Volume 5, Issue 12, December 1998
 LETTERS


Mode structure of turbulent electron temperature fluctuations in the Texas Experimental Tokamak Upgrade
View Description Hide DescriptionHigh spatial resolution electron cyclotron emission imaging (ECEI) has been employed on TEXTU [Texas Experimental Tokamak Upgrade, G. Cima et al., Phys. Plasmas2, 720 (1995)] to measureturbulent electron temperaturefluctuations using an intensity interferometric technique. With the first dispersion relation measurements in the plasma confinement region, a broadband spectral feature is identified at poloidal wave numbers consistent with expectations for electron drift waves.

Solitary radial electric field structure in tokamak plasmas
View Description Hide DescriptionThe solitary structure solution of the radial electric field in the tokamak plasmas is obtained. It is shown to be stable under an external power supply, like a biased electrode at the edge. The radial gradient is governed by the ion viscosity and the nonlinearlity of the perpendicular conductivity. The radial structure of and reduction of turbulenttransport, which belong to key issues of the high confinement mode(HMode) [F. Wagner et al., Phys. Rev. Lett. 49, 1408 (1982)], are selfconsistently determined. A bifurcation from a radiallyuniform one to a solitary one occurs at a certain applied voltage, and a hysteresis is associated.
 Top

 ARTICLES


Landau damping and transittime damping of localized plasma waves in general geometries
View Description Hide DescriptionLandau’s original derivation of the collisionless damping of smallamplitude Langmuir waves in an infinite homogeneous plasma relied on the introduction of complex velocities and was therefore somewhat difficult to interpret physically. This has inspired many subsequent derivations of Landau damping that involve only real physical quantities throughout. These “physical” derivations, however, have required the calculation of quantities to second order in the wave field, whereas Landau’s approach involved only firstorder quantities. More recent generalizations of Landau damping to localized fields, often called “transittime damping,” have followed the physical approach, and thus also required secondorder calculations, which can be quite lengthy. In this paper it is shown that when the equilibrium distribution function depends solely on the energy, invoking the timereversal invariance of the Vlasov equation allows transittime damping to be analyzed using only firstorder physical quantities. This greatly simplifies the calculation of the damping of localized plasma waves and, in the limit of an infinite plasma, provides a derivation of Landau damping that is both physical and linear in the wave field. This paper investigates the transittime damping of plasma waves confined in slabs, cylinders, and spheres, analyzing the dependence on size, radius, and mode number, and demonstrating the approach to Landau damping as the systems become large. It is also shown that the same approach can be extended to more general geometries. A companion paper analyzes transittime damping in a cylinder in more detail, with applications to the problem of stimulated Raman scattering in selffocused light filaments in laserproduced plasmas.

Collisionless damping of localized plasma waves in laserproduced plasmas and application to stimulated Raman scattering in filaments
View Description Hide DescriptionObservations of stimulated Raman scattering(SRS) in laserproduced plasmas often yield results at odds with theoretical predictions. For example, SRS is commonly seen at incident laser intensities below the theoretical threshold, and the spectrum of SRS light often extends to much shorter wavelengths than models predict. To account for these anomalies it is often proposed that SRS is occurring in highintensity, selffocused light filaments. A serious problem with this model is that plasma wavedamping rates estimated on the basis of the usual Landau theory for homogeneous plasmas would seem to rule out this explanation for many cases of interest. Damping rates for plasma waves confined to smallradius filaments, however, could be significantly different than damping rates for plane waves. Using a novel method for calculating transittime damping, this paper analyzes the collisionless damping of plasmawaveguide modes in a cylinder. It is found that the actual damping rates for waveguide modes in a suitable filament model are much less than for the plane waves in a homogeneous plasma producing the same wavelength of SRS emission. Consequently, the filament model remains viable as an explanation of the anomalous SRS observations.

Wave excitation in a modified double plasma device
View Description Hide DescriptionA modified double plasma (MDP) device is newly developed and shown to be useful for basic plasma wave experiments. Further, the mechanism of wave excitation in the MDP device is experimentally clarified. From the results the peculiarity of the device is found, that ionacoustic waves can be excited in plasmas essentially freely from the effects of stationary beam ions and other modes, such as ionbeam modes as far as linear waves are concerned. For nonlinear waves, however, ionacoustic solitons or shocks with reflected ions ahead and slower wavelike signals behind are possibly excited just as in a conventional DP device.

