Hot Magnetized Plasma Research Articles

Excitation of VLF quasi-electrostatic oscillations in the ionospheric plasma

A numerical solution of the dispersion equation for electromagnetic waves in a hot magnetized collisionless plasma has shown that, in a current-free ionospheric plasma, the distortion of the electron distribution function reproducing the downward flow of a thermal electron component and the compensating upward flow of the suprathermal electrons, which are responsible for the resulting heat flux, can destabilize quasi-electrostatic ion sound waves. The numerical analysis, performed with ion densities and electron temperature taken from the data recorded by the Interkosmos-24 (IK-24, Aktivny) satellite, is compared with a VLF spectrum registered at the same time on board. This spectrum shows a wide frequency band emission below the local ion plasma frequency. The direction of the electron heat flux inherent to the assumed model of VLF emission generation is discussed

Wave focusing near the electron cyclotron frequency in hot plasmas

Microwave transmission spectra measured on the Tore Supra tokamak [Equipe Tore Supra, in Proceedings of the 12th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Nice, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 1, p. 9] exhibit a systematic enhancement of the transmitted power at frequencies close to the electron gyrofrequency, often well beyond the corresponding level detected in vacuum. In order to explain such observations, the problem of electromagnetic wave propagation near the electron cyclotron frequency in a hot magnetized plasma is investigated in the framework of geometrical optics. The simple case of the ordinary mode injected vertically is studied by taking the finite plasma temperature and relativistic corrections to the dispersion relation into account, in contrast with the more familiar cold plasma ray-tracing approach. It is found that the ray trajectories are strongly affected by such effects in the anomalous dispersion region close to the cyclotron resonance. As a consequence of this analysis, it is shown that the local enhancement of the transmitted power observed experimentally can be explained as a focusing phenomenon related to hot-plasma corrections to the wave refractive index.

Nonlinear waves in hot magnetized plasma

Nonlinear low-frequency long wavelength waves are studied in the framework of the proposed method of the direct kinetic equation expansion in the inverse gyrofrequency power series. Nonlinear two-dimensional equations are found for perpendicular magnetosonic waves with subsequent reduction to the Korteweg–de Vries equation for quasistationary one-dimensional (QS1D) perpendicular magnetosonic wave. The dispersion is determined by the ion gyroradius ρi. Equations for nonlinear QS1D parallel Alfvén waves and QS1D oblique fast magnetosonic waves are found. It is shown that the form of the equations coincides with that one obtained from hydrodynamics but the dispersion lengths and coefficients at nonlinear terms are different. Dispersion of quasiparallel fast waves is positive and determined by the ion inertial length c/ωpi, while quasiperpendicular waves have negative dispersion determined by the ion gyroradius ρi.

Geometrical, kinetic and atomic physics effects in a two dimensional time dependent fluid simulation of ablating fuel pellets

The ablation process of hydrogen fuel pellets in hot magnetized plasmas is investigated using a newly developed two dimensional time dependent hydrodynamics code, P2D. Surface evaporation and ablated fluid flow are evolved, coupled with a kinetic calculation of the non-local heating due to slowing down of hot Maxwellian background electrons in the cold ablated plasma. Results of the neutral gas shielding model of pellet ablation are extended to include effects due to non-spherical ablation flows, proper treatment of scattering in the kinetic calculation of the hot electron heat deposition, and atomic physics processes in the ablation cloud and at the pellet surface. These effects have been considered previously, though never as a comprehensive whole. The non-spherical nature of the ablation flow reduces the ablation rate by about a factor of two, while the use of a full Maxwellian distribution for the hot electrons increases ablation by a factor of about four. With Maxwellian hot electrons, atomic physics effects (principally due to dissociation and sublimation) can reduce the ablation rate by up to a factor of two. These effects are systematically quantified using simple physical arguments and code results. For comparison with experiment, we give a simple fit to the code ablation rate results for spherical deuterium pellets: G2DGS approximately=1.65*1015Rp(cm)1.26ne(cm-3)0.35Te(eV)1.87 atoms/s, where Rp is the pellet radius and ne (Te) is the plasma density (temperature). This fit is compared with measured local ablation rates in Ohmic discharges on TFTR and JET. Predicted ablation rate profiles agree well with those on TFTR, but poorly with those on JET; pellet penetration depths agree well on both machines. Probable causes of the observed discrepancies (both experimental and theoretical) are discussed; in particular, transport processes in the post injection plasmas are shown to be able to account for some of the differences

