Volume 7, Issue 11, November 2000
 LETTERS


A possible nature of “breathing” plasmas
View Description Hide DescriptionA model for “breathing” plasmas observed in the large helical device [Y. Takeiri et al., Plasma Phys. Controlled Fusion 42, 147 (2000)] is proposed. It takes into account the synergism of radiation losses from both lowZ(carbon, oxygen) and highZ(iron) impurities in the plasma power balance.

Laser frequency upshift, selfdefocusing, and ring formation in tunnel ionizing gases and plasmas
View Description Hide DescriptionThe combined effects of tunnel ionization of gases on laser frequency upshift, defocusing, and ring formation are considered selfconsistently. A highintensity short pulse laser causes rapid tunnel ionization of a gas. The increasing plasma density leads to a decreasing refractive index, modulating the phase of the laser as it propagates and causing frequency upshift and supercontinuum generation. For laser intensity profile peaking on axis, the tunnel ionization produces a minimum of refractive index on axis, thus defocusing the laser. The defocusing reduces the ionization rate and frequency upshift. As the laser propagates over a Rayleigh length its trailing portion develops a ring shape distribution due to stronger defocusing of rays on axis than the offaxis rays, as seen in a recent experiment.

Catalytic mechanism of divertor plasma recombination provided by hydrocarbon impurities
View Description Hide DescriptionIt is shown that the hydrocarbon molecules when present in a divertorplasma, provide a powerful catalytic mechanism for volume plasma recombination at temperatures below 6–8 eV. The mechanism is based on the protoncharge exchange with and the subsequent recombination of with plasma electrons, while its catalyticproperty derives from the simultaneous creation of new hydrocarbon molecules in each charge exchange–dissociative recombination cycle. The plasma recombining efficiency of and molecules is for a factor of about 10, 30, and 40 higher than the efficiency of the similar ion conversion–dissociative recombination mechanism based on the molecule hydrogen. A 2.5% of in the divertor molecular gas has the same effect on divertorplasma recombination as the entire content of molecular hydrogen in the divertor.
 Top

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Detection of stochastic waves in plasma monolayer crystals from video images
View Description Hide DescriptionThe motion of dust particles confined in plasmamonolayer crystals is analyzed from video images, under conditions dominated by dustneutral collisions. In these crystals, dustneutral collisions will act as a random driving force, exciting phonons with a stochastic nature. The phonons are investigated using standard statistical tools, including both single and multiparticle correlation functions. Singleparticle correlations as obtained from the velocity autocorrelation function yield oscillations in a very narrow frequency band. Similar behaviors have previously been reported for strongly coupled onecomponent plasmas, and for trapped Brownian particles. Spatial correlations in the crystal lattice are studied from multiparticle correlation functions, suggesting an average wavelength slightly larger than the dimension of the crystal. Throughout the crystal, the dust velocity amplitude and polarization vary significantly, with the main variation in the radial direction out of the crystal center. This suggests the observed wave feature is a standing wave with a stochastic amplitude, dominated by its lowest eigenfrequency.

Creation of strongly coupled plasmas using intense beams of 400 MeV/u uranium ions to be generated at the Gesellschaft für Schwerionenforschung (GSI) Darmstadt SIS200
View Description Hide DescriptionThe heavy ion synchrotron, SIS18 (that has an 18 Tm magnetic rigidity), at the Gesellschaft für Schwerionenforschung (GSI), Darmstadt is a unique facility worldwide that delivers intense beams of energetic heavy ions. The GSI has plans to extend its accelerator capabilities by building a new synchrotron (SIS200) with a much higher magnetic rigidity of 200 Tm. According to the preliminary design considerations, the SIS200 will generate a uraniumbeam that will consist of at least particles and that will be delivered in a 50 ns long pulse. This beam will be used to study various interesting problems, including fragmentation of the projectile ions while passing through solid matter and creation of highdensity, strongly coupled plasmas. For the former type of studies, a particle energy of 1 GeV/u has been considered to be appropriate, while for the latter case, a lower value of 400 MeV/u has been found to be most suitable. In this paper we present, with the help of twodimensional numerical simulations, the hydrodynamic and thermodynamic response of a solid lead cylindrical target that is irradiated with the future SIS200 beam, which has a particle energy of 400 MeV/u. The beam focal spot is assumed to be circular and the power deposition profile is considered to be Gaussian along the radial direction. Calculations have also been done using a beam that has a ringshaped (annular) focal spot that interacts with solid as well as hollow lead cylinders, respectively. In all the above cases it has been assumed that the cylinder length is shorter than the range of 400 MeV/u uranium ions in solid lead so that the Bragg peak does not lie inside the target and the energy deposition is almost uniform along the particle trajectory. These simulations show that it will be possible to create extended volumes of highdensity, strongly coupled plasmas using the future SIS200 beam.

