bluuebunny/crossref_metadata_2025 huggingface dataset:
Particle distribution function in plasma and the self-consistent magnetic field
Authors: Lacina J.
Published: January 2011

The equilibrium configuration of plasma (the stationary distribution function of charged particles) and of the self-consistent magnetic field is determined on the basis of the first integrals of motion. A detailed analysis is made of the mutual relation between the resultant magnetic field B and the dependence of the distribution function on the integrals of motion; the necessary and sufficient conditions which must be satisfied by the distribution function with a minimum-B field are obtained. For the configuration with a minimum in B on the axis of symmetry, the function F(pφ) must decrease rapidly with increasing pφ in the vicinity of pφ = 0. Accordingly, the number of particles must have a maximum for particles that perform Larmor gyration around the axis (epφ < 0), and the number of particles intersecting the axis (pφ = 0), must be non-zero
Qualitative stabilizing and destabilizing effects in the macroscopic theory
Authors: Tasso H. , Schram P.P.J.M.
Published: January 2011

In the two fluid theory for a general static equilibrium without symmetry and with finite β, it is possible to obtain an equation over the velocity field perturbation. This is done by taking into account a stress tensor containing the finite Larmor radius, the viscosity arising from collisions, and the complete Ohm’s law. In this equation the space operators, with the exception of the one with the Hall term, have symmetry properties. One can see qualitatively the possible destabilizing effect of the Hall term, the stabilizing effect of the finite ion Larmor radius, the stabilizing and destabilizing effects of the viscosity.
Neutral injection into closed line magnetic traps
Authors: Bickerton R.J. , Drogman D.
Published: January 2011

The build-up of a plasma by fast neutral particle injection into a closed-line magnetic trap is studied. By contrast with the mirror-machine case, the slow plasma formed by charge exchange and ionisation is contained within the system. This slow plasma increases the efficiency of fast neutral particle trapping and, through ‘plasma pumping’, lowers the density of slow neutrals. Hence for given initial conditions of equivalent beam current, base pressure and volume a higher fast ion density can be achieved in a closed-line trap than in an open one. This higher fast ion density is accompanied in most cases by a still larger density of slow plasma. However with a sufficiently intense neutral beam the slow plasma can be heated by energy transfer to temperatures of thermonuclear interest.
Destruction of magnetic surfaces by magnetic field irregularities
Authors: Rosenbluth M.N. , Sagdeev R.Z. , Taylor J.B. , Zaslavski G.M.
Published: January 2011

A perturbation theory analogous to that of quasi-linear theory is developed to treat the behavior of magnetic surfaces, in particular to estimate their stability against field irregularities. The method exploits the similarity between the Vlasov equation and the Liouville equation for field lines. We find that a very important role is played by field resonances, that isolated resonances have a limited effect, extended over a finite width which we estimate, but as soon as resonances overlap, a very rapid destruction of flux surfaces may be expected.
Energy spreading and stabilization of plasma by applying a high-frequency electric field
Authors: Kuo-Petravić L.G. , Murphy E.G. , Petravić M. , Sinclair R.M. , Sweetman D.R. , Thompson E.
Published: January 2011

The ion cyclotron instabilities in the PHOENIX high energy injection mirror machine have been suppressed by applying oscillating electric fields. Two instabilities appear to be present. One is suppressed by energy spreading and the suppression of the other appears to be due to the effect of the applied electric fields on the electrons.
A simple model for the yield of excited hydrogen atoms as a function of gas target thickness
Authors: Berkner K.H. , Kay L. , Riviere A.C.
Published: January 2011

A simple analytical model is presented to describe the variation in the yield of excited hydrogen atoms formed by charge exchange as a function of gas target thickness. The model enables the existence of a maximum in the yield and the size of the maximum to be predicted from a minimum of cross-section information. A prediction can also be made for the amount by which the gas target thickness can be reduced in going from the value required for optimum total atom yield to that required for optimum excited atom yield. Both the ratio m of the yield at the maximum to the yield under thick target conditions and the reduction in target thickness r can be expressed in terms of only two independent variables by neglecting certain small cross-sections. Values for m and r are presented as sets of curves on one diagram.

From available cross-section data, values for m between 1.0 and 1.5 are predicted for H2, He, Ne, Ar and Xe gases for energies between 25 and 75 keV. The only experimental values of m available are those for Ne, Na and Mg reported by Il'in et al. For Ne the model predicts a value of m of 1.0 at 25 keV which is in agreement with the experiment. Although values of m up to 10 were observed by Il'in et al. for Na and Mg, there is insufficient cross-section data available as yet for these materials for predictions to be made from the model.
Approximate equations for plasmas in mirror machines
Authors: Rosenbluth M.N. , Varma R.K.
Published: January 2011

