Skin Effects in a Dusty Plasma

A multifluid MHD model is applied to study the magnetic field dynamics in a dusty plasma. The motion of plasma electrons and ions is treated against the background of arbitrarily charged, immobile dust grains. When the dust density gradient is nonzero and when the inertia of the ions and electrons and the dissipation from their collisions with dust grains are neglected, we are dealing with a nonlinear convective penetration of the magnetic field into the plasma. When the dust density is uniform, the magnetic field dynamics is described by the nonlinear diffusion equations. The limiting cases of diffusion equations are analyzed for different parameter values of the problem (i.e., different rates of the collisions of ions and electrons with the dust grains and different ratios between the concentrations of the plasma components), and some of their solutions (including self-similar ones) are found. The results obtained can also be useful for research in solid-state physics, in which case the electrons and holes in a semiconductor may be analogues of plasma electrons and ions and the role of dust grains may be played by the crystal lattice and impurity atoms.     

Analysis of the processes occurring in a submicrosecond discharge with a linear current density of up to 3 MA/cm through a thick-wall stainless-steel electrode

The state of conductors carrying a megampere current from the generator to the load is studied experimentally. It is found that the plasma produced from cylindrical stainless-steel tubes during the passage of a submicrosecond current pulse with a linear density of 3 MA/cm expands with a velocity of 5.5 km/s. Numerical results on the diffusion of the magnetic field induced by a current with a linear density of 1–3MA/cm into metal electrodes agree with the experimental data on the penetration time of the magnetic field. For a linear current density of 3.1 MA/cm, the experimentally determined electric field strength on the inner surface of the tube is 4 kV/cm. The calculated electric field strength on the inner surface of the tube turns out to be two times higher, which can be explained by plasma production on the outer and inner surfaces of the electrode.     

Study of the implosion of wire arrays at the PF-3 facility

Results of experiments on the compression of tungsten wire arrays by the plasma current sheath (PCS) of the PF-3 facility at currents of up to 2 MA are presented. The efficiency of current transportation to the wire array and switching-over of the discharge current to the array were studied. Information on the penetration of the magnetic field into the wire array obtained using microprobes made it possible to compare the obtained experimental data with the results of magnetic field measurements carried out at other high-power electrophysical devices. The intensity of plasma production from tungsten wires under the action of the plasma focus PCS is estimated. The experimental results are tested against the existing models of wire array implosion with prolonged plasma production.     

Influence of the electrons reflected from the collector on the parameters of a high-current relativistic electron beam

In plasma microwave oscillators, electrons fall onto the surface of a graphite collector, which leads to the generation of secondary electrons. The influence of the electrons reflected from the collector on the parameters of a high-current relativistic electron beam propagating in a strong longitudinal magnetic field was studied experimentally and by numerical simulations. It is shown that the penetration of the reflected electrons into the drift space can lead to a substantial increase in the depth of the potential well in the drift space, a decrease in the velocity of the beam electrons, and a broadening of the electron energy distribution function.     

Dynamics of the plasma injected into the gap of a plasma opening switch across a strong magnetic field

A method is proposed to increase the linear charge density transferred through a plasma opening switch (POS) and, accordingly, reduce the POS diameter by enhancing the external magnetic field in the POS gap. Results are presented from experimental studies of the dynamics of the plasma injected into the POS gap across a strong magnetic field. The possibility of closing the POS gap by the plasma injected across an external magnetic field of up to 60 kG is demonstrated.     

Studies of penetration of the magnetic field into electrically imploded loads in the Angara-5-1 facility

Results are presented from measurements of the distributions of the azimuthal magnetic field in aluminum, copper, molybdenum, tungsten and other wire arrays electrically imploded at currents of up to 3 MA in the Angara-5-1 facility. It is shown that the time during which the magnetic field of the current pulse reaches the array axis depends on the material of the wires or wire coating. The current of the precursor formed on the array axis before the implosion of the main load mass is measured. It is shown that the penetration of the load material with the frozen-in magnetic field into a polymer (agar-agar) foam liner is drastically different from that in the case of a wire array. It is found that the rate of current transfer to the array axis is maximum for tungsten wire arrays. The rates of plasma production during implosion of loads made of different materials are compared.     

Experimental study of the evaporation and expansion of a solid pellet in a plasma heated by an electron beam

Results are presented from experiments on the injection of solid pellets into a plasma heated by an electron beam in the GOL-3 device. For this purpose, two pellet injectors were installed in the device. The target plasma with a density of ～10¹⁵ cm^?3 was produced in a solenoid with a field of 4.8 T and was heated by a highpower electron beam with an electron energy of ～1 MeV, a duration of ～7 s, and a total energy of 120–150 kJ. Before heating, the pellet was injected into the center of the plasma column transversely to the magnetic field. The injection point was located at a distance of 6.5 or 2 m from the input magnetic mirror. Polyethylene pellets with a mass of 0.1–1 mg and lithium-deuteride pellets with a mass of 0.02–0.5 mg were used. A few microseconds after the electron beam starts to be injected into the plasma, a dense plasma bunch is formed. In the initial stage of expansion, the plasma bunch remains spherically symmetric. The plasma at the periphery of the bunch is then heated and becomes magnetized. Next, the dense plasma expands along the magnetic field with a velocity on the order of 300 km/s. A comparison of the measured parameters with calculations by a hydrodynamic model shows that, in order to provide such a high expansion velocity, the total energy density deposited in the pellet must be ～1 kJ/cm². This value substantially exceeds the energy density yielded by the target plasma; i.e., the energy is concentrated across the magnetic field onto a dense plasma bunch produced from the evaporated particle.     