Magnetosonic modes with dust mass distributions
View Description Hide DescriptionPreviously it was shown that perpendicularly propagating magnetosonic waves in a selfgravitating dusty plasma can significantly increase the Jeans length characteristic of gravitational collapse. Whereas that work was based on the presence of a single dust species, an arbitrary number of charged dust species is now considered and a modified Jeans criterion is obtained, subject to neglect of the dust thermal speeds with respect to the magnetosonic speed. As an illustration, the case of two dust masses is considered and used to justify that assumption. It is found that, in general, the criterion derived for a single (average) dust species provides an adequate approximation to the physics.

Thermodynamic equilibrium of hollow nonneutral plasmas
View Description Hide DescriptionNew annular confinement configurations of one component plasmas, corresponding to global thermal equilibria in a cylindrical Penning–Malmberg trap with an axial conductor, are investigated both numerically and analytically. In the case of infinite length plasma, analytical solutions are calculated explicitly in the limit of small Debye length. In the case of finite length plasma, the selfconsistent solution of the thermal equilibrium Poisson’s equation is obtained numerically, and the dependence of the density distribution on the different parameters of the system is illustrated.

Collisiondominated to collisionless electronfree spacecharge sheath in a plasma with variable ion temperature
View Description Hide DescriptionA theory of the nearcathode spacecharge sheath in the case when the nearcathode voltage is high enough and the presence of electrons in the sheath is unessential is developed on the basis of a fluid description of the ion motion with account of ionatom collisions and of variable ion temperature. The model spans the range of conditions from a collisionfree to collisiondominated spacecharge sheath. Detailed analytical and numerical results are presented for two models of ionatom interaction, the model of rigid spheres (constant mean free path) and the model of Maxwell molecules (constant frequency of momentum transfer). It is found, in particular, that the assumption of cold ions provides a good accuracy in the problem considered. An analytical solution has been obtained under this assumption for the model of Maxwell molecules.

Streaming instabilities in a collisional dusty plasma
View Description Hide DescriptionA pair of lowfrequency electrostatic modes, which are very similar to those experimentally observed by Praburam and Goree [Phys. Plasmas3, 1212 (1996)], are found to exist in a dusty plasma with a significant background neutral pressure and background ion streaming. One of these two modes is the dustacoustic mode and the other one is a new mode which is due to the combined effects of the ion streaming and ion–neutral collisions. It has been shown that in the absence of the ion streaming, the dustacoustic mode is damped due to the combined effects of the ion–neutral and dust–neutral collisions and the electron–ion recombination onto the dust grain surface. This result disagrees with Kaw and Singh [Phys. Rev. Lett. 79, 423 (1997)], who reported collisional instability of the dustacoustic mode in such a dusty plasma. It has also been found that a streaming instability with the growth rate of the order of the dust plasma frequency is triggered when the background ion streaming speed relative to the charged dust particles is comparable or higher than the ion–thermal speed. This point completely agrees with Rosenberg [J. Vac. Soc. Technol. A 14, 631 (1996)].

