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Volume 3, Issue 5, May 1996

A novel phase focusing mechanism in multipactor discharge
View Description Hide DescriptionIn spite of the mutual repulsion among the space charges, a new phase‐focusing mechanism is discovered whereby the leading edge of the multipactor discharge in an rf circuit grows at the expense of the trailing edge. This effect arises from the different impact energies, and hence different secondary electron yields, experienced by different portions of the discharge. This phase focusing mechanism may shape the steady‐state multipactor discharge in the form of a very tight bunch of electrons.

Electronmagnetohydrodynamic response of a plasma to an external current pulse
View Description Hide DescriptionIn this paper we examine the dynamic response of a magnetoplasma to an external time‐dependent current source in the context of electronmagnetohydrodynamics (EMHD). A combined analytic and numerical technique is developed to address this problem. The set of cold electron plasma and Maxwell’sequations are first solved analytically in the (k,ω) space. Inverse Laplace and three‐dimensional complex Fast Fourier Transform techniques are used subsequently to numerically transform the radiation fields and plasma currents from the (k,ω) space to the (r,t) space. The results show that the electron plasma responds to a time‐varying current source imposed across the magnetic field by exciting whistler/helicon waves and forming an expanding local current loop, driven by field‐aligned plasma currents. The current loop consists of two antiparallel field‐aligned current channels concentrated at the ends of the imposed current and a cross‐field Hall current region connecting these channels. The characteristics of the current closure region are determined by the background plasma density, the magnetic field, and the time scale of the current source. The results are applied to the ionospheric generation of extremely low‐frequency (ELF) and very low‐frequency (VLF) radiation using amplitude modulated high‐frequency heating. It is found that contrary to previous suggestions the dominant radiating moment of the ELF/VLF ionosphericsource is an equivalent horizontal magnetic dipole.

Generation of poloidal magnetic field in a hot collisional plasma by inverse Faraday effect
View Description Hide DescriptionGeneration of poloidal magnetic field in a hot and collisional plasma by an inverse Faraday effect is discussed. This field can either be induced by a circularly polarized laser beam (CPLB) or a plane‐polarized laser beam (PPLB). For the CPLB, an average field 〈ℜ_{ x }〉∼I _{0}λ∼11.6 MG could be produced in a DT plasma for a high intensity (I _{0}=10^{22} W/m^{2}) and shorter wavelength (λ=0.35 μm) laser. This field is essentially induced by the field inhomogeneity effect and dominates over that induced by the plasma inhomogeneity effect (〈ℜ_{ x }〉∼I ^{2/3} _{0}λ^{7/3}∼2.42 MG). The collisional and thermal contribution to 〈ℜ_{ x }〉 is just negligible for the CPLB. However, in the case of PPLB the poloidal field is generated only for a hot and collisional plasma and can be quite large for a longer wavelength laser (e.g., CO_{2} laser, λ=10.6 μm). The collisional effect induces a field 〈ℜ_{ x }〉∼0.08 kG, which dominates near the turning point and is independent of the laser parameters. However, in the outer cronal region the thermal pressure effect dominates (e.g., 〈ℜ_{ x }〉∼I ^{5/3} _{0}λ^{4/3}∼3.0 MG). Further, 〈ℜ_{ x }〉 for the p‐polarized beam is, in general, relatively smaller than that for the s‐polarized beam. Practical implications of these results and their limitations are discussed.

Simulations of electrostatic modes of non‐neutral plasmas with small aspect ratio in a Penning trap
View Description Hide DescriptionThe dependence on induced charge, experimental geometry, and temperature of electrostatic modes in very low aspect ratio non‐neutral plasmas in a Penning trap is considered. The modes are of interest as non‐destructive diagnostics of the shape of the plasmas. These investigations include equilibrium calculations of plasma shapes and profiles at finite temperature and particle‐in‐cell simulations of axisymmetric modes. The results of the simulations are compared to the zero‐temperature theory by Dubin [Phys. Rev. Lett. 66, 2076 (1991)] taken to first‐order in the aspect ratio and to experimental measurements by Weimer et al. [Phys. Rev. A 49, 3842 (1994)]. In general, it is concluded that the Dubin theory provides a means to obtain reasonable estimates of plasma parameters, including density, radius, and axial length, for plasmas in the very important regime for which the axial length is comparable to the Debye length. In addition, dependence on induced charge, equilibrium shape, and plasma temperature are identified which can likely be used to improve agreement between theory and experiment.

