Index of content:
Volume 3, Issue 8, August 1996

Orbit squeezing in a magnetic well
View Description Hide DescriptionIt is shown that the size of a charged particle’s drift orbit is squeezed, i.e., reduced, in a magnetic well in tokamak plasmas. The squeezing factor depends on the energy of the particle, being larger for higher‐energy particles. Therefore, for high‐energy particles, the size of the drift orbit depends only on the magnetic geometry. These energy‐independent drift orbits are also observed [J. A. Rome and Y.‐K. M. Ping, Nucl. Fusion19, 1193 (1979)]. The implications on the core confinement improvement physics and the confinement of the advanced fuel are discussed.

Experimentally determined profiles of fast wave current drive in a tokamak
View Description Hide DescriptionProfiles of the noninductive current, driven by direct electron absorption of fast waves in the ion cyclotron range of frequencies, have been determined for DIII‐D tokamak discharges [Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159]. The results clearly indicate the presence of centrally peaked driven current and validate theoretical models of fast wavecurrent drive.

The effects of the rotation in plasma
View Description Hide DescriptionElectric and magnetic self‐fields can exist in the rotating plasma. A self‐sustained rotation can be established in the plasma. The disturbed distribution function of rotating plasma is derived from the Vlasov equation. The propagation of waves in rotating plasma differs from that in the usual plasma. New terms for Landau damping appear. The local rotational behavior may become prevailing.

Characteristics of a weakly ionized non‐neutral plasma
View Description Hide DescriptionA scheme that allows stable confinement of a weakly ionized non‐neutral plasma is discussed. The method requires the forced rotation of the neutral gas within the trap about an axis that roughly coincides with the trap’s magnetic and mechanical axes. A number of the basic equilibrium and nonequilibrium properties of such a trapped plasma are calculated.

Effects of the ion‐beam density and velocity on the excitation of multimode soliton
View Description Hide DescriptionMultimode solitons are observed to be excited in an ion‐beam–plasma system. But, the excitation of some mode solitons of these is found to be suppressed under a certain condition depending on the density and velocity of a low‐energy ion beam, produced by the applied negative pulse. Furthermore, weak interaction between the slow‐beam soliton and ion‐acoustic soliton is also observed to cause small time lags in their trajectories on the distance–time plane.

Anomalous particle transport in a low‐temperature plasma without magnetic shear
View Description Hide DescriptionA simple shearless model for collisional drift waves in low‐temperature plasmas is analyzed to point at fluctuation‐induced anomalous plasmatransport. Spatially coherent structures do play an important role in the particle transport beyond a critical magnetic field strength. The transition from collisional to fluctuation‐inducedtransport is investigated. Special emphasis is put on analytical models for understanding the transition. The results from numerical simulations are interpreted.

Solitary kinetic Alfvén waves in the two‐fluid model
View Description Hide DescriptionEmploying the two‐fluid model, a generalized Sagdeev equation governing solitary kinetic Alfvén waves (SKAWs) and the criterion for the existence of SKAWs, which are valid for different ranges of plasma pressure parameter β, are presented. In the limit cases of β≫m _{ e }/m _{ i } and β≪m _{ e }/m _{ i }, the present results correspond, respectively, with conclusions obtained by Hasegawa et al. [Phys. Rev. Lett. 37, 690 (1976)] and by Shukla et al. [J. Plasma Phys. 28, 125 (1982)], that is, SKAWs accompanied by, respectively, hump and dip density solitons for β≫m _{ e }/m _{ i } and β≪m _{ e }/m _{ i }. However, for the case of β∼m _{ e }/m _{ i }, the present results show that SKAWs accompanied by both hump and dip density solitons are possible, and lead to KdV solitons in the small amplitude limit. In addition, the possibility for applying these results to electromagnetic spikes observed by the Freja scientific satellite is discussed [detailed information about the Freja satellite experiments can be found in serial papers presented in Space Sci. Rev. 70, Nos. 3/4 (1994)].

Current sheet formation along three‐dimensional magnetic separators
View Description Hide DescriptionIt was shown by Syrovatskii [Sov. Phys. JETP 33, 933 (1971)] that a perfectly conducting two‐dimensional magnetic field stressed externally develops a current sheet at an X point. A generalization of this analysis shows that a generic three‐dimensional magnetic field develops a closed ribbon of current along separators already existing in the field. A separator is a field line that begins and ends at different magnetic null points. A current ribbon will occur if there are two distinct separators beginning and ending at the same two nulls, thus forming a loop. The magnetic field containing the current ribbon is in force‐free equilibrium. An expression is found for the net current induced in the ribbon, and the magnetic energy stored by it, in terms of the amount of external stress. An electric field parallel to the current will facilitate reconnection and will dissipate the current and release the stored energy.