By expanding in terms of the parameter ϵ=ion Larmor radius/plasma radius (ϵ ≪ 1), sets of approximate equations are obtained from Vlasov's equation for the low-β inhomogeneous plasma equilibria which occur in the inhomogeneous magnetic fields of the mirror machines. The different sets correspond to different physical regimes which require different ordering of the parameters. Thus at very low densities (b2 = 4πnMc2/B2 ≪ 1), it is essential to order various terms in Vlasov's equation such that the precessional drift velocity is of the same order as the frequency of the motion. This implies ω≈ϵ4Ωi for a “long-thin” machine (r∼ϵ2 ρ), and ω≈ϵ2 Ωi for “short-fat” machine (r∼ρ). In either case the “closed” equation for the phase-averaged zero-order distribution function is found to be identical to the Northrop-Teller “Liouville equation” for the guiding centre with the μ∇B and the curvature drifts appearing in the same order as the frequency of the motion. For a high density plasma (b2 = 4πnMc2/B2 ≫ 1) the terms are ordered such that ω≈ϵ2Ωi for a “long-thin” machine (the finite Larmor radius case). The set of approximate equations for this case and the resulting eigenvalue equation are found to be completely analogous to those for the cylindrical geometry as found by Rosenbluth and Simon. In particular, for the “special case” of Rosenbluth and Simon the m = 1 mode is found to be neutral stable, in the absence of gravity as in the hydromagnetic limit.
Flute instability in mirror machines at very low densities
Authors: Varma R.K.
Published: January 2011

The flute instability of low-β axially symmetric plasma confinement devices is studied. From the set of equations for the low-density case, without an equilibrium space-charge potential, and with a near δ-function distribution of energies appropriate to neutral injection devices, a variational principle is derived for the three-dimensional mirror machine geometry. In general, for small electron temperatures the variational principle furnishes a dispersion relation which for given trial functions is cubic. Two roots of the cubic furnish the stability criterion. The third root describes a density-independent mode of oscillation at a frequency equal to the ion precessional frequency, and is identified with the density-independent mode observed in the ALICE machine. The order of magnitude of the critical plasma density for flute instability is the same as that obtained by previous authors using the drift approximation, but by use of the variational principle the present author is able to obtain a more quantitative stability criterion, in particular an estimate of the effect of the finite plasma length. The critical plasma density is presented as a function of the ratio of the length to the radius of the plasma.
Inhomogeneous development of a plasma through quasi-linear theory
Authors: Bloomberg H.
Published: January 2011

A quasi-linear perturbation expansion is used to study the evolution of a localized disturbance introduced in a homogeneous plasma characterized by a distribution function having a small “bump” on its tail. For this problem first-order theory of the Vlasov equation predicts the development of growing waves. The curtailment of this instability through a plateau development in v space is given through the second-order corrections. During the curtailment process the distribution function develops weak time and space dependence. There is shown an energy transfer balance between the growing waves and the particles with bump velocity which are part of the “background” distribution function and those which are second order in the “disturbance” distribution. Comparison with earlier quasi-linear theory is made.
The electrostatic energy per degree of freedom of a two-temperature plasma
Authors: Klevans E.H. , Primack J.R.
Published: January 2011

The electrostatic energy per degree of freedom of a two-temperature fully ionized plasma was calculated by Rostoker, using resonant integral approximations. His results include the contributions from plasma waves and ion waves. In this note it is shown that the non-resonant contribution from electrons, i.e. the contribution from other than plasma waves, is important for the same wavelengths for which ion waves are important. Also, the validity of the resonant approximations in the ion wave region is examined by comparing Rostoker's results with those obtained by computer calculation. Although Rostoker's results give good qualitative agreement, significant quantitative disagreement is found. A more accurate approximation procedure is presented which gives better agreement with computer results.
Cyclotron instability of a plasma in magnetic mirror machines
Authors: Davydova T.A. , Dnestrovsky Yu.N. , Kostomarov D.P.
Published: January 2011

The authors consider cyclotron instability in a homogeneous plasma with anisotropic non-monotonic ion distribution in velocity space. In the plane of the parameters and τ = ϵ⊥i/ϵ‖i (where ω0e is the plasma frequency of the electrons, ωi is the Larmor frequency of the ions, ϵ⊥i and ϵ‖i are the transverse and longitudinal energy of the ions respectively) regions are constructed by numerical methods which correspond to the unstable states of a plasma at cyclotron resonances of different orders. The authors study the dependence of these regions on electron temperature, the dimensions of the trap, and the width of the ion transverse-velocity distribution peak. The stability of a plasma in machines of the Ogra-2 type is discussed. It is shown that the results of recent experiments on the Phoenix device aimed at suppressing cyclotron instability cannot be explained by broadening of the ion distribution peak. To stabilize the oscillations in this machine it is sufficient to increase the temperature of the electrons to 30 – 50 eV, which is apparently what happens in the experiment.
Plasma instability in the electric field of an ion-cyclotron wave
Authors: Sizonenko V.L. , Stepanov K.N.
Published: January 2011

The authors investigate the stability of a collisionless plasma in which the ions are moving relative to the electrons at right angles to the applied magnetic field, under the influence of the electric field of an ion-cyclotron wave, with a velocity u⃗⊥ that is less than or commensurate with the thermal velocity of the ions vi. They study the excitation of longitudinal electrostatic oscillations with frequency and growth rate significantly greater than the gyrofrequency of the ions, but significantly less than that of the electrons, and with a wavelength significantly less than that of the ion-cyclotron wave.

