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Kinetic method of investigating oscillations and stability of inhomogeneous plasma in a helical magnetic field
Authors: Mikhailovskaya L.V. , Mikhailovsky A.B.
Published: January 2011

A new method based on the use of the kinetic Vlasov equation is suggested to investigate oscillations and stability of inhomogeneous plasma in a helical magnetic field of cylindrical symmetry. A dielectric permeability tensor has been obtained for the plasma configuration mentioned. Exceeding the limits of hydrodynamics permits one to study oscillations with a wavelength of the order of the Larmor radius of the particles. In addition such an approach makes it possible to take into consideration interaction between the resonance particles and the wave thus permitting investigations of the "kinetic" mechanisms of oscillation buildup. These questions have also been discussed in an earlier article of one of the authors.

The advance that is achieved in the present work consists of consideration of the curvature and shear of the magnetic field lines. With consideration of these quantities equations have been obtained that make it possible to investigate the behaviour of drift waves that are unstable in the case of a magnetic field with straight and parallel lines, and also waves that have been discussed by Suydam. We discuss the effect of a buildup of convective perturbations with resonance electrons that is connected with their motion along the lines of force. Such an effect takes place when the hdyrodynamic instability of Suydam is stabilized because of the large Larmor radius of the ions. The buildup effect mentioned is analogous to the "residual-instability" effect but considerably stronger than the latter if plasma pressure is small compared to magnetic pressure. This effect exists if there is a temperature gradient.

It is shown that in a plasma that is in a gravitational field and confined by a straight magnetic field, an analogous effect of drift buildup of flute perturbations is possible
Plasma acceleration by electromagnetic and magnetostatic field gradients
Authors: Consoli Térenzio , Hall R.B.
Published: January 2011

The movement of charged particles in electromagnetic and magnetostatic field gradients is examined. It is shown that when the orientation and amplitude of such gradients are suitably arranged, the mean force in relation to time acting on these particles remains constant in direction. Discussed are this mean force and, more generally, the validity of the theory of mean value in relation to time.

The results are applied to the case of a low-density plasma, and a brief description is given of four possible applications of a device based upon such forces: as injector, plasma propellant, vacuum pump and direct converter of thermal energy into u.h.f. electromagnetic energy. Orders of magnitude are stated. In two annexes, the authors determine the limits of validity of the theory based on mean value, and a comparison is made with an exact theory. The curves obtained are described and classified by analogue computer.
Convective and viscous fluxes in strongly rotating tokamak plasmas
Authors: Stacey W.M.
Published: January 2011

A formalism is presented for interpreting convective and viscous energy fluxes derived from experimental data and for correcting for them in the interpretation of measurements of the conductive heat flux. The corrections are shown to be significant in two JET pulses, suggesting that they should be taken into account in the experimental determination of thermal diffusivity in strongly rotating tokamak plasmas. A supplementary theory for ion and impurity particle fluxes, which retains ambipolarity in the presence of large anomalous electron fluxes, is presented. A theory, based upon gyroviscosity (the basis for which remains controversial), for the radial flux of toroidal momentum is presented and is shown to be in reasonable agreement with experiment for two JET pulses.
Plasma boundary phenomena in tokamaks
Authors: Stangeby P.C. , McCracken G.M.
Published: January 2011

Effects of the plasma boundary can have a substantial influence on the behaviour of the entire plasma in tokamaks. Progress in the field, particularly that over the last decade, is reviewed, with emphasis on experimental observation. Simple modelling for interpretation is also included.
Interpretation of measurements of the global momentum and energy confinement times in strongly rotating tokamak plasmas
Authors: Stacey W.M.
Published: January 2011

A model is presented for the self-consistent interpretation of the global momentum and energy confinement times and the central rotation velocities measured in plasmas that are rotating at speeds comparable to their thermal speed. This model incorporates corrections for non-steady state and represents the effect of radial density, temperature and velocity profiles. The momentum transport model is based upon gyroviscosity theory, which remains controversial. Good agreement between measured and predicted rotation frequencies and momentum confinement times is obtained for a collection of JET data and for one TFTR beam power scan. The energy confinement is shown to be degraded by a viscous energy flux, which is predicted to account for up to one fourth of the total energy loss for the JET data and for one half of the energy confinement degradation measured in the TFTR beam power scan. This implies that the measured energy confinement times in strongly rotating plasmas are significantly shorter than the times of energy confinement against conductive and convective transport processes.
Collective motion of an electron or ion gas at multiples of the cyclotron frequency
Authors: Johnston J. R. , Moore Richard L.
Published: January 2011

