Showing papers in "Plasma Physics in 1968"
TL;DR: In this paper, a collisionless Boltzmann equation with the approximation that the scale length of the equilibrium is long compared to the ion gyro radius is used to determine the stability of an experimental configuration such as the multipole.
Abstract: A method is described for the detailed investigation of electrostatic instabilities in real experimental geometries. These have frequently been discussed in the plane slab model, and modifications of it, but the present work includes all geometrical effects from the outset. The starting point is the collisionless Boltzmann equation with the approximation that the scale length of the equilibrium is long compared to the ion gyro radius. The main interest is in perturbations of low frequency but of arbitrary wavelength, which may be comparable to the ion Larmor radius. Thus several instabilities such as drift wave, flute or trapped particle, come within the scope of the theory. Expressions are first obtained for the contribution to the charge density produced by an arbitrary electrostatic perturbation affecting particles whose unperturbed orbits are (i) trapped between magnetic mirrors; (ii) circulating around closed field lines; (iii) tracing out a magnetic surface. Together with Poisson's equation these expressions lead, via the appropriate Nyquist contours, to stability criteria valid for arbitrary equilibria. Finally it is shown how this method leads to a differential equation whose solution will determine the stability of an experimental configuration such as the multipole.
197 citations
TL;DR: In this article, a theory for the process of irradiation of finite solid targets of light atoms (H2, D2, Li) by giant laser pulses is proposed, and the properties of the plasma produced are studied and the conditions to be satisfied in order to obtain an isotropic plasma are given.
Abstract: A theory is proposed for the process of irradiation of finite solid targets of light atoms (H2, D2, Li) by giant laser pulses. The properties of the plasma produced are studied and the conditions to be satisfied in order to obtain an isotropic plasma are given.
162 citations
TL;DR: In this article, an ideal hydromagnetic model was used to examine the nature of the energy sources that can drive the instability of the exchange in a single-dimensional graph. But the model was not applied to the real world.
Abstract: Interchange instabilities are examined using an ideal hydromagnetic model. The nature of the energy sources that can drive the instability is clarified.
117 citations
TL;DR: Far field effective potential of charged particle in Vlasov plasma, discussed inverse third power law for shielding test particles as discussed by the authors, and discussed the inverse third-power law for testing test particles.
Abstract: Far field effective potential of charged particle in Vlasov plasma, discussing inverse third power law for shielding test particles
95 citations
TL;DR: In this paper, a system of hydrodynamic equations for the description of a collisionless plasma is derived, which is an extension of those of CHEW et al. (1956).
Abstract: A system of hydrodynamic equations for the description of a collisionless plasma is derived. The equations for motion perpendicular to the magnetic field are an extension of those of CHEW et al. (1956). Hydrodynamic description of motion along the magnetic field is possible if v||t0/L|| is a small parameter (v|| is the thermal velocity parallel to the magnetic field, t0 the characteristic time, L|| the characteristic length scale for variation of macroscopic quantities along the magnetic field). The method of deriving the hydrodynamic equations is an extension of a method used by GRAD (1949). This extension is necessary because in collisionless plasma thermal energy is not equally distributed over all degrees of freedom. Therefore one has to consider two heat-flux vectors for the transport in thermal energy of parallel and perpendicular degrees of freedom separately. These independent heat-flux vectors are caused by gradients of the parallel and perpendicular temperature respectively. Thus one arrives at a system of equations for 16 moments of the distribution function.
89 citations
TL;DR: In this article, exact solutions of the steady-state hydromagnetic equations with a solenoidal velocity field were derived for appropriate boundary conditions in a helical geometry, where the solenoid velocity field is defined as a linear combination of the velocity field and the steady state.
Abstract: Exact solutions of the steady-state hydromagnetic equations with a solenoidal velocity field are derived for appropriate boundary conditions in a helical geometry.
63 citations
TL;DR: In this paper, the propagation and collisionless absorption of electromagnetic waves propagating in non-uniformly magnetized plasmas with regions of cyclotron resonance are computed.
Abstract: The propagation and collisionless absorption of electromagnetic waves propagating in non-uniformly magnetized plasmas with regions of cyclotron resonance are computed. The particle dynamics associated with motion in a non-uniform magnetic field near cyclotron resonance is considered explicitly. Above a critical plasma density complete wave absorption is predicted. At high plasma densities particles with high velocities along the field lines are heated preferentially whereas at lower densities the slower particles gain more energy per particle from the wave. At high densities the wave is attenuated by the high energy tail of the velocity distribution; this dissipation is shown to be consistent with the uniform field results of Stix. The lack of heating observed in Princeton ioncyclotron wave absorption experiments is resolved by considering the wave launching efficiency.
