Index of content:
Volume 3, Issue 2, February 1996

Tokamak configurations with reversed magnetic shear and a peaked current density profile
View Description Hide DescriptionRecent experiments suggest that the reversal of magnetic shear in the central region of a tokamak plasma has beneficial effects on plasma transport. In this Letter, it is shown that a hollow toroidalcurrent density distribution is not a necessary condition for the existence of tokamak equilibria with reversed magnetic shear.

On plasma crystal formation
View Description Hide DescriptionIt is shown that charged dust grains in a sheath region with plasma ion flow can attract each other in the wake potential cone of an upstream dust particulate. Because of the periodic nature of the potential, periodic structures of the dust grains can be formed in a base plane of the cone.

Stability of a thermal plasma jet
View Description Hide DescriptionThe stability of a slab model of a jet moving in an external plasma is investigated, assuming the configuration to be characterized by a general heat‐loss function. Numerical results are obtained for the growth rates of unstable modes, both for symmetric and asymmetric perturbations for equal parallel magnetic fields along or transverse to the propagation vector in the wide and slender jet approximations. Special configurations of an incompressible jet moving past a thermal plasma and also of a thermal plasma moving past an incompressible static plasma are also considered.

Streaming instability in the grain charge fluctuations
View Description Hide DescriptionHighly charged massive dust grains present in a dusty plasma may exhibit charge fluctuations in response to certain types of oscillations incorporated in the plasma. In this situation the grain charge becomes a time‐dependent and self‐consistent dynamic variable. The consequent modifications in the collective properties of a dusty plasma in response to longitudinal space‐charge waves are investigated. It is shown this new effect gives rise to purely damped modes, in addition to causing a collisionless damping of the normal modes.

Flux limiting due to electron impact excitation energy loss
View Description Hide DescriptionLarge radiation losses in the electron energy balanceequation due to electron impact excitation can cause the parallel scale length to become small enough that a short mean‐free path expansion becomes questionable for the high‐speed tail electrons. It then becomes necessary to limit the parallel electron heat flux so that it remains below its free‐streaming value nT ^{3/2}/m, where n, T, and m are the electron density, temperature, and mass. A Boltzmanninelastic scattering col‐ lision operator is adopted to investigate whether electron impact excitation can lead to a self‐consistent flux limit by depleting the electron tail.

Magnetization and other characteristics of exact relativistic dispersion of circularly polarized radiation in a magnetized plasma
View Description Hide DescriptionA relativistic determination has been made of the zero frequency magnetic moment field [the inverse Faraday effect (IFE)], synchrotron radiation, and other consequences of the exact dispersion relation of a circularly polarized wave propagating in a two‐component, cold, magnetized plasma. The relativistically correct Faraday angle of rotation of the plane of polarization of the electromagnetic (EM) wave due to the variation of the dispersion rates of the right‐ and left‐circularly polarized components of the wave has been obtained. For Alfvén wave frequencies (wave frequency less than the ion gyrofrequency), a relativistically correct analysis of the interesting new features which appear due to the predominance of the wave‐induced ion dynamics over electron motion is also presented.

The resistive interchange mode in the presence of equilibrium flow
View Description Hide DescriptionThe influence of a sub‐Alfvénic equilibrium flow along the magnetic field and a weak fluidviscosity on the resistive gravitational interchange mode is investigated in plane slab geometry. With a uniform resistivity, the current layer is subject to both tearing and interchange so that a degree of mode‐mixing is inevitable. In contrast to the tearing mode which is destabilized, sub‐Alfvénic flow is shown to have a stabilizing effect on the linear resistive interchange mode.

A three‐circulation theorem for relativistic plasmas
View Description Hide DescriptionIt is shown that the sum of three circulations (hydrodynamic, magnetic, and thermal) is constant in time for each component of a perfect relativistic plasma. A constraint for the initial configuration (‘‘Weber/Ertel case,’’ the lines of canonical vorticity lie on surfaces of constant entropy) leads to zero potential vorticity also for later times; this is generally realized in inhomogeneous flow equilibria for which the explicit time‐dependence of Clebsch potentials is given. Equilibrium states of warm relativistic plasmas with vanishing thermal circulation are discussed.

Collisionless damping of a quasilinear Langmuir wave packet
View Description Hide DescriptionCollisionless damping of a one‐dimensional packet of Langmuir waves with random phases localized in the direction of its propagation is described by using quasilinear equations. A peculiar minimum principle is proposed for reducing this quasilinear problem to a simple graphic analysis of the packet initial spectrum.

