bluuebunny/crossref_metadata_2025 huggingface dataset:
Theory of high-frequency heating of an inhomogeneous high-temperature plasma
Authors: Dolgopolov V.V. , Stepanov K.N.
Published: January 2011

We investigate Čerenkov absorption by a plasma of the energy of an electromagnetic field created by azimuthal electric currents flowing in a long coil around a plasma cylinder. The density of external currents has the form of a traveling wave j=j0 cos (kz—ωt) δ (r—R) (R is the radius of the coil). The frequency of the field is considerably smaller than the ion cyclotron frequency. Gas-kinetic plasma pressure n0(Te + Ti) is assumed small compared with the magnetic pressure H0
2/8π. Plasma density n0, electron temperature Te and ion temperature Ti are taken to be functions of the radius.

In the present study expressions have been found for the energy absorbed by plasma per unit time. Absorption is maximal when the phase velocity of the wave ω/k is of the order of the thermal velocity of the ions νi = (Ti/mi)½ (mi is the ion mass). If the radius of the plasma is of the order of the radius of the coil and of the order of the wavelength 1/k, then for ω/k ∝ νi the mean energy gained by one particle per unit time, in order of magnitude, equals dW/df = H∼2ωTi/H0
2 where H∼ = 4πj0/c is the amplitude of the alternating magnetic field.

For a strongly non-isothermal plasma (Te ≫ Ti) heating increases drastically if the phase velocity of the wave is near the velocity of sound in a collisionless plasma νs = (Te/mi)½

Expressions have also been obtained for energy absorbed by an inhomogeneous plasma for coils of finite lengths.
Role of the antenna screen angle during ICRF heating in JET
Authors: Bureš M. , Jacquinot J.J. , Start D.F.H. , Brambilla M.
Published: January 2011

Two comparative heating experiments were carried out to test the role of the antenna screen angle during high power ICRF heating in JET. In the first experiment the magnetic field was practically aligned with the screen elements, whereas in the second experiment the toroidal field was reversed and the angle between the elements and the field was 25°. There were clear differences in the impurity influx, the heating efficiency and the coupling resistance between discharges with normal field and discharges with reversed field. The results indicate the impact of the Faraday screen design on the levels of RF enhanced metal influxes originating at the screen. This should be of particular relevance for the ICRF antennas in a reactor where, in contrast to small devices, most of the interaction between the RF fields and the plasma edge is expected to take place around the antenna structures because of the highly localized RF field patterns. A numerical code based on three-dimensional single-pass and full wave calculations of antenna-plasma coupling, including an arbitrary angle between the screen elements and the magnetic field, can qualitatively reproduce the observed difference in the coupling resistance. The experimental results are discussed with regard to possible mechanisms that can account for the observed differences in the two cases studied.
Physical mechanism of ion entrainment by the electron space charge in acceleration by the gradients of static magnetic and of electromagnetic fields
Authors: Bardet Rene , Consoli Terenzio , Geller Richard
Published: January 2011

A theory of the physical mechanism of ion entrainment by accelerated electrons is presented. It is shown that under the influence of these fields the electrons describe helixes whose diameter and pitch vary along the axis of motion as a function of the difference between the cyclotron frequency and the frequency of the applied hf field. The space charge thus created accelerates the ions. The coupling between the equations of motion of the electron and ion fluids calls for the introduction of a tensor mass; viz., that of the relativistic mass of the electrons in the two equations inxandydescribing the transverse movement of the electrons, and that of the ions in the axial motion equation inz. The physical consequences of this theoretical study are then discussed, and three typical experimental results are given that illustrate three of these consequences.
Multiparticle aspects of turbulent-plasma theory
Authors: Galeev A. A. , Karpman V. I. , Sagdeev R. Z.
Published: January 2011

A review is given of theoretical work performed in connection with a new approach to the theory of a weakly turbulent plasma. The essence of this approach is the representation of turbulent plasma as an aggregate of weakly interacting gases of particles (ions, electrons) and quasi-particles (collective oscillations). In such a scheme are included also instability effects (playing the role of sources in the kinetic equations for quasi-particles). As applications of this method, which is thus a generalization of the known quasi-linear theory, some anomalous transfer phenomena that appear as the result of different types of plasma instability have been discussed.
Ionlzation of fast hydrogen atoms in a strong magnetic field
Authors: Bohovik E. S. , Busol F. I. , Kovalenko V. A. , Skibenko E. U. , Yuferov V. B.
Published: January 2011