It is shown that, when the ion temperature Ti is significantly higher than the electron temperature Te. electron-acousticoscillations are excited in the plasma. The excitation of these oscillations by resonance ions is possible even when u⊥ ≪ vi. When Te ≫ Ti ion-acoustic oscillations are excited in the plasma, the build-up of these oscillations by the ions being the result of absorption by resonance electrons. When Te ⪆ Ti oscillations are excited if the velocity of the ion beam u⊥ is somewhat greater than the thermal velocity of the ions.

When Ti ≫ Te. the reactive effect of the oscillations causes the function representing resonance ion distribution in the beam direction to level off and form a plateau. When Te ≫ Ti the unstable ion-acoustic oscillations spread the resonance electron distribution function, which is equivalent to electron heating, and slow down the ion beam.
Measuring the electron temperature of a powerful pulsed discharge
Authors: Zemtsov Yu.K. , Pismenny V.D. , Rakhimov A.T.
Published: January 2011

The electron temperature of a plasma (Ne ∼ 1017 cm−3) produced by a powerful pulsed discharge was measured by the relative intensity of the spectral lines from lithium-like impurity ions (NV, OVI). For such calculations it is necessary to know the population of the different ionic levels; this was found by solving a system of balance equations describing the processes which give rise to population and depopulation of levels. It has been found that under experimental conditions (Ne ∼ 1017 cm−3) the population of the lower levels of the ions under consideration is close to a Boltzmann population, relative to the ground state. The higher levels are in thermodynamic equilibrium with continuum but the population of these levels, relative to the ground state, is considerably smaller than a Boltzmann population. Calculations have been made of the α-corrections which show the deviation from a Boltzmann population relative to the ground state. With these corrections it was possible to obtain internally consistent values of the electron temperature (Te ∼ 20-30 eV) over the entire emission spectrum (from 150 Å to 2000 Å).
Landau damping and the moments method
Authors: Sedláček Z.
Published: January 2011

It is shown that if the continuous spectrum of the infinite mauix belonging to the moment equations is taken into account, results completely equivalent to those obtained from the linearized Vlasov equation, including the Landau damping, are recovered. In fact, such procedure can be viewed as an alternative to the usual method of solving the Vlasov equation by integration along the unperturbed trajectory.
Propagation of compressional and torsional Alfven waves under identical plasma conditions
Authors: Cross R.C. , Lehan J.A.
Published: January 2011

Though many authors have separately studied torsional and compressional Alfven waves, no measurements made on both waves for the same plasma conditions have been reported. This paper presents such measurements for several different sets of plasma conditions. For each set of conditions, velocity and attenuation measurements were made for each wave and by comparing with theoretical curves, the values of the various parameters determining the wave propagation were obtained. The compressional and torsional wave measurements gave independent estimates of the parameters. The two sets of parameters show a broad agreement which is particularly significant since de-coupling of the ions from the neutrals is taking place over the frequency range for which the measurements were made. The torsional wave measurements do, however, imply a higher total density and lower percentage ionization than the compressional wave measurements. The existence of this difference implies that non-uniformity of the radial density distribution is affecting the wave propagation.
Destruction of magnetic surfaces by magnetic field irregularities: Part II
Authors: Filonenko N.N. , Sagdeev R.Z. , Zaslavsky G.M.
Published: January 2011

The present work is a continuation of the paper by Rosenbluth et al. (Nucl. Fusion 6 (1966) 297) and concerns the investigation of problems associated with the condition for the existence of magnetic surfaces in closed systems of the stellarator type. The unperturbed geometry of the magnetic field is produced by a straight helical field. Exact equations for the motion of the magnetic field lines are put into Hamiltonian form and action-phase variables are introduced. The authors study the effect on magnetic field geometry of a perturbation that is periodic with respect to the co-ordinate along the toroidal axis. It is shown that, if the perturbation is greater than some critical value, the motion of those field lines that are at a sufficient distance from the toroidal axis is similar to Brownian motion and leads to the destruction of the magnetic surfaces. The authors derive the explicit form of the condition forstochastic instability of the magnetic field lines and estimate the coefficient of field line diffusion from the volume. With the above method it is possible to consider the most important form of perturbation in stellarator systems, occurring when the cylindrical, helical field is bent into a torus. Irrespective of the magnitude of the correction for the toroidality of the geometry, destruction of the magnetic surfaces occurs near the separatrix of the unperturbed magnetic field, and this effectively reduces the region bounded by the separatrix of the perturbed field. When the toroidal perturbations are small, the destruction is of a stochastic nature. It follows from the estimate made of the region where destruction takes place that the maximum shear permissible in toroidal systems is substantially limited. In conclusion, the authors present computer calculation results illustrating the stochastic nature of the destruction of the magnetic surfaces.
Status report on MHD electrical power generation–IAEA/ENEA International Liaison Group on MHD Electrical power generation
Authors: Lindley B. C.
Published: January 2011

The present status of commercial large-scale MHD electrical power generation is reviewed in the light of information presented at the Third International Symposium on MHD Electrical Power Generation (Salzburg, 1966) and of subsequent developments. Research and development activities, and the state of evaluation of engineering and economic factors are assessed in respect of open-cycle MHD power plant, closed-cycle MHD power plant, and the associated electromagnet.