53 citations
TL;DR: In this paper, the dispersion equation for electron plasma waves in a strong magnetic field has been solved numerically where the plasma density profile is assumed to be either uniform or parabolic and the electron energy distribution Maxwellian.
Abstract: The propagation of electron plasma waves along a cylindrical plasma column in a strong magnetic field has been studied both theoretically and experimentally. The dispersion equation for such waves has been solved numerically where the plasma density profile is assumed to be either uniform or parabolic and the electron energy distribution Maxwellian. Dispersion curves have been computed for the m = 0 azimuthal mode and compared with experimental points obtained from a thermally ionized plasma in a strong magnetic field over the range of electron density 107-1010 cm-3.
50 citations
44 citations
TL;DR: In this article, the authors describe measurements made with very small Langmuir probes in gaseous afterglow plasmas at room temperature where conditions for a study of this kind are expected to offer particular advantages.
Abstract: A diversity of opinion exists at the present time concerning the interpretation of single Langmuir probe characteristics, in particular with respect to the location of space potential and the determination of charged particle number densities from the characteristics This work describes measurements made with very small Langmuir probes in gaseous afterglow plasmas at room temperature where conditions for a study of this kind are expected to offer particular advantages A comparison is made of the values of electron densities obtained from the characteristics using six methods which are commonly used Good agreement is found to exist between those deduced from the orbital limited characteristics in the accelerating region for electrons and those calculated from the probe current at the inflexion point of the characteristics That these are also in tolerable agreement with those obtained using the intersecting tangents method is thought to be fortuitous
38 citations
TL;DR: In this paper, it was shown that a considerable reduction in the length of the accelerator can be achieved by combining impact-heating with subsequent spherical implosion of the thermonuclear material in the target area.
Abstract: It was previously shown (WINTERBERG, 1963, 1964; HARRISON, 1963) that it may be possible to ignite a small thermonuclear explosion of controllable size by the acceleration of macroscopic particles up to velocities of 108 cm/sec. One method which promises to reach high velocities is the acceleration of a superconductor by a travelling magnetic wave (WINTERBERG, 1966a; MAISONNIER, 1966; WINTERBERG, 1966b). For velocities which are required to ignite a thermonuclear reaction the accelerator would become at least 10 km long. It is shown that a considerable reduction in the length of the accelerator can be achieved by combining impact-heating with subsequent spherical implosion of the thermonuclear material in the target area. Although it seems to be very difficult to perform a spherical implosion by a macroparticle hitting a target, it is, however, easy to see that the shape of the chosen geometry of the imploding cavity is not important, but rather the behavior in time of the relative change of the imploding volume. By properly shaping the macroparticle and the target, imploding cavities may be formed for which this change is the same as that for a spherical cavity. Therefore, the results derived for imploding spherical cavities can be applied.
TL;DR: In this article, 3.5 MV electrons in 30,000 A, 30 nsec pulses diverging at a half-angle of 5° have been projected through a 2 cm diameter area of 0.05 mn metal foil and upon the end of a 50, 000 A linear pinch discharge in argon.
Abstract: Using a recently developed machine, 3.5 MV electrons in 30,000 A, 30 nsec pulses diverging at a half-angle of 5° have been projected through a 2 cm diameter area of 0.05 mn metal foil and upon the end of a 50,000 A linear pinch discharge in argon. The self-magnetic fields of the linear discharge and of the injected beam pinch the relativistic beam and deliver the 3000 joules of pulse energy to a 0.6 cm diameter spot on a metal target on the far end of the pinch tube at distances of more than 160 cm. The reverse current induced in the ionized linear pinch column by the passage of the relativistic pulse is equal or nearly equal and opposite to the injected current, as anticipated theoretically, and the reduction in radius due to the pinch effect also agrees with theory.
TL;DR: In this paper, the behavior of a fully ionized plasma composed of one type of atom and subjected mainly to electromagnetic forces (waves) is treated analytically, and a strictly analytical periodic solution of the nonlinear initial equations is obtained when the ion oscillation is neglected.