Influence of asynchronous actuation of the Angara-5-1 facility modules on the penetration of the magnetic field inside a wire array

The influence of asynchronous actuation of the Angara-5-1 facility modules on the implosion symmetry of the wire array plasma in the Z-pinch mode is studied. It is shown that an increase in the r.m.s. jitter in the start times of the modules leads to an appreciable azimuthal asymmetry of magnetic field penetration inside the wire array and, as a consequence, to an increase in the duration of the soft X-ray pulse, a decrease in its power, and a shift of the Z-pinch with respect to the array axis. Necessary conditions for axisymmetric pinch implosion are determined. Experimental data on the magnitude and azimuthal distribution of the current (magnetic field) inside the wire array were obtained from magnetic probe measurements. The position of the Z-pinch with respect to the wire array axis was determined from two-dimensional X-ray images and radial optical streak images.     

A semi-analytical model for calculating the penetration depth of a high energy electron beam in a water phantom with a magnetic field

PurposeAs an electron beam is incident on a uniform water phantom in the presence of a lateral magnetic field, the depth-dose distribution of the electron beam changes significantly and forms the well-known ‘Bragg peak’, with a depth-dose distribution similar to that of heavy ions. This phenomenon has pioneered a new field in the clinical application of electron beams. For such clinical applications, evaluating the penetration depth of electron beams quickly and accurately is the critical problem.MethodsThis paper describes a model for calculating the penetration depth of an electron beam rapidly and correctly in a water phantom under the influence of a magnetic field. The model was used to calculate the penetration depths under different conditions: the energies of electron beams of 6, 8, 12 and 15 MeV and the magnetic induction intensities of 0.75, 1.0, 1.5, 2.0 and 3.0 T. In addition, the calculation results were compared with the results of a Monte Carlo simulation.ResultsThe comparison results indicate that the difference between the two calculation methods was less than 0.5 cm. Moreover, the computing time of the calculation model was less than a second.ConclusionsThe semi-analytical model proposed in the present study enables the penetration depth of the electron beam in the presence of a magnetic field to be obtained with a computational efficiency higher than that of the Monte Carlo approach; thus, the proposed model has high potential for application.     

Decay instability of a laser pulse propagating in a transverse direction in a magnetized plasma

The decay instability of a lser pulse propagating across an external magnetic field in a subscritical plasma is investigated analytically and numerically. It is shown that, when the relaxation of the pulse is taken into account, the hydrodynamic growth rate of the decay instability is slower than that obtained earlier in the constant-amplitude pump wave approximation. The results of numerical simulations by a particle-in-cell method demonstrate that an increase in the amplitude of the parametrically excited waves is accompanied by a decrease in their group velocity; in this case, up to 85% of the laser energy is converted into the energy of the plasma particles. It is found that, under resonance conditions, the magnetic field acts to increase the energy of the accelerated ions that escape from the plasma slab through its front boundary.     

Near field of a loop antenna operating in plasma in the whistler frequency range

The structure of the RF magnetic field in the vicinity of a loop antenna operating in the whistler frequency range has been studied experimentally and theoretically. The experiments were performed over a wide frequency range at different values of the plasma density, electron temperature, and ambient magnetic field strength. It is shown that, when a loop antenna is smaller than the wavelength of a quasi-longitudinal whistler, the structure of the magnetic field of such an antenna is nearly the same as that of the field of a current-carrying loop in vacuum; otherwise, the RF field is localized near the antenna wire. The results of numerical calculations agree with the measured field distributions. The antenna field is calculated by expanding it in the eigenmodes of a magnetized plasma with allowance for not only propagating but also nonpropagating (exponentially decaying) waves, which make the main contribution to the near field. An analytic estimate of the depth to which the RF magnetic field of a loop antenna penetrates into the plasma is obtained.     

Passage of electromagnetic waves through the critical surface

A study is made of the passage of electromagnetic waves through the critical surface at small angles between the plasma density gradient and the magnetic field. Expressions are derived for the transmission and reflection coefficients of electromagnetic oscillations that are periodic in the direction transverse to the density gradient. The penetration of wave beams is also analyzed. In the case of a wide beam, the incident and transmitted ray trajectories are shown to be mirror-image about the resonance surface. Behind the resonance surface, a narrow incident wave beam generates a beam propagating along the magnetic field.     