Nonlinear growth of the double tearing mode
View Description Hide DescriptionA theory for the growth of the double tearing mode in the early nonlinear stage is presented. The equations governing the nonlinear evolution of double tearing modes are formulated and are solved in different parameter regimes. When the phase difference between the two islands is π, the coupling of the two islands plays a destabilizing role. The island growth is of the form w∼t in the early nonlinear stage. The instability condition for the nonlinear double tearing mode is found, and is the same as that for the linear double tearing mode. When current profile is flattened near the two rational surfaces, the coupling plays the dominant role in determining the nonlinear growth.

A model realization of self‐organized criticality for plasma confinement
View Description Hide DescriptionA model for plasmatransport near marginal stability is presented. The model is based on subcri‐ tical resistive pressure‐gradient‐driven turbulence. Three‐dimensional nonlinear calculations based on this model show effective transport for subcritical mean profiles. This model exhibits some of the characteristic properties of self‐organized criticality. Perturbative transport techniques are used to elucidate the transport properties. Propagation of positive and negative pulses is studied. The observed results suggest a possible explanation of the apparent nonlocal effects ob‐ served with perturbative experiments in tokamaks.

Turbulent transport in mixed states of convective cells and sheared flows
View Description Hide DescriptionLow‐order mode coupling equations are used to describe recent computer simulations of resistive‐g turbulent convection that show bifurcations for the onset of steady and pulsating sheared mass flows. The three convective transport states are identified with the tokamak confinement regimes called low‐mode (L‐mode), high‐mode (H‐mode), and edge‐localized modes (ELMs). The first bifurcation (L→H) and the second bifurcation (H→ELMs) conditions are derived analytically and compared with direct solutions of the 6‐ODE mode coupling equations. First an exact expression is given for the energy transfer rate from the fluctuations to the sheared mass flow through the triplet velocity correlation function. Then the time scale expansion required to derive the Markovian closure formula is given. Markovian closure formulas form the basis for the thermodynamic‐like L–H models used in several recently proposed models.

Analyses of three shock interactions in magnetohydrodynamics: Aligned‐field case
View Description Hide DescriptionThe paper deals with the confluence of three shock waves at a point, in a magnetohydrodynamic (MHD)fluid. Based on the three‐shock theory, the equations governing the flow field in the vicinity of the intersection point are obtained. The three shock confluences in field‐aligned cases are studied here using shock polars, revealing that only seven combinations of three shock types are possible. The relations among (a) the combinations of incident and reflected shock types, (b) the angle between incident and reflected shocks, and (c) the streamline deflection angle across the reflected shock are shown. As an example of application, the flow field induced by a supersonic MHDflow over a concave double wedge is studied both analytically and numerically.

Lyapunov exponents and particle dispersion in drift wave turbulence
View Description Hide DescriptionThe Hasegawa‐Wakatani modelequations for resistive drift waves are solved numerically for a range of values of the coupling due to the parallel electron motion. The largest Lyapunov exponent, λ_{1}, is calculated to quantify the unpredictability of the turbulent flow and compared to other characteristic inverse time scales of the turbulence such as the linear growth rate and Lagrangian inverse time scales obtained by tracking virtual fluid particles. The results show a correlation between λ_{1} and the relative dispersion exponent, λ_{ p }, as well as to the inverse Lagrangian integral time scale τ_{ i } ^{−1}. A decomposition of the flow into two distinct regions with different relative dispersion is recognized as the Weiss decomposition [J. Weiss, Physica D 48, 273 (1991)]. The regions in the turbulent flow which contribute to λ_{1} are found not to coincide with the regions which contribute most to the relative dispersion of particles.

Three‐dimensional fluid simulations of tokamak edge turbulence
View Description Hide DescriptionThree‐dimensional (3‐D) simulations of drift‐resistive ballooning turbulence are presented. The turbulence is basically controlled by a parameter α, the ratio of the drift wave frequency to the ideal ballooning growth rate. If this parameter is small [α≤1, corresponding to Ohmic (OH) or low confinement phase (L‐mode) plasmas], the system is dominated by ballooning turbulence, which is strongly peaked at the outside of the torus. If it is large [α≥1, corresponding to high confinement phase (H‐mode) plasmas], field line curvature plays a minor role. The turbulence is nonlinearly sustained even if curvature is removed and all modes are linearly stable due to magnetic shear. In the nonlinear regime without curvature the system obeys a different scaling law compared to the low‐α regime. The transport scaling is discussed in both regimes and the implications for OH, L‐mode, and H‐mode transport are discussed.

Collisionless particle orbits in a torsatron with the complicated magnetic‐field harmonic spectrum. I. Particle orbits topology
View Description Hide DescriptionCharged particle orbits are investigated in a torsatron with the complicated magnetic‐field harmonic spectrum when distant, high‐order harmonics are present. The structure of the local magnetic wells in such a torsatron is considered. Conditions for the appearance of the additional local magnetic wells along the field line (toroidal‐ripple wells) due to the distant harmonics effect are obtained. It is shown that in a torsatron, the particles which are trapped in such wells have the largest radial deviations among all types of trapped particles. The analytical conditions under which the toroidal‐ripple wells are dangerous for the particle confinement (criteria of the strong toroidal‐field ripple) are derived.

