Bifurcations of axisymmetric plasma equilibrium in a tokamak

Bifurcation of solutions to the Grad–Shafranov-type equation for helically symmetric plasma near the threshold for tearing instability are analyzed. Quadratic and cubic nonlinearities were added to the linear dependence of the current density on the helical flux. Depending on the character of nonlinearity, two types of bifurcation can be observed, the “small” and the “large” ones. The small bifurcation is typical of cubic nonlinearity and reveals itself in the growth of the magnetic island from zero as the profile parameter increases above the instability threshold. The large bifurcation is typical of quadratic nonlinearity and causes jumplike formation of a large-scale magnetic island upon exceeding the instability threshold. As the profile parameter decreases below the instability threshold, the large-scale island continues to persist for some time (the hysteresis effect) and then suddenly disappears.     

Formation of a Z-pinch during electromagnetic compression of a nonquasineutral current filament

A study is made of the structure of a relativistic current filament with the azimuthal magnetic field B_θ in the range 4πn _e m _e c²?B _θ ² 4πn _i m _i c², when the plasma quasineutrality near the filament axis is violated and a narrow peak in electron density is formed there. The ion dynamics in a strong radial electric field of the filament on time scales of about several inverse ion plasma frequencies ω _pi ^?1 is investigated. The initial ion pressure prevents the ion plasma component from compression to infinitely high densities under the action of the electric field and leads to the formation of a dense hot plasma core near the axis of the Z-pinch on time scales of about a dozen ω _pi ^?1 . The compression of the ion component in the axial region gives rise to a collisionless “unloading” shock wave that propagates away from the axis and is accompanied by the vanishing of the radial ion velocity behind the shock front, the accumulation of positive charge near the axis, and the formation of a steady-state ion density profile. It is shown theoretically that ion-ion dissipation manifests itself as the destruction of the hot core of the formed Z-pinch on picosecond time scales. This may serve to explain the explosions of “hot points” in a current-carrying plasma.     

Shock structure formation in dusty plasmas

The problem of the evolution of a perturbation in a dusty plasma and its transformation into a nonlinear wave structure is considered. A computational method that allows one to solve the set of nonlinear evolutionary equations describing variable-charge dust grains, Boltzmann electrons, and inertial ions is developed. Exact steady-state solutions corresponding to ion-acoustic shock structures associated with anomalous dissipation originating from dust grain charging are found taking into account the effect of electron and ion charge separation. The role of this effect increases with the speed of the shock. The evolutions of an initial soliton (which is a steady-state wave solution in a plasma containing dust grains with a constant charge) and an initially immobile perturbation with a constant increased ion density are investigated. In a charge-varying dusty plasma, the soliton evolves into a nonsteady shock wave structure that propagates at a constant speed and whose amplitude decreases with time. The initially immobile perturbation with a constant increased ion density evolves into a shock structure similar to a steady-state shock wave. In the latter case, the compression shock wave is accompanied by a rarefaction region (dilatation wave), which finally leads to the destruction of the shock structure. The solution of the problem of the evolution of a perturbation and its transformation into a shock wave in a charge-varying dusty plasma opens up the possibility of describing real phenomena (such as supernova explosions) and laboratory and active space experiments.     

Nonlinear ion flux caused by a periodic ion-acoustic wave in plasma with two-temperature electrons

The propagation of periodic ion-acoustic waves in plasma with two-temperature electrons and cold ions is analyzed. The equations for the wave potential are derived in the first- and second-orders of the perturbation theory, and their nonsecular periodic solutions are obtained. The average nonlinear ion flux is determined, and its properties are studied as functions of the ratios between the densities and temperatures of the cold and hot electron components. The conditions are analyzed under which the ion flux is co- or counter-directed to the wave propagation direction. For the case in which, depending on the plasma parameters, the ion flux at a given wave amplitude can be either positive or negative, the domains of existence of positive and negative ion fluxes in the “temperature ratio-density ratio” plane are determined.     

Ion-acoustic “Houston's horse” effect

The structure of an ion-acoustic forerunner excited by a shock wave in a weakly ionized plasma is studied. It is shown that, when the shock velocity exceeds the ion-acoustic speed, a soliton bunch is produced at the perturbation front. The increase in the shock velocity to a certain critical value is accompanied by an increase in the soliton amplitude. A further increase in velocity leads to an explosive-like collapse of the bunch, which results in a decrease in the medium resistance. This phenomenon is analogous to the “Houston's horse” effect in narrow-channel hydrodynamics.     

