Session FI1 - Transport Theory.
INVITED session, Tuesday morning, November 16
Grand I, The Westin Seattle

[FI1.01] Transport in zonal flows in analogous geophysical and plasma systems

Zonal flows occur naturally in the oceans and the atmosphere of planets. Important examples include the zonal flows in Jupiter, the stratospheric polar jet in Antarctica, and oceanic jets like the Gulf Stream. These zonal flows create transport barriers that have a crucial influence on mixing and confinement (e.g. the ozone depletion in Antarctica). Zonal flows also give rise to long-lasting vortices (e.g. the Jupiter red spot) by shear instability. Because of this, the formation and stability of zonal flows and their role on transport have been problems of great interest in geophysical fluid dynamics. On the other hand, zonal flows have also been observed in fusion plasmas and their impact on the reduction of transport has been widely recognized. Based on the well-known analogy between Rossby waves in quasigeostrophic flows and drift waves in magnetically confined plasmas, I will discuss the relevance to fusion plasmas of models and experiments recently developed in geophysical fluid dynamics. Also, the potential application of plasma physics ideas to geophysical flows will be discussed. The role of shear in the suppression of transport and the effect of zonal flows on the statistics of transport will be studied using simplified models. It will be shown how zonal flows induce large particle displacements that can be characterized as Lévy flights, and that the trapping effect of vortices combined with the zonal flows gives rise to anomalous diffusion and Lévy (non-Gaussian) statistics. The models will be compared with laboratory experiments and with atmospheric and oceanographic qualitative observations.

[FI1.02] L-H Transition Simulations in Divertor Geometry

Recent results are presented on turbulence in tokamak boundary plasmas and its relationship to the L-H transition, in a realistic divertor geometry. These results are obtained from the 3D nonlocal electromagnetic turbulence code BOUT (X.~Q.~Xu and R.~H.~Cohen, Contrib.~Plasma Phys.), 38, 158 (1998)., which models the boundary plasma using fluid equations for plasma vorticity, density, electron and ion temperature and parallel momentum. With sources added in the core-edge region and sinks in the SOL, BOUT follows the self-consistent profile evolution together with turbulence. Under the DIII-D tokamak L-Mode conditions, the dominant source of turbulence is pressure-gradient-driven resistive X-point modes (X.~Q.~Xu, R.~H.~Cohen, G.~D.~Porter, et al., accepted by Nuclear Fusion) (1999).. These modes are electromagnetic and curvature-driven in the outside mid-plane region but become electrostatic near X-points due to magnetic shear and collisionality. Classical resistive ballooning modes at high-n coexist with these modes but are sub-dominant. Results indicate that, as the power is increased, these modes are stabilized by increased turbulence-generated velocity shear, resulting in an abrupt suppression of high-n turbulence and formation of a pedestal, as is characteristic of the H mode transition. The simulations provides approximate quantitative agreement with experimental measurements of the pedestal width and height and the radial electric field. The relationship of the large pedestal pressure gradient to ELMs will be discussed.

Additionally, an analytic model of weakly collisional heating and potential formation from dissipation accompanying the resistive X-point mode is presented; this model may account for observations in some DIII-D shots of higher temperatures near the X-point than at the mid-plane (M.~J.~Schaffer et al., Bull.~APS), 43, 1889 (1998)..

[FI1.03] ExB Shear Flows and Electromagnetic Gyrofluid Turbulence

Low frequency drift wave turbulence is computed with a three dimensional finite difference model of the six-moment electromagnetic gyrofluid equations for both electrons and ions. The resulting dynamical system represents fluidlike ExB turbulence in planes perpendicular to the magnetic field, in competition with dissipative kinetic shear Alfven waves coupling the planes together --- an extension of drift Alfven turbulence to the collisionless, hot-ion regime. Axisymmetric flux surface geometry with arbitrary shaping and aspect ratio is modelled in globally consistent flux tube form.

The qualitative character of the turbulence is the same for parameters corresponding to core and edge plasma regions. The radial dependence of transport follows from the parallel/perpendicular scale ratio of the equilibrium profile. Statistical analysis of the fluctuations indicates nonlinear drift wave/ITG mode character in all relevant parameter regimes, excepting only the onset of ideal ballooning. Electron Landau damping is the principal dissipation channel; finite collisionality introduces no qualitative changes.

Magnetic flux surface geometry has decisive quantitative effects, including on the parameter dependence. ExB shear is not strongly generated by the turbulence, but it arises through the neoclassical equilibrium and therefore can play a role in state transitions. Preliminary results suggest that a strong temperature dependence in this equilibrium ExB shear may yield a natural mechanism for the L-to-H transition observed in tokamaks.

