Separation of the heavy and light ion components in a plasma flow propagating in a curvilinear magnetic field

The propagation of a metal plasma jet in a transport system with a curvilinear magnetic field was studied experimentally. The jet was generated by a pulsed vacuum arc discharge with a composite (W + Fe) cathode. Spatial separation of ions of the cathode material was observed at the exit from the system. The ions of the lighter element (Fe) were concentrated in the inner part of the cathode plasma jet deflected by the magnetic field. The jet is also found to be deflected along the binormal to the magnetic field lines due to plasma drift in the crossed magnetic and electric fields. The degree of mass separation of elements is shown to increase with increasing jet deflection along the binormal. The maximum value of the mass separation efficiency reaches 45, the effective value being 7.7.     

Concerning arc discharge in a transverse magnetic field

The retrograde motion of an arc in a transverse magnetic field is attributed to the onset of a tangential flow of gas or vapor. The physics of a polarized plasma jet conducting the current between the cathode and anode is discussed.     

Formation of shock waves in a discharge plasma in the presence of a magnetic field

The effect of an external magnetic field on the dynamics of shock waves generated in an argon plasma due to both explosive processes on the cathode and expansion of the spark channel has been studied experimentally. It is shown that the expanding plasma of the cathode spot forms a shock wave and that the application of a longitudinal magnetic field decelerates the radial expansion of the cathode plasma. It is found that the intensities of some argon spectral lines increase in the presence of a magnetic field.     

Formation of a cylindrical ion beam in the field of an axisymmetric system of ring currents at a low Hall current

A study is made of the structure of an accelerating layer with a closed Hall current and the geometry of an ion beam in an external magnetic field created by an arbitrary axisymmetric system of ring currents under conditions such that the Hall current can be ignored. It is shown that the ion trajectories are perpendicular to the magnetron cutoff surface for electrons and that the cathode plasma boundary coincides with a magnetic field line. A magnetic field configuration is found in which the cutoff surface is a plane surface perpendicular to the axis of the system. It is shown that, for a small ratio of the gyroradius of the electrons (in terms of the maximum energy acquired by them in the layer) to the characteristic size of the structure, such a configuration provides sufficient means to ensure the formation of slightly converging ion beams or those that are essentially parallel to the system axis.     

Numerical study of a DRAKON-type closed magnetic configuration with a spatial axis

Results are presented from numerical studies of the magnetic field lines and the charged-particle trajectories in the magnetic system of the DRAKON device and of its curvilinear element—the KREL with magnetic mirrors. For the KREL, mirror ratio values are found that do not worsen the particle-drift compensation. The dimensions of the input region for the electrons injected into the KREL to create the beam-plasma discharge are calculated. Calculations show that, in the paraxial approximation, after multiple passes around the device, the magnetic field lines and trajectories of individual transit particles form a system of embedded toroidal surfaces with circular cross sections. When symmetrically changing the current distributions in the coils of the device, these surfaces shift with respect to their previous positions, but their shape remains the same. For the DRAKON device with helical KRELs, the shift of the drift surfaces with respect to the magnetic surfaces, as well as the flow of the longitudinal diamagnetic currents from the KRELs into the rectilinear regions, is found as a function of the pitch angle θ of the KREL helix.     

Investigation of plasma characteristics in an unbalanced magnetron sputtering system

Results are presented from experimental studies of a magnetron sputtering system for different configurations of the magnetic field above the cathode surface. The current-voltage characteristics of a magnetron discharge at different working gas pressures (0.08–0.3 Pa) and currents in the unbalancing coil were studied. The production and transport of charge carriers in a magnetron discharge with an unbalanced magnetic field was investigated by means of probe measurements of plasma characteristics and ion energies in the region between the substrate and the magnetic trap at the cathode surface. The radial distributions of the ion current density, plasma potential, and floating potential in the unbalanced operating mode are found to have pronounced extrema at the magnetron axis. It is shown that the plasma density near the substrate can be increased considerably when the axial magnetic field is high enough to efficiently confine plasma electrons and prevent their escape to the chamber wall.     

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.     

Formation of electrode sheaths during the acceleration of a magnetized plasma

A study is made of the motion of a plasma with a frozen-in magnetic field along the electrode surfaces in the direction transverse to the magnetic field. A one-dimensional problem of an electrode sheath is formulated in which all of the quantities depend only on the coordinate orthogonal to the electrode surface. Viscous plasma heating, plasma cooling via heat conduction, and other kinetic effects are taken into consideration. Account is also taken of the effect of plasma acceleration and of the related current that is transverse to the electrode surfaces and, due to the Hall effect, carries the magnetic flux away from the cathode and toward the anode. Solving the one-dimensional problem with a constant electric current and constant magnetic field shows that, in a sheath that forms near the cathode, the solution becomes self-similar, the plasma mass grows linearly, and the electron magnetization parameter remains unchanged. It is found that the anode sheath cannot be described in the magnetohydrodynamic approximation, according to which the plasma density in the sheath rapidly vanishes, while the current through the sheath remains constant. This difficulty can be overcome by incorporating some of the nonhydrodynamic effects (primarily, electron dispersion), thereby making the problem physically correct. Solving the problem numerically shows that a decrease in the plasma density in the anode sheath due to the Hall effect gives rise to additional significant plasma acceleration.     

Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron 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.     

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.     

