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.     

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.     

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.     

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.     

Decay instability of a lower hybrid wave

A study is made of the decay instability of a lower hybrid wave with a finite wave vector (k ₀≠0) and a large amplitude such that the oscillatory velocity of the electrons with respect to the ions cannot be neglected. It is shown that, depending on the angle between the propagation direction of the lower hybrid wave and the external magnetic field and the angle through which the wave is scattered, the decay instability is primarily governed either by the oscillatory electron motion with respect to the ions or by the nonlinear response of the plasma to the lower hybrid wave propagating in it. The role of the nonlinear frequency shift in the saturation of the lower hybrid decay instability is clarified.     

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.     

Hydrodynamic model of the penetration of a magnetic field into a plasma with two ion species

Hydrodynamic equations are presented that describe the dynamics of a plasma with two ion species in a magnetic field such that . It is shown that there exists a range of values of the ratio of the plasma density to the magnetic field, ν_ii/ω_Bi<(Z ² M/m)^1/4, within which the frictional force caused by ion-ion collisions dominates over that caused by electron-ion collisions. In this range, the effective conductivity, which governs the magnetic field diffusion, is lower than the conventional electron-ion conductivity by a factor of $\sqrt {M/m}$ and can be as low as σ ? enc/B. The equations derived for this three-component plasma make it possible to self-consistently incorporate local changes in the partial mass and partial charge of each of the ion species in relative motion. The characteristic features of the equations obtained are analyzed by applying them to describe the propagation of a current sheath in a transmission line filled with a multispecies plasma. An analogy is drawn between magnetic phenomena in a plasma with two ion species and in a so-called dusty plasma.     

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.     

Evolutionary sheath structure in magnetized collisionless plasma with electron inertia

A classical hydrodynamic model is methodologically formulated to see the equilibrium properties of a planar plasma sheath in two-component magnetized bounded plasma. It incorporates the weak but finite electron inertia instead of asymptotically inertialess electrons. The effects of the externally applied oblique (relative to the bulk plasma flow) magnetic field are judiciously accented. It is, for the sake of simplicity, assumed that the relevant physical parameters (plasma density, electrostatic potential, and flow velocity) vary only in a direction normal to the confining wall boundary. It is noticed for the first time that the derived Bohm condition for sheath formation is modified conjointly by the electron inertia, magnetic field, and field orientation. It is manifested that the electron inertia in the presence of plasma gyrokinetic effects slightly enhances the ion Mach threshold value (typically, M _i0 ≥ 1.139) toward the sheath entrance. This flow supercriticality is in contrast with the heuristic formalism (M _i0 ≥ 1) for the zero-inertia electrons. A numerical illustrative scheme on the parametric sheath features on diverse nontrivial apposite arguments is constructed alongside ameliorative scope.     

Effect of the radial electric field on the results of measurements of the poloidal rotation of a tokamak plasma by charge exchange recombination spectroscopy

Abtract The effect of the radial electric field E _r on the results of measurements of the poloidal rotation of a tokamak plasma by charge exchange recombination spectroscopy is considered. It is shown that the emission line shift arising from the finite lifetime of the excited state of the ions is proportional to E _r. For helium ions, the maximum shift corresponds to the poloidal rotation velocity, which is about one-third of the drift velocity in the crossed radial electric (E _r) and toroidal magnetic (B _t) fields. __________ Translated from Fizika Plazmy, Vol. 27, No. 11, 2001, pp. 1050–1052. Original Russian ? 2001 by Romannikov, Chernobai.     

Nonlinear dynamics of Kelvin-Helmholtz instability in a finite-width plasma flow

The nonlinear stage of Kelvin-Helmholtz (KH) instability in a finite-width plane-parallel plasma flow is analyzed. The analysis is performed by means of two-dimensional numerical simulations with the use of ideal magnetohydrodynamic equations describing isothermal plasma flows propagating along the magnetic field. The influence of the magnetic field strength, the plasma temperature, and the ratio of the flow width to the width of the transition layer on the formation of vortex layers and large-scale flow perturbations is investigated. It is shown that, if the wavelength of periodic perturbations is shorter than the flow width, the symmetric and antisymmetric modes develop in a qualitatively similar manner. For waves with wavelengths longer than the flow width, the development of such modes is very different due to the mutual influence of the flow boundaries. Analysis of the development of instability at different values of the Alfvén Mach number M _A shows that long-lived vortices with a characteristic scale length on the order of the flow width appear in a weak magnetic field for both symmetric and antisymmetric modes; however, the vortex geometries for these modes are different. In a strong magnetic field, M _A ～ 5, the phase of vortex decay for both types of modes occurs faster than in a weak field; however, in the case of an antisymmetric mode, large-scale perturbations of the flow boundary are retained for a longer time. Analysis of the evolution of the initial disturbance produced by an ensemble of random small perturbations (noise) at different plasma temperatures shows that, for a flow width comparable with the width of the transition region, the development of KH instability is always antisymmetric in character and leads to well-developed large-scale perturbations of the flow as a whole. For a cold plasma with C _S < 0.5U (where C _S is the speed of sound and U is the flow velocity), in contrast to hot plasma with C _S > 0.5U, the development of KH instability leads to the growth of the antisymmetric mode even if the flow width is much larger than the width of the transition region.     