Wave equations for a relativistic magnetoplasma

The linearized relativistic Vlasov-Maxwell system for a hot inhomogeneous relativistic magnetized electron plasma is studied through particle orbit theory using the techniques of Fourier transform. An analytical integral expression in the (k, omega )-space is obtained for the current density for waves propagating across an externally applied uniform static magnetic field (k is the wavenumber and omega is the wave frequency). After applying inverse Fourier transform, differential equations for the electric field are obtained from the expression for the current density combined with Maxwell's equations. These fully relativistic equations are correct up to second order in rc/L. where rc is the electron gyroradius and L is the gradient length of the plasma inhomogeneity.

Exact algebraic dispersion relations for wave propagation in hot magnetized plasmas

A new model is presented for the treatment of wave propagation along an external magnetic field in a hot collisionless plasma. The analysis is based on the so-called polynomial distribution functions along the magnetic field, and takes account of enhanced fractions of high-energy particles, which are characteristic of rarefied and magnetized astrophysical plasmas, in comparison with the bi-Maxwellian distributions. These new distributions permit the derivation of general dispersion relations that are exactly valid for waves with Im (ω) > 0, and represent good approximations for those with Im (ω) > 0. Furthermore, the explicit form of the dispersion relations is shown to be valid for distribution functions of different shapes. Because of their algebraic structure, the solution of the dispersion relations can be shown to be equivalent to the determination of the roots of complex-valued polynomials. The cold plasma, the Maxwellian plasma and the so-called quasi-Maxwellian plasma appear in this formalism as asymptotic and special cases. The reliability of the model is demonstrated with the calculation of dispersion curves, growth and damping rates for several standard modes, and by comparing it with previous calculations carried out using explicit Maxwellian distributions. Finally, the tendency of the solar wind to generate ion-cyclotron waves is investigated as a first, new application.

Inhibition of electron thermal conduction by electromagnetic instabilities

Heat flux inhibition by electromagnetic instabilities in a hot magnetized plasma is investigated. Low-frequency electromagnetic waves become unstable due to anisotropy of the electron distribution function. The chaotic magnetic field thus generated scatters the electrons with a specific effective mean free path. Saturation of the instability due to wave-wave interaction, nonlinear scattering, wave propagation, and collisional damping is considered. The effective mean free path is found self-consistently, using a simple model to estimate saturation level and scattering, and is shown to decrease with the temperature gradient length. The results, limited to the assumptions of the model, are applied to astrophysical systems. For some interstellar clouds the instability is found to be important. Collisional damping stabilizes the plasma, and the heat conduction can be dominated by superthermal electrons.

Dynamics and gravitational interaction of waves in nonuniform media.

We derive the generally covariant equations describing the propagation of waves with an arbitrary dispersion relation in a nonuniform, nondissipative medium. The back-reaction of the waves on the medium is expressed in terms of the wave energy-momentum tensor. The formalism is based on variations of the Lagrangian of the system with respect to the wave amplitude and phase and the particle orbits. The Lagrangian approach is considered in detail in the context of a cold, unmagnetized plasma. It is shown that the inertial mass of a photon in a plasma, namely the plasma frequency, is also its gravitational mass. Extremely precise experiments are needed to measure the gravitational free fall of phonons, plasmons, or photons in laboratory media. Finally, we indicate how the formalism can be extended to hot magnetized plasmas.

Ultrarelativistic excitation of beat waves in a hot magnetized plasma

A theoretical investigation is made on the nonlinear relativistic excitation of an electrostatic electron plasma wave at the beat frequency of two high-power colinear laser beams in a hot, homogeneous and magnetized plasma. The relativistic Vlasov equation expressed in gyrokinetic variables has been employed to find the nonlinear response of the magnetized plasma electrons. It is noted that the power density associated with the excited beat wave is much higher for the relativistic consideration than that for the nonrelativistic consideration.