Transit‐time scattering and heating of a relativistic electron beam in strong Langmuir turbulence
View Description Hide DescriptionA Fokker–Planck theory is developed to describe the diffusion in momentum space of a beam of relativistic electrons due to multiple transit‐time interactions with an ensemble of coherent Langmuir wave packets. The theory incorporates two ingredients: a perturbed‐orbit calculation of the momentum change of a test particle during a single transit‐time interaction, and an ensemble average of the resulting Fokker–Planck coefficients based on the statistical properties of strong Langmuir turbulence. An approximate analytic solution of the Fokker–Planck equation is obtained for the case of a strongly collimated beam, and is used to interpret measurements of energy and pitch‐angle scattering in relativistic‐electron‐beam (REB) experiments. Fokker–Planck coefficients are also calculated for a weakly collimated beam. It is shown that the theory correctly predicts the amount of energy scattering in REB experiments, but underestimates the pitch‐angle scattering regardless of the distribution of wave packet orientations and the degree of collimation of the beam. This discrepancy may be a product of the approximate wave‐packet structure assumed in the analysis, or of systematic errors in the experimental data; alternatively, it may imply that a non‐transit‐time process is responsible for part of the pitch‐angle scattering observed.

On self‐consistent stationary propagation of relativistically coupled electromagnetic and electrostatic waves in cold electron‐ion plasma
View Description Hide DescriptionA general self‐consistent theory is presented for one‐dimensional stationary propagation of relativistically coupled electromagnetic and electrostatic waves. A finite amplitude plane wave solution is found to be always unstable against modulation. A modulated finite amplitude plane wave solution is found in a narrow region of the frequency, and the possibility for a solitary wave solution and its properties are discussed.

Application of the separatrix map to study perturbed magnetic field lines near the separatrix
View Description Hide DescriptionIn this paper a generalized separatrix map to study perturbed magnetic field lines in a confined magnetic system with the separatrix is discussed. The separatrix map is an iteration transform for the magnetic flux and a toroidal angle at a certain cross section after one period of the unperturbed trajectory. The map can be derived from magnetic field line equations and can be shifted along the toroidal angle, depending on the point of interest. Different asymptotic forms of the shifted separatrix map, with respect to the distance between the cross section of the toroidal angle and the X point, are considered, and their invariant properties are discussed in regard to the renormalization transformation of the perturbation amplitude. A method to find the map’s parameters for any specific magnetic system is proposed. It is shown that the shifted separatrix map can be directly applied to obtain magnetic footprints at the divertor plates, and to study chaotic scattering of field lines.

Reflection of modified Korteweg–de Vries solitons in a negative ion plasma
View Description Hide DescriptionReflection of modified Korteweg–de Vries solitons from the sheath in front of a negatively biased metal disk is experimentally investigated in a negative ion plasma. Both rarefactive and compressive solitons are reflected and the polarity of the reflected solitons is the same as that of the incident solitons. The points of reflection for the rarefactive and compressive solitons are at different locations. As the magnitude of the negative bias potential that is applied to the reflector is increased, the two reflection points move away from the reflector. An interpretation in terms of the sheath characteristics is presented.

Low‐beta equilibrium and stability for anisotropic pressure closed field line plasma confinement systems
View Description Hide DescriptionA formalism has been developed to analyze the equilibrium and stability of low‐beta anisotropicpressureplasmas confined in closed field line magnetic systems. This formalism, based on a joint use of paraxial (long‐thin) and low‐beta approximations, allows self‐consistent equilibrium and stability consideration of rather general magnetic systems with nonuniform axis curvature and longitudinal profiles of toroidal and multipole poloidal field. Strong pressureanisotropy, corresponding to enhanced plasma pressure in mirror cells of the system, may also be considered. Nonconventional features of anisotropicpressure equilibria have been revealed. Application of the above formalism to the recently proposed linked mirrorneutron source (LMNS) confirms the basic principles of the LMNS concept, but calculations based on this formalism have appreciably corrected some LMNS parameters. The LMNS longitudinal pressure profile and magnetic field distribution are optimized.

Interpretation of ion cyclotron emission from sub‐Alfvénic fusion products in the Tokamak Fusion Test Reactor
View Description Hide DescriptionIon cyclotron emission (ICE) has been observed during neutral beam‐heated supershots in the TokamakFusion Test Reactor (TFTR) [Phys. Rev. Lett. 72, 3526 (1994)] deuterium–tritium campaign at fusion product cyclotron harmonics. The emission originates from the outer midplane edge plasma, where fusion products initially have an anisotropic velocity distribution, sharply peaked at a sub‐Alfvénic speed. It is shown that the magnetoacoustic cyclotron instability, resulting in the generation of obliquely propagating fast Alfvén waves at fusion product cyclotron harmonics, can occur under such conditions. The time evolution of the growth rate closely follows that of the observed ICE amplitude. Instability is suppressed if the fusion products undergo a moderate degree of thermalization, or are isotropic. In contrast, the super‐Alfvénic fusion products present in the outer midplane of the Joint European Torus (JET) [Nucl. Fusion33, 1365 (1993)] can drive the instability if they are isotropic or have a broad speed distribution. This may help to account for the observation that fusion product‐driven ICE in JET persists for longer than fusion product‐driven ICE in TFTR supershots.