Ion–neutral collision effects on Alfvén surface waves
View Description Hide DescriptionIt is well established that in magnetized partially ionized plasmas, the dispersion of the shear Alfvén waves is strongly influenced by the ion–neutral collisions. In the case of inhomogeneous plasmas, the study of these collisions on Alfvén surface waves can become important, especially in understanding resonant absorption of Alfvén waves. In this paper, the dispersion equation for the surface waves in partially ionized plasma along a plasma–plasma interface is derived and it is shown that ion–neutral collisions can cause a drastic change in the Alfvén surface waves’ propagation characteristics. For the case when ion–neutral coupling is weak, the wave propagates along the interface with the natural frequency of Alfvén surface waves in the charged medium without friction. When coupling is strong, this frequency is determined by the mass densities of both ions and neutrals in both media. When the ionization fraction is low, these two frequencies can differ by several orders of magnitude. There also exists a range of frequencies, depending on the collisions, in which the surface waves do not propagate. The damping of surface waves due to ion–neutral collisions can be very small in the case of strong coupling. For weak coupling, this damping can become large due to large collision frequencies. The effect of this on the resonant absorption of surface waves is discussed briefly. The possibility of propagation of surface waves along thin plasma–plasma interfaces is also considered in the context of some astrophysical systems.

Modes localized to open magnetic field lines
View Description Hide DescriptionA constructive mathematical proof is given for the existence of modes localized to a single magnetic field line, which give rise to ballooning modes and to the Alfvén continuous spectrum. The unity of these two classes of modes is emphasized.

Ion oscillation modes in inhomogeneous plasmas
View Description Hide DescriptionUsing the reductive perturbation method, the carrier wave modulation of ion acoustics waves in inhomogeneous plasma is investigated. It is shown that such a process can be described by a Nonlinear Schrödingertype equation (NLStype) equation.

Surface waves in a magnetized plasma
View Description Hide DescriptionElectrostaticsurface waves propagating along the interface between a warm magnetized plasma and vacuum are investigated by deriving the relevant dispersion relations using a fluid model. The general dispersion relation for arbitrary orientation of the magnetic field and the propagation vector is derived in a closed form and certain special cases (when the magnetic field is directed parallel and perpendicular to the boundary surfaces) are analyzed numerically.

Generalized reduced magnetohydrodynamic equations
View Description Hide DescriptionA new derivation of reduced magnetohydrodynamic(MHD)equations is presented. A multipletimescale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves,equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shearAlfven wave time scale), which is the time scale of interest for MHDinstability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergencefree magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson [Phys. Fluids 18, 875 (1975)].

Computational investigation of single mode vs multimode Rayleigh–Taylor seeding in Zpinch implosions
View Description Hide DescriptionA series of twodimensional magnetohydrodynamic calculations have been carried out to investigate single and multimode growth and mode coupling for magneticallydriven Rayleigh–Taylor instabilities in Z pinches. Wavelengths ranging from 5.0 mm down to 1.25 mm were considered. Such wavelengths are comparable to those observed at stagnation using a random density “seeding” method. The calculations show that wavelengths resolved by less than 10 cells exhibit an artificial decrease in initial Fourier spectrum amplitudes and a reduction in the corresponding amplitude growth. Single mode evolution exhibits linear exponential growth and the development of higher harmonics as the mode transitions into the nonlinear phase. The mode growth continues to exponentiate but at a slower rate than determined by linear hydrodynamic theory. In the two and three mode case, there is clear evidence of mode coupling and inverse cascade. In addition, distinct modal patterns are observed late in the implosion, resulting from finite shell thickness and magnetic fieldeffects.

The threedimensional stability of steady magnetohydrodynamic flows of an ideal fluid
View Description Hide DescriptionThe stability of steady magnetohydrodynamic flows of an ideal incompressible fluid to small threedimensional perturbations is studied. Two new conditions sufficient for linear stability of steady magnetohydrodynamic flows are obtained by the energy method.

Wake potentials in nonuniform dusty magnetoplasmas
View Description Hide DescriptionIt is shown that the presence of equilibrium density gradients in a magnetized dusty plasma can introduce new types of driftlike waves. These give rise to oscillatory wakepotentials, which can focus ions and attract dust grains of similar polarity. Using a test particle approach, typical profiles for wakepotentials are obtained in several interesting cases. It is found that the effective attraction length is independent of the magnetic field strength for high density dusty plasmas, whereas it is larger for larger magnetic fields in a lowdensity dusty plasma. Furthermore, the dust attraction takes place predominantly in the inhomogeneous region of the dusty plasma having smaller lattice periodicity for smaller scale length of the density inhomogeneity.

Parametric instability on an annular beam induced by a periodic beamchannel boundary
View Description Hide DescriptionIn the framework of the general Nishikawa formalism for parametric instabilities the coupling is examined of the plasma oscillations to the density modulations of an annular electron beam, modulated by an axially periodic beamchannel boundary commonly used in microwave sources. It is found that the instability is present when the distance between the beam and the channel boundary is larger than the periodic length of the boundary. It is also found that the growth rate of the instability is independent of the beam current and depends only on the beam velocity and the periodic length of the beamchannel boundary.