The MHD power generator is attractive in that energy is extracted directly from that of the flow of working fluid. The generator itself is of simple static construction, thus permitting high maximum cycle temperature, high specific power output and potentially much larger unit size than may ultimately be achievable with turbomachinety. In principle, these features should offer increased thermal efficiency and reduced capital cost compared with conventional plant.

In the ‘open-cycle’ MHD system electrical energy is extracted directly from the flow of a plasma formed by the seeded products of combustion of a hydrocarbon fuel. The ‘closed-cycle’ MHD system similarly employs a working fluid which may be a seeded inert gas (helium, neon, argon) or a pure alkali metal. Operation may be based on the gas turbine or Brayton cycle, or incorporate steam plant (for the lower range of temperature) based on the condensing or Rankine cycle. In the case of the open-cycle MHD system, installations are being constructed or already operating successfully with hundreds of MW thermal input and tens of MW electrical output, and substantial effort has been devoted to other aspects of the plant. It is concluded that a pilot-scale power station is technically feasible but that the economics of MHD steam plant are not fully established.

Research and development towards the closed-cycle MHD system is at an earlier stage, and there are fundamental aspects of plasma behaviour relating to instabilities and the feasibility of utilizing magnetically-induced non-equilibrium ionization which have to be resolved. Engineering and economic evaluation of system concepts requires attention. Closed-cycle systems operated on a condensing or Rankine cycle with liquid-metal MHD generators are also at an early stage of development. There is as yet insufficient information on the performance of various liquid acceleration schemes and MHD generators to allow assessment for commercial plant, although for special applications (e.g. space vehicle power systems) the concept is attractive.

Superconducting electromagnets are technically and economically necessary for MHD power systems which, in almost all respects, derive benefit from operation at higher magnetic fields. Field levels of 5 – 7 T are attainable at present, and there are good prospects for further development to large size and higher fields.
Equilibrium of finite larmor radius plasma with anisotropic pressure
Authors: Lacina J.
Published: January 2011

The relations that exist between the pressure tensor, the electric current density in plasma and the selfconsistent magnetic field for equilibrium plasma configurations in magnetic mirror systems are derived and discussed. The analysis starts from the distribution function of equilibrium plasma derived in earlier work. It is found that the pressure tensor (appearing in these relations) is diagonal, with Pξξ ≠ Pφφ ≠ Pηη (Pξξ, Pφφ are the pressure components perpendicular to the lines of force, Pηη that along the lines of force). The plasma pressure in magnetic mirror systems is usually strongly anisotropic also in the plane perpendicular to the lines of force (Pξξ differs considerably from Pφφ) and the approximation Pφφ ≈ Pξξ ≡ P⊥ can no longer be used. This anisotropy is due to the strong dependence of the distribution function on the integral ; the cause of this strong dependence lies in the finite Larmor radius (real plasma consists of spatially bounded beams with Larmor radius of the same order as the plasma radius). Because of the curvature of the magnetic surfaces, the relations between the macroscopic quantities are affected by both longitudinal and perpendicular plasma anisotropy. Equations describing these relations are derived in the paper for finite β = 8πP/B2 and in the approximation β ≪ 1.
Plasma instabilities due to ion temperature gradients
Authors: Porkoláb M.
Published: January 2011

The dispersion relation for an inhomogeneous, low-pressure, collisionless magnetized plasma with ion temperature gradients is solved numerically in the regime where the plasma dispersion function cannot be expanded in a power series. The plasma is found to be unstable to low frequency, electrostatic perturbation at least in the range , 0.2 ⪅ Te/Ti lap; 5, ω ⪅ k‖vi, and possibly for a wider range of parameters (where ri as the ion Larmor radius, T the temperature, vi the ion thermal velocity, k⃗ the wave vector). It is believed that the magneto-ionic acoustic waves observed in a thermal potassium plasma are manifestations of such instabilities. Additional experimental evidence is given in support of this assertion.
Dynamics of three-wave processes in plasmas
Authors: Fedorchenko V.D. , Muratov V.I. , Rutkevich B.N.
Published: January 2011

Travelling waves with a frequency of the order of 109 c/s were excited in a plasma column and their non-linear interaction with the ionic sound waves (f = 104 c/s) was observed.

At various distances from the input the authors recorded combination spectra showing the dynamics of the processes involved: the travelling wave amplitude decreases and, at a distance of 29 cm from the input, falls to zero, its energy being redistributed to numerous satellites. The energy redistribution process is not periodic.