Collisionless particle orbits in a torsatron with the complicated magnetic‐field harmonic spectrum. II. Adiabatic invariants of particle motion
View Description Hide DescriptionCharged particle orbits are investigated in a torsatron with the complicated magnetic‐field harmonic spectrum where the distant, high‐order harmonics (the harmonics of the toroidal‐field ripple) are present. The investigation is carried out on the basis of the adiabatic invariants of particle motion. The validity of the analytical expressions for the adiabatic invariants derived in the previous works are examined for the case of the torsatronmagnetic field perturbed by the toroidal‐field ripple of the arbitrary value and periodicity. For a torsatron–heliotron [K. Uo, J. Phys. Soc. Jpn. 16, 1380 (1961)] where the TF ripple of the magnetic field of periodicity equals twice the number of the helical field periods, exact analytical expressions for the adiabatic invariants of motion are derived for all possible kinds of particle orbits.

Wavelet analysis of ADITYA edge turbulence: Evidence of non‐linear interaction
View Description Hide DescriptionThe edge turbulence in the ADITYA tokamak [Phys. Rev. Lett. 69, 1375 (1992)] is examined using wavelet analysis techniques. The wavelet filters are used to separate low and high frequency components. The filtered plasma density and floating potential fluctuations show leptokurtic non‐Gaussianity (kurtosis, K≳3) at high frequencies, whereas, the low frequency components are nearly Gaussian. The recently developed wavelet bicoherence technique [Phys. Plasmas 2, 3017 (1995)] is extended to the Mexican hat wavelet. When the data are examined using wavelet bicoherence technique, it is found that the turbulent density and potential signals exhibit episodes of quadratic interaction in which low and high frequency components are coupled.

Outflow boundary conditions for the moments of a particle distribution function
View Description Hide DescriptionThe constraints on the moments of a distribution function satisfying an outflow condition are given. When a kinetic equation is approximated by a finite system of equations for the moments, the appropriate number of boundary conditions is found by analysis of the characteristics of the system.

Modeling of sawtooth destabilization during radio‐frequency heating experiments in tokamak plasmas
View Description Hide DescriptionSawtooth oscillations in tokamaks have been stabilized using ion cyclotron resonance heating (ICRH), but often reappear while ICRH continues. It is shown that the reappearance of sawteeth during one particular ICRH discharge in the Joint European Torus (JET) [Campbell et al., Phys. Rev. Lett. 60, 2148 (1988)] was correlated with a change of sign in the energy δW associated with m=1 internal kink displacements. To compute δW, a new analytical model is used for the distribution function of heated minority ions, which is consistent with Fokker–Planck simulations of ICRH. Minority ions have a stabilizing influence, arising from third adiabatic invariant conservation, but also contribute to a destabilizing shift of magnetic fluxsurfaces. As the minor radius of the q=1 surface rises, the stabilizing influence of minority ions diminishes, and the shape of the plasma cross section becomes increasingly important. It is shown that an increase in ICRH power can destabilize the kink mode: this is consistent with observations of sawteeth in JET discharges with varying levels of ICRH. It is suggested that the sawtooth‐free period could be prolonged by minimizing the vertical extent of the ICRH power deposition profile.1996 American Institute of Physics

A possible hybrid dissipative trapped electron ion temperature gradient mode
View Description Hide DescriptionThe effects of dissipative trapped electrons on ion temperature gradient‐driven instability (η_{ i }mode) in tokamakplasmas are considered. A sheared slab geometry is adopted and a linearized fluid model of ion temperature gradient(ITG)mode including dissipative trapped electrons, which are described by means of the well‐known formula of the nonadiabatic electron response [P. L. Similon and P. H. Diamond, Phys. Fluids 27, 916 (1984)], is presented. Results show that in tokamakplasmas not only is there a modification of the dissipative trapped electrons on the η_{ i }mode, but also there may exist an intrinsic oscillationmode, namely, a hybrid dissipative trapped electron ion temperature gradient mode. The higher the dissipative trapped electron fraction, the more it drives the η_{ i }mode, that is, when the trapped electron fraction is sufficient high and the trapped electrons are dissipated strongly, the mode is dominated by the trapped electron dynamics and propagates in the electron diamagnetic direction. These analytical results can be reduced to the usual predictions of the ion temperature gradient‐driven instability in the absence of the dissipative trapped electron. Numerical results further show that (a) there may be a hybrid dissipative trapped electron ITGmode and the dissipative trapped electron effect is a destabilizing effect on this mode; and (b) when the trapped electron fraction is sufficiently high and the trapped electrons are dissipated strongly, the mode is determined by the trapped electron dynamics. These conclusions are in agreement with the experimental observations in the latest simulated tokamak experiment on the Columbia Linear Machine [J. Chen and A. K. Sen, Phys. Rev. Lett. 72, 3997 (1994)].