Session UI1 - Turbulence, Internal Transport Barriers and Turbulent Transport.
INVITED session, Friday morning, October 31
Kiva, ACC

[UI1.001] Turbulence and Propagation in Plasma: Mean Field Theory and Intermittency Corrections

Following the lead of pioneers such as Kadomtsev and others, virtually all models of turbulence and transport in confined plasmas tacitly or explicitly presume a local balance between growth and dissipation. However, very simple arguments indicate that for inhomogeneous turbulence, radial scattering is an unavoidable by-product of nonlinear coupling. Thus, turbulence propagation and spreading are generic and ubiquitous, and it is impossible to formulate a purely local balance condition to characterize the saturated state. Here, we discuss recent progress in the theory of turbulence propagation. This phenomenon is closely related to the well-known problem of calculating the spreading of a ``turbulent spot" in a fluid. A generalized spectral intensity equation is derived, including spatially dependent excitation, local nonlinear transfer to dissipation, and spatial spreading and scattering effects, via nonlinear diffusion. The basic theory is derived via a standard Fokker-Planck analysis, but extensions to fractional kinetics (which does not presume a quasi-Gaussian transition probability distribution function) are under study. We calculate the expansion rate of a turbulent region, the depth to which it penetrates a linearly stable zone, and the saturated profile, including propagation effects. Interestingly, we show that propagation is generically SUB-diffusive, with diffusive scaling emerging as an upper bound. Thus turbulence propagation is intrinsically different from, but related to, the ``avalanche" phenomena. Also, avalanches are intrinsically intermittent, while turbulent spreading can be either ``mean field" or intermittent, in character. We discuss observations of turbulence propagation in gyrokinetic simulations, and comment on propagation as a mechanism for breaking of GyroBohm scaling.

[UI1.002] Non-linear Paradigm for Drift Wave - Zonal Flow interplay: coherence, chaos and turbulence

Non-linear equations for the slow space-time evolution of the radial drift wave (DW) envelope and zonal flow (ZF) amplitude have been self-consistently derived for a model nonuniform tokamak equilibrium within the coherent 4-wave drift wave-zonal flow modulation interaction model of Chen, Lin and White(chen00). For the sake of simplicity, in this work we assume electrostatic fluctuations; but our formalism is readily extended to electromagnetic fluctuations(chen01).

In the local limit, i.e. neglecting equilibrium profile variations, the coherent 4-wave DW-ZF modulation interaction model has successfully demonstrated spontaneous generation of ZFs and non-linear DW/ITG-ZF dynamics in toroidal plasmas(chen00). The present work is an extension of previous analyses to allow both (slow) temporal and spatial variations of the DW/ITG radial envelope; thus, it naturally incorporates the effects of equilibrium variations; i.e., turbulence spreading and size-dependence of the saturated wave intensities and transport coefficients(lin99). This approach makes it possible to treat equilibrium profile variations and non-linear interactions on the same footing, assuming that coupling among different DWs on the shortest non-linear time scale is mediated by ZF only. At this level, the competition between linear drive/damping, DW spreading due to finite linear (and nonlinear) group velocity(lin02,chen02,kim02) and non-linear energy transfer between DWs and ZF, determines the saturation levels of the fluctuating fields. Despite the coherence of the underlying non-linear dynamics at this level, this system exhibits both chaotic behavior and intermittency, depending on system size and proximity to marginal stability(chen02).

The present model can be further extended to include longer time-scale physics such as 3-wave interactions and collisionless damping of zonal flows.

\beginthebibliography9 \bibitemchen00 Liu Chen, Zhihong Lin and Roscoe White, Phys. Plasmas 7, 3129, (2000). \bibitemchen01 L. Chen, Z. Lin, R.B. White and F. Zonca, Nuclear Fusion 41, 747, (2001). \bibitemlin99 Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and P. H. Diamond, Phys. Rev. Lett. 83, 3645, (1999). \bibitemlin02 Z. Lin, S. Ethier, T.S. Hahm and W.M. Tang, Phys. Rev. Lett. 88, 195004, (2002). \bibitemchen02 L. Chen, R.B. White and F. Zonca, Zonal flow dynamics and size-scaling of anomalous transport; paper 2D02. Presented at the International Sherwood Theory Conference, Corpus Christi, Texas, April 28-30, 2003. \bibitemkim02 E.-J. Kim, P.H. Diamond, M. Malkov et. al., Nonperturbative models of intermittency in drift wave turbulence:towards a probabilistic theory of anomalous transport, submitted to Nucl. Fusion, (2003).

\endthebibliography

[UI1.003] Nonlocal Closures for Plasma Fluid Simulations

Theoretical tools applied to lab and astrophysical plasmas tend toward two extremes: kinetic models rife with physics but operating for short times and fluid models employing simplified closure relations but operating for long times. Until computers are fast enough to calculate kinetic physics over resistive times, efforts to extend plasma fluid models to handle a wider range of physics are critical. In this work, we generalize the program of fluid closure to capture kinetic effects in nonlocal, integral forms for higher-order fluid moments. These closures embody collisional, particle-trapping and Landau physics by integrating the fluid drives and closure moments along characteristics of the distribution function, F. The inversion of an operator that includes these physical effects begins with an expansion in eigenfunctions of the collision operator. Next, the characteristics of F are identified by diagonalizing the resultant system of hyperbolic equations. Integrating and taking the closure moments of F results in coupled Volterra equations involving the fluid drives and closures. It is shown that the collisional and nearly collisionless limits of these integral equations match onto previous expressions. In addition to significantly advancing the realism of previous fluid closures, integration along comparatively few (\sim 100)characteristics represents a significant reduction in work compared to kinetic treatments that follow millions of particles. These characteristics uncover the essential velocity-space dependence of F and hence render this closure scheme suitable for simulation of long time scale behavior. As a specific example, we conclude this talk by discussing the incorporation of these closures in plasma fluid simulations of neoclassical tearing modes in ITER-relevant discharges.