Effects of a homogeneous magnetic field on erythrocyte sedimentation and aggregation

Effects of a homogeneous static magnetic field on erythrocyte sedimentation rate (ESR) have been assessed by using the standard Westergren method. A magnetic field of 6.3 T in the vertical direction only slightly enhanced ESR in saline solution, which was consistent with an effect on cell orientation. On the other hand, the magnetic field greatly enhanced ESR in plasma. It took a long time (about 20 min) for an ESR change to occur in plasma in response to the magnetic field. The effects in plasma were too large to originate only from cell orientation and were clearly distinct from a magnetic field-induced Boycott effect under an inhomogeneous magnetic field. A morphological examination and the nonlinear time course of the sedimentation in plasma indicated that the magnetic field increased cell aggregation and thereby enhanced ESR in plasma. Bioelectromagnetics 18:215–222, 1997. © 1997 Wiley-Liss, Inc.     

Role of the Hall flute instability in the interaction of laser and space plasmas with a magnetic field

The interaction of an expanding laser plasma with a uniform external magnetic field is studied over a wide range of experimental parameters (for a plasma energy of up to 300 J and a magnetic induction of up to 8 kG). By analyzing the data from these and other experiments, as well as the results of simulations with the use of a two-fluid Hall plasma model, it was found for the first time that the flute instability of the plasma boundary plays a decisive role in the process of the plasma cloud expansion. It is shown that, when the ion Larmor radius is sufficiently large, this instability can significantly affect the maximum radius of the diamagnetic cavity of the plasma cloud and the deceleration of its front by the magnetic field. A physical model based on the Hall effect is proposed to explain such influence. The model adequately describes data from one-dimensional simulations, as well as from experiments with quasi-spherical laser plasma clouds. The results obtained can be helpful in interpreting the data from active magnetospheric experiments with barium plasma clouds (such as AMPTE) and analyzing the plasma dynamics in future ICF reactors and propulsion systems with a magnetic field for direct conversion of fusion energy into electric energy.     

Distinctive features of collisionless gradient drift instabilities in a high-β plasma in a highly nonuniform magnetic field

A set of Vlasov-Maxwell equations for collisionless electromagnetic drift instabilities of high-β plasma configurations with a nonuniform magnetic fields is solved. The effect of the transverse static magnetic field variation and magnetic field line curvature, as well as the plasma temperature and density gradients, is considered. It is shown that, in a nonuniform magnetic field, the behavior of the instabilities differs substantially from that in a uniform field. Electromagnetic modes propagating strictly transverse to the lines of the static magnetic field are analyzed in detail, and unstable solutions are obtained for both extraordinary and ordinary waves. Numerical results show that, in the latter case, instability occurs when the magnetic field decreases toward the periphery and the plasma temperature and density gradients are oppositely directed.     

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.     

Magnetohydrodynamics of a weakly ionized plasma: Ambipolar magnetic diffusion and shock front structure

Kinetic equations with the BGK collision integral are used to derive MHD equations for a weakly ionized plasma that are applicable over a broad range of magnetic field strengths. In strong magnetic fields, a substantial contribution to the transverse diffusion of the magnetic field comes from the ambipolar magnetic diffusion, which is associated with the motion of both the charged component and the magnetic field against the background of the neutral plasma component. The problems of the magnetic field diffusion in a weakly ionized plasma and the shock wave structure are solved.     

Properties of a low-pressure inductive RF discharge I: Experiment

Results are presented from experimental studies of low-pressure inductive RF discharges (including those with a capacitive component) employed in plasma technology. It is shown that both the RF power absorbed in the plasma and the electron density depend nonmonotonically on the external magnetic field. Discharge disruptions occurring at critical values of the magnetic field and the spatial redistribution and hysteresis of the plasma parameters were observed when varying the magnetic field and RF generator power. The parameters of the plasma of low-pressure (0.5–5 mTorr) inductive RF discharges were investigated, and the discharge properties related to the redistribution of the RF generator power between the plasma and the discharge external circuit were revealed. The experiments were performed with both conventional unmagnetized inductive plasma sources and plasma sources with a magnetic field.     

Excitation of magnetic fields by a circularly polarized laser pulse in a plasma channel

The excitation of quasistatic magnetic fields by a circularly polarized laser pulse in a plasma channel is considered. It is shown that, to second order in the amplitude of the electric field of the laser pulse, circular rotation of the plane of polarization of the laser radiation in a radially nonuniform plasma gives rise to a nonlinear azimuthal current and leads to the excitation of the radial and axial components of the magnetic field. The dependence of the magnetic field distribution over the plasma channel on the spatial dimensions of the pulse and on the channel width is investigated for a moderate-power laser pulse. The structure of the magnetic fields excited by a relativistic laser pulse in a wide plasma channel is analyzed.     

Peculiarities of collisionless drift instabilities in poloidal magnetic configurations

Results of the numerical analysis of collisionless drift instabilities as applied to magnetic configurations with a purely poloidal magnetic field are presented. Instabilities caused by the gradients of the ion and electron temperatures and plasma density are considered within a wide range of wavenumbers. An electromagnetic model taking into account the finite plasma pressure and magnetic field curvature is formulated for configurations with a nonuniform magnetic field.