Showing papers in "Plasma Physics in 1973"
TL;DR: In this article, the effect of the strength of the interaction varies significantly with energy over the widths of the distributions of two Maxwellian distributions of particles, and this effect is considered for fusion (both D-T and D-D).
Abstract: The interaction of two Maxwellian distributions of particles will differ from the interaction of the two particles at their respective Maxwell averages if the strength of the interaction varies significantly with energy over the widths of the distributions. This effect is considered here in particular for fusion (both D-T and D-D) for the mean energy of the reacting particles as a function of temperature and for the spectrum of the neutrons produced.
416 citations
TL;DR: In this paper, a drift kinetic equation is derived which contains higher order effects and the upper bound appropriate to the drift ordering is only imposed so that the result is quite general and can be reduced to previous drift equations.
Abstract: A drift kinetic equation is derived which contains higher order effects. The upper bound appropriate to the drift ordering is only imposed so that the result is quite general and can be reduced to previous drift equations. The differential geometry of the magnetic field enters only trivially and a single recursion suffices to obtain the desired result.
177 citations
TL;DR: In this paper, an integral equation for the density of the neutral gas in a plasma is derived starting from the Boltzmann equation, where inelastic collisions are considered only as charge exchange and ionisation.
Abstract: Starting from the Boltzmann equation for the neutral gas in a plasma, an integral equation for the density of the neutral gas is derived. Inelastic collisions are taken into account only as charge exchange and ionisation. The integral equation is solved numerically. It is shown that the reflection mechanism of neutral particles from the wall modifies the density profile. The distribution function of the charge exchange neutrals deviates from a Maxwellian, and for fast particles (v>vth) we obtain f0 approximately v-1exp(-(v2/vi)). The total particle and energy fluxes on the wall are also calculated.
61 citations
TL;DR: The total longitudinal force which acts on a high-frequency heated plasma column is derived for any arbitrary absorption mechanism as mentioned in this paper, which results in particle drifts and poloidal fields which may be relevant to toroidal plasma confinement.
Abstract: The total longitudinal force which acts on a high-frequency heated plasma column is derived for any arbitrary absorption mechanism. This force arises from any departure from longitudinal symmetry (longitudinal plasma motion, a single travelling wave, etc.). It results in particle drifts and poloidal fields which may be relevant to toroidal plasma confinement. High-frequency power of order 105 W is sufficient to replace the driving electric field in a moderate scale tokamak.
42 citations
TL;DR: In this paper, the ion acoustic wave response to an impulse disturbance is experimentally examined for two different exciting mechanisms: double-plasma (D-P) and plate excitation methods.
Abstract: The ion acoustic wave response to an impulse disturbance is experimentally examined for two different exciting mechanisms. The differences and similarities are noted for the double-plasma (D-P) and plate excitation methods. The observed response agrees well with that predicted from a self-similar study of a fluid equation model which includes the effects of Poisson's equation.
35 citations
TL;DR: In this article, the dynamics of four nonlinearly interacting coherent coherent magnetohydrodynamic (MHD) waves (plasmons) is investigated and exact analytical solutions are obtained which describe the time behaviour of the amplitudes and phases of the waves.
Abstract: The dynamics of four non-linearly interacting coherent magnetohydrodynamic (MHD) waves (plasmons) is investigated. Exact analytical solutions are obtained which describe the time behaviour of the amplitudes and phases of the waves. The analysis of the solutions shows that they vary periodically. The periods of variation are also found for various types of coherent interacting MHD waves.
28 citations
TL;DR: In this paper, the electrostatic potential rise is calculated across a perpendicular shock wave, in the approximation that the resistive shock heating results solely in an increase of electron, and not ion, temperature.
Abstract: The electrostatic potential rise is calculated across a perpendicular shock wave, in the approximation that the resistive shock heating results solely in an increase of electron, and not ion, temperature. The result is applicable to shocks in which the ions undergo some other form of irreversible heating, such as viscous heating. A simple relation is obtained between the electrostatic potential rise and the jumps in magnetic field and electron temperature, making possible a relatively simple indirect measurement of electron heating from magnetic and electric probe data.
26 citations
TL;DR: In this paper, the general electromagnetic problem of coupling a magnetized, hot electron-ion plasma column to an arbitrary r.f. exciting field which is periodic along the column axis is considered.