Abstract: The behaviour of a fully ionized plasma composed of one type of atom and subjected mainly to electromagnetic forces (waves) is treated analytically. The problem is described by relativistic field equations and equations of motion. The general fundamental equations lead to a special system of equations yielding wave solutions in which all partial waves have the same space-time constant phase velocity. This system of equation provides: A strictly analytical periodic solution of the non-linear initial equations. The solution describes a transverse, circularly polarized electromagnetic wave. An analogous solution is obtained for a fully ionized plasma composed of electrons and k (= 1, 2, 3...) types of ions. The ions orbit in phase. The magnitudes of their orbital velocities depend on the charge and mass of the individual types of ions. A strictly analytical periodic solution of the non-linear initial equation obtained when the ion oscillation is neglected. The solution describes a longitudinal electric wave. The phase velocity of the wave has to be greater than the maximum absolute value of the longitudinal electron velocity caused by the electric field. This exact statement is dependant on a corresponding relation resulting from the Landau damping between the phase velocity and the mean thermal electron velocity. An approximate steady-state solution of the non-linear initial equations for the simultaneous coupling of the plasma, transverse and longitudinal waves. Purely longitudinal electric waves result in a constant plasma electron drift velocity (second-order): The plasma electrons stream toward the waves. A transverse plane polarized electromagnetic wave (first-order) is coupled with a plane polarized electromagnetic wave (third-order): the third-order wave oscillates at three times the frequency of the first-order wave and has a maximum amplitude which is directly proportional to the electron rest density of the wave-free plasma when the plasma frequency is sufficiently smaller than the first-order wave frequency.
TL;DR: In this paper, a two-dimensional model simulating the effects of magnetic curvature variation, magnetic shear and particle trapping is adopted to investigate the stability of a closed toroidal configuration in the high temperature collisionless regime.
Abstract: In view of investigating the stability of a closed (toroidal) configuration in the high temperature collisionless regime, a two-dimensional model simulating the effects of magnetic curvature variation, magnetic shear and particle trapping is adopted. Use is made of the Vlasov equation including finite Larmor radius and wave-particle resonance effects. Low frequency electrostatic modes are considered. Then two types of wave having the same periodicity L as the magnetic curvature, or localized in a region where curvature is unfavourable, are found. One has the frequency of the known drift wave and the other (the flute-`gravitational' wave) has frequency determined by the average favourable curvature along the lines of force. The latter wave is stabilized by imposing that L be sufficiently short as to ensure good ion communication making ion Landau damping effective. The former one by imposing that L make the effects of longitudinal ion sound wave prevail over the effects of ion inertia on their transverse motion. If the lines of force are not closed or if they are closed but their length is much larger than L, drift waves with wavelength larger than L have to be considered. In the first case they can be stabilized by shear, in the second case, waves with transverse wavelengths short enough as to make the effects of transverse inertia prevail over those of longitudinal ion inertia, remain unstable. The influence of trapped particles is investigated, finding that it contributes to reducing growth rates. Stability conditions are given for the most significant cases observing that, for non-hydromagnetic types of mode, they are easier than those obtained for the collisional regime. It is recalled that while no wave localized in a region of unfavourable curvature was found in the high temperature collisional regime, a wave driven by the known drift mechanism but localized over distances shorter than L can be found in the collisionless regime.
TL;DR: In this article, small amplitude oscillations in bounded beam-plasma systems with a sharp interface between two plasma media present were investigated and the dynamic character of the electromagnetic wave field was taken into account, which makes it possible to go beyond the quasistatic approximation usually employed.
Abstract: The present work investigates the small amplitude oscillations in bounded beam-plasma systems with a sharp interface between two plasma media present. The dynamic character of the electromagnetic wave field is taken into account which makes it possible to go beyond the quasistatic approximation usually employed. The space charge and current of the beam travelling along the external magnetic field are assumed to be compensated. The thermal motion of plasma and beam particles is neglected. Oscillation frequency and growth rates have been found for whistlers and waves corresponding to the quasistatic approximation, in a cylindrical plasma waveguide with a low density beam moving near the axis.
TL;DR: In this article, the authors investigated the behavior of a plasma with hot electrons (Te? 30 keV, ne? 3? 1010 cm-3), obtained by electron cyclotron resonance heating in an adiabatic trap.
Abstract: An investigation is made of the behaviour of a plasma with hot electrons (Te ? 30 keV, ne ? 3 ? 1010 cm-3), obtained by electron cyclotron resonance heating in an adiabatic trap. An instability is observed which leads to rapid loss of the energy of transverse plasma motion in a time ~ 1 ?sec. The instability is accompanied by radiation near the electron cyclotron frequency and its second harmonic. Simultaneously the ejection of hot electrons is observed, both along and perpendicular to the magnetic lines of force. A possible theoretical explanation of the observed phenomena is considered.
TL;DR: In this article, an analysis of the mechanism whereby strong variable electric fields occur in an ion beam in which the space charge is compensated by the electrons which the beam produces in a rarefied gas is given.