To determine the fraction of 30 keV hydrogen atoms that were ionized by the Lorentz force in a magnetic field up to 60 kG, we performed a direct measurement, unlike the experiment of Sweetman who evaluated the neutral flux following charge exchange. The beam of neutral hydrogen atoms was obtained from charge exchange of a 30 keV proton beam on a supersonic jet of carbon dioxide in a vacuum of residual pressure 5 × 10−7 torr; the beam strength, measured with a small inertial calorimeter (thermocouple) calibrated by an ion beam, was nearly constant during the magnetic pulse. Electrons were removed by a weak electric field. The ions were measured with three collectors (before, in and after the central magnetic field of 2.2 cm radius); at fields above 25 kG all the ions appeared at the central collector that had a sensitivity 0.5 nA. At fields of 55 to 60 kG, the fraction (5 to 4) × 10−4 of the hydrogen atoms were ionized by Lorentz ionization, that is an ion current about 0.05 μA and an equivalent neutral current about 100 μA. From 32 to 51 kG, ionization is from the state n=9, for larger fields from n=8.
Plasma confinement in a toroidal magnetic field and with a conducting diaphragm
Authors: Shafranov V.D.
Published: January 2011

Consider a plasma column maintained in equilibrium in a toroidal magnetic field and its shape defined by a diaphragm. The maximally admissible value of β = 8 πp/B2 for such a retention is βmax = 4 b/π2R in which b is the small radius and R the large radius of the toroidal chamber containing the plasma.
Necessity of the energy principles for magnetostatic stability
Authors: Laval G. , Mercier C. , Pellat R.
Published: January 2011

Three energy principles for magnetostatic stability are known that are supposed to give necessary and sufficient conditions. For this reason their minimization has been the subject of a lot of work in plasma physics. Indeed one can easily justify the sufficiency of the conditions of stability devised from these energy principles. But to the demonstrate their necessity one usually assumes that the operators of the perturbed linearized motions have a complete spectrum of eigenfunctions in the space of square integrable functions. We show the weakness of that assumption and propose two new demonstrations of the necessity of energy principles for stability that require less stringent assumptions. The first demonstration involves some properties of the Laplace transform. In the second one we use the integral invariants of the linearized motion. The conclusions in both cases are identical: if one finds a trial function which makes the potential energy negative, the equilibrium is unstable. We give lower and upper bounds for the growth rate of the unstable perturbation.
Lorentz dissociation of H3+ in DCX-1
Authors: Haste G.R. , Dunlap J.L. , Postma H. , Reber L.H.
Published: January 2011

The experimental device DCX-1 has, in the past, observed proton trapping resulting from Lorentz dissociation of H2+ which was formed from the dissociation of H3+ within a water vapor cell. This letter presents evidence for proton trapping resulting from Lorentz dissociation of H3+ itself, with the H3+ coming directly from a duoplasmatron ion source. The evidence rests upon a measurement of the proton loss rate, which is proportional to the trapping rate. At high pressures the trapping rate is proportional to the pressure, a characteristic of gas dissociation. At low pressures, however, the trapping rate approaches a constant, independent of the pressure. This indicates another trapping mechanism, Lorentz dissociation, which is independent of pressure.
Spatially periodic plasma structures appearing in fast heavy-current discharges
Authors: Kvartskhava I. F. , Kervalidze K. N. , Gvaladze Yu. S. , Zukakishvili G. G.
Published: January 2011

We discuss recent theta- and z-pinch experiments performed to investigate the spatially periodic structure of a heavy-current plasma. A heavy-current plasma seeks to form a periodic structure whose basic elements are the E filaments (oriented along the electric field) and the H filaments (oriented perpendicular to the electric field). By means of Rogowski belts and magnetic probes we measured the distributions of plasma currents and magnetic fields. Almost all the plasma current was concentrated in the E filaments that are the elementary z pinches, whereas relatively very small currents flowed along the H filaments. The initial magnetic field stimulated plasma breakup into filaments that were parallel to the field lines. The E- and H-filament systems had a certain stability and they affected the discharge dynamics in a definite manner. Related to them in particular was the excitation of a “tongue” plasma instability in theta pinches.

We studied qualitatively several mechanisms that are possible in forming E- and H-filament systems and are based on plasma drift motion in sheared electric and magnetic fields.
Flute instability of a plasma with non-zero ion Larmor radius and non-zero pressure
Authors: Mikhilovsky A. B. , Tsypin V. S.
Published: January 2011

From a system of equations for description of the flute instability, it is shown that the stabilizing effect of the non-zero Larmor radius occurs not only in a zero-pressure plasma, but also in a non-zero (finite) pressure plasma.
Plasma Losses in a Q-device
Authors: D'Angelo N. , Goeler S.v.
Published: January 2011

Probe and microwave measurements support the view that the ordinary plasma of a Q-device is suitably described by the “equilibrium” model. An apparent discrepancy between Motley's results, giving considerable support to the “equilibrium” model, and those of Grieger and others appears to be resolved by consideration of probe losses.
Effect of an electric field on the spectrum of oscillations in an inhomogeneous plasma
Authors: Baikov I.S. , Bogdankevich L.S. , Rukhadze A.A.
Published: January 2011