Abstract: The general electromagnetic problem of coupling a magnetized, hot electron-ion plasma column to an arbitrary r.f. exciting field which is periodic along the column axis is considered. The plasma is described by fluid theory and the absorbed r.f. power is computed in a broad frequency range (from omega omega ce). The influence of all parameters is systematically investigated and the often startling effects of axial propagation, electron temperature, TE or TM mode of exciting field and boundedness of the plasma are emphasized. Finally the distribution of r.f. energy between ions and electrons is discussed.
24 citations
TL;DR: In this paper, it was shown that the minimum value of the magnetic field above which the plasma can be sustained appears to be a function of gas pressure, and when the pressure is high enough, this minimum field varies with the plasma density in a manner similar to that of the first Bernstein mode.
Abstract: Some properties have been investigated of a plasma which is maintained by microwave excitation whose frequency omega is greater than the electron gyromagnetic frequency Omega e. The absorption of high frequency energy is completely achieved in spite of a low collision rate. It is found that the minimum value of the magnetic field above which the plasma can be sustained appears to be a function of gas pressure. Furthermore, when the pressure is high enough, this minimum field varies with the plasma density in a manner similar to that of the first Bernstein mode.
22 citations
TL;DR: In this paper, the axial variation of the ambipolar potential in a mirror machine is presented for an angular ion distribution which is not maximum at theta = pi /2(theta =Arc tg(nu 1/nu 11)).
Abstract: The calculation of the axial variation of the ambipolar potential in a mirror machine is presented for an angular ion distribution which is not maximum at theta = pi /2( theta =Arc tg( nu 1/ nu 11)). In this condition the potential presents a dip at the mid-plane; cold ions can be trapped in the electrostatic well. The cold ion density is calculated.
22 citations
TL;DR: In this paper, the motion of a satellite in a collisionless plasma, parallel to the magnetic field is simulated in a Q-machine and the effects of a parallel ion temperature and of the self consistent electric field are discussed.
Abstract: The motion of a satellite in a collisionless plasma, parallel to the magnetic field is simulated in a Q-machine. Previous theories are extended to include the effects of a parallel ion temperature and of the self consistent electric field. The measurements appear to be well explained by the present theory; in particular the coupling of the wake with ionic Bernstein modes is demonstrated. When the cross-sectional area of the obstacle is made to vary in time, the propagation of a 'magneto ballistic pseudo wave' the properties of which are connected to those of the steady wake is predicted and observed. This experiment is used as a measurement of the ion mean velocity and of the ion perpendicular temperature in a Q-machine.
TL;DR: In this paper, the complete dispersion equation governing small-amplitude quasi-longitudinal oscillations of hot homogeneous anisotropic plasma has been solved numerically for a wide range of plasma parameters.
Abstract: Damping of quasi-longitudinal plasma oscillations in the lower hybrid frequency range has been investigated. The complete dispersion equation governing small-amplitude quasi-longitudinal oscillations of hot homogeneous anisotropic plasma has been solved numerically for a wide range of plasma parameters. Temporal damping rates of stable eigen oscillations and spatial damping rates of externally driven plasma waves are given. The lower hybrid dispersion curves are presented. The straight-line orbit approximation and the influence of distant collisions on the ion resonant interaction are discussed. The results obtained indicate that the wave energy is preferentially given to the ion perpendicular motion while an efficient energy transfer to the electrons requires a large electron velocity spread along the field lines.
TL;DR: In this article, the characteristics of plasma produced by a TEA-CO2 laser have been studied using an interferometer, a charge collector and a particle analyser, and the influence of the incident wavelength on these characteristics has been investigated.
Abstract: The characteristics of plasma produced by a TEA-CO2 laser have been studied using an interferometer, a charge collector and a particle analyser. The influence of the incident wavelength on these characteristics has been investigated.
TL;DR: In this paper, the axial electron density of an axisymmetric plasma was determined without inverting an integral equation using the angle of refraction of a laser beam as a function of incident beam lateral displacement.