Sheath modification in the presence of dust particles
View Description Hide DescriptionNegatively charged dust particles are expected to modify the local sheath potential where they are in equilibrium. In the conditions of a hot cathode discharge, sheath profiles are deduced from the measurement of ion drift velocities, with dust particles in suspension and without. In the unperturbed potential profile, the surface potential of an isolated dust particle, its charge, and its potential energy can be estimated as a function of the position in the sheath. In the presence of dust particles, an average increase of the ion drift velocity is measured showing a modification of the local sheath profile. This experimental result suggests that the dust particle charge due to the plasma particle fluxes in the sheath, modifies in turn the local plasma particle distributions.
 Nonlinear Phenomena, Turbulence, Transport

Nonlinear electron beam interaction with a whistler wave packet
View Description Hide DescriptionThe nonlinear evolution of a thin monoenergetic electron beam injected in a magnetized plasma and interacting with a whistler wave packet through Cherenkov resonance is considered. It is shown that effective dissipation due to whistlers’ wave field leakage out of the bounded beam volume to infinity (effective radiation outside the beam) strongly influences the evolution of the beam electrons’ distribution. Selforganization of beam structure leads to the formation of electron bunches continuously decelerated by waves. In the presence of effective energy losses, the phases of all waves in the packet can become strongly correlated and thus can prevent the stochastic phase mixing required for validity of quasilinear theory. In the asymptotic stage of the beam–waves interaction, dynamically stable electron bunches are present together with a diffusion plateau in the velocity distribution; these nonlinear structures allow the beam to radiate wave energy on a significative distance from its injection point.

Gyrocentergauge kinetic theory
View Description Hide DescriptionGyrocentergauge kinetic theory is developed as an extension of the existing gyrokinetictheories. In essence, the formalism introduced here is a kinetic description of magnetized plasmas in the gyrocenter coordinates which is fully equivalent to the Vlasov–Maxwell system in the particle coordinates. In particular, provided the gyroradius is smaller than the scalelength of the magnetic field, it can treat highfrequency range as well as the usual lowfrequency range normally associated with gyrokinetic approaches. A significant advantage of this formalism is that it enables the direct particleincell simulations of compressional Alfvén waves for magnetohydrodynamic(MHD) applications and of rf (radio frequency) waves relevant to plasma heating in space and laboratory plasmas. The gyrocentergauge kinetic susceptibility for arbitrary wavelength and arbitrary frequency electromagnetic perturbations in a homogeneous magnetized plasma is shown to recover exactly the classical result obtained by integrating the Vlasov–Maxwell system in the particle coordinates. This demonstrates that all the waves supported by the Vlasov–Maxwell system can be studied using the gyrocentergauge kinetic model in the gyrocenter coordinates. This theoretical approach is so named to distinguish it from the existing gyrokinetictheory, which has been successfully developed and applied to many important lowfrequency and long parallel wavelength problems, where the conventional meaning of “gyrokinetic” has been standardized. Besides the usual gyrokineticdistribution function, the gyrocentergauge kinetic theory emphasizes as well the gyrocentergauge distribution function, which sometimes contains all the physics of the problems being studied, and whose importance has not been realized previously. The gyrocentergauge distribution function enters Maxwell’sequations through the pullback transformation of the gyrocenter transformation, which depends on the perturbed fields. The efficacy of the gyrocentergauge kinetic approach is largely due to the fact that it directly decouples particle’s gyromotion from its gyrocenter motion in the gyrocenter coordinates. As in the case of kinetic theories using guiding center coordinates, obtaining solutions for this kinetic system involves only following particles along their gyrocenter orbits. However, an added advantage here is that unlike the guiding center formalism, the gyrocenter coordinates used in this theory involves both the equilibrium and the perturbed components of the electromagnetic field. In terms of solving the kinetic system using particle simulation methods, the gyrocentergauge kinetic approach enables the reduction of computational complexity without the loss of important physical content.