Formation of charge-exchange ion flows near the exit from the stationary plasma thruster acceleration channel

Ion currents onto the exit plane of the acceleration channel of a stationary plasma thruster model were measured using electrostatic probes the collecting surfaces of which could be oriented either upstream or downstream with respect to the thruster plume. Using the results of measurements, the so-called “back” flows of charge-exchange ions onto the exit plane are estimated. It is shown that the back ion flows are the most intense in the close vicinity of the thruster, but do not exceed 0.6% of the total ion flow from the thruster. The formation of steady-state ion flows near the exit from the acceleration channel of a stationary plasma thruster is simulated numerically by using a three-dimensional kinetic model that describes the dynamics of ions and neutral atoms exhausting from the acceleration channel and produced in the thruster plume and takes into account resonance charge exchange of ions with neutral atoms. The distribution of the back ion current density in the exit plane is determined. The effect of the flow rate of the working gas through the cathode on the distributions of the neutral atom density and charge-exchange ion flows is demonstrated. The obtained results can be used to analyze the effect of the thruster plume on the charge state of the surfaces located in the vicinity of the thruster.     

Effect of viscosity on the plasma decay in a magnetic field

The effect of viscosity on the evolution of an axisymmetric plasma column in a longitudinal magnetic field is considered. It is found that, under the action of viscosity, the plasma density profile tends to become Gaussian.     

Specific features of the radial distributions of plasma parameters in the initial segment of a supersonic jet generated by a pulsed capillary discharge

Results are presented from spectroscopic studies of the initial segment of a supersonic plasma jet generated by a pulsed capillary discharge with an ablative carbon-containing polymer wall. Specific features of the spatial distributions of the electron density and intensities of spectral components caused, in particular, by the high electron temperature in the central zone, much exceeding the normal temperature, as well as by the high nonisobaricity of the initial segment of the supersonic jet, are revealed. Measurements of the radiative properties of the hot jet core (the intensity and profile of the H_α and H_β Balmer lines and the relative intensities of C II lines) with high temporal (1–50 μs) and spatial (30–50 μm) resolutions made it possible to determine general features of the pressure and temperature distributions near the central shock. The presence of molecular components exhibiting their emission properties at the periphery of the plasma jet allowed the authors to estimate the parameters of the plasma in the jet region where “detached” shock waves form.     

Theory of the ICR heating of a plasma column: Methodological note

A set of wave equations is derived that describes electromagnetic waves at frequencies on the order of the ion gyrofrequency in a plasma column with an arbitrary electron temperature. This set takes into account, in particular, the resonant interaction of electrons with waves in the transit-time magnetic pumping regime. The effect of the amplification of the electromagnetic fields of current-carrying antennas by the plasma is analyzed. The evolution of the fields with an increase of plasma density from a zero value (vacuum) is considered. The main parameters are determined for minority ion cyclotron resonance heating in the planned EPSILON system.     

Quality factor of a plasma waveguide and contraction of laser-induced breakdown waves in gases

A previously developed plasma-waveguide model of a long laser spark in atmospheric-pressure gases is used to describe the evolution of a plasma waveguide produced in the course of electric breakdown and to analyze energy dissipation in it. The requirements are formulated for the plasma density profile to be steep enough in order that the threshold conditions for electric breakdown can be satisfied, and the conditions are determined under which the distortion of the plasma density profile can lead to a decrease in the diameter of the breakdown wave.     

Reversion of thermic-shock effect on ram spermatozoa by adsorption of seminal plasma proteins revealed by partition in aqueous two-phase systems

Centrifugal counter-current distribution (CCCD) in a dextran, Ficoll, poly(ethylene glycol) two-phase system was used to study the effect of seminal plasma proteins on the partition behaviour of ram spermatozoa exposed to thermal shock. Ram spermatozoa freed from seminal plasma by a ‘swim-up’ procedure were submitted to thermal shock and fractionated by CCCD. Cell viability decreased from 68% to 18% after the treatment, showing a slight displacement of the cells from the right (where a higher enrichment of live cells is found) to the centre of the profile. A change of the distribution profile was shown in the presence of either ram or bull seminal plasma. Bull seminal plasma was able to move the profile to the right, whereas ram seminal plasma increased the proportion of cells with enhanced affinity for the lower dextran-rich phase. Plasma proteins isolated from both seminal plasmas moved the profile to the right. In addition, cell viability rose to 48% after the CCCD run in the presence of ram plasma proteins. This restoring effect was lost when ram plasma proteins were thermally denatured. Bovine serum albumin was not only unable to move the profile to the right but even promoted displacement of the profile to the left. This negative effect was also observed when proteins from bull seminal plasma were in the presence of protein-free ram seminal plasma. However, proteins isolated from ram seminal plasma still restored the profile in the presence of bull seminal plasma freed from proteins. The results presented here strongly suggest that seminal plasma proteins are absorbed by a spermatozoal surface previously exposed to thermic shock. These proteins would exert a highly specific protective effect on ram spermatozoa. In addition, in the ram seminal plasma there must be some factor which avoids this adsorption.     

