approximation, the magnetic vortex structure in a hot plas mamanifests itself in the appearance of a “hole” in the plasma density.     

Electrostatic electron vortex structure in a plasma in an external magnetic field

A previously developed method for describing vortex structures is used to construct electrostatic vortices in a plasma in an external magnetic field. An equation for the radial electric field that gives rise to azimuthal electron drift in crossed electric (E _r ) and magnetic (B _z ) fields is derived without allowance for the magnetic field of the electron currents. Two types of the resulting electrostatic vortex structures with a positive and a negative electric potential at the axis are analyzed. The results obtained are compared with experimental data on vortex structures.     

Kelvin-Helmholtz instability for a bounded plasma flow in a longitudinal magnetic field

Kelvin-Helmholtz MHD instability in a plane three-layer plasma is investigated. A general dispersion relation for the case of arbitrarily orientated magnetic fields and flow velocities in the layers is derived, and its solutions for a bounded plasma flow in a longitudinal magnetic field are studied numerically. Analysis of Kelvin-Helmholtz instability for different ion acoustic velocities shows that perturbations with wavelengths on the order of or longer than the flow thickness can grow in an arbitrary direction even at a zero temperature. Oscillations excited at small angles with respect to the magnetic field exist in a limited range of wavenumbers even without allowance for the finite width of the transition region between the flow and the ambient plasma. It is shown that, in a low-temperature plasma, solutions resulting in kink-like deformations of the plasma flow grow at a higher rate than those resulting in quasi-symmetric (sausage-like) deformations. The transverse structure of oscillatory-damped eigenmodes in a low-temperature plasma is analyzed. The results obtained are used to explain mechanisms for the excitation of ultra-low-frequency long-wavelength oscillations propagating along the magnetic field in the plasma sheet boundary layer of the Earth’s magnetotail penetrated by fast plasma flows.     

Study of Plasma Flow Modes in Imploding Nested Arrays

Results from experimental studies of implosion of nested wire and fiber arrays at currents of up to 4 МА at the Angara-5-1 facility are presented. Depending on the ratio between the radii of the inner and outer arrays, different modes of the plasma flow in the space between the inner and outer arrays were implemented: the sub-Alfvénic (V _r < V _А ) and super-Alfvénic (V _r > V _А ) modes and a mode with the formation of the transition shock wave (SW) region between the cascades. By varying the material of the outer array (tungsten wires or kapron fibers), it is shown that the plasma flow mode between the inner and outer arrays depends on the ratio between the plasma production rates ?_in /?_out in the inner and outer arrays. The obtained experimental results are compared with the results of one-dimensional MHD simulation of the plasma flow between the arrays. Stable implosion of the inner array plasma was observed in experiments with combined nested arrays consisting of a fiber outer array and a tungsten inner array. The growth rates of magnetic Rayleigh?Taylor (MRT) instability in the inner array plasma at different numbers of fibers in the outer array and different ratios between the radii of the inner and outer arrays are compared. Suppression of MRT instability during the implosion of the inner array plasma results in the formation of a stable compact Z-pinch and generation of a soft X-ray pulse. A possible scenario of interaction between the plasmas of the inner and outer arrays is offered. The stability of the inner array plasma in the stage of final compression depends on the character of interaction of plasma jets from the outer array with the magnetic field of the inner array.     

Stability of localized MHD perturbations in confinement systems with closed magnetic field lines

Conditions are determined for the stability of a finite-pressure plasma against perturbations localized near a magnetic field line in a magnetic confinement system without average minimum-B. The marginal stability (ω²=0) is achieved at the pressure profile p∝U ^?5/3 (where $U = \oint {\frac{{dl}}{B}}$ ), provided that the pressure is lower than a certain critical value above which an unstable incompressible mode in which the displacement as a function of the coordinate along the field line has zeros appears at some magnetic field line.     

Kelvin-Helmholtz instability in a bounded plasma flow

Kelvin-Helmholtz instability in a three-layer plane geometry is investigated theoretically. It is shown that, in a three-layer system (in contrast to the traditionally considered case in which instability develops at the boundary between two plasma flows), instability can develop at an arbitrary ratio of the plasma flow velocity to the ion-acoustic velocity. Perturbations with wavelengths on the order of the flow thickness or longer can increase even at a zero temperature. The system can also be unstable against long-wavelength perturbations if the flow velocity at one of the boundaries is lower than the sum of the Alfvén velocities in the flow and the ambient plasma. The possibility of applying the results obtained to interpret the experimental data acquired in the framework of the CLUSTER multisatellite project is discussed. It follows from these data that, in many cases, the propagation of an accelerated particle flow in the plasma-sheet boundary layer of the Earth’s magnetotail is accompanied by the generation of magnetic field oscillations propagating with a velocity on the order of the local Alfvén velocity.     

Field-dependent specific-heat of the pure and diluted 4f electron system Yb4As3

The experimental field-dependent specific heat of the polydomain pure Yb₄As₃ and diluted (Yb_1−xLu_x)₄As₃ (x = 0.01, 0.03) systems is presented and compared with that calculated by the numerical quantum transfer-matrix method. The simulations have been performed using the S = 1/2 antiferromagnetic Heisenberg model with the transverse staggered field (appearing as a result of the antisymmetric Dzyaloshinskii-Moriya interaction) and a uniform magnetic field perpendicular to the staggered field. In the model calculations the fixed microscopic parameters have been taken and the impurity distribution has been considered. A significant improvement with respect to the previous results is shown.     

