Boundary conditions for the electromagnetic field in a waveguide with a thin-walled annular plasma in the context of application to plasma microwave electronics

Effective boundary conditions for the electromagnetic field of the slow surface waves of a thinwalled annular plasma in a metal waveguide are derived and justified. With the boundary conditions obtained, there is no need to solve field equations in the plasma region of the waveguide, so that the dispersion properties of plasma waveguides can be investigated analytically for an arbitrary strength of the external magnetic field. Examples are given that show how to use the effective boundary conditions in order to describe surface waves with a normal and an anomalous dispersion. The boundary conditions are then employed to construct a theory of the radiative Cherenkov instabilities of a thin-walled annular electron beam in a waveguide with a thinwalled annular plasma. The single-particle and collective Cherenkov effects associated with low-and high-frequency surface waves in an arbitrary external magnetic field are studied analytically. The method of the effective boundary conditions is justified in the context of application to the problems of plasma relativistic microwave electronics.     

Generation of terahertz radiation in the reflection of a laser pulse from a dense plasma

The generation of low-frequency (terahertz) electromagnetic radiation in the reflection of a laser pulse from the boundary of a dense plasma is considered. Low-frequency wave electromagnetic fields in vacuum are excited by a vortex electric current that is induced at the plasma boundary by the ponderomotive force of the laser pulse. The spectral, angular, and energy parameters of the low-frequency radiation, as well as the spatiotemporal structure of the emitted waves, are investigated. It is shown that for typical parameters of present-day laser plasma experiments, the power of terahertz radiation can amount to tens of megawatts.     

Nonlinear dynamics of the interaction of a modulated electron beam with a plasma

The excitation of plasma waves during the injection of an unmodulated and a density-modulated electron beam into a semi-infinite cold plasma is investigated. It is shown that the Langmuir oscillation energy accumulated in the plasma increases substantially near the plasma boundary and that the dimension of the region where the Langmuir oscillation energy is localized decreases with time.     

Tearing instability in a tokamak with a noncircular cross section

Using a straight-column model to describe tokamak plasma with a noncircular cross section, it is shown how to (i) find the boundary of tearing instability from the condition of existence of a magnetohydrodynamic plasma equilibrium different from that of a straight cylinder by solving a two-dimensional linear boundary-value problem with a second-order equation with respect to the flux coordinate and (ii) find the spatial structure of the tearing mode and the corresponding effective Δ' when there is only one resonance magnetic surface in the plasma for a given axial wavenumber by solving some kind of a boundary-value problem for the perturbation. The proposed approach is illustrated by numerical calculations for the case of an elliptical cross section as an example.     

Dynamics of a magnetic field in dusty plasma

The problem of the expansion of a magnetic field in a complex (e.g., dusty) plasma is considered, with a focus on the effects produced by the independent transport of charged components that does not break plasma quasineutrality. Solutions to a set of nonlinear equations are obtained for different initial and boundary conditions. In particular, it is shown that the field rapidly penetrates into the plasma when the dust is charged negatively and does not penetrate at all when the dust charge is positive.     

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.     

Dissipation of Energy of an AC Electric Field in a Semi-Infinite Electron Plasma with Mirror Boundary Conditions

Absorption of the electromagnetic energy in a semi-infinite electron plasma is calculated for an arbitrary degree of the electron gas degeneracy. Absorption is determined by solving the boundary-value problem on the oscillations of electron plasma in a half-space with mirror boundary conditions for electrons. The Vlasov?Boltzmann kinetic equation with the Bhatnagar–Gross–Krook collision integral for the electron distribution function and Maxwell’s equation for the electric field are employed. The electron distribution function and the electric field inside plasma are searched for in the form of expansions in the eigenfunctions of the initial set of equations. The expansion coefficients are found for the case of mirror boundary conditions. The contribution of the plasma surface to absorption is analyzed. Cases with different degrees of electron gas degeneracy are considered. It is shown that absorption of the electromagnetic energy near the surface depends substantially on the ratio between the electric field frequency and the volumetric electron collision frequency.     

Thermal nonlinearity of potential surface waves at a plasma-metal interface

A study is made of the effect of the heating of plasma electrons in the field of a potential surface wave on the wave dispersion properties. The wave is assumed to propagate along the boundary between a metal and a finite-pressure plasma. Different mechanisms for electron energy losses are considered in the weak heating approximation. The spatial distribution of the plasma electron temperature under nonlocal heating conditions is derived on the basis of the electron energy balance equation. Expressions for the spatial damping rate and the nonlinear shift of the wavenumber are analyzed for different values of the plasma parameters. The results obtained are valid for both semiconductor and gaseous plasmas.     

