The detailed dynamics underlying the self-generation of magnetic flux (‘‘dynamo’’) in reversed-field pinches (RFPs) is investigated with a three-dimensional magnetohydrodynamic code. A novel energy diagnostic is used to identify the path taken in Fourier space by the poloidal magnetic field energy as it is converted to axial magnetic field energy by the dynamo. At high values of the pinch parameter, Θ, and Lundquist number, S, the dynamo can be alternatingly dominated by quasilinear and nonlinear processes in a quasiperiodic fashion. Quasilinearly, the m=1 modes can reverse the axial field by themselves. However, m=0 modes are crucial to produce the nonlinear dynamo that triggers quasiperiodic relaxations. The same causal mechanism is likely to be responsible for the experimentally observed sawteeth.
Here, we propose and analyze a technique for active suppression of tokamak edge turbulence. Suppression occurs due to the effects of a sheared radial electric field generated by externally driven radio-frequency waves. Plasma flow is induced by radially varying wave-driven Reynolds and magnetic stresses, and opposed by neoclassical damping. For Alfvenic flow drive, the predicted shear flow profile is determined by ion inertia and electron dissipation effects. Results indicate that a modest amount of absorbed power is required for edge-turbulence suppression. More generally, several novel results in the theory of momentum transport by electromagnetic fluctuations are presented. 52.35.Ra, 52.55.Fa The understanding and control of turbulent transport of heat and particles are the principal obstacles confronting controlled fusion research today [1]. Progress toward this end has been aided by the discovery of various improved confinement regimes. Foremost of these is the H mode [2], in which a transport barrier spontaneously forms at the plasma periphery or edge, resulting in the development of steep density and, occasionally, temperature gradients. Prior to the formation of this barrier, i.e., during the L mode, this periphery region is characterized by large electromagnetic and density fluctuation levels, indicating a region of strong edge turbulence [3]. Recently, the L-*H transition has been observed to coincide with the onset of large poloidal flows in the edge region [4]. Such flows are thought to be symptomatic of a strongly sheared inward electric field, which in turn can suppress turbulence and transport via shear-enhanced decorrelation [5]. The transport barrier then forms as a consequence of the turbulence suppression. Indeed, recent studies of edge shear layer structure in non-//-mode discharges indicate that shear decorrelation is likely to play an important role in regulating edge transport in all confinement regimes [6].In this Letter, we discuss the suppression of turbulence using sheared electric fields generated by externally driven radio-frequency (rf) waves. This technique for turbulence suppression has several potential advantages over the spontaneous L-•// transition. First, it allows enhanced confinement with Er > 0, thus preventing the undesirable impurity accumulation characteristic of spontaneous H mode (with £';^<0), and facilitating ash removal. Second, the proposed technique can render edge localized mode (ELM) [7] control feasible, via confinement control. Third, rf flow drive permits controlled, perturbative experiments on the L-* H transition and angular momentum transport. Finally, rf flow drive does not suffer from the limitations intrinsic to electrodedriven flows [8] or from the disadvantages of wallsputtering associated with flow drive by neutral-beam injection [9]. While rf flow drive is possible in a broad range of frequencies, we focus here on Alfven-wave flow drive. This frequency range of flow drive has inherent basic physics interest outside the realm of magnetic fusion. ...
The theory of radio frequency induced ion Bernstein wave- (IBW) driven shear flow in the edge is examined, with the goal of application of shear suppression of fluctuations. This work is motivated by the observed confinement improvement on IBW heated tokamaks [Phys. Fluids B 5, 241 (1993)], and by previous low-frequency work on RF-driven shear flows [Phys. Rev. Lett. 67, 1535 (1991)]. It is found that the poloidal shear flow is driven electrostatically by both Reynolds stress and a direct ion momentum source, analogous to the concepts of helicity injection and electron momentum input in current drive, respectively. Flow drive by the former does not necessarily require momentum input to the plasma to induce a shear flow. For IBW, the direct ion momentum can be represented by direct electron momentum input, and a charge separation induced stress that imparts little momentum to the plasma. The derived Er profile due to IBW predominantly points inward, with little possibility of direction change, unlike low-frequency Alfvénic RF drive. The profile scale is set by the edge density gradient and electron dissipation. Due to the electrostatic nature of ion Bernstein waves, the poloidal flow contribution dominates in Er. Finally, the necessary edge power absorbed for shear suppression on Princeton Beta Experiment-Modified (PBX-M) [9th Topical Conference on Radio Frequency Power in Plasmas, Charleston, SC, 1991 (American Institute of Physics, New York, 1991), p. 129] is estimated to be 100 kW distributed over 5 cm.
From extensive simulation of simple local fluid models of long wavelength drift wave turbulence in tokamaks, it is found that conventional notions concerning directions of cascades, locality and isotropy of spectral transfer, frequencies of fluctuations, and stationarity of saturation do not hold for moderate to long wavelengths (kps< 1). In particular, at long wavelengths, where spectral transfer of energy is dominated by the EX B nonlinearity, energy is carried to short scale (even in two dimensions) in a manner that is anisotropic and highly nonlocal (energy is efficiently passed between modes separated by the entire spectrum range in a correlation time). At short wavelengths, transfer is dominated by the polarization drift nonlinearity. While the standard dual cascade applies in this subrange, it is found that finite spectrum size can produce cascades that are reverse directed (Le., energy to high k) and are nonconservative in enstrophy and energy similarity ranges (but conservative overall). In regions where both nonlinearities are important, cross-coupling between the nonlinearities gives rise to large nonlinear frequency shifts which profoundly affect the dynamics of saturation by modifying the growth rate and nonlinear transfer rates. These modifications produce a nonstationary saturated state with large amplitude, long period relaxation oscillations in the energy, spectrum shape, and transport rates. Methods of observing these effects are presented.
As a model for the hot [βe(Ls/iLT)2 ≳1] turbulent tokamak edge, the nonlinear saturated state of the high-βe limit of microtearing turbulence is examined. This mode couples magnetic and electron temperature fluctuations. Using mixing length analysis and a variational calculation of the renormalized eigenmode equations, a magnetic fluctuation level and turbulent radial correlation length are derived. The resulting anomalous thermal diffusivity for auxiliary heating scales as T7/4e n−3/20 I−5/3p P 5/6H R7/3, where Te is the electron temperature, n0 is the density, Ip is the toroidal plasma current, PH is the heating power, and R is the major radius.
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