This paper contains an explanation for phenomena found in laboratory plasmas by many investigators. When a magnetic field is present, either the ion component or the electron component (but not both simultaneously) may rotate with a mean angular velocity equal to its cyclotron frequency. In such a case, the periodic electric and magnetic force fields induced by certain types of collective oscillations of the velocity field cooperate in such a way that rotating wave patterns are formed. These rotating waves fall into two groups. The frequency of the first group is the well-known plasma frequency. The second group has two frequencies—one near a multiple of the cyclotron frequency, and the other, much lower, at the square of the plasma frequency divided by a multiple of the cyclotron frequency. The field of motion of the first group of waves is periodic along the direction of the magnetic field. The field of motion for the second group of waves is given by

where

and

These fields of motion are in agreement with the experiments which have found that the higher harmonics of the cyclotron frequency can be excited to a much higher degree than previous theory had predicted.
Influence of Hall current on the stability of the pinch
Authors: Buti B. , Dixit M. S. , Nayyar N. K. , Trehan S. K.
Published: January 2011

The Hall current has no effect on the hydromagnetic stability of a sheet pinch that has a trapped axial magnetic field and is surrounded by perfectly conducting walls.
Project MACETIE (Multistage adiabatic compression and equi-temperature irreversible expansion)
Authors: Uchida Taijiro , Hamada Shigeo , Miyamoto Kenro , Fujita Junji , Inoue Nobuyuki , Kawasaki Sunao , Katsumata Saburo
Published: January 2011

The principle of Project MACETIE and the preliminary experiment are described. The basis of our plan is the thought that the goal of controlled thermonuclear fusion may be accessible by the multistage alternating processes of adiabatic compression and irreversible expansion of plasma. In the latter process, the plasma compressed by a strong magnetic field is expanded into a region of weaker magnetic field. A static consideration of this expansion suggests that plasma temperature will not change appreciably in this process, and a second adiabatic compression of plasma in the weak field may further increase its temperature. Preliminary experiments are being carried out to examine the foregoing principle of irreversible expansion.
A review of cyclotron harmonic phenomena in plasmas
Authors: Crawford F.W.
Published: January 2011

In recent years, cyclotron harmonic phenomena have been encountered in many branches of plasma physics. For example, anomalously high noise radiation near the electron and ion cyclotron harmonic frequencies (nωce, nωci) has been observed from plasmas used in thermonuclear fusion studies. Transmission resonances near (nωce) have been detected in the laboratory in perpendicular propagation experiments, while satellite explorations have established the existence of ionospheric resonance effects near these frequencies. The substantial volume of experimental data accumulated on cyclotron harmonic phenomena can be interpreted qualitatively, and in some cases quantitatively, in terms of cyclotron harmonic waves whose propagation has been predicted for warm plasmas in a magnetic field. The review gives a brief outline of the theory, and concentrates on the basic physical mechanisms of the effects observed experimentally. These phenomena are of considerable practical importance in the understanding of processes occurring in fusion study devices, other laboratory discharges, and the ionosphere. There are several potential applications to plasma diagnostics; the paper concludes with a brief discussion of them.
Plasma compression by light pressure
Authors: Caruso A. , Gratton F.
Published: January 2011

For giant pulse lasers with light amplifier, the rise time of the pulse is 0.001 nsec, the duration is 1 nsec. The light from the laser, focused on a speck (10 μ) of solid material, by its pressure can overbalance the pressure of a high temperature and high density plasma. The initial stage of a plane system is briefly studied and, in more detail, the subsequent dynamics.
Longitudinal propagation of a microwave beam in a laboratory plasma near the cyclotron resonance
Authors: Sharp L.E. , Hooker C.A.
Published: January 2011

A microwave beam (8-mm wavelength) was propagated parallel to the confining magnetic field in a plasma. To identify the transmission bands, the electron density and the magnetic field were slowly varied (in time) to separate the transmission bands of the left-hand circularly polarized wave from the right hand wave, above and below the electron cyclotron resonance. The experimental data show good agreement with the dispersion relations derived more than thirty years ago for ionospheric propagation.
Magnetohydrodynamic ionizing shock waves
Authors: May R.M. , Tendys J.
Published: January 2011

The theory of magnetohydrodynamic “switch-on” shock waves is well understood when the electrical conductivity is large ahead of the shock front. If the conductivity is zero, the analysis is more difficult. Kulikovskii and Lyubimov have shown in principle how the solution proceeds in this case; there are two regions in the shock front, separated by a temperature T* above which the electrical resistivity is smaller than the viscosity and thermal conductivity. We apply this general theory to the switch-on ionizing shock wave, and we provide a method for calculating T*. The shock velocity and the flow parameters behind the front are then obtained in terms of the parameters ahead of the front and the magnitude of the jump in the transverse magnetic field.
End losses from a theta pinch
Authors: Taylor J.B. , Wesson J.A.
Published: January 2011

A simple model for the flow of plasma from the ends of a theta pinch is used to calculate the steady state plasma loss rate. The flow is similar to hydrodynamic flow in a flexible nozzle; special attention must be paid to the conditions in the “throat” of the nozzle. The plasma loss rate is then a function of the plasma parameters and the mirror ratio of the coil—when this is appropriately defined. Graphs and convenient formulas for the loss are provided.
Analogue computation of instability growth rates in finite conductivity magnetohydrodynamics
Authors: Kontos J.
Published: January 2011