[UI1.004] Control of Internal Transport Barriers in Alcator C-Mod

Recent studies of internal transport and double transport barrier regimes in Alcator C-Mod have explored the limits for forming, maintaining, and controlling these plasmas. C-Mod provides a unique platform for studying such discharges: the ions and electrons are tightly coupled by collisions with T_i/T_e=1, and the plasma has no internal particle or momentum sources. The double-barrier ITB can be induced at will using off-axis ICRF injection on either the low or high field side of the plasma with either of the available ICRF frequencies (70 or 80 Mhz). When EDA H-mode is accessed in ohmic plasmas, the double barrier ITB forms spontaneously if the H-mode is sustained for at least 2 energy confinement times. The ITBs formed in both ohmic and ICRF heated plasmas are quite similar regardless of the trigger method. They are characterized by strong central peaking of the electron density, and reduction of the core particle and energy transport. Control of impurity influx and heating of the core plasma in the presence of the ITB have been achieved with the addition of central ICRF power in both ohmic H-mode and ICRF induced ITBs. The radial location of the particle transport barrier is dependent on the toroidal magnetic field and not on the location of the ICRF resonance. A narrow region of decreased electron thermal transport, as determined by sawtooth heat pulse analysis, is found in these plasmas as well. Transport analysis indicates that reduction of the particle diffusivity in the barrier region allows the neoclassical pinch to drive the density and impurity accumulation in the plasma center. Examination of the gyrokinetic stability at the trigger time for the ITB suggests that the density and temperature profiles are inherently stable to ITG and TEM modes in the core at and to the inside of the ITB location.

[UI1.005] Role of Trapped Electron Mode Turbulence in Internal Transport Barrier Control in Alcator C-Mod

C-Mod experiments using off-axis ICRH produce an internal transport barrier after the transition to EDA H-Mode [1]. The barrier foot reaches the half-radius, with a peak density 2.5 times the edge density. As the density peaks, the temperature profile is relatively unaffected. The peaking is controlled by applying modest central heating power late in the discharge. Gyrokinetic turbulence simulations of the barrier formation phase, using GS2 [2,3], show a transient \eta_e-dependent, turbulent pinch similar in magnitude to the Ware pinch. Toroidal ion temperature gradient driven modes are suppressed inside the barrier foot, but continue to dominate in the outer half-radius. As the density gradient steepens further, non-resonant collisionless trapped electron modes (TEM) are driven unstable. Gyrokinetic stability analysis shows the modes are driven solely by the density gradient, have wavelengths twice the ion gyroradius, and are partially damped by collisions. After the TEM onset, the turbulent inflow reverses to become an outflow that strongly increases with the density gradient. This outflow ultimately balances the inward Ware pinch leading to steady state. Moreover, the simulated turbulent particle diffusivity closely matches that inferred from particle balance using measured density profile data and the calculated Ware pinch. This turbulent diffusivity exhibits a strong unfavorable temperature dependence that allows control with central heating.

[1] S. J. Wukitch et al., Phys. Plasmas 9 (5), 2149 (2002).

[2] M. Kotschenreuther et al., Comp. Phys. Comm. 88, 128 (1995).

[3] W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000).

[UI1.006] Beta Scaling of Transport on the DIII-D Tokamak - Is Transport Electrostatic or Electromagnetic?

The related methods of dimensional analysis, similarity, and scale invariance in physics provide a powerful technique for analyzing physical systems. Previous experiments on the JET, DIII-D, and Alcator C-Mod tokamaks have validated the principle of similarity for energy transport in high-temperature plasmas. Recently the dependence of transport on beta, the ratio of the plasma kinetic pressure to the magnetic field pressure, has been measured for H-mode plasmas on DIII-D. Experimentally determining the beta scaling helps to differentiate between various proposed mechanisms of turbulent transport since theories for which ExB transport is dominant show little change with increasing beta up to the ideal ballooning limit, while transport models that invoke electromagnetic effects like magnetic flutter transport generally have a strong, unfavorable beta scaling. These experiments on DIII-D varied the normalized beta from 1.1 to 3.0 in several steps, covering a range from 25% to 85% of the ideal no-wall beta limit, and showed that the measured thermal diffusivities and global energy confinement times (normalized to Bohm) have little dependence on beta. This weak, possibly non-existent, beta scaling of transport confirms previous observations from the DIII-D and JET tokamaks as well as the ATF torsatron. This experimental result is in marked contrast to empirical scaling relations derived from multi-machine H-mode confinement databases, such as the ITER-98(y,2) relation that contains a strong, unfavorable beta dependence. New semi-empirical scaling relations, derived from the confinement databases, that are gyroBohm-like and electrostatic predict that the fusion performance in ITER will optimize at high beta, yielding twice the fusion power as the nominal beta scenario at higher fusion gain.

Part U of program listing