A phenomenological model of the current filamentation instability driven by cathode processes in the Livermore spheromak

The current density on the open field lines of the Livermore spheromak (SSPX) typically exceeds the saturation current density of the bulk plasma. We assume that the mechanism that provides conditions for that is associated with the formation of a thin layer near the cathode surface, where both the plasma and the neutral density are higher than in the bulk plasma and where intense ionization occurs. The ions formed in this layer fall back onto the cathode, whereas electrons contribute to the high current density in the bulk plasma. The particle balance in the ionizing layer is determined by the recycling coefficient, which, in turn, depends on the cathode temperature and the sheath voltage. As it turns out, these dependences give rise to an instability that leads to the current filamentation and the formation of hot spots on the cathode surface. The instability can be characterized in a phenomenological manner without going into the details of the structure of the ionizing layer, whose effect on the instability shows up in the form of a couple of numerical coefficients of the order of one. We predict the characteristic size and the shape of the filaments (and the hot spots), which are in a general agreement with discoloration patterns on the surface of the cathode in the SSPX. If the magnetic field is tilted to the surface, the footpoints of the filaments move with a significant velocity, whose direction depends on the ratio of the ion gyroradius and the thickness of the ionizing layer. This instability, although primarily considered in conjunction with the SSPX experiment, may play a role in spherical tokamaks and other systems with coaxial helicity injection.     

Influence of a transverse magnetic field on the characteristics of a dc gas discharge

The influence of a transverse magnetic field and the working-gas pressure on the rotation frequency of the current channel, as well as on the electric field in the positive column and the cathode voltage drop in a dc gas discharge, was studied experimentally. The working gases were pure hydrogen and hydrogen-methane, hydrogen-argon, and hydrogen-argon-methane mixtures. It is shown that a transverse (with respect to the discharge current) magnetic field stabilizes a normal glow discharge against a transition to an arc discharge at specific absorbed powers above 300 W/cm³. The cathode voltage drop and the electric field in the positive column are measured. It is shown that the electric field does not depend on the magnetic field strength, whereas the cathode voltage drop increases with increasing magnetic field. It is found that the rotation frequency of the current channel is a complicated function of the discharge parameters and attains 400 Hz.     

Formation of space-charge bunches in a multivelocity-electron-beam-based microwave oscillator with a cathode unshielded from the magnetic field

The influence of the magnitude and configuration of the magnetic field on the parameters of electron bunches formed in a multivelocity electron beam is analyzed. It is shown that the use of a cathode unshielded from the magnetic field and a nonuniform magnetic field increasing along the drift space enables the formation of compact electron bunches. The ratio between the current density in such bunches and the beam current density at the entrance to the drift space reaches 10⁶, which results in a substantial broadening of the output microwave spectrum due to an increase in the amplitudes of the higher harmonics of the fundamental frequency.     

On the possibility of reflection of Alfvén waves in a curvilinear magnetic field

The propagation of Alfvén waves in a plasma immersed in a curvilinear magnetic field is investigated by using a 2D model. The waves are described by a 1D equation that formally coincides with the equation for the case of a quasi-uniform straight magnetic field with a modified Alfvén velocity that takes into account the longitudinal dependence of the Lame coefficients. It is shown that toroidal and poloidal Alfvén modes depend differently on the magnetic-field geometry. In the case of a 2D plane-parallel configuration of the magnetic field, poloidal modes are efficiently reflected from regions where the magnetic field lines sharply converge or diverge. This effect can result in the formation of open-field-line Alfvén quasi-resonators.     

MHD flows in the channels of plasma accelerators with a longitudinal magnetic field

Plasma flows caused by the interaction of the discharge current with the azimuthal magnetic self-field in coaxial channels (nozzles) of plasma accelerators are strongly affected by the longitudinal field produced by external conductors. A two-dimensional MHD model of flows in channels in the presence of a longitudinal magnetic field is proposed. Depending on the ratio between the characteristic values of the longitudinal and azimuthal field components, one of three types of flow is established in the channel: super-Alfvén, sub-Alfvén, or combined. The properties of different types of flows are analyzed. The acceleration process in sub-Alfvén flows differs qualitatively from that in regimes without a longitudinal field in transitions between the kinetic, thermal, and magnetic energy components.     

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.     

Specific features of virtual cathode formation and dynamics with allowance for the magnetic self-field of a relativistic electron beam

The conditions and mechanisms of virtual cathode formation in relativistic and ultrarelativistic electron beams are analyzed with allowance for the magnetic self-field for different magnitudes of the external magnetic field. The typical behavior of the critical current at which an oscillating virtual cathode forms in a relativistic electron beam is investigated as a function of the electron energy and the magnitude of the uniform external magnetic field. It is shown that the conditions for virtual cathode formation in a low external magnetic field are determined by the influence of the magnetic self-field of the relativistic electron beam. In particular, azimuthal instability of the electron beam caused by the action of the beam magnetic self-field, which leads to a reduction in the critical current of the relativistic electron beam, is revealed.     

Optical studies of plasma inhomogeneities in a high-current pulsed magnetron discharge

Results are presented for experimental studies of the plasma glow in a high-current pulsed magnetron discharge by using a high-speed optical frame camera. It is found that the discharge plasma is inhomogeneous in the azimuthal direction. The plasma bunches rotate with a linear velocity of ∼1 cm/μs in the direction of electron Hall drift, and their number is proportional to the discharge current. Plasma inhomogeneities in the form of plasma jets propagate in the form of plasma jets from the cathode region toward the anode. It is shown analytically that the formation of inhomogeneities is caused by the necessity to transfer high-density electron current across the magnetic field.     

Radio-frequency stabilization of a nonequilibrium plasma accelerator

Results of experimental studies of the effect of an external RF field on the excitation of oscillations in a magnetoplasmadynamic plasma accelerator are presented. It is found that applying an RF field can suppress the drift component of low-frequency oscillations in the ejected plasma flow. The experimental data agree with the concept of stabilization of the plasma accelerator by the magnetic component of the field generated by the RF current loop. The conditions under which the RF field stabilizes the generation of the plasma flow are determined, and the factors limiting the stabilization efficiency are revealed.