The instability growth rates for a uniformly distributed current in a cylinder of fluid with finite conductivity were computed by analogue computer for comparison with digital computer solutions. The analogue computer does not use the dispersion relation; in view of the very coarse finite differences it used, the order of magnitude agreement is considered satisfactory. The analogue computer is economical in equipment and time for finding roughestimates of the instability growth rates.
Acceleration of plasma electrons
Authors: Stefanovsky A. M.
Published: January 2011

The author studied plasma electron acceleration in toroidal devices where electron beam equilibrium on the annular orbit is secured by image currents appearing in a metallic housing that covers the vacuum chamber. The initial plasma was created in a toroidal magnetic field with the aid of electron injection along the lines of force of that field and neutral gas ionization in the chamber. The first series of experiments showed that the overwhelming majority of plasma electrons do not accelerate after the creation of an electric field up to 150 V/cm; at the same time powerful oscillations are excited in the plasma. These oscillations appear as a result of the effect on the plasma, of a non-uniform electric field. The results obtained in this series of experiments are analogous to those obtained on plasma betatrons.

In the second series of experiments the accelerating electric field was created uniformly and simultaneously along the column of the preliminary plasma. Comparison of the plasma density obtained with the aid of a probe technique, and measurement of the currents that appeared in the plasma show that probably all plasma electrons are initially accelerated by the electric field. Subsequently, however, for reasons that are unclear so far, acceleration ceases and the plasma current becomes a purely ohmic current. Measurement of the x-ray energy that appeared in experiments with an accelerating field of 250 V/cm shows that the electron component of the plasma is, under these conditions, heated by a short electric field pulse (1.7 × 10−7 sec duration) to a temperature of 50 - 70 keV. It is assumed that these effects can be very significant for obtaining large accelerated currents in plasma betatrons. In a denser plasma, one does not succeed in accelerating the electrons to relativistic energies; however, the superposition of a strong electric field can be applied with success for heating the electron component of the plasma.
The effect of shear on flute instability in a dilute plasma
Authors: Mikhailovskaya L. V. , Mikhallovsky A. B.
Published: January 2011

In this paper we consider the flute oscillation of a plasma in a helical, cylindrically symmetrical magnetic field, with shear not equal to zero, at an arbitrary value of the parameter β = 8π p/B
2, particularly where β → 0. Suydam's familiar stabilization criterion loses its validity if β < (Me/Mi) (k ⊥ ϱ)2 (in a low-density plasma), and that it is replaced by the criterion θ > 4(Me/Mi)1/2 (a/R) [1 + (C/CA)2]1/2

The combined stabilizing action of shear and a finite ion Larmor radius makes it possible to eliminate flute instability over the whole range of densities. (A plasma without shear, on the other hand, and with a density in the range a/R < (C/CA)2 ≳ 1 would be unstable no matter how large the Larmor radius of the ions.)
Heating a plasma by means of magnetic pumping
Authors: Dawson John M. , Uman Myron F.
Published: January 2011

We present two models for the heating of a cylindrical plasma by an oscillating magnetic field. The model for collisional heating, applicable at low temperatures and high densities, is extended to include dissipative effects. Both linear and nonlinear numerical calculations yield heating times which agree for moderate values of the modulation index. A model for collisionless transit-time heating, applicable at high temperatures, is extended to include the self-consistent electric fields; the ions are treated by means of a Vlasov equation and the electrons are treated as a fluid in equilibrium. Inclusion of the electric fields enhances the heating rate by as much as a factor of four. Heating rates calculated from the two theories are in essential agreement when the mean free path of the ions is comparable to the length of the pumping section.
Kinetic theory of electromagnetic waves in a bounded plasma
Authors: Kondratenko A.N.
Published: January 2011

Propagation of electromagnetic surface waves in an infinite plasma layer is examined in kinetic approximation. The problem is solved with the Fourier method. The dispersion equation obtained is investigated (a) for high-frequency oscillations in which the average thermal velocity of the electrons υTe and of the ions υTi is much smaller than the phase velocity of wave V
Φ; and (b) for low-frequency oscillations (ion-acoustic waves) in which υTe≫ VΦ≫ υTi

For high-frequency oscillations, wave damping is proportional to υTe, and not exponentially small as it is for a volume wave in an infinite plasma. As is known, damping of an ion-acoustic volume wave in an infinite plasma is caused by plasma electrons, and the ion contribution to damping is exponentially small if V
Φ≪ υTi. In the case of an ion-acoustic surface wave, a large and sometimes even fundamental contribution to damping is made by plasma ions whose damping fraction is proportional to υTi. The reason for so large a damping in both high-frequency and low-frequency waves is Cerenkov absorption of the wave energy by plasma particles that is particularly considerable in the short-wave components of the Fourier expansion of the surface wave.
Plasma equilibrium in a toroidal chamber with a travelling magnetic field
Authors: Volkov T.F.
Published: January 2011

The displacement was found of the center of a plasma column in a toroidal chamber that is maintained in equilibrium by the average pressure of the high-frequency travelling magnetic field H and the dc magnetic field ℋ of the longitudinal surface currents. The travelling hf magnetic field is created by passing ac currents with specially selected phases through the annular conductors enveloping the chamber. It is assumed that these conductors do not affect the distribution of the dc magnetic field, which is assumed to be the same as in a single ideally conducting toroid. The solution is performed in assuming that toroidality is small (expansion in powers with respect to 1/R; R is the large radius of the torus).