Instability of a broadband Langmuir wave spectrum in a dusty plasma
View Description Hide DescriptionThe nonlinear interaction between broadband Langmuir waves and electrostatic dust–acoustic perturbations in a uniform collisional dusty plasma is considered, taking into account the combined effects of the Langmuir waveponderomotive force and the electron Joule heating nonlinearity. This coupling is governed by a Liouville equation for a Langmuir wave packet and an equation for a dust–acoustic perturbation that is driven by the ponderomotive and thermal forces of the random phase Langmuir waves. The mode coupling equations are then Fourier decomposed to derive the nonlinear dispersion relation. The latter is analyzed numerically for a Gaussian Langmuir wave spectrum, by taking parameters that are relevant for lowtemperature dusty plasma discharges. It is found that a broadband spectrum of Langmuir waves is subjected to a rapidly growing modulational instability in a dusty plasma.

Electron magnetohydrodynamic turbulence in a highbeta plasma. I. Plasma parameters and instability conditions
View Description Hide DescriptionThe interaction of a dense discharge plasma with a weak external magnetic field has been studied experimentally. The electron pressure exceeds the field pressure and forms a magnetic hole in the plasma interior. The ions are unmagnetized, while the electrons are in a transition regime from none to full magnetization. The electron confinement changes from Boltzmann equilibrium to magnetic confinement. The pressure balance equation does not describe the diamagnetism because ambipolar drifts oppose the diamagnetic drift. The net drift exceeds the sound speed by an order of magnitude and produces a strong twostream crossfield instability. Although its spectrum is close to the lower hybrid instability, there are significant differences from the classical lower hybrid instability, e.g., the presence of strong magnetic fluctuations. These fall into the regime of electron magnetohydrodynamics (EMHD) with unmagnetized but mobile ions. While the EMHD turbulence is the main focus of the two following companion papers, this first paper describes the plasmadiamagnetism and basic parameters that lead to the instability.

Electron magnetohydrodynamic turbulence in a highbeta plasma. II. Single point fluctuation measurements
View Description Hide DescriptionA magnetic void is created by high electron pressure in a large nonuniform laboratory plasma. A strong instability is observed in regions of high pressure and magnetic field gradients. It is associated with the electron diamagnetic drift through the essentially unmagnetized ions. Its spectrum is broad and peaks near the lower hybrid frequency. The coupled fluctuations in density, electron temperature,plasma potential, and magnetic field are measured with probes and crosscorrelated. The temporal correlation extends only over 1–2 oscillations. The fluctuations propagate in the direction of the electron diamagnetic drift but at the lower ion acoustic speed. In the saturated regime of the instability, the fluctuation waveforms are highly nonlinear. Density cavities with % are formed with steepened density rise at the trailing edge. The associated high pressure gradient forms a diamagnetic current sheet. Positive density perturbations are smaller %), broader, and produce regions of weak magnetic fields where the electrons become nearly unmagnetized. Amplitude distributions of nonlinear density, magnetic field, and current waveforms are evaluated. The threedimensional magnetic fieldfluctuations are analyzed with hodograms. The direction of the average wave vector points essentially across the mean field in the direction of the diamagnetic drift. The magnetic fluctuations can be interpreted as highly oblique electron whistlers, the density fluctuations as sound waves, but both modes are coupled in a highbeta plasma.Fluctuations in the electric and magnetic fields lead to a timeaveraged electron drift, i.e., anomalous transport, across the mean field.

Electron magnetohydrodynamic turbulence in a highbeta plasma. III. Conditionally averaged multipoint fluctuation measurements
View Description Hide DescriptionA large discharge plasma is generated whose electron pressure exceeds that of an external magnetic field. A magnetic cavity exists in the plasma interior. The ions are unmagnetized while the electron magnetization varies from complete to none. In the region of pressure and field gradients a strong instability is observed. It is a crossfield instability driven by the electron diamagnetic drift through the unmagnetized ions, creating large density and magnetic fieldfluctuations near the lower hybrid frequency that propagate at the sound speed in the diamagnetic drift direction. The basic plasma parameters leading to the instability have been presented in Part I of three companion papers. Spectra, correlations, amplitude distributions, and magnetic hodograms derived from singlepoint fluctuationmeasurements have been presented in Part II. These led to the discovery of density cavities and current sheet formation by nonlinear wave steepening. The present Part III deals with multipoint fluctuationmeasurements using online conditional averaging, which resolves the structure of typical fluctuations in space and time. Propagation velocity and coherence of the flutelike density perturbations is measured. The topology of the magnetic fluctuations and associated current density is investigated and shown to consist of flux ropes of negative selfhelicities. Superposition of the nonuniform mean field and fluctuating fields yields the net field and current density. Instantaneous field lines and magnitude distributions in threedimensional space are presented for a turbulent highbeta plasma. The results suggest that the demagnetization of electrons in large positive density fluctuations provides a new saturation mechanism for the instability.