Abstract: An analysis is given of the mechanism whereby strong variable electric fields occur in an ion beam in which the space charge is compensated by the electrons which the beam produces in a rarefied gas. An experimental study has been made of the nature of the plasma instabilities responsible for the dynamic decompensation of the beam and effective means of controlling these instabilities have been found. The results are more or less applicable to all physical systems in which intense ion beams in a strong magnetic field are used, for example electromagnetic isotope-separators and plasma traps with external injection of fast ions.
TL;DR: In this article, a theoretical study of axially symmetric oscillations in a bounded beam-plasma system is presented, where the external magnetic field is assumed to apply along the symmetry axis and the dynamic character of wave fields is taken into account.
Abstract: A theoretical study has been made of the axially symmetric oscillations in a bounded beam-plasma system. The external magnetic field is assumed to apply along the symmetry axis and the dynamic character of wave fields is taken into account. The excitation of plasma oscillations in a waveguide is investigated in the presence of a low density beam passing near the axis. Frequencies and growth rates have been obtained for the quasi-static approximation, for `whistler mode' and magnetohydrodynamic waves.
TL;DR: In this paper, surface waves at the interface between two plasma media in the presence of a beam of charged particles are considered and the potential oscillations of high frequency electron oscillations are investigated.
Abstract: The present paper considers surface waves at the interface between two plasma media in the presence of a beam of charged particles. The thickness of the transition layer between two media is supposed to be much less than the wavelength. Special attention has been paid to the study of potential oscillations. The excitation of high frequency electron oscillations has been considered for a configuration, consisting of a plasma and a weak beam conterminous with a vacuum. The authors have also studied instabilities in the region of low frequencies for the case, when the system, consisting of ions at rest and drifting electrons, is conterminous with a vacuum.
TL;DR: In this paper, an exact analytic dispersion relation is derived for the case where the true collision integral in the Boltzmann equation is replaced by a Fokker-Planck term and a BGK term.
Abstract: The longitudinal oscillations of a weakly ionized plasma in a constant external electric field have been studied. An exact analytic dispersion relation is derived for the case where the true collision integral in the Boltzmann equation is replaced by a Fokker-Planck term and a BGK term. Comparisons with some previous results are made.
TL;DR: In this article, the authors investigated small-amplitude oscillations in bounded beam-plasma systems with collisions taken into account, and the frequencies and growth rates were obtained for potential oscillations, as well as for helicons.
Abstract: The present work investigates small-amplitude oscillations in bounded beam-plasma systems with collisions taken into account. The beam travelling along the magnetic force lines is supposed to be compensated. The interface between two plasma media is considered to be sharp, hence the wavelength is much greater than the thickness of the transition layer. Special attention is paid to the oscillations of plasma layers confined by conducting plates. The frequencies and growth rates have been obtained for potential oscillations, as well as for helicons.
TL;DR: In this paper, a very thin current sheet is produced by induction, supporting a β = 1 plasma, which is found to be stable for a period of time, which depends on density, and is longer than expected from existing theories of resistive tearing instability.
Abstract: A very thin current sheet is produced by induction, supporting a β = 1 plasma. It is found to be stable for a period of time, which depends on density, and is longer than expected from existing theories of resistive tearing instability. At the end of this period, the sheet is rapidly destroyed. This destruction occurs when the electron density is lower than a critical value: an initial breakthrough at one point gives rise to a magnetic field across the sheet which drives the whole current layer out of equilibrium. It is shown that this breakthrough cannot be produced either by unstable ion drift waves or by electrons of the plasma running away, as already observed in other experiments. A new mechanism is needed to explain these results.
TL;DR: In this article, two high power r.f. generators, each capable of delivering pulses of 7 periods at a frequency of 3.10 Mc/s, are triggered, one generator produces an oscillating axial current in the preionized plasma while the other induces an oscillated azimuthal current.
Abstract: Helium gas at a pressure of 60 mtorr is contained in a discharge tube of 4.8 cm dia. and 49 cm length which is equipped with end electrodes and is situated within a multi-turn solenoid. The gas is preionized by means of an axial current pulse of 9.5 kA amplitude and 32 μsec duration. Following the preionization pulse, two high power r.f. generators, each capable of delivering pulses of 7 periods at a frequency of 3.10 Mc/s, are triggered. One generator produces an oscillating axial current in the preionized plasma while the other induces an oscillating azimuthal current. The generators are adjusted to give equal Bθ and Bz peak amplitudes at the inner wall of the discharge tube. These peak amplitudes reach a maximum value of 2.2 kG. When the two oscillating currents are dephased by 90°, the plasma experiences the continuous magnetic pressure exerted by a rotating field. Streak photographs show that the plasma separates from the tube wall and implodes towards the axis. Framing pictures show that cylindrical symmetry is maintained during this implosion. The implosion stage of the pinch is shown to be well represented by a solution of the appropriate snowplow equation. 1.1 μsec after the initiation of the r.f. discharge, luminosity again appears in the region of the tube wall and stays there for the remainder of the discharge. This light is associated with the production of conducting material at the wall and a subsequent growth of currents in this material. Measurements made of the time variation of the inductance of the pinch support this conclusion.