The conditions for detachment of the column from the chamber walls in a quasi-static regime, is evaluated in the following manner. Let a plasma column of radius α be in equilibrium in a cylindrical chamber of radius b (R = ∞) at a distance δ from the walls. If the column is bent into a torus, then for detachment of the plasma from the chamber walls it is necessary that δ be larger than the displacement of the center of the plasma column Δ (a,b) = b – δ. The condition for detachment, δ > Δ (b – δ, b), limits β, the ratio of plasma pressure to full magnetic-field pressure (time average of H plus ℋ).

In a concrete case that is close to the experiments described in ref. 1 (R=35 cm, b=4 cm, and 12 waves of the travelling magnetic field fill the length of the torus), the formula is

h = ℋa/Hb is the ratio of x at the surface of the plasma column to H near the current conductors (on the surface of the chamber). From this formula it follows that for large longitudinal currents (h
2 > 0.49), detachment is impossible. From table I we can find the maxima of β for which, with preset h
2, a column can exist that is detached from the chamber walls. As is seen from this table, the conditions for detachment are very stringent.
Cerenkov absorption of Alfvén waves and of fast magneto-acoustic waves in an inhomogeneous plasma
Authors: Dolgopolov V.V. , Stepanov K.N.
Published: January 2011

We investigate Cerenkov electron absorption of low-frequency electromagnetic waves in an inhomogeneous plasma cylinder. Formulas were obtained for the energy absorbed by plasma, and for the damping factor where there is no resonance layer. A sharp boundary leads to a strong absorption increase. For a resonance layer containing a point at which the radial wave number becomes infinite, there occurs a strong absorption increase (if the phase velocity of the wave is the order of thermal-electron velocity, then the damping rate is the same order as the frequency). The radial and axial components of the electric field of the wave then increase sharply in the resonance layer. The increase in absorption is caused by the axial component of the electric field. Formulas were derived for the electric field strength inside the resonance layer, for the high-frequency power that is absorbed by the layer; and for the width of the layer.
Longitudinal dielectric constant of the classical plasma — I
Authors: Coste J.
Published: January 2011

Starting from the work of Guernsey on the system of the two first equations of the BBGYK hierarchy, we show that an approximate solution of these equations may be found in the limit of high frequency or short wave length, and we derive general expressions for the longitudinal dielectric constant ε (k, ω) of the plasma. Limiting cases are considered: zero frequency [equilibrium quantities are derived from ε (k, 0)]; and frequencies much higher than the inverse relaxation time.
Longitudinal dielectric constant of the classical plasma — II
Authors: Coste J.
Published: January 2011

We study the contribution of electron-electron correlations to ε (k, ω), by considering the case of a one component plasma. This contribution is compared to that due to the electron-ion correlations. A resonance effect is found at ω = 2 ωp. From ε (k, ωp) we derive a formula for the damping of the plasma oscillations.
Normal modes of plasma oscillation
Authors: Trocheris Michel
Published: January 2011

The present paper is concerned with the well-known problem of electrostatic waves in a uniform collisionless plasma, in the linearized approximation. Although much work has already been done on this problem, a number of questions still arise. In particular a slightly unstable wave corresponds to an exact normal mode solution, whereas a slightly damped wave has a much more limited meaning: it is encountered by solving the equations with initial conditions in the manner first introduced by Landau.

In this paper a new type of normal mode is introduced which can represent damped waves as well as unstable ones, thus preserving the continuity between both kinds of waves. This is possible by considering the distribution function as a linear functional, or as an analytic function defined for complex values of the velocity. A complete system of such normal modes is formed. The spectrum consists of discrete eigenvalues corresponding to waves, either growing or damped, together with a continuum that may be chosen to have an imaginary part such that it corresponds to rapidly damped transients. An expansion formula is derived and the expansion given by Van Kampen and Case is recovered as a special case. This expansion is used to solve the equation for the distribution function and the relation to the solution by Laplace transformation is discussed.
Effect of a cold-plasma component on the stability of an inhomogeneous hot plasma
Authors: Baikov I.S.
Published: January 2011