The effect of an inhomogeneous electric field on the spectrum of low-frequency oscillations of a spatially inhomogeneous plasma contained by a strong magnetic field is investigated in the approximation of geometrical optics. The curvature of the lines of force of the containing magnetic field is considered by introducing an effective gravitational field. The cases of a plane and a cylindrical geometry of the inhomogeneous plasma are discussed. Based on the kinetic equation with self-consistent field, expressions are obtained for the longitudinal dielectric permeability characterizing oscillations derivable from a potential of the electromagnetic field in the plasma. Analysing of the oscillation spectra demonstrated a considerable influence of the inhomogeneous electric field on the low-frequency oscillations of the plasma for the case in which this field is comparable to or greater than the thermal field. The electric field has the strongest influence on the long-wave flute and drift oscillations. In plane geometry for an inhomogeneous plasma these oscillations are suppressed under the action of the electric field, the conditions of stabilization improving as the electric field increases. On the other hand, in cylindrical geometry, the increase of the electric field does not, generally speaking, improve the conditions for suppression of the flute oscillations of an inhomogeneous plasma. This is the result of the azimuthal rotation of the cylindrical plasma column under the action of the crossed radial electric and longitudinal magnetic fields leading to a renormalization of the effective gravitational field. In a cylindrical inhomogeneous plasma, therefore, an effective suppression of the flute instability is possible only in a thin layer near the plasma surface.
Faust 1 — A hardcore discharge stability experiment
Authors: Aitken K.L. , Hopkins K.J. , Bickerton R.J. , Hardcastle R.A. , Reynolds P.
Published: January 2011

A hardcore discharge stability experiment is described in which the final configuration is obtained by the radial inward collapse of the plasma sheath from the wall of the tube. By varying the initial conditions an axial field of arbitrary sign can be trapped within the annular plasma column. The construction and mode of operation of the apparatus is fully described.

The gas currents were the order of 50 kA and rod currents were 120 kA, so that the current in the gas was less than half that in the rod at all times. The general behaviour of the discharge was examined and the effects of pressure, preionization and trapped axial field studied. A detailed examination was made of a representative set of conditions with electric, magnetic and double Langmuir probes. These measurements, together with quantities derived from them, are discussed and the derived values of electron temperature and kinetic pressure are compared with the directly measured values. The validity of the pressure balance analysis is considered in the light of these results.

The discharge, without trapped axial field, showed a high degree of reproducibility and the observed fluctuations were of low amplitude (<10%) and low frequency (∼500kc/s) in both electric and magnetic field and in particle density. The last showed a well-defined annular sheath until late in the halfcycle; the radial profiles of azimuthal and axial current densities, kinetic pressure, temperature, and particle density showed good agreement. With trapped axial field, however, the discharge showed a reduction in stability, especially with trapped reverse field which introduces a null in the total axial field. Even with these, the most unstable conditions, the fluctuations were still relatively small (<20%) and of low frequency (∼1 Mc/s). The stability of the discharge is quantitatively compared with stability theory and the results discussed.
Hydromagnetic waves in a partially ionized hydrogen plasma
Authors: Malein A.
Published: January 2011

This paper gives further experimental verification of the theory of fast hydromagnetic waves. By a suitable choice of plasma conditions the compressional wave is propagated in a partially ionized cylindrical hydrogen plasma at frequencies below the ion cyclotron frequency. The propagation constants of the wave are measured experimentally by observing the phase velocity and attenuation over a fixed distance. Other plasma parameters, with the exception of the neutral density are measured independently.

To obtain good experimental agreement with the theoretical curves computed from the measured data, it is necessary to postulate a considerable neutral particle density in the plasma. This gives rise to loading of the wave, observable as a reduction in the Alfvén speed, and also to wave damping not explicable by resistive effects alone. The enhanced loading produced by neutral particles is unaffected by variations in magnetic field and the fitted value of neutral density derived from wave cut-off data is in agreement with that calculated from attenuation measurements.
Collision damping of transverse electron plasma oscillations
Authors: Jain R.K.
Published: January 2011

The effect of collisions on the transverse plasma oscillations has been studied by using a relaxation model for the collision term. With the Fourier-Laplace transform method, a general dispersion relation for the oscillations of an infinite uniform plasma has been derived. We obtain
and

where ω is the frequency of oscillations, ωp is the plasma electron frequency, k is the wave propagation vector, v is the damping due to collisions, v
coll is a phenomenological collision frequency, and ν0 is the mean thermal velocity. The real part (a) is consistent with the results of earlier authors and the imaginary part (b) gives the damping of the oscillations by the collisions.
Instability of a hot-cathode discharge in a magnetic field at low pressures
Authors: Vlasov M.A. , Dobrokhotov E.I. , Zharinov A.V.
Published: January 2011

The authors present results of the investigation of an incandescent-cathode discharge in an equipotential volume in a magnetic field of 2000 Oe. In the pressure range studied, 2 × 10−6 to 10−4 Torr, there is formed a plasma column negatively charged in relation to the surrounding walls. It is established that, when the pressure of the neutral gas is increased, such a discharge becomes unstable. A plasma torch is formed which rotates steadily in the direction of the electrons and escapes from the region of the primary beam. The torch is a result of plasma polarisation in the primary electron beam when there is azimuthal non-uniformity of density and a difference between the ion and electron drift velocities. If the pressure is increased further the steady rotation vanishes and intensive oscillations with a continuous frequency spectrum develop in the discharge. The fundamental principles underlying this discharge behaviour are explained. By means of a simplified model an expression for the rotation frequency of the torch is obtained and confirmed qualitatively by experiment.
Preionization and shock-wave ionization in a crossed-field plasma source
Authors: Brand G.F. , Chung S.K. , Robinson L.C.
Published: January 2011

