Showing papers in "Plasma Physics in 1975"

Propagation of ion-acoustic waves in a multi-component plasma

Abstract: The authors derive the Korteweg-de Vries equation in a multicomponent plasma that includes any number of positive and negative ions. The solitary wave solutions are also found explicitly for the case of isothermal and non-isothermal electrons.

Gigawatt microwave from an intense relativistic electron beam

Abstract: Microwave generation experiments were carried out on a multimegavolt electron accelerator (33 MV, 80 kA) X-band microwave power as high as approximately 1 GW was measured Results are compared with a non-linear theory of unstable resonant interaction between a TE waveguide mode of the electron drift tube and an electron cyclotron wave on the beam

Thermal conduction in laser fusion

Abstract: The treatment of thermal conduction in the context of laser-driven fusion is examined critically. Expressions are given for electron and ion conductivity and for electron-ion equilibration after a discussion of the applicability of pre-existent formulations, supplemented by some new analysis, to the relevant density-temperature regime which includes Fermi degeneracy (with some judicious interpolation where the theories fail). The sensitivity of the fusion calculations to these considerations is illustrated by comparing the history of a typical laser-pellet interaction computer with the present coefficients and with the classical Spitzer set.

Electrostatic electron-cyclotron waves in plasma with a loss-cone distribution

Abstract: An analytical investigation and numerical solutions of the dispersion equation for electrostatic waves in plasma with a loss-cone velocity distribution are presented. The general structure of the dispersion branches is elucidated and the maximum growth rates found for different sets of plasma parameters. The results obtained provide a basis for treating magnetospheric and laboratory experimental results concerning electrostatic waves with frequencies close to (m+1/2) omega c.

Resistive Tearing Modes in a Sheet Pinch with Shear Flow

Abstract: Resistive tearing modes are analysed in a plane sheet pinch with shear bulk plasma flow present. A perturbation theory using asymptotic series is applied for small resistivity and sero viscosity. The analyticity problems arising in the vicinity of singular points are taken into account. For a suitably defined solution uniform convergence is proved and the scaling law for the growth rate derived. The instability region is shown to depend on the function fluid kinetic energy magnetic field energy where both stabilization and destabilization are possible effect of the shear flow. The relationship to the Kelvin-Helmholtz instability is discussed.

Non-linear plasma transport equations for high flow velocity

Abstract: Collision terms for plasma transport equations are derived from the Fokker-Planck equation without the usual linearization in U=flow velocity/thermal velocity. A 13-moment ansatz for the distribution functions includes the linearized dependence of the collision terms on viscous pressure and heat flow in the transport equations for momentum, energy, viscous pressure and heat flow. The masses and temperatures of the species are arbitrary. An expansion in U is made and the lowest non-vanishing terms are retained. The resulting system is discussed. The nonlinear terms in U may be important even for moderate U. All analytic results were obtained with the symbolic computer language REDUCE.

Production of dense thermonuclear plasmas by intense ion beams

Abstract: For very high density plasmas, large energy accumulation within a small volume is required. As an alternative to laser- or relativistic electron-beams, the employment of intense non-relativistic beams of heavy ions is considered. Because of the rather low ion velocities, the beams can be axially compressed thereby shortening the duration of the beam pulse and increasing the beam power by perhaps several orders of magnitude. The low ion velocities make it possible to build up the beam rather slowly in about approximately 10-6 sec, prior to its axial compression and delivery to the target. This long build up time may permit the use of cheap inductive energy storage devices to drive the beam. In case capacitors are used one can simply pulse the beam with the upper terminal of a Marx generator.

The coupled mode approach to nonlinear wave interactions and parametric instabilities

Abstract: The non-linear interaction of a few coherent, weakly damped longitudinal and transverse waves in an unmagnetized plasma is considered by means of the coupled mode theory. Using the equations describing the non-linear wave interactions the threshold electric fields and initial growth rates of a number of parametric instabilities are calculated. The following four instabilities, all of which are relevant to laser fusion are considered: (i) the parametric ion-acoustic-Langmuir wave integration, (ii) the two plasmon decay, (iii) stimulated Raman scattering and (iv) stimulated Brillouin scattering. All these instabilities are driven by a large amplitude electro-magnetic wave.