Nonlinear evolution of double tearing modes
View Description Hide DescriptionThe linear and nonlinear behaviors of the tearing mode is systematically studied for nonmonotonic qprofiles on the basis of the reduced magnetohydrodynamics(MHD)equations in cylindrical geometry, and some new features about the double tearing mode are revealed. The linear eigenmode scales as a resistive internal mode for a small distance between two rational surfaces with the same qvalue, and as the tearing one for large New nonlinear phenomena appear in the tearing mode regime and for shorter The linear eigenfunction shows sharply localized fluid motion at both resonant surfaces and small but global convective motion between the resonant surfaces; consequently the mode goes through a Rutherfordtype regime. When the islands have grown enough, the mode shows explosive growth. This results from the nonlinear coupling among the higher harmonics, so that the inner and outer magnetic islands interact with each other leading to an internal disruption.

Experimental determination of attractor dimension of E×B turbulence
View Description Hide DescriptionThe time series analysis method for chaotic attractor dimension by Grassberger and Procaccia [P. Grassberger and I. Procaccia, Physica D 9, 189 (1983)] was applied to fluctuations due to an rotational flute mode in the Columbia Linear Machine (CLM) [G. A. Navratil, J. Slough, and A. K. Sen, Plasma Phys. 24, 184 (1982)]. After frequency domain filtering, the results show that the fluctuations carry a dimension close to three. A dimension of three supports a possible threewave mode coupling process revealed in bicoherence studies. The Grassberger Procaccia method was also performed on cases where partial feedback suppression was applied to the instability. It is shown that feedback does not alter the attractor dimension of the instability, supporting previous findings that the linear feedback only affects the linear drive of the instability, and not its nonlinear saturation mechanism.

Chaotic behavior of iontemperaturegradient driven driftdissipative modes
View Description Hide DescriptionA new set of nonlinear mode coupling equations for finite amplitude lowfrequency electromagnetic waves has been derived for nonuniform, resistive, magnetized electronion plasma with sheared flows. At equilibrium, the plasma is assumed to have density, iontemperature, magnetic field, and velocity gradients. The temporal behavior of the nonlinear mode coupling equations is found to be governed by eight coupled equations, which are the generalization of the Lorenz and Stenflo equations, admitting chaotic trajectories. The linear stability of the generalized Lorenz–Stenflo system of equations is also presented under different approximations. The results of the present investigation should be helpful in understanding the wave phenomena in space and tokamakplasmas.

Molecular dynamics evaluation of selfdiffusion in Yukawa systems
View Description Hide DescriptionSelfdiffusion coefficients of Yukawa systems in the fluid phase are obtained from molecular dynamics simulations in a wide range of the thermodynamical parameters. The Yukawa system is a collection of particles interacting through Yukawa (i.e., screened Coulomb) potentials, which may serve as a model for charged dust particles in a plasma or colloidal particles in electrolytes. The selfdiffusion coefficients are found to follow a simple scaling law with respect to the system temperature, which is consistent with the universal scaling (i.e., temperature scaling independent of the ratio of interparticle distance to screening length) observed by Robbins et al. [J. Chem. Phys. 88, 3286 (1988)] if the fluid system is near solidification. Also discussed is the velocity autocorrelation function, which is in part used to determine the selfdiffusion coefficients through the Green–Kubo formula.