An experimental investigation into the development of ionization in a cylindrical crossed-field plasma source is described. The observations are based mainly on microwave diagnostic methods; 35-Gc/sec interferometry is supplemented by measurements of the reflection of 10-Gc/sec waves from the plasma surface, enabling observations far above the density range normally accessible to microwave methods. We find that there are two stages of ionization. For the first, or pre-ionization stage, measured values of the electron density under various preparation conditions are presented, and estimated values of collision frequency are used for the calculation of the conductivity of the pre-ionized gas. Observations are made of the second stage of ionization, wherein a supersonic ionization front propagates through the pre-ionized gas raising it to a highly ionized state. Front velocities are measured for various pressures, magnetic induction fields and currents. Microwave reflections are used to monitor the build-up of ionization following the arrival of the ionization front at the end of the plasma vessel.
Hydromagnetic shock fronts with collisionless dissipation
Authors: Bardotti G. , Cavaliere A. , Engelmann F.
Published: January 2011

The structure of a hydromagnetic shock front wherein an electrostatic turbulence continuously develops from a two-stream instability, is investigated to aim at orders of magnitude for the width of the front, the heating of electrons and ions, and the magnitude of excitation of fluctuations. Use is made of a stationary macroscopic model that includes two phenomenological parameters. The meaning of these is examined on the basis of a microscopic theory of weak turbulence; an argument is put forward which shows that an appreciable heating of electrons can be consistent with such a regime. Conditions entailing a turbulent shock are given.
Efficiencies for plasma jet collisions in a homogeneous magnetic field
Authors: Evrard P. , Jacquinot J. , Leloup C. , Poffe J. P. , Waelbroeck F.
Published: January 2011

Collisions of plasma puffs, whose characteristics (density and velocity) vary considerably, are studied in a homogeneous longitudinal magnetic field. It is verified that the puffs meet head on. Collisions of dense (ni ≥ 4⋅1014 cm−3) and relatively slow (v0 ≥ 107 cm s−1) puffs are “efficient”, that is the initial kinetic energies of the puffs are converted into thermal energy of the ions in the resulting plasma. Faster and less dense puffs interact little (incomplete conversion of kinetic into thermal energy). The limit between efficient and inefficient collision corresponds to that which is expected from the test particle model. The slowing down of our puffs is thus ensured mainly by ion-ion interactions. The use of electric probes and the examination of the evolution of the plasma produced by collision show that this plasma does not exhibit any rapid radial motion.
Oscillations of a beam plasma in a high-frequency electric field
Authors: Gorbunov L. M. , Silin V. P.
Published: January 2011

Potential oscillations are considered in a system consisting of a neutral and completely ionized plasma and a neutral beam of charged particles in a highfrequency electric field. Under certain conditions, the uniform external high-frequency field leads to a broadening of the instability region and to an increase of the growth rate.
Finite resistivity instabilities of a sheet pinch
Authors: Wesson John
Published: January 2011

The finite (nonzero) resistivity instabilities of a sheet pinch are studied by numerical analysis in terms of normal modes. Results are obtained for the tearing, rippling and gravitational modes and their dependence on conductivity, on wavelength, on the gravitational field, on the position of k · B = 0 and on the positions of the walls. Comparison is made with the analysis of Furth, Killeen and Rosenbluth.
Electrostatic stability of gyrating electron streams
Authors: Canobbio E.
Published: January 2011

Two wide classes of velocity distribution functions suitable for confinement in “open-ended” containment fields may lead to electrostatic (linear) instability of an infinite homogeneous plasma in a uniform magnetic field. They are the anisotropie distributions with a preponderance of the particle energy being directed perpendicular to the magnetic lines (distributions which may also be set up by such situations as resonant heating, charge exchange losses and energetic particle injection) and the double streams resulting from the axial oscillations of the trapped particles between two magnetic mirrors. We are concerned here with a plasma constituted by electrons which spiral around the magnetic lines of force with a large (but not relativistic) perpendicular velocity and by ions which move almost axially. We consider in particular the effects associated with the finite radius of the streams. The discussion of the stability of such a system is of some relevance to the injection and accumulation experiments in progress at Saclay in the Pléiade and Circé machines. The validity of the electrostatic approximation made throughout the paper is investigated in an appendix.
Flux of D+ions with pléiade
Authors: Bardet R. , Consoli T. , Consolino J. , Geller R. , Gormezano C. , Jacquot B.
Published: January 2011

In the first part, a method is described for measuring fluxes of deutrons with energies over 20 keV. The method relies on the detection of alpha particles from the T(d, n)4He reaction produced by the bombardment of a tritiated titanium target. The second part describes the experimental results obtained with a mixed-field (static magnetic + HF) accelerator called plélade.
Critical voltage of a rotating plasma
Authors: Lehnert B. , Bergström J. , Holmberg S.
Published: January 2011