Ion acceleration in a dipole vortex in a laser plasma corona

Particle-in-cell simulations show that the inhomogeneity scale of the plasma produced in the interaction of high-power laser radiation with gas targets is of fundamental importance for ion acceleration. In a plasma slab with sharp boundaries, the quasistatic magnetic field and the associated electron vortex structure produced by fast electron beams both expand along the slab boundary in a direction perpendicular to the plasma density gradient, forming an extended region with a quasistatic electric field, in which the ions are accelerated. In a plasma with a smooth density distribution, the dipole magnetic field can propagate toward the lower plasma density in the propagation direction of the laser pulse. In this case, the electron density in an electric current filament at the axis of the magnetic dipole decreases to values at which the charge quasineutrality condition fails to hold. In electric fields generated by this process, the ions are accelerated to energies substantially higher than those characteristic of plasma configurations with sharp boundaries.     

Identification of the plasma boundary shape and position in the Damavand tokamak

A series of experiments and numerical calculations have been done on the Damavand tokamak for accurate determination of equilibrium parameters, such as the plasma boundary position and shape. For this work, the pickup coils of the Damavand tokamak were recalibrated and after that a plasma boundary shape identification code was developed for analyzing the experimental data, such as magnetic probes and coils currents data. The plasma boundary position, shape and other parameters are determined by the plasma shape identification code. A free-boundary equilibrium code was also generated for comparison with the plasma boundary shape identification results and determination of required fields to obtain elongated plasma in the Damavand tokamak.     

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.     

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.     

High-frequency surface waves at a plasma-metal interface: I. Linear model

A study is made of the dispersion properties of surface waves at a plasma-metal interface under thermodynamically nonequilibrium conditions such that a space charge sheath forms at the plasma boundary. In the simplest model, the sheath is described as a dielectric with a given permittivity. The wave parameters in a highly collisional plasma are discussed. The effect of interaction between waves propagating near the opposite plasma boundaries is considered, in particular, for space charge sheaths of different thicknesses. Conditions are determined under which the parameters of surface waves are substantially altered by the plasma-sheath geometric resonance.     

Transition radiation generated by a short laser pulse at a plasma-vacuum interface

A theory is presented of the generation of low-frequency transition radiation by a short laser pulse at a plasma-vacuum interface. The wave electromagnetic fields are excited by the vortex electric current that is generated at the plasma boundary by the ponderomotive force of the laser field. The spectral, angular, and energy parameters of the transition radiation, as well as the spatiotemporal structure of the emitted waves in vacuum and in plasma, are investigated. It is shown that the parameters of the transition radiation depend essentially on the ratio of the laser pulse duration to the plasma oscillation period. Under conditions typical of present-day laser-plasma experiments, the transition electromagnetic radiation is generated in the terahertz frequency range and its power can reach several megawatts.     

Theory of transverse surface electromagnetic waves propagating along a plasma-metal boundary with a finite radius of curvature in a magnetic field

The spectra of electromagnetic waves propagating perpendicular to the axis of a plasma-filled metal waveguide in a magnetic field are studied with allowance for the effects exerted upon the wave frequency by the radial plasma density variation and by the emission of waves through a narrow axial slit in a waveguide wall. The case of wave propagation along the boundary between a plasma and a cylindrical metal waveguide wall with a periodically varying radius of curvature is also considered. The electromagnetic properties of the plasma are described by a dielectric tensor in the hydrodynamic approximation. The spatial distribution of the wave field is determined by the method of successive approximations. Results are presented from both analytical and numerical investigations. Analytical expressions for the corrections to the wave frequency due to the emission of the wave energy from the waveguide and due to the slight corrugation of the waveguide wall are obtained. The rates of wave damping due to the emission of the wave energy through a narrow axial slit and due to collisions between the plasma particles are found. The correction to the frequency that comes from the periodic variation of the radius of curvature of the plasma surface is calculated to within terms proportional to the square of the small parameter describing the azimuthal corrugation of the waveguide wall. The effect of the radial plasma density variation on the dispersion of the surface modes is examined both analytically and numerically.     

Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field

The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a secondorder ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calculated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maximum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counter-directed ion flux.     

Pressure insensitivity of a high-β quasi-isodynamic stellarator

The sensitivity of a high-β quasi-isodynamic stellarator equilibrium with respect to changes of the plasma pressure is investigated. It is shown that a plasma boundary near to the high-β boundary exists with the property that the magnetohydrodynamic and drift-kinetic properties of the associated low-β plasma are similar.     

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.     

Pressure profiles of a plasma confined by the magnetic field of a ring current

Pressure profiles p(ψ) marginal with respect to convective instability in a toroidal tubular plasma confined by the magnetic field of an internal levitated ring current and external ring currents are studied as functions of the shape of the magnetic separatrix. Configurations are found in which the maximum plasma pressure in a finite-width layer near the plasma boundary decreases by two orders of magnitude at the expense of artificially raising the effective length (characterized by the integral ∮dl/B) of the magnetic field lines near the separatrix surface. It is shown that, in the case of a straight cylindrical tubular plasma, which is the limiting case of a toroidal configuration with an arbitrarily large aspect ratio, the sufficient condition for the plasma to be MHD stable against both convective and kink perturbations is satisfied for local values β≤0.4. __________ Translated from Fizika Plazmy, Vol. 26, No. 6, 2000, pp. 519–528. Original Russian Text Copyright ￠ 2000 by Popovich, Shafranov.