Kinetic models of current sheets with a sheared magnetic field

Thin current sheets, whose existence in the Earth’s magnetotail is confirmed by numerous spacecraft measurements, are studied analytically and numerically. The thickness of such sheets is on the order of the ion Larmor radius, and the normal component of the magnetic field (B _z ) in the sheet is almost constant, while the tangential (B _x ) and shear (B _y ) components depend on the transverse coordinate z. The current density in the sheet also has two self-consistent components (j _x and j _y , respectively), and the magnetic field lines are deformed and do not lie in a single plane. To study such quasi-one-dimensional current configurations, two kinetic models are used, in particular, a numerical model based on the particle-in-cell method and an analytical model. The calculated results show that two different modes of the self-consistent shear magnetic field B _y and, accordingly, two thin current sheet configurations can exist for the same input parameters. For the mode with an antisymmetric z profile of the B _y component, the magnetic field lines within the sheet are twisted, whereas the profiles of the plasma density, current density component j _y , and magnetic field component B _x differ slightly from those in the case of a shearless magnetic field (B _y = 0). For the symmetric B _y mode, the magnetic field lines lie in a curved surface. In this case, the plasma density in the sheet varies slightly and the current sheet is two times thicker. Analysis of the dependence of the current sheet structure on the flow anisotropy shows that the sheet thickness decreases significantly with decreasing ratio between the thermal and drift plasma velocities, which is caused by the dynamics of quasi-adiabatic ions. It is shown that the results of the analytical and numerical models are in good agreement. The problems of application of these models to describe current sheets at the magnetopause and near magnetic reconnection regions are discussed.     

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.     

Alfvén resonance heating in Uragan-2M torsatron

Uragan-2M is a medium-size torsatron with reduced helical ripples. This machine has the major plasma radius R = 1.7 m, the average minor plasma radius r _p ≤ 0.24 m and the toroidal magnetic field B ₀ ≤ 2.4 T. The Alfvén resonance heating in a high k _‖ regime is advantageous for small size machines since it can be realized at smaller plasma densities than the minority and second harmonic heating. The Alfvén resonance heating is examined numerically in the approximation of radially non-uniform plasma cylinder with identical ends. The numerical model for wave excitation and propagation accounts for the longitudinal electron thermal motion and the finite ion gyroradius which allow the model to treat correctly the propagation and damping of the kinetic Alfvén wave in hot plasma. A compact antenna consisting of four loop elements is chosen to provide operation in a high k _‖ regime. The major drawback of such an approach is the presence of plasma peripher y heating owing to unavoidable excitation of low k _‖ Alfvén resonances. Calculations show that, with the proper choice of heating regime, the periphery heating has an acceptable level and the major part of the power is deposited inside plasma column.     

Electron leakage mechanism in a plasma-filled magnetically insulated transmission line

It is shown that relativistic electron current can propagate across the magnetic field B ₀ over a distance d much larger than the electron gyroradius, r ₀ ? m _e v _z c/(eB ₀) ? d. This current is driven by the Hall electric field, which is generated on a spatial scale equal to the magnetic Debye radius r _B = B ₀/(4πen _e) and causes the electrons to drift in crossed electric and magnetic fields. For a plane equilibrium current configuration, analytic profiles of the electron velocity and electron density are calculated and the electric and magnetic fields are determined. The results obtained are used to explain electron leakages in magnetically insulated transmission lines filled with a plasma expanding from the electrodes. Equations describing an equilibrium configuration of the ions and electrons that drift simultaneously across a strong magnetic field are derived.     