The accessible voltage levels have been determined for a rotating plasma device in which the confinement region surrounds a ring-shaped coil that is suspended by a single rod. (i) There exists a sharply defined critical voltage and a corresponding velocity limit which cannot be exceeded by a moderately large power input. This is clearly shown with the present apparatus where the plasma voltage slowly approaches the critical level from below and where the insulator consists only of a narrow rod. (ii) The critical voltage increases with the mean radial ratio r
0/r
w in the plasma. This ratio is defined by a magnetic field line which intersects the midplane of the device at a radial distance r
0 from the axis of symmetry, and cuts the end insulator at the corresponding distance r
w. (iii) The results can be explained by an interaction between the plasma and a neutral gas layer at the insulator surface that limits the velocity to the critical value v
c earlier introduced by Alfvén. As a consequence, the velocity limit becomes (r
0/r
w)v
c in the equatorial plane. Deductions of the corresponding voltage limit agree with the experiments, (iv) The plasma is heavily disturbed even by a very small obstacle which is introduced in the equatorial plane. This indicates that the losses of the system are small under normal operation, (v) So far the stability, is not influenced by the fact that most of the field lines pass freely around the confinement region and do not end upon an insulator surface.
Convective modes driven by density gradients
Authors: Coppi B. , Laval G. , Pellat R. , Rosenbluth M.N.
Published: January 2011

The effects of magnetic shear on the drift instability, driven by a density gradient, are investigated. Both the collisional and the collisionless regimes are considered and it is found that in many cases this instability is of convective type, propagating away from the point where k·B = 0. Stability conditions are derived, showing that in the collisional regime the amount of shear necessary to stabilize the drift mode is generally less than that required to stabilize the resistive normal mode driven by unfavourable magnetic curvature. Since a less severe condition is instead obtained for the modes driven by a favourable magnetic curvature, an indication in favour of minimum-B toroidal systems is deduced. In the collisionless regime only moderate amounts of shear are required to completely stabilize the convective density-gradient drift mode.
Self-consistent magnetic field and integrals of plasma motion
Authors: Lacina J.
Published: January 2011

A general solution of the Vlasov equation for the stationary axisymmetric distribution function of charged particles in plasma, together with a self-consistent solution of the Maxwell equations.

is found and physically interpreted.

The orthogonal natural system of coordinates of a magnetic field jointly with magnetic induction B and the integrals of motion are first determined. The spatial dependence of the resultant magnetic field is discussed in considerable detail and criteria for the existence of minimum-B are established. It is indicated that currents in plasma itself create configurations with a minimum-B on the axis of symmetry under the following necessary and sufficient exact conditions. (1) There must exist a minimum value of B in the longitudinal direction at r = z = 0 (mirror field):

(2) It must be, at r = z = 0, that –(4π/c) (∂iφ/∂r)> ½∂2
B/∂z2, where r, φ, z are the cylindrical coordinates, and iφ the electric current in the plasma.
Hamilton-Jacobi theory applied to Vlasov's equation
Authors: Pfirsch D.
Published: January 2011

Solutions of Vlasov's equation are given in terms of the Hamilton-Jacobi function S for the characteristics. Such solutions are appropriate in order to derive equations for macroscopic quantities which are of interest, for instance, in turbulence theories. In this context it is important that the Hamilton-Jacobi-theory leads to a simple straightforward nonsecular perturbation theory. The method is applied to a one-dimensional plasma which is homogeneous in the unperturbed state.
Kelvin instability in current-carrying cold plasmas
Authors: Talwar S.P. , Kalra G.L.
Published: January 2011

The electrostatic instability paused by a tangential discontinuity of velocity in two semi-infinite homogeneous regions of a cold and collisionless plasma subject to a uniform magnetic field is investigated using two fluid equations. A general dispersion relation is derived allowing for interstreaming of charged particles in each region in addition to a slippage of one region over the other. Special cases are then discussed and the criteria for stability, monotonic instability and growing wave instability are derived.
High-beta plasmas in theta pinches and cusp experiments
Authors: Ribe F.L.
Published: January 2011

High-β plasmasare those whose diamagnetic currents react strongly on the confining magnetic field. Examples of such plasmas, in which the field is largely excluded from the plasma, are those in linear θ pinches and cusp-compression devices. In the former, measurements show β (the ratio of particle and magnetic pressures) to lie typically in the range 0.6 to 0.9. The sheath which separates the plasma from the confining magnetic field has the dimension c/ωpi (the ion collisionless skin depth), indicating that sheath ions carry the current. θ-pinch and cusp experiments are described in which the basic limitation on plasma containment is end-or cusp loss. In both cases the dimension of the loss ‘hole’, out of which plasma flows, is found to be a few ion Larmor radii. A simple theoretical argument is given to show that gross flute instabilities depend sensitively on the collisionless or collision-dominated nature of the high-β plasma. In the case of θ pinches experimental evidence for this effect is given, and its relevance to stabilization of a toroidal θ pinch is discussed.
Persistence of MHD-stability in the two-fluid model
Authors: Schram P.P.J.M. , Tasso H.
Published: January 2011

