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Dec 1994

Volume 1, Issue 12, pp. 3725-4122

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Transition to turbulence in a crossed‐field gap

P. J. Christenson and Y. Y. Lau

Phys. Plasmas 1, 3725 (1994); http://dx.doi.org/10.1063/1.870915 (3 pages) | Cited 26 times

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The transition from laminar to turbulent behavior of the electron sheath in a cross‐field gap is examined for the regime B≳BH, where B is the external magnetic field and BH is the Hull cutoff value. An analytic expression is presented for the critical emitted current beyond which laminar solutions cease to exist. A one‐dimensional particle code is used to corroborate the analytic theory. This code shows several interesting properties when the emitted current exceeds the critical value. Chief among them is the presence of a turbulent microsheath near the cathode surface. The electrostatic potential in the gap’s vacuum region is found to oscillate at a frequency that is quite insensitive to the emitted current and to the electrons’ emission velocity. © 1994 American Institute of Physics.
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52.27.Jt Nonneutral plasmas
84.47.+w Vacuum tubes
52.59.Mv High-voltage diodes

Explosion of soliton in a magnetic field

Katsuhiro Nishinari, Kanji Abe, and Junkichi Satsuma

Phys. Plasmas 1, 3728 (1994); http://dx.doi.org/10.1063/1.870910 (3 pages) | Cited 1 time

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A dynamics of a solitary pulse of the electrostatic ion cyclotron wave that propagates perpendicular to an applied magnetic field is considered. It is shown that the solitary wave will be singular in some range of parameters in the system, such as the plasma density and the magnitude of an applied magnetic field. This fact shows that there is a possibility of controlling the place where explosion of the solitary wave occurs. © 1994 American Institute of Physics.
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52.35.Sb Solitons; BGK modes
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)

A new class of cold fluid non‐neutral plasma equilibrium

K. Avinash

Phys. Plasmas 1, 3731 (1994); http://dx.doi.org/10.1063/1.870911 (3 pages) | Cited 2 times

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Using a variational principle a new class of cold fluid non‐neutral plasma equilibria with uniform density equal to the Brillouin limit density but which are differentially rotating are constructed. These equilibria lie asymptotically close to the usual equilibria with Brilliouin limit density and rigid rotation. The experimental significance of these results is briefly discussed. © 1994 American Institute of Physics.
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52.27.Jt Nonneutral plasmas
52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.

Method for computing the attenuation coefficient of electromagnetic waves in anisotropic plasma columns

I. Ghanashev and I. Zhelyazkov

Phys. Plasmas 1, 3734 (1994); http://dx.doi.org/10.1063/1.870912 (8 pages) | Cited 3 times

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A new and efficient method for calculating the attenuation coefficient of weakly damped electromagnetic waves traveling along wave‐guiding structures partially or entirely filled by a lossy anisotropic dielectric, in particular cold axially magnetized plasma, is proposed. The structure cross‐section geometry can be arbitrary and any nonradiating mode can be considered. In the case of plasma columns, they might be transversely inhomogeneous. Having obtained the attenuation coefficient, it is straightforward to find out the axial structure of plasma columns sustained by the waves themselves. The method is applied to azimuthally symmetric and dipolar waves in cylindrical plasma columns and it is found to reproduce all known theoretical results within its applicability. © 1994 American Institute of Physics.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.80.Pi High-frequency and RF discharges

Convective amplification of drift‐acoustic waves in sheared flows

F. L. Waelbroeck, J. Q. Dong, W. Horton, and P. N. Yushmanov

Phys. Plasmas 1, 3742 (1994); http://dx.doi.org/10.1063/1.870848 (9 pages) | Cited 6 times