Attenuation of energetic helium beams in fusion plasmas
View Description Hide DescriptionThe efficiency of plasma heating and diagnostics based on using atomic beams or neutralized ion fluxes depends crucially on the atomic processes involved in the stopping of the atoms. These processes have been studied in detail for helium atoms in the energy range from 25 keV/u to 2.5 MeV/u. The processes considered include both the ground state and the excited states of the atoms, thus allowing for the multistep electron loss in collisions with the plasma constituents. Special attention is paid to electron loss from the atoms in metastable states. The effective beam stopping cross section and attenuation factor have been calculated for a wide variety of beam and plasma parameters. The atomic database necessary for these calculations has been documented using the best data available at present. The results are also given in terms of convenient analytic fits. Special calculations have been carried out for the helium probing beam and neutralized alpha particles in International Thermonuclear Experimental Reactor (ITER) [Kikuchi et al., Fusion Eng. Design 16, 253 (1991)] plasmas.

A nonlinear model for the singular surface response
View Description Hide DescriptionThe issues concerning the response of a plasma, at or near a singular surface, to a magnetic perturbation with a phase velocity different from the plasma flow velocity, are important for a number of phenomena. Among these are ideal and nonideal magnetohydrodynamic stability of plasmas with shear flow or a flow relative to a resistive wall, sensitivity of rotating plasma to field errors, and the ‘‘locked mode’’ phenomenon. Models for the singular surface response have been tested against results from ‘‘magnetic braking’’ experiments in DIII‐D [R. J. La Haye et al., Nucl. Fusion 32, 2119 (1992)]. Previous models are found unable to account for all of the experimental observations. A new heuristic nonlinear model presented in the paper may account for the observations. A key element in the model is turbulence developed at the singular surface; the turbulence is assumed driven by the singular layer dissipation and is assumed to impede the singular current through an anomalous resistivity. When the perturbation amplitude is sufficiently large, a positive feedback mechanism exists, since in the regime of interest, dissipation increases with decreasing singular current. For small perturbation amplitudes this mechanism is not operative so that previous models for the response may be valid.

Turbulent transport in low‐β plasmas
View Description Hide DescriptionLow‐frequency electrostaticfluctuations are studied experimentally in a low‐β plasma, with particular attention to their importance for the anomalous plasmatransport across magnetic field lines. The presence of large coherent structures in a turbulent background at the edge of the plasma column is demonstrated by a statistical analysis. The importance of these structures for the turbulenttransport is investigated. The study is extended by a multichannel conditional analysis to illustrate detailed properties and parameter dependences of the turbulenttransport.

Stochastic ion behavior in subharmonic and superharmonic electrostatic waves
View Description Hide DescriptionThe dynamics of a charged particle in a magnetic field perturbed by electrostatic waves propagating transverse to the magnetic field has been investigated. Depending on the number of perturbing waves, the magnitude of the perturbation and the perturbation frequency (ν=r/s=ω/ω_{0}, where r and s are relatively prime integers, and ω_{0} is the cyclotron frequency), the particle motion can exhibit either a small deviation from simple cyclotron motion or stochastic motion over phase space. The latter case is found to correspond to particle heating and anomalous transport. In the case of cyclotron harmonic perturbations (superharmonic case, s=1), the phase space of the particle is covered by a stochastic web, inside of which the particle motion is chaotic. The particle can, in principle, be heated to very high energy. However, if the wave frequency is some fraction of the ion cyclotron frequency (subharmonic case, s≥2), the heating range is limited.

Effect of elastic scattering on stochastic ion heating by electrostatic waves
View Description Hide DescriptionThe dynamics of an ion interacting with an electrostatic wave propagating perpendicularly to a static magnetic field in the presence of elastic ion‐neutral scattering is investigated. Superharmonic (ω/ω_{0}∈I) and subharmonic (ω/ω_{0}=r/s≤1) perturbations are studied. Here, ω and ω_{0} are the wave and the ion cyclotron frequency, respectively, and r and s are relatively prime integers. Without elastic collisions, the ion is found to exhibit either quasi‐regular or stochastic motion in phase space depending on the wave frequency, wave amplitude, and the initial position and velocity of the particle. Quasi‐regular and stochastic behavior are found to be exclusive with respect to each other. In the presence of elastic collisions, the entire phase space becomes accessible to the ion irrespective of the initial conditions. The heating rate is generally found to depend on the ratio γ_{ m }/ω (where γ_{ m } is the momentum loss rate) and is enhanced compared to the collisionless case.