Intermittent particle transport in twodimensional edge turbulence
View Description Hide DescriptionInterchange turbulence in two dimensions is investigated in the scrapeoff layer (SOL) of fusion devices, when driven by a constant core particle influx. Contrary to the standard gradientdriven approach, density is allowed to fluctuate around its average profile. Transverse transport exhibits some of the features of selforganized critical systems, namely inward and outward avalanches, together with a frequency spectrum decrease in and at intermediate and high frequencies, respectively. An avalanche occurs when the local radial density gradient exceeds the critical one. A selfsustained particle flux then follows the large radial structures of the electric potential. As observed experimentally, the radial profile of density relative fluctuations decreases from the wall into the core plasma, while that of electric potential relative fluctuations peaks inside the SOL. Equilibrium density exhibits the experimental exponential decrease. An analytical expression of the SOL width is obtained, which maximizes the linear growth rate, when the poloidal modulation of electric potential equilibrium is taken into account. The parametric dependencies of are compared to experimental data.

Solitary Alfvén wave in an electron positron ion plasma
View Description Hide DescriptionSolitary Alfvén waves in electron positron ion plasmas are investigated. The Alfvén wave is shown to have an exact solitary wavesolution for a small but finite value of β. It is shown that the existence regions are different if the value of β is changed; however, the change in simply changes the soliton width.

Scaling of spectral anisotropy with magnetic field strength in decaying magnetohydrodynamic turbulence
View Description Hide DescriptionSpace plasmameasurements,laboratory experiments, and simulations have shown that magnetohydrodynamic(MHD)turbulence exhibits a dynamical tendency towards spectral anisotropy given a sufficiently strong background magnetic field. Here the undriven decaying initialvalue problem for homogeneous MHDturbulence is examined with the purpose of characterizing the variation of spectral anisotropy of the turbulent fluctuations with magnetic field strength. Numerical results for both incompressible and compressible MHD are presented. A simple model for the scaling of this spectral anisotropy as a function of the fluctuating magnetic field over total magnetic field is offered. The arguments are based on ideas from reduced MHD (RMHD) dynamics and resonant driving of certain nonRMHD modes. The results suggest physical bases for explaining variations of the anisotropy with compressibility, Reynolds numbers, and spectral width of the (isotropic) initial conditions.

Nonlinear interaction of whistler waves with a modulated thin electron beam
View Description Hide DescriptionThe nonlinear theory of a thin modulated electron beaminteraction with a monochromatic whistler wave is considered. The selfconsistent set of differential equations describing the wave amplitude evolution and the beam particle motion has been solved by a computer code. Results issued from the numerical solution of the differential system are discussed, namely the physical features of the nonlinear beam–wave interaction (trapping, slowing down of the beam, wave damping, multiple bunching, beam focusing), as well as the influence of the physical parameters on the wave emission: beam energy and density, initial beam velocity distribution, and beam current modulation. It has been shown that the trapped particles are the source of the emission; they are decelerated in phase with the wave and remain in Cherenkov resonance with it owing to a nonlinear shift of the parallel wave number. No quasiperiodic exchange of energy between the wave and the particles has been observed. Time evolution of the wave amplitude and the particle energy has been explained by a simple model, as well as the multibunched structures appearing in the particle dynamics for certain physical parameters.

Wave propagation and absorption simulations for helicon sources
View Description Hide DescriptionA twodimensional (2D), finitedifferencecomputer code is developed to examine helicon antenna coupling, wave propagation, collisionless Landau, and collisional heating mechanisms. The code calculates the electromagnetic wave fields and power absorption in an inhomogeneous, cold, collisional plasma. The current distribution of the launching antenna, which provides the full antenna spectra, is included in the model. An iterative solution that incorporates warm plasma thermal effects has been added to the code to examine the contribution of collisionless (Landau) wave absorption by electrons. Detailed studies of the wave fields and electron heating profiles at low magnetic fields where both Trivelpiece–Gould (TG) and helicon (H) modes are present, are discussed. The effects of the applied uniform magnetic field 2D density profiles neutral gas pressures of 1–10 mTorr and the antennaspectrum on collisional and collisionless wave field solutions and power absorption are investigated. Cases in which the primarily electrostatic (TG) surface wave dominates the heating and the power is absorbed near the edge region and cases in which the propagating helicon wave transports and deposits its energy in the core plasma region are examined.

Observation of collisionless thermalization of a plasmoid with a fieldreversed configuration in a magnetic mirror
View Description Hide DescriptionA systematic translation study of fieldreversed configurations (FRCs) has been conducted on the FRC Injection Experiment (FIX) machine [Okada et al., in Fusion Energy 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 2, p. 229]. Plasma density and temperature of a translated FRC moving at supersonic speed are measured in the downstream magnetic mirror of FIX to verify a shock jump there when the FRC is reflected. A significant jump is observed. Moreover, the time evolution of the Carbon V Doppler profile is measured both quasiparallel and perpendicular to the direction of FRC motion. Distinct transitions from Gaussian to nonGaussian shapes are clearly seen in both profiles before and after the shock jump. Also, the ion meanfree path in the downstream magnetic mirror is calculated to be much longer than the characteristic width of the shock jump. These results indicate that the thermalization of flow energy in the translated FRC in the mirror is produced by a collisionless process, implying that this heating mechanism can be realized even in a reactor regime.