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The evolution of wave packets is investigated in a cold‐ion plasma model with sheared magnetic and velocity fields. Wave packets may be amplified by the drift Kelvin–Helmholtz mechanism even when the velocity shear is such that normal modes are stable. It is shown that the logarithm of the convective amplification can be an order of magnitude greater than the logarithm of the steady‐state amplification often taken as the measure of convective instability. For a given wave number, the maximum of either of these amplifications decreases only as the inverse of the perpendicular component of the velocity shear. © 1994 American Institute of Physics.
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52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.30.-q Plasma dynamics and flow

Analytic calculation of certain scattering parameters from a mode conversion analysis of X‐mode–O‐mode coupling

C. S. Ng and D. G. Swanson

Phys. Plasmas 1, 3751 (1994); http://dx.doi.org/10.1063/1.870849 (14 pages) | Cited 2 times

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Certain fast wave scattering parameters from a sixth order mode conversion equation, which represents the coupling of five propagating wave branches in an inhomogeneously magnetized plasma, are shown to be independent of absorption. However, the mode conversion coefficient C23 between the X‐mode and the O‐mode where both propagate in the same direction is not one of these. A recently developed analytical method is applied to calculate C23 and one of the nonzero reflection coefficients. Empirical formulas are found for these two coefficients. The result shows that C23 is not exactly independent of absorption, but for many cases has an unusually weak dependence. This explains a previous numerical result showing that C23 is independent of absorption to numerical accuracy. The coefficient C32 is also calculated by the same method and is shown to be equal to C23 as required by a proven reciprocity relation. The weak dependence of C23 on absorption has to be taken into consideration by any theory that attempts to treat a five branch problem as two separated three branch problems. © 1994 American Institute of Physics.
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52.25.Os Emission, absorption, and scattering of electromagnetic radiation
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
42.25.Bs Wave propagation, transmission and absorption
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma

Structure of Alfvén waves at the skin‐depth scale

G. J. Morales, R. S. Loritsch, and J. E. Maggs

Phys. Plasmas 1, 3765 (1994); http://dx.doi.org/10.1063/1.870850 (10 pages) | Cited 48 times

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This analytical study demonstrates that shear Alfvén waves having transverse scale on the order of the electron skin depth exhibit a collisionless divergence determined by propagation cones that emanate from the edges of the exciting structures. Axial current channels are found to spread radially due to the skin effect up to the cone trajectories and at distances of a few wavelengths from the exciter develop radial diffraction patterns. For values of the collision frequency slightly larger than the wave frequency resistive diffusion allows the axial currents to expand beyond the cone trajectories. © 1994 American Institute of Physics.
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.25.Gj Fluctuation and chaos phenomena
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma

Experimental observation of Alfvén wave cones

Walter Gekelman, David Leneman, James Maggs, and Stephen Vincena

Phys. Plasmas 1, 3775 (1994); http://dx.doi.org/10.1063/1.870851 (9 pages) | Cited 50 times

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The spatial evolution of the radial profile of the magnetic field of a shear Alfvén wave launched by a disk exciter with radius on the order of the electron skin depth has been measured. The waves are launched using wire mesh disk exciters of 4 mm and 8 mm radius into a helium plasma of density about 1.0×1012 cm−3 and magnetic field 1.1 kG. The electron skin depth δ=c/ωpe is about 5 mm. The current channel associated with the shear Alfvén wave is observed to spread with distance away from the exciter. The spreading follows a cone‐like pattern whose angle is given by tan θ=kAδ, where kA is the Alfvén wave number. The dependence of the magnetic profiles on wave frequency and disk size are presented. The effects of dissipation by electron–neutral collisions and Landau damping are observed. The observations are in excellent agreement with theoretical predictions [Morales et al., Phys. Plasmas 1, 3765 (1994)]. © 1994 American Institute of Physics.
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.70.Gw Radio-frequency and microwave measurements

Phase space evolution in linear instabilities

F. G. E. Pantellini, D. Burgess, and S. J. Schwartz

Phys. Plasmas 1, 3784 (1994); http://dx.doi.org/10.1063/1.870852 (8 pages) | Cited 2 times