Relativistic second-harmonic generation in a laser-produced plasma

In this paper the relativistic second-harmonic generation of a high-power laser radiation in a laser-produced plasma has been studied theoretically in the presence of a self-generated magnetic field. The relativistic Vlasov equation has been employed for the nonlinear response of the electrons in the hot magnetized plasma. It is observed that the power conversion efficiency of the generated second harmonic wave is much higher for relativistic calculations than that for nonrelativistic calculations.

Path‐integrated growth of electrostatic waves: The generation of terrestrial myriametric radiation

It is generally accepted that electrostatic wave energy is the source of terrestrial myriametric radiation (TMR), but there are several theories to suggest how this energy is converted into TMR. The linear mode conversion “window” theory of Jones (1976, 1980), which in the past has been considered by some to be too inefficient to account for the observed wave amplitudes, is considered here. First, the ray tracing program HOTRAY is described. This program is used to trace electromagnetic and electrostatic waves in a hot magnetized plasma and to calculate the path‐integrated growth rates for a realistic unstable particle distribution function. A density model is constructed from wave observations made by DE 1 of an event where TMR was beamed to northern and southern latitudes from a source very close to the magnetic equator. Ray tracing shows that backward propagating electrostatic waves can refract into electromagnetic Z mode waves and transport energy to the so‐called radio window at the equator. At this point, mode conversion of energy into O mode radiation is assumed to take place. Ray tracing of O mode radiation from the radio window shows that TMR is beamed to northern and southern latitudes as observed and as predicted by the theory. Path‐integrated growth rates show that the electrostatic waves amplify by a factor ≥42 from the background fluctuation level before reaching the window. This is sufficient to account for the observed TMR wave amplitudes which require the waves to amplify by a factor ≥20. Increasing the depth of the loss cone, or increasing the hot plasma density, to within observed limits, increases the wave amplification up to a factor of 104. Strong Landau and cyclotron damping from the hot plasma component restricts the efficient transfer of energy to the radio window to within a few tenths of a degree in latitude about the magnetic equator. Thus the strongest TMR is emitted from the equator. In general, TMR beamed to northern latitudes from radio windows north of the equator is stronger than that beamed to southern latitudes; conversely, TMR beamed to northern latitudes from radio windows south of the equator is generally weaker than that beamed to southern latitudes. It is shown that electrostatic wave energy can still be transported efficiently to the radio window for magnetic field intensity variations of 1 or 2%. Thus the generation of TMR is not sensitive to variations in the magnetic field strength of this magnitude.

Beat wave current drive with intense pulsed free-electron lasers

High power free-electron lasers make possible new methods for driving current in toroidal devices with electromagnetic waves. Earlier considerations of beat wave current drive are applied to a hot magnetized plasma and an arbitrary beat wave. Here the beating of two electromagnetic waves resonantly excites a low frequency beat wave that accelerates and heats electrons and leads to a current. The absolute current drive efficiency depends nonlinearly on the two pump wave intensities and is constrained by the Manley-Rowe relations. Accessibility at high plasma densities is not a difficulty, but a degree of frequency tunability of the wave sources is required. Particle simulations indicate that there is good coupling to an electron velocity tail for a Langmuir beat wave with a phase velocity 1.5 to 3 times (Te/me)½, so that all of the high frequency wave source is absorbed and the beat wave damps completely on the electrons. A novel diagnostic, based on an analytical solution for the linearized Fokker-Planck equation describing electron scattering and slowing down, is added to the particle code. This permits the computation of the current drive efficiency, including both the non-linear beat wave coupling and the collisional relaxation of the electron distribution. A realistic scenario for a beat wave current drive experiment in the Livermore Microwave Tokamak Experiment is calculated using the TORAY toroidal ray tracing code, and the scaling to an engineering test reactor plasma is described.