By applying geometrical optics, the author investigates the effect of a volume component of cold plasma on the low-frequency oscillation spectrum and on the local stability conditions of an inhomogeneous hot plasma contained by a strong magnetic field. Allowance is made for the curvature of the lines of force of the containing magnetic field by introducing an effective gravitational field. The author points to the existence in such a system of a low-frequency oscillation branch, that is “electron” sound, with a frequency proportional to the square root of the ratio of hot to cold plasma densities. For very low cold-plasma densities a hydrodynamic growth of long-wave and short-wave oscillations of the inhomogeneous plasma results from the excitation of an “electron-acoustic” oscillation branch by the gravitational drift of the ions. For higher cold-plasma densities one observes a resonant growth of low-frequency plasma oscillations with frequencies approaching those of the diamagnetic particle drift. Further increases in the cold-plasma density such that the frequency of the electron sound exceeds all the drift frequencies of the plasma lead to an expansion of the stability region of the inhomogeneous plasma.
Errors in the use of mass analyzers in plasma physics
Authors: Fleischmann H.H. , Ashby D.E.T.F. , Larson A.V.
Published: January 2011

This note discusses sources of error in the use of charged-particle analyzers to determine the ionic species and energies in plasma streams, with particular reference to the widely used electrostatic instrument. Space-charge expansion within the analyzer leads to an upper limit on the size of the entrance aperture. This limit, which depends on the ion energy and density, is less than the proper Debye shielding distance that is often considered a sufficient limit. For ion energies below a few hundred eV and densities above 1010 cm−3 the aperture requirement is impractical. Therefore the possibility of reducing the plasma density by means of single apertures or multi-hole screens is considered. These considerations are supported by measurements on plasma gun outputs. The best criteria for proper operation of the analyzer are that the integral over the output spectrum equal the number of incident ions and that the output intensity be proportional to the area of the entrance hole.
Thermal radiation of an inhomogeneous plasma layer
Authors: Dolgopolov V.V.
Published: January 2011

This study discusses the radiation from an arbitrary inhomogeneous isotropic layer (of a plasma, for example, when the radiation frequency greatly exceeds the electron cyclotron frequency). With the fluctuation-theory method we obtain a formula for radiation intensity that depends on the solutions of two linear homogeneous second-order differential equations whose coefficients are determined by the distributions of density and temperature in the layer. We discuss in detail: 1) Radiation from a semi-infinite homogeneous dielectric; 2) Radiation from a layer with a smoothly changing dielectric permeability when the geometrical-optics method is applied; 3) Radiation from a layer with a smoothly changing dielectric permeability when there are regions inside the layer in which the real portion of dielectric permeability vanishes and the geometrical-optics method is inapplicable owing to the smallness of the imaginary portion. The formula for radiation intensity remains finite but exponentially small even when the imaginary portion of the dielectric permeability approaches zero. If the wave length of the radiated wave is of the order of the thickness of the inhomogeneous transparent layer inside which dielectric permeability vanishes, the radiation intensity is of the order of the radiation intensity of a black body.
Magnetic viscosity and the stability of superposed fluids in a magnetic field
Authors: Singh Surindar , Hans Harikrishan
Published: January 2011

The effect of magnetic viscosity is investigated in two simple stability problems — Rayleigh-Taylor instability and Kelvin-Helmholtz instability of superposed fluids. In the Rayleigh-Taylor instability, perturbations perpendicular to the magnetic field are suppressed. In the Kelvin-Helmholtz instability, a magnetic field transverse to the direction of streaming velocities in general opposes the development of instability.
Theory of the hydrodynamic stability of inhomogeneous plasma fluxes
Authors: Lovetsky E.E. , Rukhadze A.A.
Published: January 2011

The stability of a multicomponent flow of cold inhomogeneous plasma with respect to conservative electromagnetic oscillations is investigated in two-fluid hydrodynamics. It is shown that, when there is a strong external axial magnetic field parallel to the plasma flux, the inhomogeneous plasma may be unstable with respect to short-wave oscillations described by the methods of geometrical optics. When there is no external magnetic field only long-wave oscillations, for whose description geometrical optics cannot be employed, are unstable; short-wave oscillations are unstable even when there is a magnetic field. The instabilities considered can develop when there is no beam instability in the plasma, and longwave instability is possible even in a currentless plasma (plasma jet). The long-wave instability is by its nature analogous to the Rayleigh flow instability of an ideal fluid with an inhomogeneous velocity profile.
Probing a plasma by electromagnetic waves
Authors: Dnestrovsky Yu.N. , Kostomarov D.P.
Published: January 2011

The authors examine the problem of determining the spatial density distribution of a magnetized plasma containing cold electrons by using the measured phase difference between the incident and reflected waves in a given frequency range. With the methods of geometrical optics the problem yields Volterra's integral equations of the first kind. If the external magnetic field is homogeneous the equations are linear; otherwise they are nonlinear. The equations are studied by numerical methods. The authors also consider the absorption of electromagnetic waves in relation to the problem of probing a plasma.
Interaction of fast plasmoids with magnetic field barriers
Authors: Chwaszczewski S.
Published: January 2011

A useful way of obtaining more accurate information about the processes that occur when fast plasmoids are trapped in magnetic traps is to investigate the interaction of the fast plasmoids with the barriers of magnetic fields that are constant or variable in time. The results obtained may be valuable in helping to clarify questions concerning the acceleration of plasmoids by variable magnetic fields and to explain some of the processes involved in penetration of the magnetic field by the plasma. To investigate the effects of the interaction between fast plasmoids and magnetic field barriers a coaxial plasma gun of the Marshall type was constructed. When the optimum conditions for operating the gun had been established plasmoids with a speed of 1.3 × 107 cm/s and an initial density of 2.5 × 1013 ion pairs per cma were obtained.