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A simple and powerful way to investigate the linear evolution of particle distribution functions in kinetic instabilities in a homogeneous collisionless plasma is presented. The method can be applied to any kind of instability, provided the characteristics (growth rate, frequency, wave vector, and polarization) of the mode are known and can also be used to estimate the amplitude of the waves at the end of the linear phase of growth. Two didactic examples are used to illustrate the versatility of the technique: the Alfvén Ion Cyclotron (AIC) instability, which is electromagnetic, and the Electron Ion Cyclotron (EIC) instability, which is electrostatic. © 1994 American Institute of Physics.
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52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.25.Dg Plasma kinetic equations
52.20.Dq Particle orbits

Discrete spectra of compressional Alfvén eigenmodes in inhomogeneous magnetohydrodynamic plasma

I. M. Rutkevich and M. Mond

Phys. Plasmas 1, 3792 (1994); http://dx.doi.org/10.1063/1.870940 (15 pages) | Cited 4 times

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The spectrum of the compressional Alfvén eigenmodes in a magnetohydrodynamic (MHD) current‐carrying inhomogeneous plasma column is obtained analytically. A MHD model that is adequate for calculating the compressional Alfvén spectra in large tokamaks like the Joint European Torus (JET) [Plasma Physics and Controlled Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 27] and Tokamak Fusion Test Reactor (TFTR) [Plasma Physics and Controlled Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 9] is employed. It is shown that the radial nonuniformities of the plasma density give rise to various types of localization of the eigenmodes. Thus, the global, near‐axis, near‐wall, and annulus spectra are identified and studied. The eigenfrequencies and domains of localization of the various eigenmodes, as well as their range of existence in parameter and wavelength space, are determined and investigated. The effects of finite ion gyrofrequency on the MHD eigenmodes are examined, and a perturbation scheme for calculating the modified eigenfrequencies and localization domains is presented. Numerical calculations of a set of near‐axis eigenmodes for the JET parameters is given as an example for the applicability of the MHD model. Finally, the relevancy of the eigenmodes to plasma heating in large tokamaks is discussed. © 1994 American Institute of Physics.
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.50.-b Plasma production and heating

Improved stability condition for rotating plasmas

Eliezer Hameiri and Hanno A. Holties

Phys. Plasmas 1, 3807 (1994); http://dx.doi.org/10.1063/1.870853 (7 pages) | Cited 7 times

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It is shown that the conservation of flow circulation along magnetic field lines can be used to improve on the δW stability criterion for rotating plasmas by adding to the energy integral a positive definite term. The improvement is most effective for ballooning modes in systems with a closed‐line magnetic field. Such systems are investigated, both when the flow is sheared and when it is unsheared. In the unsheared case, instabilities grow exponentially in time, while, if the flow is sheared, an instability eventually saturates. The time‐asymptotic behavior of such solutions is obtained and is different from the asymptotic behavior when the magnetic field is sheared. © 1994 American Institute of Physics.
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52.30.-q Plasma dynamics and flow
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Fa Tokamaks, spherical tokamaks

Direct measurement of velocity space transport in a plasma

Jeffrey Bowles, Roger McWilliams, and Nathan Rynn

Phys. Plasmas 1, 3814 (1994); http://dx.doi.org/10.1063/1.870854 (12 pages) | Cited 9 times

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The direct measurement of the velocity space transport of ions in a plasma is reported. Measured diffusion and convection coefficients are compared to the calculated Fokker–Planck coefficients for a fully ionized plasma. The measurements were made in a Q‐machine barium plasma (Ti=Te= 0.17 eV, 5×108≤n≤8×109 cm−3) with both high and low fluctuation levels. At low fluctuation levels the measured coefficients agree with classical collision theory. Coefficients measured in the presence of large amplitude fluctuations generally are larger and have different velocity dependences. Test particle distributions are created and interrogated using the technique of optical tagging. The short‐time (≪90° collision time) relaxation of the test particle distribution function was measured as a function of density and temperature of the background plasma and as a function of the velocity of the test particle distribution. The values of the convection and diffusion coefficients were extracted from these measurements. Longer time relaxations (∼90° time) also were measured. © 1994 American Institute of Physics.
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52.25.Fi Transport properties