Scaling of magnetic turbulence with Lundquist number in relaxed state devices
View Description Hide DescriptionThe scaling of magnetic turbulence with Lundquist number, B̃(S), as generated by the dynamo in reversed‐field pinches and spheromaks, is addressed. A theoretical framework is described, showing how the fluctuations arise from the dynamo and what dynamics determine the B̃(S) scaling. There are two limits of the dynamo. For a discrete (sawtoothing) dynamo, the time average of the magnetic fluctuations is given by B̃∝S ^{0}, but it is argued that the averaged flux surface destroying magnetic field fluctuations scale as B̃_{br}∝S ^{−1/2}. For a continuous dynamo, with a steady‐state saturated turbulent spectrum, the magnetic field perturbations scale as B̃∝S ^{−1/4}. Previous theories of S scaling are reviewed.

Nonlinear stopping power of ions in plasmas
View Description Hide DescriptionThe study of the nonlinear stopping power of ions in plasmas is of fundamental importance for various applications. One example is the energy loss of heavy ions passing through a plasma. Due to the high non‐equilibrium charge states specific to heavy ions, the plasma regime with coupling parameters 1/N _{ D }<1 and Z _{ p }/N _{ D }≳1 (N _{ D }∼ number of electrons in a Debye sphere, Z _{ p }charge of the ion) is of interest. In this regime, the Vlasov‐Poisson system cannot be linearized, rather a fully nonlinear treatment is required. In the present paper, the Vlasov‐Poisson system is solved numerically by using the capability of the new generation of massively parallel supercomputers. The results are compared with the standard dielectrictheory and a recent binary collision approach. It is demonstrated that nonlinear effects lead to a strongly reduced Bragg‐peak for Z _{ p }/N _{ D }≳1. In the nonlinear regime, the scaling of the stopping power is close to a Z _{ p } ^{3/2} law, which is found to be characteristic for the nonlinear stopping power, if the influence of close collisions on the induced potential is treated properly.

Electrical conductivity for nonideal partially ionized alkali plasmas
View Description Hide DescriptionThe electrical conductivity is calculated for partially ionized Li, Na, K, Rb, and Cs plasmas starting from quantum kinetic equations which account for collision terms of free and bound particles including many body effects. The scattering cross sections entering the conductivity are calculated in T matrix approximation. The description of electron‐atom scattering is based on the close coupling system of equations considered in the adiabatic exchange model. The plasma composition is determined from generalized mass action laws valid for nonideal plasmas.

Contribution of Yushmanov‐trapped electrons to a thermal dike
View Description Hide DescriptionA substantial amount of Yushmanov‐trapped electrons are generated as a result of electron cyclotron resonance heating employed for generating a thermal dike in an open magnetic field configuration. The production rate and the energy spectrum of the trapped electrons are calculated by using a heating response function. The calculated energy spectrum of the end‐loss electrons driven from the Yushmanov‐trapped region indicates a reduction in power efficiency of the thermal dike. The potential profile modified by the Yushmanov‐trapped particles tends to reduce their production rate, leading to a stationary state. Their significance to a thermal dike basic experiment in the end region of the GAMMA 10 tandem mirror [Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 2, p. 651] is discussed.

Plasma diagnostics using synchrotron radiation in tokamaks
View Description Hide DescriptionEmission of synchrotron radiation for electron temperaturediagnostics in dense and hot tokamakplasmas is discussed. This novel diagnostic scheme is motivated by the need to overcome several limitations of the familiar first and second harmonic method, caused by cutoff, refraction, and harmonic overlap. Emission at high harmonics is not restricted by density and temperature upper limits, and the method is then particularly appropriate for reactor relevant regimes. This method yields global information on the electron temperature profile, since the source of high harmonic emission is poorly localized in space. Synchrotron radiation is emitted by electrons over a wide spectrum of energies, ranging from thermal to superthermal values, and is therefore also useful to investigate deviations of the electron velocity distribution from the Maxwellian. In contrast, the source of the optically thick low harmonic radiation is highly localized in the ordinary space near the resonance points, which implies that the energy of the emitting electrons lies in the subthermal range. The basic theory of the method is presented and illustrated by numerical applications, for plasma parameters of relevance for International Thermonuclear Experimental Reactor (ITER) [ITER‐JCT and Home Teams, Plasma Phys. Controlled Fusion37, A19 (1995)].

