Volume 11, Issue 6, June 2004
 LETTERS


Hamiltonian description of convectivecell generation
View Description Hide DescriptionThe nonlinear statistical growth rate for convective cells driven by driftwave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic iontemperaturegradientdriven modes at small ion temperature, and (ii) weakly electromagnetic collisional DWs are noted.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Wiebel instability of microwave gas discharge in strong linear and circular pulsed fields
View Description Hide DescriptionBeing much weaker than the atomic fields, the gas breakdown produced by highpower pulsed microwave fields is investigated in the nonrelativistic case. The distribution function of the electrons produced by the interaction with intense linearly and circularly polarized microwave fields is obtained and it is shown that it is in a nonequilibrium state and anisotropic. The discharge mechanism for the gas atoms is governed by electronimpactavalancheionization. By analyzing the instability of the system and by finding its growth rate, it is shown that the instability which is governed by the anisotropic property of the distribution function is Wiebel instability.
 Inertially Confined Plasmas, Dense Plasmas, Equations of State

Modeling of stimulated Brillouin scattering near the criticaldensity surface in the plasmas of directdrive inertial confinement fusion targets
View Description Hide DescriptionThe nonlinear propagation of laser beams, smoothed by spatial and temporal bandwidth, near the critical density surface of directdrive inertial confinement fusion targets has been modeled. The interplay between filamentation and forward and backward stimulated Brillouin scattering(SBS) is described in the presence of light reflected from the critical density surface and high absorption of light near the critical density. The spectrum of backscattered light develops a red shift due to SBS, which can be seeded by the reflection of light from the critical surface. The intensity of backscattered light decreases moderately as the bandwidth of smoothing by spectral dispersion is increased.
 Nonlinear Phenomena, Turbulence, Transport

Expansion of dust grains in electron depleted twotemperature–ion plasma
View Description Hide DescriptionThe nonlinear space–time evolution of an expanding electron depleted dusty plasma into a vacuum region is numerically investigated without imposing the quasineutrality approximation. Based on hydrodynamicequations a Lagrangian algorithm is developed. A small group of dust particles is accelerated ahead of the dominant plasma expansion by a local electric field set up by massless ions rushing into the vacuum region. Dust wave breaking and associated dust bunching is found to take place limiting therefore the time scale of the simulation.
 Magnetically Confined Plasmas, Heating, Confinement

Integrated pedestal and core modeling of Joint European Torus (JET) triangularity scan discharges
View Description Hide DescriptionSimulations of four Joint European Torus (JET) [Rebut et al., Nucl. Fusion25, 1011 (1985)] type I ELMy high confinement mode discharges in a triangularity scan are carried out using the JETTO integrated modeling code [Erba et al., Plasma Phys. Contolled Fusion39, 261 (1997)] with a predictive core transport model and a pedestal model that includes the effects of edge localized modes(ELMs). The pedestal pressure gradient is limited by the magnetohydrodynamic(MHD)ballooning modeinstability, which triggers ELM crashes in these simulations. The validation of the pressure gradient limit used in the simulations is confirmed by a stability analysis carried out using the HELENA and MISHKA codes [Mikhailovskii et al., Plasma Phys. Rep 23, 713 (1997)]. The MHD stability analysis includes infinite ideal ballooning, finite ballooning, and low kink/peeling modes. It is shown that higher triangularity plasmas have easier access to the second stability region, which allows the edge pressure gradients in the higher triangularity discharges to increase to higher levels.
 Nonlinear Phenomena, Turbulence, Transport

Exact solutions for axisymmetric ideal magnetized plasma steady state with incompressible poloidal flow
View Description Hide DescriptionThe steady state equations of an axisymmetric ideal magnetized plasma with incompressible poloidal flow and toroidalmagnetic field are investigated. The state is governed by a second order elliptic partial differential equation of the stream function. New exact analytic solutions to this equation associated with cuspmirrorlike, divertortokamaklike, and looplike configurations are obtained. The latter solutions have not appeared in literature as far as we know.
 Lasers, Particle Beams, Accelerators, Radiation Generation