The characteristic wave interaction time is found to be short (τ ∼ 10−8 s), which indicates the efficiency of the process and enables conclusions to be drawn regarding the determinacy of the interacting wave phases (δω⋅τ ≪ 1).
Kinetics of slightly relativistic plasma, I
Authors: Trubnikov B.A.
Published: January 2011

The kinetics of a slightly relativistic plasma is discussed on the basis of Darwin's Lagrangian, taking into account in the first non-vanishing approximation the effects of interaction retardation. Since the corresponding Hamiltonian cannot be written down explicitly, the author has devised a means of applying Bogolyubov's method using correlation functions to the case of a Lagrangian formalism involving velocity-dependent binary interaction.
Larmor radius and collisional effects on the combined Taylor and Kelvin instabilities in a composite medium
Authors: Hans H. K.
Published: January 2011

The simultaneous effects of ion Larmor radius and collisions with neutral atoms are investigated on Kelvin-Helmholtz and Rayleigh-Taylor configurations. It is found that the Kelvin configuration is stable if both finite Larmor radius effects and the collisions are taken into account for all wave-numbers greater than the critical value U/2ν. When the system is unstable, it is found that, whereas the Larmor radius has a stabilizing influence, a collision frequency has a stabilizing effect when it is small and a destabilizing effect when it exceeds a certain value. In the case of the Rayleigh-Taylor configuration it is found, however, that the collisions have a stabilizing influence.
Contribution to the theory of magnetic pumping of an inhomogeneous collisional plasma
Authors: Nemov V.V. , Stepanov K.N.
Published: January 2011

The authors consider the heating, by magnetic pumping, of a radially non-uniform plasma cylinder of non-uni form radius located in a longitudinal, constant and uniform magnetic field B. An oscillating magnetic field having the form of a travelling wave with phase velocity ω/k of the order of the ionic thermal velocity is produced by means of external azimuthal electric currents. The frequency of the oscillating field ω is significantly less than the reciprocal of the ion-ion collision time 1/τi, and the ion cyclotron frequency ωi, the plasma electrons are magnetized (the electron cyclotron frequency is considerably greater than the reciprocal of the electron-electron collision time), and the plasma pressure is significantly less than the magnetic pressure.

Simple expressions are obtained for the energy absorbed per unit time by the plasma as a result of dissipative effects: ion viscosity and longitudinal electronic heat conduction (Joule losses play a minor role in magnetic pumping). Particular attention is paid to the case of acoustic resonance, where the inhomogeneous plasma contains a layer in which the velocity of sound is equal to the phase velocity of the excited wave. In this situation the absorption of energy by the plasma increases sharply and the increase in plasma temperature T is determined to within an order of magnitude by the relation dT/dt ∼ ωT(B∼/B)2, where B∼is the amplitude of the oscillating magnetic field at the axis.
Three-turn helical magnetic configuration with shear and minimum B̄
Authors: Aleksin V.F. , Sebko V.P.
Published: January 2011

The authors investigate the magnetic configuration of a three-turn helical magnetic field through which an axial current flows and which has three spatial magnetic axes. It is shown that, near the spatial axes, the cross-sections of the magnetic surfaces are ellipses lying in the planes perpendicular to the axes. The parameter values for which the configuration concerned possesses, near one of the spatial axes, an angle of torsion of the magnetic field lines, shear and minimum average magnetic field is considered.
Cusp containment and thermonuclear reactors
Authors: Spalding I.J.
Published: January 2011

Existing theories of the cusp containment of quiescent plasma are reviewed. Some technical and economic requirements of any fusion reactor are then summarized and used to deduce the probable dimensions of open-ended high-β reactors. It is shown that such reactors must be long, pulsed, and of very high output power. Crucial physical problems are the microstability of the high-β plasma boundary and, to a lesser extent, problems associated with energy transport by hot electrons.

Assuming that these physical and technological problems are capable of solution, it is shown that mirror-symmetric versions of the hybrid-cusp discussed previously by Bickerton may have significant advantages over the simpler linear θ-pinch geometry.
Screening of a high-density plasma from neutral gas
penetration
Authors: Lehnert B.
Published: January 2011

In several experiments on a magnetically confined plasma and under certain conditions
of a fusion reactor in stationary operation, neutral gas will be present in the
regions surrounding the plasma. The inflow of neutrals and the outflow of plasma by
diffusion or free streaming is studied in this paper, both for closed and open-ended
systems:

In a closed bottle neutral gas will not be able to penetrate through the cool
boundary layers into the hot core of a high-density plasma. At plasma densities
above 1021 m−3 the energy losses from interaction with
the neutrals become negligible compared to the thermonuclear power production,
but not at densities below 1019 m−3. This is due to the
fact that the penetration depth of the neutrals depends on the ionization rate
and becomes about 10−3 and 0.1 m at the densities 1021
and 1019 m−3. Further, the neutral gas inflow will be
delayed by diffusion through a cool boundary region of sufficiently high
density. In stationary operation the plasma density will be determined by the
magnetic field strength and the density of the surrounding neutral gas. A
condition for stable heat balance in a boundary region of finite thickness is
deduced in this paper.