Study of the termination phase of plasma production and the formation of magnetic flux breakthroughs during wire array implosion

The phenomenon of magnetic flux breakthrough into a wire array during its implosion was studied experimentally at the Angara-5-1 facility. It is shown that breakthroughs develop in the final stage of plasma production from the wire material and occur near the initial wire position. The spatial distributions of the azimuthal magnetic field within tungsten, molybdenum, copper, and aluminum wire arrays were studied using magnetic probes. The distributions of the azimuthal magnetic field B _φ(z, t) along the array height in different stages of implosion were measured, and the characteristic dimensions of regions with a nonuniform magnetic field that appear during magnetic flux breakthroughs at the outer boundary of the wire array plasma were determined. The dimensions of these regions are compared with those of the regions with depressed plasma radiation observed in frame and time-integrated X-ray images. The dynamics of the distribution B _φ(z, t) in regions with a nonuniform magnetic field during breakthroughs of the azimuthal magnetic flux is compared with that of the spatial distribution of pinch radiation in the frame X-ray images in different stages of implosion. The experimental data on the characteristics of spatially nonuniform breakthroughs of the magnetic flux into the wire array are analyzed using the plasma rainstorm model proposed by V.V. Aleksandrov et al. (JETP 97, 745 (2003)). The plasma density in the region of magnetic flux breakthrough is estimated.     

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.     

Generation of dense multicharged ion flows from an ECR plasma confined in a quasi-gas-dynamic magnetic cusp trap

The possibility of generating dense multicharged ion beams with a current density as high as ～1 A/cm² from an ECR plasma confined in a quasi-gas-dynamic cusp trap is studied both theoretically and experimentally. The most important advantages of this type of ion source are that the plasma in the cusp is stabile against MHD perturbations and that a trap intended to operate at fairly high pump-field frequencies (above 30 GHz) is relatively inexpensive. A theoretical model of confinement of a high-density nonequilibrium ECR plasma (T _e ? T _i ) in an open magnetic trap is proposed and results are presented from model experiments with an ～30-cm-long cusp trap (here, by the cusp length is meant the volume of a paraxial magnetic tube divided by the area of its cross sections in magnetic mirrors) pumped by a pulsed microwave field with a frequency of 37.5 GHz and power of 100 kW. The possibility of achieving a quasi-gas-dynamic regime of plasma confinement of an ECR plasma in a cusp trap is demonstrated. Ion beams with a average ion charge number of 2–4 (depending on the sort of working gas) and current densities unprecedented for ECR sources are obtained. Good agreement between theoretical and experimental results makes it possible to reliably predict the ion beam parameters that can be achieved at even higher microwave frequencies.     

Spatial distribution of the RF power absorbed in a helicon plasma source

The spatial distributions of the RF power absorbed by plasma electrons in an ion source operating in the helicon mode (ω _ci < ω < ω _ce < ω _pe ) are studied numerically by using a simplified model of an RF plasma source in an external uniform magnetic field. The parameters of the source used in numerical simulations are determined by the necessity of the simultaneous excitation of two types of waves, helicons and Trivelpiece-Gould modes, for which the corresponding transparency diagrams are used. The numerical simulations are carried out for two values of the working gas (helium) pressure and two values of the discharge chamber length under the assumption that symmetric modes are excited. The parameters of the source correspond to those of the injector of the nuclear scanning microprobe operating at the Institute of Applied Physics, National Academy of Sciences of Ukraine. It is assumed that the mechanism of RF power absorption is based on the acceleration of plasma electrons in the field of a Trivelpiece-Gould mode, which is interrupted by pair collisions of plasma electrons with neutral atoms and ions of the working gas. The simulation results show that the total absorbed RF power at a fixed plasma density depends in a resonant manner on the magnetic field. The resonance is found to become smoother with increasing working gas pressure. The distributions of the absorbed RF power in the discharge chamber are presented. The achievable density of the extracted current is estimated using the Bohm criterion.     

Drift-Alfvén turbulence in a tokamak wall plasma

The behavior of turbulent fluxes in the vicinity of a resonant point m/n=q(x _res) in a plane wall plasma layer in a tokamak is studied by numerically analyzing the nonlinear MHD equations in a four-field electromagnetic model. Simulations show that, as the electron temperature at the plasma edge increases, the intensity of turbulent particle flux decreases, reaching its minimum value, and then increases. Such behavior is found to be due to the stabilizing effect of the electron drift velocity (V _y0∼dT _e0/dx) in the equation for the longitudinal component of the magnetic potential. It is shown that, at a strong toroidal magnetic field, turbulent transport processes conform to the gyro-Bohm scaling, which gradually passes over to the Bohm scaling as the field decreases. __________ Translated from Fizika Plazmy, Vol. 30, No. 5, 2004, pp. 387–397. Original Russian Text Copyright ￠ 2004 by Shurygin.