During investigation of plasmoid interaction with the barrier of a constant magnetic field, compression of the plasma was observed at low field intensities. At high magnetic field intensities the density of the plasmoids penetrating the barrier decreased until the plasma was completely reflected by the barrier. Using the model of a collisionless plasma, equations were obtained for the distribution of electromagnetic fields along the radius of a plasmoid passing through the barrier. By comparing the solution of this equation with the measured diamagnetic signal the electron gas density in the plasmoid was determined; it was found to be in agreement with results obtained with a twin probe. The interaction of plasmoids with the barrier of a variable magnetic field is determined not only by the amplitude of the field intensity, but also by a whole set of interaction phases. New values characterizing these phases were introduced for convenience. The reflection, partial penetration and acceleration of the plasmoids was measured for different interaction parameters.
Polarized pyrometric probe: principles of operation and measurement of plasma particle energy
Authors: Bardet R. , Geller R.
Published: January 2011

The polarized pyrometric probe is a thermally insulated electrostatic probe made of tungsten or carbon. Unlike the Langmuir probe, its operating characteristic is located beyond the knees on the curve indicating ion and electron saturation. In hot, dense plasmas (where the Langmuir probe is difficult to use), the radiance of this probe, inferred from the temperature reading on the pyrometer, is compared with the productVI(voltage times current) of the characteristic. It is then easy to calculate the energy of the particles and to estimate their density. The principle underlying these measurements is explained and illustrated by two experimental applications for ions of 300 and of 1200 eV.
Field dissociation probabilities of Field dissociation probabilities of
Authors: Wind H.
Published: January 2011

For 31 highly excited states of Field dissociation probabilities of a value of the dissociation probability as a function of the electric field is computed. The field range is from 5 × 103 to 1 × 105 V/cm. The accuracy, mainly governed by the neglect of the Stark shift, is 5 to 7 per cent. There is good agreement with experimental observations.
Stability of flute oscillations with wave-plasma resonances
Authors: Timofeev A. V.
Published: January 2011

The flute oscillations of a hot-ion plasma in a non-uniform magnetic field are discussed. It is shown that resonances, at which the phase velocity of the waves is the same as the velocity of the ion Larmor drift, can have a stabilizing effect. In particular, with careful selection of the resonance characteristics, one can control the most dangerous “mode 1” of the flute oscillations. Also examined are resonances of the second type, which appear only in an electric field; at them the phase velocity of the wave is the same as the velocity of the plasma electric drift. In the presence of such resonances, the natural frequencies of the flute oscillations become complex of necessity and, accordingly, the oscillations themselves either grow or are damped.
Resistive instabilities in a diffuse linear pinch
Authors: Coppi Bruno , Greene John M. , Johnson John L.
Published: January 2011

The effects of small electrical resistivity, viscosity, and thermal conductivity on hydromagnetic instabilities for diffuse linear pinch configurations are considered. For finite-pressure systems, higher order equations must be solved than in previous work that was applicable to stellarator or slab geometries. A careful treatment of the problem of matching the perturbed solution across the boundaries that separate a resistive layer from outer hydromagnetic regions clarifies the relationship between resistive instabilities and the ordinary hydromagnetic instabilities that are obtained from the ideal equations. In a similar way consideration of various limiting cases brings out the connection between the different resistive modes. The manner in which thermal conductivity and viscosity assert themselves is exhibited, and for a special configuration it is shown explicitly how viscosity can exert a small stabilizing effect. Aside from this, instabilities are found whenever the pressure decrease is outward.
Cesium plasmas in a magnetic field with variable curvature: Experiments
Authors: D'Angelo N. , von Goeler S.
Published: January 2011

As the radius of curvature of the magnetic lines decreases from its normal value R = ∞, one observes in the thermally ionized cesium plasma the excitation of several “modes” of low-frequency (5 to 30 kc/sec) “drift” waves and additional plasma losses. “Toroidal equilibrium” has been analyzed both theoretically and experimentally. The connection between the low-frequency drift waves and the additional losses is discussed.
Drifts and plasma losses in Q devices with curved magnetic fields: Calculations
Authors: Von Goeler S. , Smith C. G. , D'Angelo N.
Published: January 2011

The conditions of toroidal equilibrium prevailing in a Q device with curved magnetic lines have been analyzed from the two-fluid equations. The density profiles are calculated to second order in an expansion in reciprocal powers of the radius of curvature. The main features of the equilibrium are toroidal and E × B drifts that, to first order, give rise to shifts of the plasma column and, to second order, to plasma losses. These calculations can account for the experimental observations without invoking low-frequency “drift” waves on confinement.
Plasma electric noise of a steady hf discharge in a magnetic field
Authors: Vdovin V.L. , Rusanov V.D. , Frank-Kamenetsky D.A.
Published: January 2011