Current driven ion cyclotron waves in collisional plasma

Abstract: The stability of obliquely propagating ion cyclotron waves to current flow along the magnetic field lines, in a fully ionised plasma, is examined using fluid equations. It is shown that when a certain threshold current is exceeded, instability results through normally dissipative terms like parallel resistivity, thermal conductivity, etc.

Test charge potentials in turbulent plasmas

Abstract: The potential of stationary test charge in a uniform quiescent Maxwellian plasma decreases exponentially at distances larger than the Debye length. The possibility that the potential may decrease in a significantly different manner in a turbulent plasma was investigated. The far field potential in a weakly turbulent magnetized plasma was derived, in order to calculate collision frequencies. The effects of turbulence on the scattering of laser light by plasmas is also discussed.

Absorption of electromagnetic waves in a radially inhomogeneous plasma at high magnetic fields

Abstract: The paper deals with the experimental study of the absorption of microwave energy in plasma in a strong magnetic field, omega ce/ omega >>1, where omega ce and omega are the electron cyclotron and wave frequency respectively. The microwave energy is delivered to the plasma by a cylindrical helical structure. The experiments have verified the possibility of efficient absorption of the microwave energy for ratios up to omega ce/ omega =14. It was found that the absorption is practically independent of the magnetic field, and for magnetic fields lying in the interval omega ce/ omega in (1, 14) is nearly constant.

Analysis of light scattering data from relativistic plasmas

Abstract: The relativistic theory developed by previous authors for the spectral profile of a Thomson scattered wave is applied to the highest temperatures expected from currently planned fusion machines (25 keV). Adequate procedures for data reduction and error analysis are described and applied to experimental results collected on TFR. These computations yield corrected temperatures and error bars which differ already considerably from those obtained by the usual procedures. The temperatures are as much as 35 per cent lower, and the errors 50 per cent less, than the corresponding classical values.

Spherical electric probe in a continuum gas

Abstract: The problem of a spherical electric probe in a continuum gas without chemical reactions is re-examined when the dimensionless probe potential omega p is large and comparable to rho p, the ratio of probe radius to the ion Debye length. An asymptotic scheme for omega p to infinity shows that the ion-sheath region near the probe and the quasi-neutral region further away are separated by a single transition region which must be carefully matched to them. The properties of the transition equation are investigated in some detail, and numerical results are obtained determining the second-order (ion) current to the probe. Universal curves are given for the first- and second-order currents when the electron temperature equals the ion temperature.

Linear two-stream instability of warm relativistic electron beams

Abstract: The linear dispersion relation for a warm relativistic electron beam propagating through a cold plasma is studied. The beam electrons have the same energy, but there is a spread in their directions of motion. Numerical solutions have been obtained for the fastest growth rate delta for wave vectors k at various angles to the direction of propagation of the beam. It is found that even for very strong beams ( alpha 1/3 gamma >>1; alpha =nb/np) the hydrodynamic phase, when delta varies as alpha 1/3, during which waves parallel to the beam axis grow in the same fashion as if the beam were cold, plays an important role. The kinetic phase ( delta varies as alpha ) occurs only after the angular spread reaches large values.

Ablation of hydrogen pellets in hydrogen and helium plasmas

Abstract: Measurements on the interaction between solid hydrogen pellets and rotating plasmas are reported. The investigations were carried out because of the possibility of refuelling fusion reactors by the injection of pellets. The ablation rate found is higher than expected on the basis of a theory of a shielding neutral gas layer.