Langevin equation versus kinetic equation: Subdiffusive behavior of charged particles in a stochastic magnetic field

R. Balescu, Hai‐Da Wang, and J. H. Misguich

Phys. Plasmas 1, 3826 (1994); http://dx.doi.org/10.1063/1.870855 (17 pages) | Cited 35 times

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The running diffusion coefficient D(t) is evaluated for a system of charged particles undergoing the effect of a fluctuating magnetic field and of their mutual collisions. The latter coefficient can be expressed either in terms of the mean square displacement (MSD) of a test particle, or in terms of a correlation between a fluctuating distribution function and the magnetic field fluctuation. In the first case a stochastic differential equation of Langevin type for the position of a test particle must be solved; the second problem requires the determination of the distribution function from a kinetic equation. Using suitable simplifications, both problems are amenable to exact analytic solution. The conclusion is that the equivalence of the two approaches is by no means automatically guaranteed. A new type of object, the ‘‘hybrid kinetic equation’’ is constructed: it automatically ensures the equivalence with the Langevin results. The same conclusion holds for the generalized Fokker–Planck equation. The (Bhatnagar–Gross–Krook) (BGK) model for the collisions yields a completely wrong result. A linear approximation to the hybrid kinetic equation yields an inexact behavior, but represents an acceptable approximation in the strongly collisional limit. © 1994 American Institute of Physics.
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05.20.Dd Kinetic theory
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
52.25.Gj Fluctuation and chaos phenomena
52.35.Ra Plasma turbulence

Nonlinear dynamo in ABC flow: The Hall effect

B. Galanti, N. Kleeorin, and I. Rogachevskii

Phys. Plasmas 1, 3843 (1994); http://dx.doi.org/10.1063/1.870856 (7 pages) | Cited 8 times

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Nonlinear evolution of the magnetic field generated by a prescribed deterministic flow of a conducting fluid in form of the Arnold–Beltrami–Childress (ABC) flow is studied numerically. The nonlinearity is caused by the Hall effect. After the linear regime, the Hall term in the induction equation becomes important, leading to saturation of the magnetic field. The oscillations of the magnetic field which characterize the linear regime fade away into a steady state regime. The structure of the magnetic field can be viewed as a sum of two components: a field of the integral scale and a small‐scale field. The large‐scale field contains most of the energy of the system, whereas the energy of the small‐scale field is very small. These results demonstrate significant difference between the actions of two types of nonlinearity in terms of the magnetic field: the Ampère force and the Hall effect. © 1994 American Institute of Physics.
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52.30.-q Plasma dynamics and flow
52.65.-y Plasma simulation
41.20.-q Applied classical electromagnetism
47.52.+j Chaos in fluid dynamics

Experimental study of two‐dimensional electron vortex dynamics in an applied irrotational shear flow

D. L. Eggleston

Phys. Plasmas 1, 3850 (1994); http://dx.doi.org/10.1063/1.870857 (7 pages) | Cited 12 times

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An electron column in a modified Malmberg–Penning trap is used to study the behavior of a single two‐dimensional vortex in an imposed irrotational shear flow. Phosphor screen images are presented, showing the dispersion of a vortex in a strong shear flow. The images show a variety of phenomena, including the fission of the original vortex, the emission, stretching, and entrainment of filamentary arms, and turbulent diffusion. The vortex lifetime is measured as a function of applied shear, with vortex strength independently adjustable. These data are compared to the predictions of a fluid theory, which correctly identifies the key dimensionless parameter (shear rate/vorticity) and its critical value. The experimental lifetime of a vortex in a strong shear is found to be the same as the dispersion time of a patch of zero vorticity. The lifetime of an unsheared vortex appears to be limited by a slow diffusion that gradually weakens the vortex. © 1994 American Institute of Physics.
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52.27.Jt Nonneutral plasmas
47.32.C- Vortex dynamics
52.35.Ra Plasma turbulence
47.15.ki Inviscid flows with vorticity