As an alternative to a fusion device where the plasma is surrounded by an
ultra-high vacuum region, it is therefore possible to surround a high-density
plasma by a neutral gas blanket. The latter should be dense enough for released
wall impurities to diffuse only slowly towards the plasma boundary. With a
superimposed stream of neutral gas along the plasma boundary, the impurities
can then be removed before reaching the plasma.

In an open-ended system, thin layers of neutral gas are formed by plasma
particles which escape along the magnetic field and recombine at the end walls.

The theory agrees with measurements of the density of a fully ionized plasma
as a function of the applied magnetic field and the density of the surrounding
neutral gas. It also suggests that Bohm diffusion has not been present in
earlier experiments with rotating plasmas where the density was found to decay
at a very slow rate during free-wheeling.
A study of plasma stability in sheared magnetic fields
Authors: Davidson James N. , Kammash Terry
Published: January 2011

In this review paper the basic equations for the study of the stability of inhomogeneous plasma in sheared magnetic fields are derived and examined for normal mode and wave-packet perturbations. Special emphasis is placed on the detailed mathematical formalisms usually employed in the analysis of such problems, and numerous known examples are used as applications.
Theoretical limitations to the Hall acceleration mechanism in the polytron machine
Authors: Dunnett R.M.
Published: January 2011

In the ‘polytron’ a series of cusp magnetic fields is superimposed on a toroidal discharge. Stability is improved by favourable field curvature, and containment will be good if the plasma acquires a substantial velocity relative to the cusps. This can be achieved by a Hall acceleration mechanism. In this paper a hydromagnetic analysis is presented in which realistic time variations of electric and magnetic fields are allowed, and plasma self-fields are included. An upper bound is set to the acceleration obtainable from a given cusp system and expressed as a critical electric field Ec. The existence of Ec is confirmed experimentally, and it is possible to reproduce experimental waveforms approximately by inserting appropriate parameters into the equations. The effect of a toroidal magnetic field is also considered and a criterion derived for its maximum permissible value. In designing a fusion device this criterion could be an important consideration.
Magnetogravitational instability of a Vlasov plasma
Authors: Bajaj N.K. , Tandon J.N.
Published: January 2011

A complete derivation of the moment equations of a Vlasov plasma has been presented separately for the three density domains, namely the high-density regime (b→0), the moderate-density regime [bϵ ≃ O(1)] and the low-density regime [bϵ2 ≃ O(1)] with b as the ratio of Alfvén velocity to light velocity and ϵ = a/L where a is the ion Larmor radius and L, the characteristic length of the system. These moment equations are then employed to investigate the effect of finite β (= particle pressure/magnetic pressure) on gravitational flute instability of a non-uniform plasma. It is shown that the effect of finite β is one of stabilization.
Kinetic instability of flute oscillations
Authors: Kopecký V.
Published: January 2011

The author considers the effect of resonance particles drifting under the influence of magnetic field inhomogeneity with a velocity close to the phase velocity of flute oscillations on those oscillations. He investigates the instability of these oscillations at densities below the critical density of the hydrodynamic flute instability Ra/d2 ≪ 1 (R – radius of curvature of the magnetic field lines, a – transverse dimension of the plasma, d – Debye radius).

It is shown that, when resonance particles are present, the branch of oscillations with frequency (ω0 – ionic plasma frequency, ωc – ionic cyclotron frequency, k – transverse wave number) is always unstable. For an ion transverse velocity distribution function having the form of a δ-function with an admixture of hot ions, it is shown that the branch of oscillations with a frequency only slightly dependent on density and close to (v0 – mean ion velocity) is also unstable. Both instabilities also occur in the hydrodynamically stable case; i.e. when the magnetic field lines are convex with respect to the plasma.
Influence of ballooning effects on plasma stability in closed systems
Authors: Shafranov V. D. , Yurchenko E.I.
Published: January 2011

A general criterion of hydromagnetic plasma stability in the infinite electrical conductivity approximation is applied to smooth closed systems. As in the pioneering work of Mercier, the authors use the method of expansion with respect to the deviation from the magnetic axis. The effects of ballooning instability and of magnetic well deepening due to ballooninginduced stretching of the plasma column are clearly distinguished in this criterion. The above effects cancel out with an accuracy to within the square of the ellipticity of the magnetic surface cross-sections. Even in magnetic systems with a comparatively shallow magnetic well, ballooning instability does not therefore lead to a serious limitation on plasma pressure.