Growth of a ring ripple on a Gaussian beam in a plasma
View Description Hide DescriptionThe growth of a ring ripple, riding on an intense Gaussian laser beam, through plasma has been studied. The amplitude ratio p of the ripple and the beam and the dimensionless width of the ripple are chosen as significant coordinates. It is observed that the positive quadrant of the p, space can be divided in three distinct regions corresponding to steady divergence, oscillatory divergence and oscillatory convergence of the ripple. The variation of ripple width with distance of propagation has been obtained for typical points in the three regions. Collisions, ponderomotive force, and relativistic dependence of mass on quiver velocity have been considered as the mechanisms, which introduce nonlinearity.
 Basic Plasma Phenomena, Waves, Instabilities

Collective behavior of ion Bernstein waves in a multiionspecies plasma
View Description Hide DescriptionCollective behavior of ion Bernstein waves propagating perpendicular to an external magnetic field is studied with attention to the effect of multipleion species. In a thermalequilibrium, multiionspecies plasma, a great number of Bernstein waves are excited near the harmonics of many different ion cyclotron frequencies. The autocorrelation function of the quasimode consisting of these waves is initially damped and is not recovered to its initial value. This is predicted by the theory and is confirmed by numerical calculations and by particle simulations. It is also demonstrated by particle simulations that a perpendicular macroscopic disturbance is damped in a multiionspecies plasma. The electricfield energy associated with this disturbance is significantly reduced and is transferred to the ions, indicating that the presence of multipleion species affects the energy transport.
 Lowtemperature Plasmas, Plasma Applications, Plasma Sources, Sheaths

Critical assessment of a twodimensional hybrid Hall thruster model: Comparisons with experiments
View Description Hide DescriptionA discussion is presented on the results and predictive capabilities of a twodimensional (2D) hybrid Hall effect thruster (HET) model. It is well known that classical (collisioninduced) crossfield electron transport and energy losses are not sufficient to explain the observed HET characteristics. The 2D, quasineutral, hybrid discharge model uses empirical parameters to describe additional, anomalous electron transport and energy loss phenomena. It is shown that, for properly adjusted empirical parameters, the model can qualitatively reproduce the observed thruster behavior over a large range of operating conditions. The ionization and transittime oscillations predicted by the model are described, and their consequences on the timeaveraged thruster properties are discussed. Finally, the influence of the empirical parameters on the model results is shown, especially on quantities that can be measured experimentally.
 Lasers, Particle Beams, Accelerators, Radiation Generation

Near steadystate orbits and injection in free electron lasers with ionchannel guiding
View Description Hide DescriptionA numerical and an analytical investigation of near steadystate orbits in free electron lasers(FELs) with ionchannel guiding are carried out and two kinds of orbits are found. Injection of electrons is studied numerically using an adiabatically tapered wiggler field and ionchannel density. A considerable reduction in the amplitude of oscillations about steadystate orbits was found. Near steadystate orbits, to second order in wigglerinduced velocity, are found in FELs with axial magnetic field guiding.
 Magnetically Confined Plasmas, Heating, Confinement

Effects of flow shear on temperature gradient driven short wavelength modes
View Description Hide DescriptionThe effects of flow shear on the temperature gradient driven short wavelength ion (SWITG) modes and electron temperature gradient (ETG) modes are investigated in a sheared slab. The SWITG mode can be stabilized at arbitrary β when the E×B velocity shear, reaches above a critical value. Since the SWITG mode has a lower frequency, a lower is needed to stabilize the SWITG mode than to stabilize the conventional ITGmode. However, the critical values of for stabilization of both SWITG and conventional ITGmodes are much less than where and are ion thermal speed and the scale length of density gradient. Contrastively, the ETG mode cannot be stabilized until the is larger than Similarly, a parallel velocity shear with order has significant effects on the SWITG mode but is too small to influence the ETG mode. The different behaviors of flow shear effects on the SWITG and ETG modes may indicate that the ETG mode is more reasonable than the SWITG as the candidate responsible for anomalous electron thermal transport.