Electron cyclotron resonance heating in a pulsed mirror experiment

Abstract: Using a plasma, generated by contact ionization, in a pulsed mirror device, a microwave pulse is used for electron cyclotron resonance heating (ECRH). The average electron energy was found by measuring the X-ray bremsstrahlung spectrum from the plasma after peak compression, and the energy obtained was measured as a function of applied electric field. The results show a saturation of heating in agreement with the theory of ECRH of Lieberman and Lichtenberg (1973). Computer calculations of the average electron energy and the energy distribution were in good agreement with the experimental data.

Parametric excitation of ion-cyclotron waves

Abstract: A modulated magnetic field is shown to parametrically excite a pair of oppositely polarized waves propagating along the magnetic field, one of which is an ion-cyclotron wave. The growth rate and threshold of the instability are calculated and compared with the results for the low-frequency Alfven wave. It is found that the excited cyclotron wave's frequency is close to the ion-cyclotron frequency omega ci only if the pump frequency is much greater than omega ci.

Energy principle for two-dimensional resistive instabilities

Abstract: An energy principle for 2-d resistive instabilities has been found. It leads to a necessary and sufficient condition for stability allowing the use of test functions. One simple consequence is that the current density in a plasma with arbitrary cross section should not increase to the outside. Otherwise the plasma would be unstable against resistive instabilities.

Action conservation in the presence of a high-frequency field

Abstract: Even in the presence of a high-frequency field, which strongly modifies the plasma normal modes and their coupling coefficients, the Manley-Rowe condition for action conservation remains valid.

Numerical parameter studies for the dense plasma focus

Abstract: The magnetohydrodynamic equations are solved using an explicit numerical scheme for the focus geometry together with the electrical circuit equation. The influence of varying circuit parameters, focus apparatus dimensions and filling pressure on the discharge characteristics, especially the maximum current, and the plasma variables in the pinch phase are examined and compared with experimentally determined neutron outputs. An experimentally derived scaling law for the dependence of maximum neutron output on bank energy, filling pressure, and length of the inner electrode is confirmed by the results of the MHD computations.

Plasma heating in the presence of parametric instabilities in a magnetic field

Abstract: Heating of a magnetically confined plasma column in a mirror device is studied when high power microwave pulses are injected with frequencies well above the ion plasma frequency but below the electron plasma and the electron cyclotron frequencies. The fundamental aspects of the parametric instability are in agreement with theory. It is found that in this frequency regime for pulse times of the order of 10 mu sec or less, mainly the tail of the electron and the ion distribution function are heated. The number of particles populating these tails amount to a few percent (5 per cent) for the available input powers (P

High speed photographic studies of the equilibrium and stability of the atc tokamak

Abstract: High speed photographic studies of the equilibrium and stability of the atc tokamak have been performed. Framing speeds of 26000 pictures per sec were achieved as were effective shuttering times of 5 musec. Streak photography with time resolution of 15 musec was also performed. Studies of the disruptive instability enabled the radial expansion velocity of the plasma cross section to be determined. Differences in the form of the negative spike on the loop voltage between disruptions which led to the plasma interacting with the limiter and those which did not were found. A histogram giving the relative occurrence of disruptive instabilities vs the q of the plasma just before the disruption was constructed.

Generation of an intense stationary wave in modulated beam-plasma systems

Abstract: The basic equations and numerical results which describe the non-linear interaction of a weak, modulated electron beam with a single, stationary one-dimensional wave, excited in a cold, magnetic field-free plasma, are presented and discussed. The effect of all possible irreversible processes (e.g. plasma turbulence) accompanying this interaction is simulated by a constant, effective collision frequency nu eff of plasma electrons. Starting from the non-linear Poisson equation, expressions for the amplitude and phase of the beam-excited wave are derived and then solved numerically, together with the equations of motion of the beam electrons. The results are compared with those of the time-dependent model. Considerable differences which can be detected experimentally are established.