The plasma is produced by magneto-acoustic techniques in a glass tube situated in a constant magnetic field. The plasma flows out continuously along the axis into the measuring chamber at whose centre the magnetic field varies from 700 to 2500 Oe. A hydrogen plasma was studied at pressures of (5 to 1) × 10−3 Torr. The active high-frequency power put into the discharge was 4 kW. The temperature of the electrons varied from 4 to 10 eV, and the electron concentration at the centre of the chamber was 1 × 1010 to 4 × 1012 cm−3. The density of the plasma and the temperature of the electrons were determined mainly by electric probes. Further, the density and temperature of the electrons were checked by a microwave technique (for which the Fabry-Perot interferometer was used) as well as by optical methods.

In the range from 10 to 200 kHz, intensive (∼1 V) electric noise with first-harmonic frequencies of several tens of kHz was discovered and investigated by means of dual electric and capacitative and double capacitative probes. The relationship between this noise and the plasma parameters was studied, and discussed from the point of view of the “universal” plasma instability.
Stability of a spatially inhomogeneous current-carrying plasma
Authors: Bogdankevich L.S. , Rukhadze A.A.
Published: January 2011

The oscillation spectrum of a spatially inhomogeneous current-carrying plasma is analysed in conditions where all the plasma electrons are in motion relative to quiescent ions. Along with the density and temperature of the particles, the directed motion of the electrons, i.e. the plasma current, is considered to be inhomogeneous. The analysis shows that in certain cases this directed motion can be a cause of instability in a current-carrying plasma. The author establishes criteria for the instabilities of such a plasma in various frequency ranges and suggests ways of averting them. In particular, he draws attention to a dynamic method of suppressing instabilities by means of the current itself, in conditions where the plasma current is variable in time.
Cross sections for collisions of electrons with hydrogen atoms and hydrogen-like ions
Authors: Percival I.C.
Published: January 2011

On the basis of a limited critical review of present theory and experiment, cross sections are recommended for the ionization of any level of hydrogen or any hydrogenic ion by electrons, for the excitation of any level from the ground level and n→n + 1 excitation from higher levels. Individual angular momentum and Stark states of the levels are not considered. We rely on a few experimental results for excitation and ionization, together with theoretical estimates of relative cross sections to obtained recommended cross sections for a variety of processes, which are inaccessible to direct experiment. The normalized energy of the incoming electron is ℰ = E/U where E is the energy of the incoming electron, and U the ionization energy of the atom or ion. A normalized cross section is defined as where Z is the nuclear charge, n the initial principal quantum number and Q the cross section. The recommended normalized cross sections for ionization are

The cross section QR,1→n(ℰ) for excitation of neutral hydrogen from the ground level n = 1 to the n = 2 level is presented graphically. The recommended cross section for excitation to an arbitrary final level is

For any excitation of neutral hydrogen from a level n ≠ 1 to a neighbouring level, the cross sections of Saraph are recommended. The recommended cross sections for excitation of the ground levels of ions are more complicated, but are based on the Born cross sections for neutral hydrogen.
Stability of plasma cylinder in a time-dependent magnetic fleld
Authors: Vandakurov Yu.V.
Published: January 2011

The stability of an ideally conducting plasma cylinder in a strong, time-dependent magnetic field is studied in the magnetohydrodynamic approximation. When there is no radial movement of particles the configuration is stable (the stability in question is that of a non-rotating plasma column in one longitudinal field, although the current along the cylinder axis and the rotation of the medium are taken into account in some of the sections of this work). The superposition of the time-dependent component of the longitudinal magnetic field may produce the following three types of instability: (1) In a contracting cylinder the long-wave perturbations may become unstable; when this happens the development time is inversely proportional to (|m|−1)½, where m is the perturbation mode. This is an instability of the Rayleigh-Taylor type. The effect is studied by means of a homogeneous plasma column model in which the compression velocity is linearly dependent on the radius and the magnetic pressure distribution is parabolic; (2) In a plasma in which the compression or expansion velocity is of the same order as the thermal speeds, non-radial natural oscillations may build up. In particular, the bands of instability are narrow for cylinder pulsations of small amplitude, while the growth rate is proportional to the amplitude of the pulsations. The most dangerous resonance occurs if the pulsation frequency is close to the sum of the two oscillation freqviencies (or twice the frequency of one oscillation); (3) Instability occurs in an inhomogeneous plasma contained by a strong magnetic field on which a parallel field of small amplitude and high frequency is superposed (it is assumed that the frequency is much greater than the ratio of thermal speeds to plasma column radius). The development time of the perturbations is inversely proportional to the amplitude of the alternating field component and decreases abruptly near frequencies exceeding ion cyclotron frequency. In this region a build-up occurs of highfrequency non-radial natural oscillations that are independent of the co-ordinate along the cylinder. The most stable configuration has a uniform density distribution and a sharp boundary, and the growth rates are proportional to the square root of the ratio of the boundary layer thickness to the cylinder radius. The author suggests that the effect considered in this work is the cause of the high level of diffusion observed at the ion cyclotron resonance.
Radial distribution of plasma formed in simple mirror machines by field ionization of fast neutral atoms
Authors: Murphy E.G. , Riviere E.G. , Sweetman D.R.
Published: January 2011