Abstract: A mathematical analysis is developed which allows the axial electron density of an axisymmetric plasma to be determined without inverting an integral equation The required input includes the angle of refraction of a laser beam as a function of incident beam lateral displacement Data at several wavelengths are required to eliminate contributions to the refractivity due to atoms and ions Either long laser wavelengths or large electron densities are necessary to cause measurable refraction angles Experimental data have been collected at several wavelengths for a stable argon arc discharge at atmospheric pressure The analysis of these data yield electron densities which are in good agreement with thermodynamic calculations
TL;DR: In this paper, the locus of the beam electrons with reference to energy, position and wave phase is described, and the experiment follows theory until saturation, in which the beam and wave do not follow prediction in that the wave decays and the beam particles become trapped at velocity smaller than the wave velocity.
Abstract: The result of a measurement of the locus of the beam electrons with reference to energy, position and wave phase, is described. The experiment follows theory until saturation. Subsequently the beam and wave do not follow prediction in that the wave decays and the beam particles become trapped at velocity smaller than the wave velocity. Two candidates for the untrapping are the transverse electric field and cyclotron damping, both of which are present in this wave. The damping transfers energy into the plasma, while the transverse electric field transfers energy into transverse motion of the beam electrons. Thus, it is possible that longitudinal beam energy is lost finally to the plasma and/or transverse beam energy.
TL;DR: The concept of non-magnetic effective inductance is experimentally verified in this paper and the acceleration and containment of the Polytron is shown to be given by a particle equation mi(dvphi /dt)=ZeEphi and occurs in thin sheaths in the ring cusp planes.
Abstract: The Polytron is a toroidal plasma configuration, using 36 magnetic cusps joined point-to-point. This paper presents observations of the acceleration and containment of the plasma. Measurement of the force on the plasma shows that the initial acceleration is given by a particle equation mi(dvphi /dt)=ZeEphi and occurs in thin sheaths in the ring cusp planes. The concept of a non-magnetic effective inductance is experimentally verified. However rapid, although not complete loss of plasma occurs after 1 mu sec for argon, limiting the electron temperature to 30 eV at an electron density of 1020 m-3. This loss is expected and an energy balance at this time implies that electron thermal conduction causes the principal loss of energy. After this loss, the rest of the plasma drifts to the outer wall of the vacuum vessel after about 3 mu sec.
TL;DR: In this article, the equilibrium of a helically symmetric, current-carrying low-beta plasma was investigated by solving the equation CurlB=sB self-consistently in helical symmetry.
Abstract: The equilibrium of a helically symmetric, current-carrying low- beta plasma is investigated. The force-free magnetic field B=BH+BJ, generated by a current Je=CurlBJ=sB(s=const.) in a straight l=2 stellarator vacuum field BH, is calculated by solving the equation CurlB=sB self-consistently in helical symmetry. In order to impose the appropriate boundary conditions at the limiter, a self-consistent free-boundary problem is solved. The magnetic field configuration, the current distribution, the magnetic surfaces and the rotational transform are calculated.
TL;DR: In this article, the random fluctuation spectrum of the electron density is calculated by orbital statistics for arbitrary electron velocity distributions, and for a velocity dependent collision frequency nu, it is shown that collisions produce two effects: spectral broadening due to phase interruption, and spectral narrowing due to a reduction of the forward velocity by dynamical friction.
Abstract: The random fluctuation spectrum of the electron density is calculated by orbital statistics for arbitrary electron velocity distributions, and for a velocity dependent collision frequency nu . It is shown that collisions produce two effects: spectral broadening due to phase interruption, and spectral narrowing due to a reduction of the forward velocity by dynamical friction. For a Maxwellian velocity distribution all results are expressed in terms of the error function of complex argument and, for constant nu , they are practically equivalent to results obtained earlier from the autocorrelation function of a Brownian particle.
TL;DR: In this paper, the authors investigated the iso-thermalization of strongly anisothermal magnetized collisionless plasmas by collective electromagnetic interactions with the aid of particle-in-cell simulation methods.
Abstract: The iso-thermalization of strongly anisothermal magnetized collisionless plasmas by collective electromagnetic interactions is investigated with the aid of particle-in-cell simulation methods. The iso-thermalization process is found to be strongly dependent on the initial ratio of the two temperatures involved, Tperpendicular to /T/sub ///: the higher Tperpendicular to /T/sub /// the stronger the relaxation. For sufficiently large Tperpendicular to /T/sub /// values the iso-thermalization is complete. The time evolution of the instability (i.e. the built up and decay of the electromagnetic turbulence) and of the particle relaxation (iso-thermalization) for several initial conditions is presented and discussed. These results should provide a guide for elaborating a fully non-linear theory.