Model for collisional fast ion diffusion into Tokamak Fusion Test Reactor loss cone

C. S. Chang, S. J. Zweben, J. Schivell, R. Budny, and S. Scott

Phys. Plasmas 1, 3857 (1994); http://dx.doi.org/10.1063/1.870858 (14 pages) | Cited 11 times

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An analytic model is developed to estimate the classical pitch angle scattering loss of energetic fusion product ions into prompt loss orbits in a tokamak geometry. The result is applied to alpha particles produced by deutrium–tritium fusion reactions in a plasma condition relevant to Tokamak Fusion Test Reactor (TFTR) [Proceedings of the 14th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Würzburg, 1992 (International Atomic Energy Agency Vienna, 1992)]. A poloidal angular distribution of collisional fast ion loss at the first wall is obtained and the numerical result from the transp [‘‘A standard D–T supershot simulation’’ (to be published in Nucl. Fusion, 1994)] code is discussed. The present model includes the effect that the prompt loss boundary moves away from the slowing‐down path due to reduction in banana thickness, which enables one to understand, for the first time, the dependence of the collisional loss rate on Zeff. © 1994 American Institute of Physics.
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52.55.Pi Fusion products effects (e.g., alpha-particles, etc.), fast particle effects
52.55.Fa Tokamaks, spherical tokamaks
52.25.Fi Transport properties

Radiation‐driven turbulence at the plasma edge in toroidal devices

L. A. Charlton, J.‐N. Leboeuf, B. A. Carreras, and V. E. Lynch

Phys. Plasmas 1, 3871 (1994); http://dx.doi.org/10.1063/1.870859 (12 pages) | Cited 13 times

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The radiation drives for plasma edge parameters are reexamined. By including the electron density gradient, the radiation drive through density fluctuations can be strongly destabilizing even in a parameter regime away from force balance. This results in the dominance of the magnitude of the radiation power (γn drive) over its derivative (γT drive) for plasma edge parameters of Ohmic tokamak discharges. This leads to instability over a range of poloidal mode numbers much broader than in the case of the γT drive and to temperature fluctuations of opposite phase to the density fluctuations. Nonlinear numerical calculations show that this opposite phase relationship persists nonlinearly. As a consequence, the fluctuations induce a heat flux that is observed to be inward, while the particle and energy fluxes that they generate are calculated to be outward. © 1994 American Institute of Physics.
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52.25.Gj Fluctuation and chaos phenomena
52.35.Ra Plasma turbulence
52.65.-y Plasma simulation

Effect of magnetic field on the distribution of ions striking a planar target

P. B. Parks and S. I. Lippmann

Phys. Plasmas 1, 3883 (1994); http://dx.doi.org/10.1063/1.870926 (7 pages) | Cited 4 times

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The angular distribution of ions striking a planar target surface which has an obliquely inclined magnetic field at the surface is considered. The results have potentially important ramification for divertor surface sputtering and impurity transport in tokamak plasmas. © 1994 American Institute of Physics.
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52.40.Hf Plasma-material interactions; boundary layer effects

Fast wave poloidal flow generation in a plasma

C. Y. Wang, E. F. Jaeger, D. B. Batchelor, and K. L. Sidikman

Phys. Plasmas 1, 3890 (1994); http://dx.doi.org/10.1063/1.870860 (6 pages) | Cited 14 times