The authors present estimates of the critical plasma pressure for a two-turn stellarator and for systems with helical and axial symmetry.
Flute instability in an axially symmetric plasma with finite ion Larmor radius
Authors: Dnestrovsky Yu.N. , Kostomarov D.P. , Suzdaltseva L.F.
Published: January 2011

Solving numerically the integro-differential equation for plasma oscillations, the authors study the effect of the size of the ion Larmor radius ri and of an intrinsic electric field on the flute instability of a plasma. It is shown that, in a dilute plasma (, where ω0i and ωi, are the plasma and Larmor frequencies of the ions), effects attributable to the finiteness of ri are small and cannot explain the stabilization of oscillations in the Phoenix device. Intrinsic electric fields due to an excess of ions improve the stability of such a plasma. If the magnetic field gradient is small (aH'/H ∼ 0.1, where a is the characteristic dimension of the plasma) and the Larmor radius is of reasonable size (ri ∼ 0.2a). a relatively dense plasma surrounded by a conducting sheath may be stable.
Gyroresonant particle acceleration in a non-uniform magnetostatic field
Authors: Canobbio E.
Published: January 2011

Particle motion in inhomogeneous magnetostatic and high-frequency fields at the gyroresonance is studied in the limit of a large number of particle revolutions in the resonance region. The role played by the magnetic mirror, Doppler and relativistic effects, wave attenuation and radiation pressure on particle acceleration is discussed. The time dependence of the orbital magnetic flux, the velocity along the magnetic lines of force and the width of the resonance region are calculated. An upper limit is found for the energy of the particle, when the effect of the magnetic field of the wave partially compensates for the change in mass with energy.

The non-linear method we use is exact in the limit of many revolutions. It generalizes the results established by C.S. Roberts and S.J. Buchsbaum in a special case, to the more complex situation proposed by T. Consoli for injecting, accelerating and confining a hot plasma in a magnetic trap. A number of numerical examples are presented for various conditions. The energy transfer to the particles at the parametric resonances is also investigated.

The space charge field which develops along the magnetic lines of force in a plasma accelerating structure is taken into account in the equations from the very beginning by assuming (Consoli) that the electron guiding centres move with the velocity of the ions.
Influence of the shape and magnitude of the discharge current pulse on plasma containment and heating in Tokamak-3
Authors: Mirnov S.V.
Published: January 2011

The author systematizes the results of measurements of plasma energy and energy replacement time as a function of the shape and magnitude of the discharge current pulse. It has already been established that the maximum transverse energies E⊥ and energy replacement times τE in Tokamak-3 are reached 2-3 ms after the peak of the discharge current I. I n this paper, the author shows how E⊥(t) and τE(t) depend on the shape of the discharge current pulse and the duration of the discharge. An attempt is made to connect the observed relationships with the current density distribution. The internal (ℓi) and external (Lext = 2 ln(b/a)) self-inductance coefficients of the plasma column are measured and, on the basis of the results, an estimate is obtained of the shear averaged over the radius a. Hypotheses are advanced regarding the nature of the processes which determine the observed patterns of behaviour. One possible explanation is the presence of either dissipative helical instability (tearing mode) or overheat instability in the initial stage of the discharge and during the current rise.
Drift instabilities of a magnetized turbulent plasma
Authors: Krivorutsky E.N. , Makhankov V.G. , Tsytovich V.N.
Published: January 2011

The authors investigate the influence of a developed high-frequency plasma turbulence on the spectrum and build-up of drift oscillations. It is shown that, even in the case of relatively weak turbulence, W/n0 Te ≪ 1 (W being the turbulence energy), there is a critical value Wcr such that when W > Wcr the spectrum and build-up of drift oscillations change radically. When W > Wcr, high-frequency turbulence may lead to stabilization of drift oscillations for large temperature gradients (d ln T/d ln n0 > 2). The analysis is limited by the assumption that the plasma electrons are magnetized, which means that a drift kinetic equation can be used in describing them. The authors consider the role of both potential and non-potential turbulent pulsations at frequencies of the order ωpe = (4π n0 e2/me)½ and the limiting cases of isotropic andone-dimensional turbulence. A new class of turbulent-plasma instabilities with non-linear drift is found.
Non-linear skin effect in a conducting cylinder
Authors: Breus S.N. , Kurdyumov V.N.
Published: January 2011

The paper examines the penetration into a plasma cylinder of a quasi-stationary electromagnetic field excited by a wave of azimuthal surface current travelling parallel with the cylinder axis and located at some distance from the surface of the plasma. Since in this instance the variable magnetic field is considerably higher than the electric field its influence on the movement of particles in the plasma was taken into account. Within the limits of a hydrodynamic approximation this factor could be reduced to the inclusion of the Hall current in Ohm's law (σ/enc) [j⃗H⃗]. A solution to the resulting system of nonlinear partial differential equations was found by using a computer programme somewhat analogous to the physical process by which field equilibrium distributions are established in a plasma.

The dependence of all physical magnitudes on two parameters was studied: the conductivity of the plasma o and the ratio Ω of the Hall current to the conduction current.

Allowance for non-linear effects leads to the appearance of a constant component of the longitudinal current (the carrier current), whose density never exceeds, at any point of the cylinder cross-section, the limiting value corresponding to the movement of all electrons at the phase velocity of the wave. A leakage of current towards the inner region of the plasma cylinder takes place and closed lines of current form in the cross-sections φ = const. The depth of field penetration increases with increased non-linearity, while at high plasma conductivity values the penetration depth is determined only by the value of Ω. Dissipation losses in the plasma are to all practical purposes independent of Ω.
The plasmascope: its operational features, design and applications
Authors: Dobrokhotov E.I. , Zharinov A.V. , Moskalev I.N. , Petrov D.P.
Published: January 2011

The authors analyse the specific properties of the plasmascope as a device for investigating the processes which occur in a closed-end plasma chamber immersed in a magnetic field. They indicate its advantages and possibilities, and assess how much information can be obtained with it.