Nonlinear broadband doubling of the extraordinary wave frequency in inhomogeneous magnetoactive plasma

The nonlinear resonance doubling of radio wave frequencies in inhomogeneous plasma is studied as applied to the ionosphere under the conditions of the phase synchronism between an extraordinary pump wave and its second harmonic. The synchronism is not related to plasma resonances, but is determined by the magnetic field and plasma electron density in the transparency region. The generation efficiency of the second harmonic of a transversely propagating wave is calculated for a wide frequency band lying higher than the lower hybrid resonance frequency. It is shown that this effect is physically analogous to the generation of the second harmonic of laser radiation in a nonlinear crystal. The generation efficiency of the second harmonic is determined for inhomogeneous ionospheric plasma in which the synchronism condition is satisfied in a limited frequency range. It is shown that this effect can be used for remote nonlinear diagnostics of the upper ionospheric plasma, in which the characteristic size of the synchronism region can reach several kilometers. It is proposed to use a combination of satellite and ground-based ion probes in experiments on transionospheric probing. Even if the frequency of the wave emitted from the satellite is lower than the critical frequency in the ionosphere, the frequency of its second harmonic can exceed the critical frequency, so that it can be recorded by a ground-based ion probe or a specially designed receiver. The reflected second-harmonic signal can also be detected at the satellite by using a broadband radio-frequency spectrometer.     

Physical processes of the interaction of ion and plasma streams with a target surface in a dense plasma focus device

Dynamics of the interaction of powerful streams of high-temperature plasma and fast ions generated in a device of the “Dense Plasma Focus” (DPF) type has been studied for a special case. In these experiments solid conductive targets with the shape of a plate and a tube, respectively, were placed normally and axially with respect to the Z axis of the DPF chamber on its cathode side. The secondary plasma spread out from the target surface has been examined. The shock-wave action upon the flat targets produced by the ion beam has been revealed.     

Influence of electromagnetic radiation on the shock structure formation in complex plasmas

Electromagnetic radiation effects are calculated for the case of the solar radiation spectrum in the vicinity of the Earth. The influence of the photoelectric effect on the propagation of nonlinear waves in complex plasmas is studied when the dust grains acquire large positive charges. Exact solutions to nonlinear equations in the form of steady-state shocks that do not involve electron-ion collisions are found, and the conditions for their existence are obtained. In contrast to the classical collisionless shock waves, the dissipation due to the dust charging involves the interaction of the electrons and ions with the dust grains in the form of microscopic grain currents and the photoelectric current. The nonsteady problem of the evolution of a perturbation and its transformation into a nonlinear wave structure is considered. The evolution of an intense, initially nonmoving region with a constant increased ion density is investigated. It is shown that the evolution of a rather intense nonmoving region with a constant increased ion density can result in the formation of a shock wave. In addition to the compressional wave, a rarefaction region (dilatation wave) appears. The presence of a dilatation wave finally leads to the destruction of the shock structure. The possibility is discussed of the observation of shock waves related to dust charging in the presence of electromagnetic radiation in active rocket experiments, which involve the release of a gaseous substance in the Earth's ionosphere in the form of a high-speed plasma jet at altitudes of 500–600 km.     

Electrostatic plasma turbulence and spitzer longitudinal conductivity in tokamaks

An analysis has revealed that there may be three radically different steady states of a tokamak plasma: (i) discharges in which the electron and ion transport can be described by neoclassical theory; (ii) discharges with the Spitzer longitudinal conductivity, neoclassical ion transport, and “anomalous” electron transport; and (iii) discharges in which the electron transport and ion transport are both “anomalous.” The dimensionless parameters responsible for the occurrence of the three types of discharges are determined. In accordance with the criteria derived for the achievement of different steady states, discharges of the second type are most typical of modern tokamaks and discharges of the third type can occur only if the turbulence is sufficiently strong. Discharges of the first type cannot occur in the range of the working parameters of present-day tokamaks and future tokamak reactors, but they can be ignited in a large class of magnetic confinement systems. The physical reason for the onset of different types of discharges is associated with the fact that turbulent fluctuations play very different roles in the dynamics of the ion and electron components of a finite-size magnetized plasma. The question of the self-consistency between the profiles is considered. A law is derived according to which the thermal diffusivity increases toward the plasma edge.     