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Fast wave poloidal flow generation at the plasma edge of a tokamak is studied with a one‐dimensional slab model. In the absence of mode conversion, the poloidal flow can be generated by a spatial change of plasma velocity and current density profiles due to strong minority ion power absorption at the minority ion cyclotron resonance. The electromagnetic force plays a more important role in the flow generation than does the plasma Reynolds stress. In the presence of mode conversion, the flow is mainly generated by interference between the long‐wavelength transmitted fast wave and the short‐wavelength ion Bernstein wave (IBW) from mode conversion. Flow shear generated in the presence of mode conversion varies spatially with a scale length similar to the IBW wavelength. With mode conversion, the plasma Reynolds stress becomes more important in the flow shear generation than the electromagnetic force. For both cases, the plasma Reynolds stress and the electromagnetic force are out of phase, so that the resultant flow shear is smaller than the larger of the two. The short scale length flow shear enhances the turbulence stabilization. © 1994 American Institute of Physics.  
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52.30.-q Plasma dynamics and flow
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.55.Fa Tokamaks, spherical tokamaks
52.35.Ra Plasma turbulence

Mode conversion of fast magnetosonic waves and minority ion heating in a longitudinally inhomogeneous magnetic field

O. Sakai and Y. Yasaka

Phys. Plasmas 1, 3896 (1994); http://dx.doi.org/10.1063/1.870861 (9 pages) | Cited 5 times

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Mode conversion process in ICRF (Ion Cyclotron Range of Frequencies) in a longitudinally inhomogeneous two‐ion‐species plasma is clarified in the HIEI tandem mirror experiments. Measurements of wave number parallel to the magnetic field reveal that the fast magnetosonic wave of low‐field‐side incidence converts into the slow ion‐cyclotron wave near the ion–ion hybrid resonance. The propagation of the slow wave is detected between the ion–ion hybrid resonance and minority ion cyclotron resonance layers, which shows good agreement with the calculated dispersion relation based on one‐ and two‐dimensional plasma models. Simultaneous minority ion heating is observed, and it is due to the presence of the slow wave that resonates with minority ions at the minority ion cyclotron resonance. © 1994 American Institute of Physics.
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28.52.Av Theory, design, and computerized simulation
52.55.-s Magnetic confinement and equilibrium
52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.50.Gj Plasma heating by particle beams

Comments on finite Larmor radius models for ion cyclotron range of frequencies heating in tokamaks

C. K. Phillips, J. R. Wilson, J. C. Hosea, R. Majeski, and D. N. Smithe

Phys. Plasmas 1, 3905 (1994); http://dx.doi.org/10.1063/1.870862 (3 pages) | Cited 2 times

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The accuracy of standard finite Larmor radius (FLR) models for wave propagation in the ion cyclotron range of frequencies (ICRF) is compared against full hot plasma models. For multiple ion species plasmas, the FLR model is shown to predict the presence of a spurious second harmonic ion–ion type resonance between the second harmonic cyclotron layers of two ion species. It is shown explicitly here that the spurious resonance is an artifact of the FLR models and that no absorption occurs in the plasma as a result of this ‘‘resonance.’’ © 1994 American Institute of Physics.
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52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.50.Gj Plasma heating by particle beams

Sheared rotation effects, ion‐ and electron‐temperature fluctuations, and generalized form factors on drift waves

K. Katou and H. Mamada

Phys. Plasmas 1, 3908 (1994); http://dx.doi.org/10.1063/1.870863 (7 pages)

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The effect of inhomogeneous azimuthal flows in cylindrical geometry on drift waves with non‐Boltzmann density response is investigated. Stabilization of dissipative drift waves by the inhomogeneous flow is also analyzed. Convective cells are shown to be destabilized by the discontinuous flow. Next, ion‐ and electron‐temperature fluctuations in a resistive plasma are investigated in the slab approximation, allowing for the self‐consistently stationary system parameters (electron‐ and ion‐temperature inhomogeneities, magnetic shear, and plasma currents). Their magnitude, their propagation directions, and the dependence of their stability characteristics on the system parameters are identified, distinguishing between the weakly and the strongly collisional regions. Finally, the generalized form factor for density fluctuations in ion‐temperature gradient modes is calculated. The resulting broad frequency spectrum is shown to stem from the fact that the linear growth rate is comparable to the real wave frequency. © 1994 American Institute of Physics.
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52.35.Kt Drift waves
52.25.Gj Fluctuation and chaos phenomena