Relativistic theory of absorption and emission of electron cyclotron waves in anisotropic plasmas

The weakly relativistic theory of absorption and emission of electron cyclotron waves in hot magnetized plasmas is developed for a large class of anisotropic electron distribution functions. The results are expressed in terms of the weakly relativistic plasma dispersion functions, and therefore of the well-known plasma Z-function. The particular case of a loss-cone electron distribution function is presented as a simple example.

Asymptotic approximation for the dispersion relation of a hot magnetized plasma

An asymptotic expression for the dielectric tensor e of a hot magnetized plasma is obtained employing the steepest descents method, via the transformation of the components of ε into their integral representation. The electrostatic Bernstein dispersion relation for oblique and perpendicular propagation is discussed under this treatment. It is shown that with this procedure the computation of the dispersion relation is up to 20 times faster when it is compared with the original expression, and the relative accuracy is usually as good as O·l% for a typical case.

On the local absorption of linear electromagnetic waves in electromagnetic waves in hot magnetized plasmas

A general formulation of the local power absorption density is obtained from the Vlasov equation. An explicit expression is derived for a specific case in a two-dimensional geometry.

Magnetic field dependence of the energy-equipartition frequency and the resistivity

Transport coefficients in hot magnetized plasmas may exhibit a magnetic field dependence as a consequence of Larmor radius effects during the collision process. Here we present analytical approximations and numerical results for the energy-equipartition frequency and the parallel electrical resistivity.

Decay instability of beat waves in a hot magnetized plasma.

An electrostatic electron plasma wave excited at the beat frequency of two incident laser beams is seen to decay efficiently into an ion acoustic wave and a scattered electron plasma wave in a hot collisionless plasma in the presence of a transverse static magnetic field. The Vlasov equation in terms of guiding center coordinates has been solved to find the nonlinear response of electrons in the plasma. It is observed that a strong external magnetic field may reduce the growth rate of the decay instability appreciably and the growth rate is independent of the density of the plasma.

Electromagnetic wave propagation in relativistic magnetized plasmas

An improved mathematical technique and a new code for deriving the conductivity tensor for collisionless plasmas have been developed. The method is applicable to a very general case, including both hot (relativistic) and cold magnetized plasmas, with only isotropic equilibrium distributions being considered here. The usual derivation starts from the relativistic Vlasov equation and leads to an integration over an infinite sum of Bessel functions which has to be done numerically. In the new solution the integration is carried out over a product of two Bessel functions only. This reduces the computing time very significantly. An added advantage over existing codes is our capability to perform the computations for waves propagating obliquely to the magnetic field. Both improvements greatly facilitate investigations of properties of the plasma under conditions hitherto unexplored.

Filamentation instability of beat waves in a hot magnetized plasma.

A large-amplitude longitudinal electrostatic electron plasma wave excited at the beat frequency of two laser beams is shown to be strongly unstable against the filamentation instability for arbitrary short-wavelength perturbations in the presence of an external transverse magnetic field. The Vlasov equation in terms of guiding-center coordinates has been employed to obtain the nonlinear response of electrons in the plasma. It is concluded that a strong static magnetic field efficiently reduces the growth rate of the filamentation instabilty of the excited electron plasma wave.

Kinetic damping of transverse waves

In a hot magnetized plasma large ion excursions can take place along the magnetic field lines, thereby introducing kinetic effects which cannot be treated in terms of a macroscopic fluid model. These effects are studied for transverse wave motions of ions and electrons in a homogeneous thermal plasma which is immersed in a homogeneous magnetic field. Strong kinetic wave damping is found to occur when the product kui of the wave number k and the ion thermal velocity ui exceeds the ion gyro frequency omega i. The physical mechanism of this damping originates from the ion excursions and differs from that of Landau and cyclotron damping. For plasmas having a comparatively low beta value, such as in Tokamak experiments, the present results indicate that kinetic damping becomes important only at small wave lengths, as compared to the dimensions of the plasma body. However, in high-beta systems, such as the Z-pinch, wave lengths in a large range become affected by kinetic damping, in some cases even those which are comparable to the characteristic macroscopic dimensions. This also affects the conditions of plasma stability and plasma high-frequency heating.