Single particle motion near an X point and separatrix
View Description Hide DescriptionThe motion of a single particle near an X point or separatrix in given static axisymmetric electric and magnetic fields is studied. It is shown that large classes of particles are lost on a time scale given by the distance scale on which the fields vary divided by the thermal speed. In a low beta version of the problem the results are more specific and the classes of particles are described which are either lost or confined. A preliminary, simpler problem is also treated with model fields in rectangular geometry. Although the losses are similar, the orbits near the X point exhibit a more complicated structure in phase space.

Study of electromagnetic microinstabilities in helical systems with the stellarator expansion method
View Description Hide DescriptionElectromagnetic microinstabilities in helical systems are studied by numerically solving integral eigenmodeequations, which are derived from the ion gyrokineticequation, the quasineutrality equation, the Ampère’s law, and the massless electron approximation. The stellarator expansion technique is used to evaluate finitebeta effects on the guidingcenter drift in the helical configuration, where the toroidal plasma shift and the magnetic shear strongly influence the magnetic curvature and accordingly the stability of both magnetohydrodynamics(MHD) and kinetic modes. The kinetic integral equations are shown to reduce to the ideal MHDballooning modeequation in the fluid limit, from which the Mercier criterion is obtained. For helical geometry like the Large Helical Device(LHD) [Motojima, et al., Nucl. Fusion 43, 1674 (2003)], it is confirmed that, when increasing the beta value, the ion temperature gradient mode is stabilized while the kinetic ballooning mode (KBM) is destabilized due to the unfavorable geodesic curvature resulting from the negative magnetic shear combined with the toroidal plasma shift. Also, dependencies of these kineticmode properties on the poloidal wave number and the magnetic shear are investigated. It is found that the KBMunstable parameter region is narrower than the Mercierunstable region in the LHDlike configuration.
 Nonlinear Phenomena, Turbulence, Transport

Large amplitude solitary electromagnetic waves in electronpositron plasmas
View Description Hide DescriptionWaves in electronpositron plasmas have fundamentally different dispersion characteristics due to the equal chargetomass ratios between negative and positive charges, which mix different timescales, and are of interest in understanding aspects of pulsars and active galactic nuclei, where astrophysical electronpositron plasmas occur. Earlier systematic nonlinear treatments of parallel propagating electromagnetic waves via a reductive perturbation analysis had indicated unusual results, namely a vector equivalent of the modified Korteweg–de Vries equation. The latter is nonintegrable except in the case of linear polarization when it becomes equivalent to the scalar (integrable) modified Korteweg–de Vries equation. Here large amplitude purely stationary nonlinear solitary waves are studied in their own reference frame via the McKenzie approach. The behavior of the wave magnetic field can be expressed through an energy integral that involves the Mach number of the structure. Possible solitons are superAlfvénic and occur symmetrically for positive or negative fields, owing to the obvious symmetry between positive and negative charges with the same mass. The limits on the allowable Mach numbers and soliton amplitudes have also been computed.
 Inertially Confined Plasmas, Dense Plasmas, Equations of State

Laser light and hot electron micro focusing using a conical target
View Description Hide DescriptionThe laser light propagation inside the conical target had been studied by threedimensional particleincell simulations. It is found that the laser light is optically guided inside the conical target and focused at the tip of the cone. The intensity increases up to several tens of times in a several micron focal spot. It is the convergence of hot electrons to the head of the cone that is observed as a consequence of the surface electron flow guided by selfgenerated quasistatic magnetic fields and electrostatic sheath fields. As a result, the hot electron density at the tip is locally ten times greater than the case of using a normal flat foil.
 Lowtemperature Plasmas, Plasma Applications, Plasma Sources, Sheaths

Investigation of electrical breakdown characteristics in the electrodes of cylindrical geometry
View Description Hide DescriptionAnalytical solutions of Laplace’s equation in the space between electrodes of cylindrical geometry are derived by conformal mapping. Electrical breakdownproperties of the two cylindrical electrodes are investigated by making use of the Townsend criterion and the electric potential obtained analytically. The characteristics of electrical breakdown are investigated in terms of the geometrical configurations, the cylinder radii, and the distance between the two axes of cylinders. The present theoretical expression of the breakdown analysis is applied to the special cases to discuss the wellknown electrode configurations such as the two parallel plane electrodes with infinite curvature radii, the wireplane electrodes, and the coaxial cylindrical electrodes. It is shown that the electrical field distribution determined by electrodes arrangement plays a pivotal role in the electrical breakdown phenomena.
 Magnetically Confined Plasmas, Heating, Confinement