The effect of sheared axial flow on the linear stability of the Z‐pinch
View Description Hide DescriptionA linear analysis of the ideal magnetohydrodynamic(MHD) stability of the Z‐pinch is presented in which plasma flows are included in the equilibrium. With sheared axial flows it is found that substantial stabilization of internal modes is possible for some equilibrium profiles. For this to occur equilibria with a change in fluid velocity across the pinch radius of about Mach 2 are required. However, this ignores the surrounding vacuum and for the more realistic free boundary modes flows of about Mach 4 are required to stabilize all global MHD modes. This stabilization of MHD modes is not observed for all equilibria however. This fact, combined with the supersonic flow speeds required for stability, make it unlikely that a Z‐pinch could in practice be stabilized by the introduction of sheared flow.

Comparison of two resistive ballooning mode models in transport simulations
View Description Hide DescriptionPredictive transport simulations of the temperature and density profiles have been carried out for TokamakFusion Test Reactor (TFTR) [K. Young et al., Plasma Phys. Controlled Fusion26, 11 (1984)] current, density, and heating power scans. Two competing resistive ballooningmodetheories are considered in order to examine their intrinsic magnetic‐q dependence. The theoretically derived transport model employed in this study includes drift wave contributions from the Weiland theory of trapped electron and ion temperature gradient modes, the Kwon–Biglari–Diamond neoclassical magnetohydrodynamic(MHD)theory, the Tang–Rewoldt kinetic ballooning modetheory, and either the previously used Carreras–Diamond or the recently developed Guzdar–Drake resistive ballooningmodetheories. It is found that the Guzdar–Drake theory provides the correct scaling with plasma current while maintaining a scaling with density and auxiliary heating power that is consistent with experimental data from TFTR low confinement (L‐mode) plasmas. A statistical analysis of the profile results for the current scan is included to give quantitative measures of how well simulations that include either the Guzdar–Drake or the Carreras–Diamond theory compare with the experimental data.

Modulational excitation of drift waves by a beam of lower‐hybrid waves
View Description Hide DescriptionThe results of theoretical and experimental studies on excitation of drift waves in a tokamak plasma under the conditions of experiments on lower‐hybrid (LH) plasma heating and current drive are presented. It is shown that for sufficiently strong LH pump levels the main effect resulting in the drift wave excitation is the LH wave modulational instability. It is found that the modulational excitation of long‐wavelength drift oscillations (with the wavelengths exceeding the length of the LH pump wave) is described by a dispersion equation similar to the equation for the usual hydrodynamical beam instability. This allows us to treat the excitation of the long‐wavelength drift waves as modulational excitation by a beam of the LH waves. The theoretical results obtained are compared with the data of the tokamak Tore Supra [Proceedings of the 12th International Conference on Plasma Physics and Controlled Nuclear Fusion, Nice, 1988 (International Atomic Energy Agency, Vienna, 1989), p. 9] experiment. Qualitative accordance of the theoretical and experimental results is demonstrated.

Detection of fusion neutrons from a deuterium‐proton mixed plasma in the GAMMA 10 Tandem Mirror
View Description Hide DescriptionNeutron diagnostics are applied to a deuterium plasma mixed with protons in the central cell of the GAMMA 10 tandem mirror [Inutake et al., Phys. Rev. Lett. 55, 939 (1985)]. The deuterium ions are heated with a slow ion cyclotron wave tuned to the fundamental deuterium resonance near the mid‐plane of the central cell while the plasma is sustained with the fundamental resonance heating of protons in the minimum‐B anchor cells. The measurement is based on in situ calibration to determine the transmission efficiency through machine walls and the counting efficiency of the detection system for neutrons emitted from ^{252}Cf with energy close to that in the deuterium–deuterium (D–D) fusion reaction. The observation shows that the count rate of neutrons increases with diamagnetism, and this relation is accounted for in terms of fusion reaction between deuterium ions with a transverse temperature exceeding 10 keV. Discrepancies among ion temperatures determined with different diagnostics are mostly attributed to insufficient knowledge of the profiles of plasma parameters. The results indicate that the neutron measurement can be added as a powerful diagnostic tool for hot ions if combined with more detailed profile measurements.

Toroidal coupling of ideal magnetohydrodynamic instabilities in tokamak plasmas
View Description Hide DescriptionA theoretical framework is developed to describe the ideal magnetohydrodynamic(MHD) stability properties of axisymmetric toroidal plasmas. The mode structure is described by a set of poloidal harmonics in configuration space. The energy functional, δW, is then determined by a set of matrix elements that are computed from the interaction integrals between these harmonics. In particular, the formalism may be used to study the stability of finite‐nballooning modes. Using for illustration the s‐α equilibrium, salient features of the n■∞ stability boundary can be deduced from an appropriate choice of test function for these harmonics. The analysis can be extended to include the toroidal coupling of a free‐boundary kink eigenfunction to the finite‐n ideal ballooning mode. A unified stability condition is derived that describes the external kinkmode, a finite‐nballooning mode, and their interaction. The interaction term plays a destabilizing role that lowers the instability threshold of the toroidally coupled mode. These modes may play a role in understanding plasma edge phenomena, L–H physics and edge localized modes (ELMs).