A general proof is given that all static equilibria without volume currents which are stable according to magneto-hydrodynamics (MHD) remai n stable in the two-fluid model, if resistivity and electron inertia are neglected. Therefore the Hall term in Ohm's law can onl y have a stabilizing effect, if any effect at all. This result is valid for finite beta and arbitrary geometry, whether a wall or vacuum surrounds the plasma. As a special example th e cylindrical pinch with surface currents is investigated in detail.
The yield of excited atoms in a beam formed by charge exchange in a partially ionized gas target
Authors: Berkner K.H. , King I.I. , Riviere A.C.
Published: January 2011

Beams of excited hydrogen atoms are commonly produced for neutral injection experiments by charge exchange in a gas target. The passage of the beam through the target also ionizes the gas and the amount of ionization will increase as beam intensities are increased. Measurements have been made of the effect of ionization of the gas in a charge exchange cell on the yield of excited atoms. The results are compared with calculations of the effect based on the best available experimental, theoretical or estimated collision cross-section values in that order of preference. The agreement between calculation and experiment is considered to be satisfactory and the method of calculation is used to predict the effect at higher ion densities in the cell. It is found that the population of a given excited level falls to a very small value when the ion density is greater than a critical value.
Laminar hydromagnetic waves of finite amplitude in plasmas of low temperature
Authors: Cavaliere A. , Engelmann F.
Published: January 2011

The theory of non-relativistic hydromagnetic waves of finite amplitude in a plasma is presented in a simple, but systematic way. The emphasis is on stationary disturbances in a cold plasma. The physical meaning of the cold-plasma model, especially with respect to the description of collisional and collisionless dissipation effects, is discussed.
Quasi-linear theory of Cerenkov plasma heating
Authors: Dolgopolov V.V. , Sizonenko V.L.
Published: January 2011

The authors investigate Cerenkov heating in a radially non-uniform plasma cylinder, taking into account the effect of oscillations on the ‘background’ charged particle distribution function. They derive equations for particle diffusion in velocity space which are valid for both ‘narrow’ and ‘broad’ wave packets, and also expressions for the energy absorbed by the plasma. The effect of collisions is taken into account. The energy gained per unit time by an ion is estimated for the case of ‘broad’ wave packets, when the ‘background’ distribution function is non-Maxwellian to an insignificant extent. It is shown that in the case of ‘narrow’ wave packets, when the coefficient of diffusion in velocity space (characterizing the effect of oscillations on the ‘background’ distribution function) exceeds the coefficient of diffusion due to collisions, ‘absorption saturation’ ensues and an increase in the amplitude of the electromagnetic field does not lead to an increase in absorbed energy. It is also shown that heating with ‘narrow’ wave packets is no less effective than heating with ‘broad’ wave packets, provided that the ‘background’ distribution function in the latter case is not significantly non-Maxwellian.
Factors determining beta in a theta-pinch experiment
Authors: Bodin H.A.B. , Dancy D.J.
Published: January 2011

The containment and stability of the theta pinch depend critically upon the value of beta. However, while theoretical calculations predict a value of unity on the axis, experimental results show that the value on axis is substantially less than this.

The possibility that these low experimental values are due to a small field diffusion in the early stages of the current sheath formation, followed, during the compression, by an energy loss, is examined. Using various values of γ to simulate the effects of energy loss, the variation of beta during the shock phase, and during the isentropic compression phase, is calculated.

The results are compared with observations on a Megajoule Theta pinch and it is shown that the penetration of a few hundred gauss during the sheath formation stage can account for the observed values of beta.
Evaluation of transfer coefficients in a turbulent plasma
Authors: Timofeev A.V.
Published: January 2011

A method is given of calculating and evaluating to an order of magnitude the diffusion coefficient and the frictional force in a turbulent plasma. By analogy with the expression for the ordinary diffusion velocity v⃗=D(∇N/N), in our case it is possible to introduce a coefficient of anomalous diffusion, which turns out to be equal to D ≈(cT⊥i/eH) (m/M)½ τ−2μ−5/2. The study is based on the example of a turbulent state produced by the development of cyclotronic instability in a plasma with anisotropic velocity distribution of the ions.
Quasi-linear theory of cherenkov heating of electrons in an inhomogeneous plasma
Authors: Dolgopolov V.V. , Sizonenko V.L. , Stepanov K.N.
Published: January 2011

The authors investigate, in the quasi-linear approximation, the Cherenkov absorption by plasma electrons of the energy of an electromagnetic field created by external sources. The plasma is in the form of a cylinder of non-uniform radius located in a longitudinal magnetic field and the external sources are specific azimuthal currents flowing in coils surrounding the plasma cylinder. It is assumed that the magnetic pressure significantly exceeds the gas-kinetic pressure of the plasma, that the Larmor radius of the plasma panicles is small compared with the distances within which the plasma density and the electromagnetic field change substantially, that the frequency of the field is significantly less than the electron gyrofrequency, and that the phase velocity is significantly greater than the thermal velocity of the ions, so that thermal motion of the ions can be ignored.