A neoclassical model for toroidal rotation and the radial electric field in the edge pedestal
View Description Hide DescriptionA model for the calculation of toroidal rotation velocities and the radial electric field in the edge pedestal of tokamaks is described. The model is based on particle and momentum balance and the use of the neoclassical gyroviscous expression for the toroidal viscous force. Predicted toroidal rotation velocities in the edge pedestal are found to agree with measured values to within about a factor of 2 or less, for a range of DIIID [Luxon, Nucl. Fusion 42, 614 (2002)] edge pedestal conditions.

Comparison of toroidal rotation velocities of different impurity ions in the DIIID tokamak
View Description Hide DescriptionMeasurements of the relative toroidal rotation velocities of low Z impurity ions have been made in DIIID tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] plasmas that have a strong core pressure gradient and reduced anomalous transport. They show that the differences in toroidal rotation velocities agree with predictions of neoclassical transport theory. The toroidal rotation velocities are measured via charge exchange recombination (CER) spectroscopy of the impurity species. Taking into account the nonnegligible effect of energy dependent charge exchange cross sections, quantitative agreement is found between the measured and predicted difference in toroidal rotation velocities, including the strong Z dependence. The predicted difference between the measured impurity rotation velocity and the main ion rotation velocity can be substantial and therefore care should be taken in using quantitative results from impurity rotation measurements and applying them to the bulk plasma.

A full radius gyrokinetic stability analysis for large aspect ratio finiteβ tokamaks
View Description Hide DescriptionLinear, fully gyrokinetic, full radius (global), large aspect ratio studies of Alfvénion temperature gradient mode (AITG) or kinetic ballooning modes or betainduced Alfvén eigenmodes considering only “passing” species is presented. Effects hitherto completely neglected in a full radius approach such as fluctuations and the ones which have been treated partly [Phys. Plasmas 10, 1424 (2003)] such as Shafranov shifts are included. To this end, an existing code EMGLOGYSTO has been upgraded to incorporate these effects. Among others, the most interesting results include: (i) For relatively large positive magnetic shear where is safety factor and ρ minor radius], fluctuations have a benign effect on AITG growth rates and for positive but small shear fluctuations are too weak to play any crucial role. (ii) In the later case, inclusion of Shafranov shift leads to the following: (a) Growth rates without Shafranov shift effects are in general larger than those including Shafranov shift; (b) nonmonotonous dependence of growth rates and frequencies on (c) the presence of multiple eigenmodes with competing growth rates for same values of β; (d) no sign of complete stabilization with increasing β. Finally eigenmode structures with and without Shafranov shift are reported. The growth rates and frequencies thus obtained may serve as estimates of transport coefficients and for future bench marking of the (then) global electromagnetic, gyrokinetic, time evolution codes (particleincell or otherwise).

Losses of neutral beam injected fast ions due to adiabaticity breaking processes in a fieldreversed configuration
View Description Hide DescriptionLosses of neutral beam (NB) injected fast ions from the confinement region of a fieldreversed configuration (FRC) with a strong magnetic mirror are numerically analyzed for parameters relevant to NB injection experiments on the FIX (FRC injection experiment) device [T. Asai et al., Phys. Plasmas 7, 2294 (2000)]. Ionization processes of beam particles are calculated by the Monte Carlo method. The confinement of beam ions is discussed with the concept of accessible regions that restrict the ion excursion and are determined from two constants of motion, the kinetic energy and canonical angular momentum, in the case of an axisymmetric and a steady state FRC without an electrostatic field. From the calculation of the accessible regions, it is found that all the fast ions suffer from the orbit loss on the wall surface and/or the end loss. Single particle orbits are also calculated to find a difference of confinement properties from the results by employing the accessible regions. The magnetic moment is observed to show nonadiabatic motions of the beam ions, which cause a gradual orbit loss on the wall even in a case that a strong magnetic mirror is applied. The results show that the correlation of the magnetic moment disappears as the fast ions experience the density gradient around the separatrix surface and the fieldnull points.