Emission of alfvén waves from a nonuniform MHD waveguide

The efficiency of the wave energy loss from a nonuniform MHD waveguide due to the conversion of the trapped magnetosonic waveguide modes into runaway Alfvén waves is estimated theoretically. It is shown that, if the waveguide parameters experience a jumplike change along the waveguide axis, the interaction between the waveguide modes and Alfvén waves occurs precisely at this “jump.” This effect is incorporated into the boundary conditions. A set of coupled integral equations with a singular kernel is derived in order to determine the transmission and reflection coefficients for the waveguide modes. The poles in the kernels of the integral operators correspond to the surface waves. When the jump in the waveguide parameters is small, analytic expressions for the frequency dependence of the transformation coefficients are obtained by using a model profile of the Alfvén velocity along the magnetic field. For the jump characterized by the small parameter value ε=0.3, the wave-amplitude transformation coefficient can amount to 5–10%. Under the phase synchronization condition (when the phase velocities of the waveguide modes on both sides of the jump are the same), the wave-energy transformation coefficient is much higher: it increases from a fraction of one percent to tens of percent. The transformation of fast magnetosonic waves into Alfvén waves is resonant in character, which ensures the frequency and wavelength filteringof the emitted Alfvén perturbations.     

Stiffness and rigidity of the temperature profile in a tokamak

The notions of “stiffness” and “rigidity” of the temperature profile in a tokamak are introduced and formalized. By stiffness is meant the consistency of the profile when the plasma density, boundary temperature, and heating power change. By rigidity is meant the strong dependence of the central temperature on the boundary temperature. Analytical and numerical estimates carried out in a transport model with critical temperature gradients show that, at a low boundary temperature (the L-mode), the profiles are, as a rule, stiff but are not rigid. For a sufficiently high temperature pedestal in the H-mode, there exists a parameter range in which the profiles are stiff and at the same time rigid. However, when the pedestal temperature is too high and the deposited power profile is flat, the temperature profile may be neither stiff nor rigid. This behavior of the electron temperature profile was observed in a number of H-mode discharges with high plasma densities in the DIII-D and JET tokamaks. An analysis is also made of the stiffness and rigidity of the temperature profiles in the MAST and T-10 tokamaks.     

Reflectionless passage of an electromagnetic wave through an inhomogeneous plasma layer

An exactly solvable model is used as a basis to study the reflectionless passage of a transverse electromagnetic wave through an inhomogeneous plasma containing large-amplitude, small-scale (subwave-length) structures (in particular, opaque regions) that cannot be correctly described by approximate methods. It is shown that, during the reflectionless passage of an electromagnetic wave, strong wave field splashes can occur in certain plasma sublayers. The nonuniform spatial plasma density profile is characterized by a number of free parameters describing the modulation depth of the dielectric function, the characteristic sizes of the structures and their number, the thickness of the inhomogeneous plasma region, and so on. Such plasma density structures are shown to be very diverse when, e.g., a wave that is incident from vacuum propagates without reflection through a plasma layer (wave barrier transillumination). With the cubic nonlinearity taken into account, a one-dimensional problem of the nonlinear transillumination of an inhomogeneous plasma can be solved exactly.     

Some Features of ICR Heating by a Solenoidal Antenna

A study is made of some characteristic features of ion cyclotron resonance (ICR) heating in plasma-based isotope separators. The effects associated with ion drift in the RF field of a solenoidal antenna are considered in the single-particle approximation. Estimates are obtained and numerical calculations are carried out for ICR heating in the case of a “narrow” (ρ/r ～ 1, where ρ is the ion gyroradius) plasma flow.     

Longitudinal ion source with the current self-compensation of the focused ion beam

Utilization of ballistic focusing in the longitudinal Hall-type ion source is described. It allows transformation of the ion beam shape from an “ellipsoidal” one to a linear one, as well as increasing the ion beam current density per the operating surface. Both the influence of transverse magnetic field and edge effects on the beam shape are investigated. The ion beam is charge compensated by a plasma neutralizer designed on the basis of a supplementary semi-self-maintained magnetron-type discharge and hollow cathode effect.