[FI1.04] Full Torus Gyrokinetic Calculations of Turbulence Modification by External Electric Fields in Electric Tokamak Plasmas

Global, toroidal, three-dimensional, gyrokinetic particle simulations are being performed to predict and assess plasma behavior in the large aspect ratio Electric Tokamak presently under construction at UCLA. In particular, systematic studies of the influence of externally imposed radial electric fields, such as are expected in the Electric Tokamak, on electrostatic turbulence driven by ion temperature gradients are being pursued with realistic profiles and parameters. These global gyrokinetic calculations are an outgrowth of the Numerical Tokamak Turbulence Project and are being carried out on the massively parallel computing platforms available at the National Energy Research Scientific Computer Center in Berkeley and the Advanced Computing Laboratory in Los Alamos. Results from these calculations so far indicate that significant reduction and eventual suppression of turbulence can be achieved with fields on the order of 50 V/cm which are at or below the level that is deemed achievable through RF-induced global poloidal plasma rotation in the Electric Tokamak. These calculations indicate that reduction and/or suppression result from electric field shear mitigating the ion temperature gradient drive and the electric field itself reducing the trapped particle population which also contributed to the turbulence drive. Results from studies of the influence of these externally imposed radial electric fields on the poloidal and radial correlation lengths of the turbulence will also be discussed.

[FI1.05] Ion Bernstein Wave Heating: a Tool to Modify the Plasma Profile

Research on the direct application of ion Bernstein wave (IBW) power to magnetically confined plasmas is being pursued with the aim of providing a tool to control the pressure profile. Theoretical work has shown that the Reynolds stress induced by the wave can drive localized, sheared poloidal flow.^1-2 With sufficient shearing rate, turbulence suppression should be expected. Experimental results obtained in PBX-M^3 have shown that a transport barrier, observable on all kinetic profiles, was formed in the vicinity of the IBW power deposition location. More recently, direct-launch IBW experiments were conducted in TFTR^4 in D-T plasmas during which shearing of the poloidal velocity profile was observed. A model, based on a ray-tracing calculation of the wave induced Reynolds stress, reproduces the salient experimental features^5: The observed sheared flow occurs near the tritium fifth harmonic cyclotron resonance layer and depends strongly on the tritium density in agreement with the model. Furthermore, the model reproduces the observed insensitivity of the induced rotation to the tritium density in the region between the third deuterium harmonic layer and the fifth tritium harmonic layer. Power coupling was limited to < 500 kW and the induced shearing rate was insufficient by a factor of \sim 4 to induce a transport barrier. Recent IBW results^6 obtained on FTU will also be discussed. This work was supported by the U.S. Department of Energy Contract No. DE-AC02-76-CHO-3073. ^1C.G. Craddock and P.H. Diamond, Phys. Rev. Lett. 67, 1536 (1991); ^2Biglari, et al., RF Power in Plasmas, 9th Topical Conf., AIP Conf. Proc. 244, p.376 (1991); ^3B.P. LeBlanc et al., Phys. Plasmas, 2, 741 (1995); ^4J.R. Wilson, et al., Phys. Plasmas, 5, 1721 (1998); ^5B.P. LeBlanc, Phys. Rev. Letts., 82, 331 (1999); ^6R. Cesario, 13^th Topical Conf. on the Application of RF Power to Plasmas, Annapolis, April 1999.

[FI1.06] Electron-temperature-gradient-driven turbulence

At typical perpendicular wavelengths and frequencies of \rho_e and v_te/L_n, electron-temperature-gradient-driven (ETG) modes are linearly unstable when R/L_Te exceeds a critical value. Their linear dynamics is similar to that of ion-temperature-gradient-driven (ITG) modes with the roles of electrons and ions reversed. Because of \rho_i>>\rho_e the ion response is (almost) adiabatic and D=\chi_i=0, whereas the mixing length estimate for the electron heat transport caused by ETG turbulence is given by \chi_e=\rho_e^2 v_te/L_n. However, this transport level is in general too low to be of experimental relevance. Here we present the first nonlinear simulation results for collisionless ETG turbulence obtained by various toroidal gyrofluid and gyrokinetic codes. Somewhat surprisingly, and unlike the analogous case of ITG turbulence, we find that the turbulent electron heat transport is significantly underpredicted by the mixing length estimate. This oberservation is directly linked to the presence of radially highly elongated vortices (``streamers'') which lead to very effective radial transport. The simulations indicate that \chi_e from ETG turbulence can be high enough to force R/L_Te towards its critical value in a wide region of parameter space. We will present comparisons with experimental data examining this prediction. Moreover, because of its small spatial and temporal scales, ETG turbulence is able to exist even in a large ExB shear environment and therefore sets a lower limit on \chi_e within an internal transport barrier.

Part F of program listing