The radial distribution of plasma which results from field ionization of excited atoms injected into simple mirror machines is calculated and compared with measurements made in the Phoenix machine. The excited atoms are assumed to have a level population distribution given by An
−3 where n is the principal quantum number. The fraction of the atoms ionized per unit interval along their path is obtained by calculating the quantum mechanical barrier penetration probability at each point. Finite Larmor orbit diameter, precessional drift around the field axis and finite atom beam dimensions are taken into account in obtaining the radial distribution of plasma that results from this method of injection. The plasma distribution rises to a maximum on the axis in contrast to the distribution obtained by assuming that ionization occurs immediately a critical field is reached. Good agreement with experiment is obtained both for the absolute density and for radial distributions. The fraction ionized per unit interval at the axis is calculated for the Alice and Ogra II experiments without their stabilising fields; this fraction is approximately proportional to the square root of the radial field gradient coefficient. However, the fraction ionized per unit interval is also calculated for an artificial flat-topped field shape and the results show that even in the absence of field gradient, useful trapping can be obtained. Calculations are also made of the effect of pre-ionization on the radial extent of the plasma.
Dissociation of H2+ ions by the Lorentz force
Authors: Dei Cas R. , Fumelli M. , Girard J.P. , Prévot F. , Valckx F.P.G.
Published: January 2011

In the plasma experiment of H2+ ion injection into a magnetic mirror (MMII) at Fontenay-aux-Roses, Lorentz force trapping is observed when the residual gas pressure is low enough. The measured dissociation fraction of H2+ directly extracted from the ion source is relatively high,f∼ 2×10−4, for an equivalent electric field maximumE= 3.2 × 104V/cm. This result is attributed to the abundance of ions with high vibrational levels.
Convective and absolute instability
Authors: Dysthe K.B.
Published: January 2011

Unstable systems characterized by linear partial differential equations with constant coefficients are considered. The question of convective or absolute instability has meaning only for a stated condition; then the Cauchy problem for the system is solved by Fourier and Laplace transforms. For one space dimension, we start from the solution which is written as a Laplace inversion integral, and evaluate it asymptotically (t→ ∞). For several space dimensions we start from a solution of the Cauchy problem that is written as a Fourier integral; this solution is evaluated asymptotically by the saddle point method. Six criteria distinguish between the two types of instabilities. The first is equivalent to the criterion found by Sturrock, and applies only to systems propagating in one space dimension. The fifth is more general because it applies to one or more space dimensions. The second and sixth give sufficient conditions for convective instability. The third and fourth give sufficient conditions for absolute instability.

The “bulk” of the growing wave is defined to be the part of it having the highest growth rate. The velocity associated with the bulk of the wave is calculated for unstable systems satisfying the stated condition. This velocity may be zero for an absolutely unstable system.
Radial implosion of a partially ionized plasma in a theta pinch
Authors: Green T.S. , Newton A.A. , Segre S.E.
Published: January 2011

We investigated the radial implosion of a deuterium plasma in a theta pinch in which the initial level of ionization was controlled. Measurements of the diamagnetism of the plasma during the implosion were related to the mass of gas in motion. The latter depends on the interaction between the ions and the neutral atoms. The effective cross-section for momentum transfer from ions to neutrals is 4 × 10−15 cm2, close to the charge exchange cross-section for protons and hydrogen atoms.
Current instability in an inhomogeneous plasma
Authors: Buchelnikova N.S. , Salimov R.A. , Eidelman Yu.I.
Published: January 2011

The authors investigate the development of instability when a current is passed through a strongly ionized potassium plasma of non-uniform density. The collisionless plasma, having a density of 109 to 1010 cm−3, is subjected to magnetic fields of 400 to 2000 Oe. In accordance with earlier experiments, “universal” instability in the form of drift waves is observed when no current is present. The coefficient of diffusion across the magnetic field is some two orders of magnitude greater than the classical coefficient. When a current is passed through the plasma two oscillation branches are excited: drift and ion-sound waves. With the first branch the oscillation frequency is inversely proportional to the magnetic field and the waves have an azimuthal component, the azimuthal phase velocities of all the harmonics being the same. With the second branch the oscillation frequency is independent of the magnetic field and varies inversely with the length of the system. For practical purposes, the phase velocity of the longitudinal component coincides with the ion-sound velocity. The critical drift velocity of the electrons and of the ions, at which ion-sound waves are excited, is approximately 2 × 106 cm/ sec, an order of magnitude less than the theoretical critical drift velocity for an homogeneous, almost isothermal, plasma. When the current instability is excited, the diffusion coefficient increases by a factor of 1.5 to 2.5, diffusion beginning to increase simultaneously with the increase in oscillation amplitude.