A comparison of compressible and incompressible magnetohydrodynamics in toroidal plasmas
View Description Hide DescriptionA comparison is made of the properties of compressible and incompressible magnetohydrodynamic (MHD)oscillations in toroidal plasmas. In the main part of the paper we deal with the compressible case, and it is shown that the Alfvén wave equation describing toroidal Alfvén eigenmodes (TAE modes) in a low‐β tokamak [Berk et al., Phys. Fluids B 4, 1806 (1992)], including the toroidal coupling of the shear Alfvén continuum modes with poloidal mode numbers m and m±1, can be obtained by means of an inverse aspect ratio expansion of the usual set of compressible MHDequations. This method provides an alternative, and more straightforward, approach to the analysis of such modes as compared with previous studies based on reduced MHD, or on different formulations of MHD. In the case of incompressible MHD, it is found that the Alfvén continua are strongly modified by the finite value of the toroidal component of the plasma perturbation. In particular, a large frequency gap where global eigenmodes can be found appears already to lowest order in the inverse aspect ratio in the case of incompressible oscillations.

Impact of radial transport on the quasilinear plateau formation due to electron cyclotron wave absorption
View Description Hide DescriptionNumerical simulations using a three‐dimensional Fokker–Planck code show that for small tokamaks the transport of electrons across the magnetic surfaces at a level consistent with anomalous transport has a large influence on the formation of the quasilinear plateau during electron cyclotron resonantheating. The reduction of wave absorption due to the plateau formation is much smaller when the effects of radial transport are included. This is explained by the localized nature of the resonance in velocity space and the strong dependence of resonant energy on radial position. Impact of the effect on diagnostic signals is discussed.

A kinetic model of transient effects in tokamak edge plasmas
View Description Hide DescriptionFluid descriptions are not adequate for edge plasma studies when the high collision frequency assumption fails in the presence of rapid transient processes. The results of analytic and numerical modeling of some of the non‐Maxwellian features of edge plasma transport associated with transient heating and cooling phenomena in the scrape‐off layer are presented. It is found that kinetic effects alter the heat conduction coefficient and lead to interesting critical behavior of the distribution function. The numerics are performed with the recently developed time‐dependent Fokker–Planck code ALLA.

Magnetohydrodynamic stability of an axisymmetric mirror device with ‘‘massive’’ end‐sections
View Description Hide DescriptionMagnetohydrodynamic(MHD) stability of an axisymmetric mirror device with long end‐sections filled with a collisional plasma is studied. It is shown that unstable perturbations in such a system, if they exist, are localized at a distance ∼v _{ A }/Γ near the central cell (v _{ A } is the Alfvén velocity and Γ is the growth rate). Perturbations of the magnetic field do not penetrate into regions where plasma beta is greater than unity. Therefore, regions of weak magnetic field has a stabilizing effect on MHD‐perturbations.

Tomography of full sawtooth crashes on the Tokamak Fusion Test Reactor
View Description Hide DescriptionFull sawtooth crashes in high temperature plasmas have been investigated on the TokamakFusion Test Reactor (TFTR) [Plasma Phys. Controlled Fusion33, 1509 (1991)]. A strong asymmetry in the direction of major radius, a feature of the ballooning mode, and a remaining m=1 region after the crash have been observed with electron cyclotron emission image reconstructions. The TFTR data is not consistent with two‐dimensional (2‐D) models; it rather suggests a three‐dimensional (3‐D) localized reconnection arising on the bad curvature side. This process explains the phenomenon of fast heat transfer which keeps the condition q _{0}<1.

Pressure driven tokamaks
View Description Hide Description‘‘Pressure driven tokamaks’’ are special tokamaks for which the rate of injection of energy and mass (e.g., by neutral beams) is so large that no drive for the toroidal current is needed. Examples of pressure driven tokamak equilibria are found numerically; for these examples, both the poloidal and the toroidalmagnetic fields vanish in a region around the plasma center. Thus, the ratio between the plasma pressure and the magnetic fieldpressure is large, namely of order unity. Therefore, pressure driven tokamaks appear attractive for fusion reactors; it is, however, an open question whether there exist magnetohydrodynamically stable pressure driven equilibria.