Effect of the transverse magnetic field on turbulence and parameters of a plasma column in the L-2M stellarator

The influence of magnetic configurations with magnetic hills or wells on the parameters of a plasma column and turbulence characteristics were studied in experiments in which the plasma was created and heated by a microwave beam at the second harmonic of the electron cyclotron frequency. Calculations show that, for 〈β〉=(1.5?2)×10^?, a configuration with a magnetic well takes place and the Mercier criterion for stability of the ideal MHD modes is satisfied. It is shown that the compensation of the Shafranov shift of the plasma column by a transverse (vertical) field (B _v /B ₀ =5×10^?3) leads to a configuration with a magnetic hill in which the Mercier stability criterion is violated in the central region of the plasma column. It is experimentally shown that the stored plasma energy in the magnetic-hill configuration is reduced by one-half in comparison with the magnetic-well configuration. In the case of a magnetic hill, the energy of fluctuations increases both in the plasma core and near the separatrix, and the quasi-regular components of the wavelet spectra grow. When the Shafranov shift is compensated only partially (B _v/B ₀～3×10^?3) and the system is near the instability threshold, the stored plasma energy and the central electron temperature are somewhat higher, and the radiation power of fast electrons from non-Maxwellian tails at the second harmonic of the electron gyrofrequency decreases. It is found that the wavelet spectra of fluctuations change, the coherence coefficient for spectral components increases, and the radial electric field near the separatrix decreases.     

Nonlinear dynamics of beam–plasma instability in a finite magnetic field

The nonlinear dynamics of beam–plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam?plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B ₀ = 4.5 kG (Ω ~ ωB _p ) and 20 kG (Ω _B ? ω_p). For B ₀ = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.     

Single-mode magnetic structures in a plasma with anisotropic pressure

The equations of vortex electron anisotropic hydrodynamics are used to show that, in a plasma with anisotropic pressure, the Weibel instability of short-wavelength perturbations gives rise to a large-amplitude quasi-harmonic magnetic field varying periodically as a function of time. The computed field parameters agree well with the proposed analytic estimates.     

Additional ECR heating of a radially inhomogeneous plasma via the absorption of satellite harmonics of the surface flute modes in a rippled magnetic field

A theoretical study is made of the possibility of additional heating of a radially inhomogeneous plasma in confinement systems with a rippled magnetic field via the absorption of satellite harmonics of the surface flute modes with frequencies below the electron gyrofrequency in the local resonance region, ε₁ (r ₁) = [2πc/(ωL)]², where ε₁ is the diagonal element of the plasma dielectric tensor in the hydrodynamic approximation, L is the period of a constant external rippled magnetic field, and the radical coordinate r ₁ determines the position of the local resonance. It is found that the high-frequency power absorbed near the local resonance is proportional to the square of the ripple amplitude of the external magnetic field. The mechanism proposed is shown to ensure the absorption of the energy of surface flute modes and, thereby, the heating of a radially inhomogeneous plasma.     

Multi-Year Lags between Forest Browning and Soil Respiration at High Northern Latitudes

High-latitude northern ecosystems are experiencing rapid climate changes, and represent a large potential climate feedback because of their high soil carbon densities and shifting disturbance regimes. A significant carbon flow from these ecosystems is soil respiration (R _S, the flow of carbon dioxide, generated by plant roots and soil fauna, from the soil surface to atmosphere), and any change in the high-latitude carbon cycle might thus be reflected in R _S observed in the field. This study used two variants of a machine-learning algorithm and least squares regression to examine how remotely-sensed canopy greenness (NDVI), climate, and other variables are coupled to annual R _S based on 105 observations from 64 circumpolar sites in a global database. The addition of NDVI roughly doubled model performance, with the best-performing models explaining ∼62% of observed R _S variability. We show that early-summer NDVI from previous years is generally the best single predictor of R _S, and is better than current-year temperature or moisture. This implies significant temporal lags between these variables, with multi-year carbon pools exerting large-scale effects. Areas of decreasing R _S are spatially correlated with browning boreal forests and warmer temperatures, particularly in western North America. We suggest that total circumpolar R _S may have slowed by ∼5% over the last decade, depressed by forest stress and mortality, which in turn decrease R _S. Arctic tundra may exhibit a significantly different response, but few data are available with which to test this. Combining large-scale remote observations and small-scale field measurements, as done here, has the potential to allow inferences about the temporal and spatial complexity of the large-scale response of northern ecosystems to changing climate.     

Nonlinear damping of zonal flows

The modulatonal instability theory for the generation of large-scale (zonal) modes by drift modes has been extended to the second order including the effects of finite amplitude zonal flows, ? _q . The nonlinear (second-order) sidebands are included in the perturbative expansion to derive the nonlinear equation for the evolution of ? _q . It is shown that effects of finite ? _q reduce the growth rate of zonal flow with a possibility of oscillatory regimes at a later stage.     

Limiting Parameters of the Plasma Opening Switch

Implementing programs for nuclear fusion research and X-ray generation requires the creation of superpower generators based on plasma opening switches (POSs) capable of commutating currents as high as several tens of megaamperes at output voltages of up to 5 MV and higher. The physical mechanisms limiting the POS voltage are investigated. It is shown that, as the generator voltage U _g increases, the voltage multiplication factor k = U_POS/U_g (where U_POS is the POS voltage) decreases. An explanation for such a dependence is proposed, and the maximum value of the POS voltage is estimated. A POS design that enables operating in the above current and voltage ranges is considered. The design is based on applying an external magnetic field to the POS interelectrode gap, increasing the initial generator voltage, and decreasing the linear (along the perimeter of the outer electrode) density of the charge passing through the POS during the conduction phase.     

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U₀. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2v_T/R (where v_T is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ? of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.