TL;DR: In this article, the frequency difference, sum and second harmonic currents, due to two interacting waves in a plasma with no external magnetic field, are calculated, and the oscillation frequencies are taken to be sufficiently high that ion motion can be neglected.
Abstract: The frequency difference, sum and second harmonic currents, due to two interacting waves in a plasma with no external magnetic field, are calculated. The oscillation frequencies are taken to be sufficiently high that ion motion can be neglected. We consider the regime where Landau damping is negligible compared to collisional damping. The non-linearity is due to gradients in the a.c. electric fields. The form of the zero-order isotopic and non-oscillatory part of the velocity distribution function is left arbitrary. The velocity dependences of the collision frequency of electrons with neutrals, ions and other electrons are properly accounted for. The Fokker-Planck equation in its integro-differential form and including non-linear terms is used for electron-electron collisions. The self-consistent electric field is included with non-linear terms. Results are given (a) for any degree of ionization provided the lowest frequency in the mixing process is greater than the total collision frequency and (b) for a slightly ionized gas for any ratio of oscillation to collision frequency. In the former case, it is shown that electron-electron effects do not contribute to the non-linear current arising from wave mixing but contribute to the non-linear self-consistent electric field.
TL;DR: In this article, the effect of a skin high frequency field polarized along the magnetostatic field, on the onset of the drift-cyclotron instability of an inhomogeneous plasma with warm ions was studied.
Abstract: A study is made of the effect of a skin high frequency field polarized along the magnetostatic field, on the onset of the drift-cyclotron instability of an inhomogeneous plasma with warm ions. It is found that an h.f. field of this sort removes instability on the low harmonics of the ion cyclotron frequency but that instability arises on all the higher harmonics.
TL;DR: In this article, a theory is developed which leads to an expression for the partition of energy between mechanical and magnetic modes in a turbulent magnetohydrodynamic system in the presence of a strong external field.
Abstract: A theory is developed which leads to an expression for the partition of energy between mechanical and magnetic modes in a turbulent magnetohydrodynamic system in the presence of a strong external field. Modifications to this expression due to specific plasma effects are obtained and are not significant. Results are also obtained for the frequency spectra and diffusion coefficient. Measurements of the turbulent fluctuations in the Zeta device are described, and from these, values for the partition are obtained. It is found that there is only complete agreement with the theory if an anomalous resistivity is assumed at low operating pressures.
TL;DR: In this article, an analytical approach is made to the problem of describing the toroidal equilibrium of a finite beta plasma column in the hydromagnetic approximation, where the thickness of the sheath region separating the plasma from the external magnetic field is assumed to be negligibly small compared to all other dimensions (the thin skin approximation).
Abstract: An analytical approach is made to the problem of describing the toroidal equilibrium of a finite beta plasma column in the hydromagnetic approximation. The thickness of the sheath region separating the plasma from the external magnetic field is assumed to be negligibly small compared to all other dimensions (the thin skin approximation). The deviations of this interface from toroidal cylindrical shape are treated by perturbation theory, a procedure which is consistent with the usual series expansion in powers of reciprocal aspect ratio. The formalism provides analytic expressions for the auxiliary currents necessary to produce equilibrium in toroidal theta pinch systems such as Scyllac.
TL;DR: In this article, a strictly relativistic non-linear solution describing the interaction of a stationary, circularly polarized electromagnetic wave with a cold plasma in a constant longitudinal magnetic field is derived.
Abstract: The strictly relativistic, non-linear solution describing the interaction of a stationary, circularly polarized electromagnetic wave with a cold plasma in a constant longitudinal magnetic field is derived. Apart from the a priori restriction that the plasma in the wave-plasma-magnetic field system under consideration be cold, no other restriction is imposed on the range of validity of the solution. Provided the solution exists, it is thus valid for any values of the parameters. The solution allows exact study of the resonance and cut-off behaviour of wave-plasma-magnetic field systems of the kind described. The non-linear relations between the wave, plasma and field parameters can be solved numerically without approximations. Owing to the complicated nature of the equations a special case is treated which at least conveys some idea of the general relationships.