An equation is derived for the diffusion of electrons in velocity space. From this equation it follows that the electron distribution along the velocity component perpendicular to the magnetic field does not change with time and that a plateau is formed on the curve characterizing the dependence of the distribution function on the longitudinal velocity component. The rate of formation of the plateau is different for different values of the velocity component perpendicular to the magnetic field.

In the case of narrow wave packets a diffusion equation is obtained taking Coulomb collisions into account. The slope is found of the curve characterizing the dependence of the background distribution function on the longitudinal velocity component in the steady state, where diffusion on the waves is balanced by collisions.

With narrow wave packets, if the frequency of the external currents coincides with that of the natural oscillations of the plasma cylinder (for a given wave vector value), saturation is reached in the absorption of electromagnetic field energy and, if the amplitudes of the external currents are fairly large, further amplitude increases do not lead to an increase in the absorbed power.

If, however, the external current spectrum contains wave vectors corresponding to the natural oscillations of the plasma cylinder, the formation of a plateau does not lead to absorption saturation (the absorbed power remains proportional to the square of the external current amplitude).
Resonance interaction of flute oscillations with ion Larmor drift
Authors: Timofeev A.V.
Published: January 2011

It is found that, in a regime in which flute oscillations are usually assumed to be stabilized effects of the finite Larmor radius, they are characterized by resonances with the ion Larmor drift. It is shown that a correct study of these resonances requires direct use of an integral equation, without expansion in the small Larmor radius. The initial value problem is solved by the method of Laplace transformation, and it is shown that the flute instabilities are indeed stable.
Equilibrium of a plasma pinch in a toroidal constant magnetic field and a helical high-frequency magnetic field
Authors: Gutkin T.I. , Lozovsky S.N. , Boleslavskaya G.I.
Published: January 2011

The authors consider the equilibrium of a toroidal plasma pinch in a constant magnetic field on which is superposed a helical high-frequency field produced by helical currents flowing on a toroidal surface with major radius R and minor radius rk. The helical currents are proportional to exp[i(ωt – nψ – k‖ζ)], where ω is the frequency imparted by the generator, ψ the polar angle in the meridional cross-section of the torus, and ζ is the length of arc along the major circumference of the torus.

The authors demonstrate that it is possible to achieve equilibrium with high-frequency field pressures less than the kinetic pressure of the plasma.

An expression is derived for the displacement of the pinch in the equilibrium state as a function of high-frequency field amplitude, plasma kinetic pressure, the multipolarity n, and such geometric parameters as the radius of the plasma pinch rp, the radius of the circuit rk and the radius of the torus R.

In the helical high-frequency field, the equilibrium of the plasma pinch depends to a great extent on the strength of the constant magnetic field H0, the plasma concentration N, the frequency of the variable field f = 2π/ω, and the wavelength of the helical current λ‖ = 2π/k‖.

The helical high-frequency electromagnetic field within the plasma is a superposition of two wave types. When H0 < Hcrit = the first type of wave transfers to the skin, and when H0 > Hcrit. it propagates. When k‖rp ≪ 1 and k‖rp ≪ H0/Hcrit. the field of the second type of wave differs only slightly from the vacuum field.

In the region where the first type of wave transfers to the skin, the displacement Δ of the plasma pinch decreases with increasing H0 and becomes zero when H0 = Hres = : with further increases in the magnetic field strength Δ becomes negative. H0 = Hres is the condition for resonance excitation of the helical high-frequency field within the plasma. The most effective use of high-frequency power for equilibrium containment of the plasma pinch within the torus is to be expected near this resonance on the side where Δ > 0.

The change in the sign of Δ is a consequence of a change in the direction of the force acting on the plasma. If there are two types of wave in the plasma, there appear – in addition to the forces associated with the pressure of each individual wave -forces produced by the interaction of the currents excited by one wave type with the field of the other wave type, and vice versa.

For certain parameter values, the phase relations of the fields and currents may be such that the additional forces associated with the cross interaction may work in a direction opposite to that of the forces produced by the pressure of each individual wave.

In the propagation region of the first wave, i.e. where H0 > Hcrit. positive and negative values of the plasma pinch displacement alternate (i.e. there are alternating regions of stable and unstable equilibrium respectively).
Nonlinear oscillations in a cold plasma
Authors: Davidson R.W.C. , Schram P.P.J.M.
Published: January 2011