The design elements of the plasmascope are described, together with certain techniques employed in its construction.

The results are presented of plasmascope experiments with a low-temperature plasma obtained by means of gaseous discharge with an incandescent cathode. On the basis of these results it is possible to estimate the directed-motion velocities of the plasma, the plasma potential and the electric fields, and to obtain a picture of the instantaneous plasma density distribution over the transverse cross-section of the discharge. It is shown that the characteristic states of a discharge can be identified with the help of plasmagrams.
Dispersion relations for ion cyclotron oscillations
Authors: Shoucri M.M.
Published: January 2011

The natural modes of oscillation of a cold plasma, in the presence of a longitudinal external magnetic field, are examined near the ion cyclotron frequency. It is shown that under appropriate conditions, both the ordinary and the extraordinary hydrodynamic waves can be modified, giving modes whose natural frequency is in the neighbourhood of the ion cyclotron frequency. Dispersion relations for these modes are given in the case of cylindrical geometry, and the excitation of oscillations close to the ion gyrofrequency by a small-density beam is discussed.
Temperature and density measurements in the midplane of a long theta pinch
Authors: Beach A.D. , Bodin H.A.B. , Bunting C.A. , Dancy D.J. , Heywood G.C.H. , Kenward M.R. , McCartan J. , Newton A.A. , Pasco I.K. , Peacock R. , Watson J.L.
Published: January 2011

This paper describes the measurement of the plasma parameters in an 8-metre long theta pinch. The plasma in the midplane is found to be free of end effects and energy loss for some tens of microseconds and is characterized by electron densities of 2 - 5 × 1016 electrons/cm3 and temperatures of 100 - 300 eV. The measured radial distributions of temperature and density and their dependence on voltage and filling pressure were in agreement with MHD code calculations using an anomalous resistivity previously shown to account for the diffusion in the early stages.
Inductive lenses for improved magnetic field symmetry in a corrugated theta-pinch coil
Authors: Hartz F. , Junker J. , Pohl F. , Wolf G.H.
Published: January 2011

The magnetic field distribution of corrugated theta-pinch coils is measured in an analogue experiment (experimental error 0.05%) in order to determine the perturbation of the rotational symmetry induced by the current feed slot.

The maximum deviations from rotational symmetry are found near the coil surface around the current feed slot. They have a value of a few per cent and are proportional to the width of the current feed slot. The perturbations decrease towards the coil axis to a few tenths per cent only.

The distribution of a locally varying inductance of the current transmission line is computed and applied by moulding inductive lenses into the transmission line plates. The influence of the inductive lenses is measured. Within a radial region of about 1/2 of the coil radius the perturbations are found to be reduced to the level of the experimental error. The residual perturbations outside this region are mainly attributed to the limited space available for the application of the inductive lenses in the transmission line system.
Parametric excitation of ion-sound instability in a magnetized plasma located in a high-frequency electric field
Authors: Nekrasov F.M.
Published: January 2011

The author investigates the stability of a magnetized non-isothermal (Te ≫ Ti) plasma in an alternating electric field when the field frequency Ω0 is close to the frequency of the ion-sound oscillations of the plasma.

The amplitude of the oscillatory velocity of electrons in a h.f. field is assumed to be small compared with their thermal velocity (u0 ≪ vTe
). It is shown that, for perturbations with wave number kz satisfying the resonance condition there exists in such a plasma an instability with a growth rate .

The width of the instability zone is determined in the kinetic and hydrodynamic approximations. In the hydrodynamic approximation, if one does not allow for dissipation, there is instability however small the value of . If one allows for collisionless kinetic damping of the oscillations on the electrons, the instability develops only when u0 exceeds come critical value ∼ vTe
(me/Mi)¼.
Contribution to the theory of beam heating of a plasma in an open trap
Authors: Ryutov D.D.
Published: January 2011

The author investigates the mechanism whereby an electron beam interacts with a cold plasma in an open trap t o produce fast electrons, considering in particular the case where the electron plasma frequency, calculated from the cold plasma density, is considerably greater than the electron cyclotron frequency. It is assumed that the electron beam is the source of the electrons which are involved in the acceleration process. It is also assumed that the beam is the source of Langmuir oscillations with an anisotropic spectrum and that the electrons “ejected” from the beam, after interacting with the Langmuir oscillations, diffuse radially and at the same time accelerate. With these assumptions, it is possible to solve the kinetic equation with quasi-linear collision integral and to find the distribution function of the fast electrons at each point in the trap. It is also possible to calculate the “temperature” of the fast electrons and their total energy, and to determine how these quantities depend on the magnetic field strength and on the radius of the diaphragm limiting the diameter of the plasma. The results are in good agreement with experimental data.