The ergodic limit of multipass absorption for fast wave current drive in tokamaks

K. Kupfer, C. B. Forest, C. C. Petty, and R. I. Pinsker

Phys. Plasmas 1, 3915 (1994); http://dx.doi.org/10.1063/1.870864 (13 pages) | Cited 5 times

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In many parameter regimes of interest for fast wave current drive (FWCD) in tokamaks, direct absorption of the fast wave by resonant electrons is a weak process and multipass absorption is an important issue. Although both full wave codes and ray tracing codes have been developed to model FWCD, in the multipass regime these tools are computationally intensive, and yield little insight into the nature of the solutions. In this work, an alternative approach is considered. Based on the wave kinetic equation, a natural limit emerges for the multipass regime, where wave energy density, convected along stochastic ray trajectories, uniformly fills the entire accessible phase space. In this ergodic, weak damping limit, the absorbed power density and corresponding wave‐driven current density are readily obtained by calculating the appropriate set of one‐dimensional k‐space integrals at every point in configuration space. The method is used here to model FWCD on the DIII‐D tokamak [R. I. Pinsker and the DIII‐D Team, Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 1, p. 683]. An example for reactor‐grade plasma parameters is also considered. © 1994 American Institute of Physics.
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52.50.Gj Plasma heating by particle beams
52.55.Fa Tokamaks, spherical tokamaks

Collisionless kinetic ballooning mode equation in the low‐frequency regime

L.‐J. Zheng and M. Tessarotto

Phys. Plasmas 1, 3928 (1994); http://dx.doi.org/10.1063/1.870865 (8 pages) | Cited 9 times

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The derivation of the fluid‐like kinetic ballooning mode equation from the gyrokinetic and Maxwell equations in the low‐frequency regime is revisited. The traditional results are pointed out to be ordering‐inconsistent. With the theory developed in the paper, two new effects are discovered: the small parallel‐ion‐velocity (SPIV) and the apparent mass (AM) effects. The SPIV effect is induced by the ions with parallel velocities much smaller than the thermal velocity, while the AM effect mainly by the ions with velocities comparable with the thermal velocity. The trapped‐particle contribution to the SPIV effect can be interpreted as a harmonic trapped‐particle effect, which can be even more important than the traditional bounce‐average trapped‐particle effect. The SPIV effect is shown to be more significant in ordering than the inertia effect with the AM and finite Larmor radius modifications. The application of the equation is discussed. The comparison with the ideal magnetohydrodynamic theory is made. © 1994 American Institute of Physics.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Fa Tokamaks, spherical tokamaks
52.55.Jd Magnetic mirrors, gas dynamic traps

Dynamo power balance in a reversed‐field pinch

P. Nordlund and S. Mazur

Phys. Plasmas 1, 3936 (1994); http://dx.doi.org/10.1063/1.870866 (6 pages) | Cited 5 times

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A study of the steady‐state magnetohydrodynamic dynamo power balance in the Extrap T1 reversed‐field pinch [Nucl. Fusion 34, 427 (1994)] is reported. The power transfer between the poloidal and toroidal magnetic fields is discussed in terms of a dynamo efficiency which is degraded with increasing pinch parameter Θ=Bθ(a)/〈Bϕ〉 as a consequence of a larger fraction of the input power (up to 50% at high Θ) being dissipated by the fluctuations. It is shown that this anomalous (non‐Spitzer) input power scales specifically with the power in nonlinearly driven dissipative m∊[0,2] modes. This is consistent with numerical results indicating the dynamo arises primarily from the m=1 modes. © 1994 American Institute of Physics.  
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52.55.Jd Magnetic mirrors, gas dynamic traps
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
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