In a Maxwell-fluid description large-amplitude electrostatic and electromagnetic oscillations in a cold plasma are analysed in situations where the spatial variations are one-dimensional and the ions form a fixed neutralizing background. In the electrostatic approximation a Lagrangian description following the electron motion is adopted, and exact solutions obtained in these variables in situations where multistream flow does not develop. The inversion to Eulerian coordinates is carried out explicitly for the particular example of an initial sinusoidal perturbation in density. A model describing the dispersive modifications of (weak) thermal effects is analysed showing the phase-mixing of (moderately) large-amplitude initial disturbances. After sufficient time, the electron fluid becomes stationary and a low level of electric field remains balancing the force due to pressure variations. In addition, for the case of nonlinear electrostatic oscillations perpendicular to a static magnetic field, the exact solution in Lagrangian variables shows that for a cold plasma coherent oscillations at the upper hybrid frequency are maintained indefinitely over the regions of initial excitation. Electromagnetic oscillations are considered as developing from small initial values on the background of the large-amplitude longitudinal oscillations already calculated. The resulting wave equation is analysed for several limiting cases. It is shown that for sufficiently short wavelengths of the transverse fields there exists an infinite number of narrow ranges of the wave number in which the transverse oscillations are unstable. The growth is ultimately limited by the magnetic force which was neglected in the description of the longitudinal motion. Finally, stationary solutions are studied. In the electrostatic approximation a very special class of periodic Bernstein-Greene-Kruskal waves without trapped particles is obtained. Again the electromagnetic solutions are unstable (in space), the growth being limited by the same effect as in the time-dependent problem. A simple class of special stationary solutions is obtained for the complete problem including all magnetic force terms.
Scattering of electromagnetic waves by the turbulent pulsations in an inhomogeneous magnetoactive plasma
Authors: Sakhokiya D.M. , Tsytovich V.N.
Published: January 2011

The authors consider the theory of high-frequency electromagnetic wave scattering by the turbulent pulsations in a plasma contained by an external magnetic field. They analyse in detail the effects accompanying the scattering of waves in both inhomogeneous and homogeneous magnetoactive plasmas. The effects of quasi-elastic and diffusion scattering are also analysed. The possibilities of using calculated scattering effects for diagnosing the turbulent state of a plasma are discussed.
Flute instability of a current-carrying curved plasma column
Authors: Shafranov V.D.
Published: January 2011

Suydam's criterion for an arbitrarily curved plasma column is generalized. Mercier's well-known results concerning the local stability of a plasma in the vicinity of the magnetic axis are a special case arising from this criterion. In a curved plasma column, in addition to the stabilizing effect of shear, the stabilizing role of the “magnetic well” assumes importance. The magnetic well is produced by a displacement of the magnetic axis into the region where the toroidal magnetic field is weaker. The contribution to the magnetic well made by that part of the displacement which is associated with ballooning of the plasma column as a whole exactly cancels the ballooning mode. The part of the displacement due to electrodynamic stretching of the current column creates a “vacuum” magnetic well that is independent of plasma pressure. In stability criterion, given in this paper the stabilizing role of the vacuum magnetic well manifests itself in the coefficient F, which is dependent both on the mean curvature of the plasma column and on its harmonics. The condition for stabilization by the magnetic well, F > 1, imposes a limitation on the “stability safety factor” q = 2πr Bζ (r)/LBθ. The author considers regions where there are variations in the values q ensuring stability for systems of the racetrack and spatial figure-eight types.
Closed expressions for the magnetic field in two-dimensional multipole configurations
Authors: Boris J. P. , Kuckes A.F.
Published: January 2011

Closed analytic expressions for the vector potential and the magnetic field generated by axisymmetric multipole line currents are presented. These results complement and simplify earlier work utilizing truncated infinite series. The infinite series, which arise by Fourier analyzing the angular dependence of the current distribution, are summed explicitly. For the special case of filamentary line conductors the vector potential, as well as the field components, can be summed. For this case explicit equations for the lines of force and magnetic isobars can be determined. One finds that all lines of force penetrating a cylinder whose radius is determined explicitly by the order of the multipole take on the maximum value of |B⃗| on that cylinder. Thus, for a low-density plasma composed of adiabatically gyrating charged particles, the region of possible plasma containment within the region bounded by the fixed conductors is a cylinder of circular cross-section with known radius.
Fusion research in open-ended systems
Authors: Fowler T.K.
Published: January 2011

Low-beta fusion research in open-ended magnetic geometries (mirrors) is reviewed. This material, extracted from the report of a USAEC panel convened to examine mirror research, has been edited and revised to include recent information. It is intended to present an overview of the achievements, methods and rationale of this area of fusion research. Topics covered include the scope of mirror research, classical end losses, and fusion economics, minimum-B stabilization of flute instability, theoretical and experimental results concerning loss-cone instabilities, and a summary of experiments and experimental techniques.
Convective and absolute two-stream instabilities for hot plasma
Authors: Infeld E. , Skorupski A.
Published: January 2011

The two-stream instability for arbitrary but equal temperatures of the streams is investigated. The equilibrium distribution function for a given temperature, which is the sum of two Maxwellian distributions, is approximated by resonance functions . The division of the two-stream instability into convective and non-convective is described. Non-convective instability occurs when the two streams are in opposite directions and the velocity of the slower of the two is greater than a critical value. This critical value is given with considerable accuracy by the empirical formula , where v1 is the speed of the faster stream and u0 the ‘thermal’ velocity. Comparison is made with a step-function distribution calculation performed by Sturrock.