Geometric resonances near the lower hybrid frequency

Abstract: Radio frequency waves at extremely low power and near the lower hybrid frequency are coupled inductively to a plasma cylinder. The dominance of geometric resonances is verified. The strength of anomalous damping is observed to be related to the steepness of radial density gradients; a qualitative explanation by means of linear mode conversion is discussed.

Plasma confinement in presence of magnetically shielded supports

Abstract: During recent investigations on plasma confinement by internal ring systems with magnetically shielded supports some authors have arrived at contradictory conclusions. This paper reconsiders support shielding in terms of the problems of plasma cut-off at the support surfaces, the plasma equilibrium in presence of the support field, non-adiabatic effects on transit and trapped particles, and magnetic field misalignment in the weak-field regions.

Non-linear mode-mode coupling at a plasma-vacuum transition layer

Abstract: An investigation is made of wave generation at combination frequencies for the oblique incidence of polarized electromagnetic waves on a semi-bounded plasma when the width of the plasma-vacuum transition layer is much less than the wavelength. The amplitudes of the waves radiated at combination frequencies are calculated. It is shown that the tangential electric field components of the waves at the combination frequencies are discontinuous at the plasma boundary. This explains the differences in our results from the corresponding results of earlier papers in which the tangential electric field components of higher harmonics at the plasma boundary were assumed to be continuous.

On the quasi-linear theory of momentum transfer from r.f. oscillations to a plasma including the effect of Coulomb collisions

Abstract: An investigation is made into the effect of particle dragging, which occurs when toroidal plasmas are r.f. heated by travelling waves. A generalized quasi-linear relaxation theory in a collisional plasma is developed, including the effect of the conservation of the longitudinal component of momentum. The dependence of the toroidal current on the amplitude of the r.f. field and on the plasma parameters is obtained and a saturation effect for this current is found at strong r.f. fields.

Measurement of the electron temperature and density of a helium plasma produced by a hollow cathode arc discharge

Abstract: The electron temperature and electron density of a steady state helium plasma produced by a hollow cathode arc discharge have been measured with the aid of Thomson scattering as functions of the radial distance to the plasma axis. Electron densities in the range of 1*1019 to 4*1019 m-3 and electron temperatures 0.5*105 to 2.5*105K were determined with an accuracy of 5% in both. The observed Thomson spectra indicate a Maxwell-Boltzmann velocity distribution of the electrons. The Thomson scattering measurements have been spatially extended by probe measurements.

Interferometric measurement of particle densities in cascaded arcs at atmospheric pressure

Abstract: Two wavelength interferometry is applied to a cascaded arc burning in Ar, Xe and He at atmospheric pressure. The interferometer is of the Mach-Zehnder type with a He-Ne-laser as a light source. The refractive index of the plasma is measured at the wavelengths lambda 1=6328 AA and lambda 2=33912 AA and is compared to calculated data. A contribution of excited levels to the refractive index was not found in the temperature and pressure range studied here. Using experimentally determined refractive index profiles neutral and electron density distributions are derived and compared to spectroscopically measured values. The comparison shows that the diagnostic method applied here leads to accurate particle densities without using any assumption concerning the thermodynamic equilibrium state of the plasma.

Dissipative trapped electron instability in a linear machine

Abstract: A study of the dissipative trapped electron instability is greatly simplified, both experimentally and theoretically, when posed in a cylindrical geometry. A derivation of the linear dispersion relation for a finite cylindrical system with two localized magnetic mirrors shows that a linear machine can support the instability with strong localization between the mirrors. The growth rate can be larger than 10% of the wave frequency which is approximately the drift frequency. A simple physical explanation is provided for the dynamics of the instability. An experiment was performed in a Q-machine converted to an ODE-type device in which the dissipative trapped electron instability was definitively identified through the dependence of the wave amplitude on mirror ratio, axial position, temperature gradient, electron collision frequency, and radial position. The wave, with the azimuthal mode number 1, is nearly monochromatic at approximately 50 kHz which is in the neighbourhood of the drift frequency. The density fluctuation in the wave can be as high as 30%.