TL;DR: In this paper, the linear dispersion relation is solved numerically for Te approximately Ti with particular attention given to directions of propagation away from the perpendicular to B and wavelengths longer than the electron gyroradius.
Abstract: Electrostatic waves in a Vlasov plasma of unmagnetized ions and magnetized electrons undergoing E*B and gradient B drifts are considered. The linear dispersion relation is solved numerically for Te approximately Ti with particular attention given to directions of propagation away from the perpendicular to B and wavelengths longer than the electron gyroradius. The results lead to the conclusion that this 'modified two stream instability' is probably not important in perpendicular resistive shocks.
TL;DR: In this paper, the ion energy spectrum of a turbulently-heated hydrogen plasma was measured during the first approximately 10 mu sec. During this time the energy spectrum is isotropic and well approximated by a two-temperature Maxwellian distribution.
Abstract: Measurements are reported of the ion energy spectrum of a turbulently-heated hydrogen plasma in the Cornell THM-2 experiment. The results show that the ion-heating mechanism simultaneously affects the entire length of the plasma column. Ion heating scales linearly with current, but the dependence on electric field strength is less than linear. The stored energy which drives the heating pulse is variable from 250 to 1000J. In all cases the ions account for approximately 10 percent of the total plasma energy. The efficiency of energy transfer to the plasma is approximately 4 percent, but for the most energetic condition the efficiency is found to be sensitive to the conductivity of the initially cold plasma. The H1+ energy spectrum sampled from the outer periphery of the plasma was measured during the first approximately 10 mu sec. During this time the energy spectrum is isotropic and well approximated by a two-temperature Maxwellian distribution. For the most energetic discharge the low energy component accounts for approximately 90 per cent of the ions and has Ti approximately=320 eV. The high energy component has Ti=1400 eV.
TL;DR: In this article, the authors measured the ion energy parallel to the magnetic field of a modified Penning discharge with a retarding potential energy analyzer, and the results suggest that turbulent processes previously observed in this discharge Maxwellianize the velocity distribution along a radius in velocity space.
Abstract: The distribution function of ion energy parallel to the magnetic field of a modified Penning discharge has been measured with a retarding potential energy analyzer. These ions escaped through one of the throats of the magnetic mirror geometry. Simultaneous measurements of the ion energy distribution function perpendicular to the magnetic field have been made with a charge-exchange neutral detector. The ion energy distribution functions are approximately Maxwellian, and the parallel and perpendicular kinetic temperatures are equal within experimental error. These results suggest that turbulent processes previously observed in this discharge Maxwellianize the velocity distribution along a radius in velocity space, and result in an isotropic energy distribution. The kinetic temperatures observed are on the order of kilovolts, and the tails of the ion energy distribution functions are Maxwellian for up to a factor of 7 e-folds in energy. When the distributions depart from Maxwellian, they are enhanced above the Maxwellian tail. Above densities of about 1010 particles per cem3, this enhancement appears to be the result of a second, higher temperature Maxwellian distribution. At these high particle energies, only the ions perpendicular to the magnetic field lines were investigated.
TL;DR: In this article, the moment equations of plasma physics are examined in a form that is directly Galilean invariant and is suited for taking advantage of the small charge and current densities that occur in a dense plasma.
Abstract: The moment equations of plasma physics are examined. They are arranged in a form that is directly Galilean invariant and is suited for taking advantage of the small charge and current densities that occur in a dense plasma. Further, the results are given in a form that is symmetric in the various species. For a two component plasma the mass momentum, charge, and current densities are the natural variables. When a larger number of species are present the equations become very complicated, particularly when collisional momentum exchange is included. The current does not separate cleanly from other components, and the designation of 'Ohm's Law' becomes arbitrary. The entire set of moment equations can be considered to be the generalized Ohm's Law since they are a coupled set of equations for the sources in Maxwell's equations.
TL;DR: In this paper, the current and density distributions for the non-equilibrium plasma in a segmented electrode duct are computed for values of the electron Hall parameter between 0 and 10.
Abstract: Current and density distributions for the non-equilibrium plasma in a segmented electrode duct are computed for values of the electron Hall parameter between 0 and 10. A two-dimensional, time-dependent numerical model is used. It is found that the behaviour of the plasma depends on its stability to electrothermal waves, and the ratio of segmentation length to electrode pair separation, L/H. In the unstable regime the current flow is dominated by the presence of streamers, which are approximately one-dimensional. For L/H of order unity the streamers have a beneficial influence on current conduction, i.e., the non-equilibrium plasma duct possesses a lower internal impedance than the uniform plasma duct for the same average electrical conductivity, Hall parameter and duct dimensions. For L/H much less than unity the reverse is true.
TL;DR: In this article, basic axioms of the theory of continuous media are employed to obtain the field equations and jump conditions of mixtures composed by charged species having chemical reactions and electromagnetic interactions.
Abstract: Basic axioms of the theory of continuous media are employed to obtain the field equations and jump conditions of mixtures composed by charged species having chemical reactions and electromagnetic interactions. These are: conservation of mass and charge, balance of momenta, conservation of energy, principle of entropy, and the balance laws of the Maxwell-Lorentz theory of electromagnetic fields. Relativistic effects associated with large material velocities are not incorporated into the theory. Nonlinear and linear constitutive equations are obtained for a slightly ionized plasma with diamagnetic effects and ionization. The solution of a cylindrical positive column is presented to illustrate the theory.
TL;DR: In this article, the Bennett-type identities and general solutions for relativistic electron beams in plasmas with return current and with or without an external magnetic field parallel to the beam are derived, and a general expression for the current screening factor is obtained.
Abstract: Macroscopic equilibria of relativistic electron beams in plasmas, with return current and with or without an external magnetic field parallel to the beam, are investigated in cylindrical geometry. Bennett-type identities and general solutions are derived, and special examples are considered, in particular low-net-current, quasineutral configurations. A general expression for the current screening factor is obtained. Because of screening, relaxed versions of the Alfven-Lawson conditions determine whether beam propagation is possible. These conditions are easily satisfied for low perpendicular temperatures and sufficiently diffuse density profiles of the beam; they do not limit the beam current. Only equilibria with zero total charge, nonzero total net current, and beam profiles without sharp boundary, can be obtained from the equations and boundary conditions used.
TL;DR: In this article, the authors considered the possibility of heating a Tokamak plasma with the help of a compression wave induced in the plasma by a wave guide system, where the frequency of the wave is a high harmonic of the ion cyclotron frequency.
Abstract: The possibility of heating a Tokamak plasma with the help of a compression wave induced in the plasma by a wave guide system is considered. The frequency of the wave is a high harmonic of the ion cyclotron frequency. Plasma heating cannot occur through linear resonant mechanisms. Heating due to the non-linear amplification of ion Bernstein modes is studied, taking into account the existence of the magnetic surfaces and the non-uniformity of the static field. The value of the wave field which is necessary to obtain effective plasma heating is calculated.
TL;DR: In this article, an experimental study of the mechanisms occurring in the constricted type of discharge used in ion sources has been performed, where the variation on the radius of the fireball forming at the constriction, together with the plasma potential, electron temperature and density variation through the discharge, were measured as a function of the discharge current and neutral gas flow rate and pressure.
Abstract: An experimental study of the mechanisms occurring in the constricted type of discharge used in ion sources has been performed. The variation on the radius of the fireball forming at the constriction, together with the plasma potential, electron temperature and density variation through the discharge, were measured as a function of the discharge current and neutral gas flow rate and pressure. The studies showed that the fireball grows out of the background plasma whenever local conditions require that the electron drift velocity exceed the ion sound speed. Large jumps in potential and electron temperature are found to occur across the sheath surrounding the fireball in a hydrogen discharge. In addition a maximum discharge current limitation in terms of the neutral gas flow rate was observed.
TL;DR: In this article, it was shown that ions in a laser heated plasma can be heated directly by laser induced plasma instabilities, which may explain the large neutron yields seen in some experiments involving the focusing of nanosecond laser pulses onto solid deuterium targets.
Abstract: Computer experiments and theoretical arguments suggest that ions in a laser heated plasma can be heated directly by laser induced plasma instabilities This may explain the large neutron yields seen in some experiments involving the focusing of nanosecond laser pulses onto solid deuterium targets