Zero-Turbulence Manifold in a Toroidal Plasma

Physics of Plasmas, 1997

In general, turbulent transport drives a plasma toward a state of turbulent equipartition, in which Lagrangian invariants are uniformly distributed. Different invariants decay with different rates, and in tokamaks the frozen-in law of particles in the poloidal magnetic field survives longer than the corresponding law for the toroidal field, assuming that the trapped particles dominate the turbulent transport. Therefore, the plasma profiles depend on the safety factor q(r), and the condition for convection of trapped particles is that the shear dq/dr is positive. There are two ways to suppress this convection and thereby enhance confinement. The first one is to reverse the magnetic shear. The energy of typical trapped particles then increases outward instead of inward, which suppresses instabilities. The second method is to eliminate the trapped ions by poloidal rotation, and thereby create a transport barrier.

Recent progress made with our global gyrokinetic simulations in understanding the origin of intrinsic rotation and non-diffusive transport characteristics in tokamaks is reported. Key results include the finding of an important nonlinear flow generation process due to the residual stress produced by the fluctuation intensity and the intensity gradient, acting with the zonal flow shear induced k symmetry breaking, which offers a universal mechanism to drive intrinsic rotation via wave-particle momentum exchange. This turbulence nonlinearly-driven intrinsic rotation scales close to linearly with plasma gradients and the inverse of the plasma current in various turbulence regimes, reproducing and extending empirical scalings obtained in multiple fusion devices. The underlying physics governing these characteristic dependences is elucidated. Particularly, the current scaling is found to result from the magnetic shear effect on k symmetry breaking. Highlighted results also include robust radial pinches in toroidal flow, heat and particles driven by CTEM turbulence, which emerge "in phase", and are shown to play remarkable roles in determining plasma transport. Particularly, the "flow pinch" phenomenon amazingly reproduces the experimental result of radially inward penetration of perturbed flows created by modulated beams in peripheral regions, and thus is highly illuminating. Finally, the ∇T e -driven CTEM turbulence in specific parameter regimes is found to generate remarkably large fluctuation structures via inverse energy cascades, which may have a natural connection to the generation of blobs in the edge.

Physics of Plasmas, 2009

Electrostatic drift wave turbulence in tokamak plasmas with reversed magnetic shear is studied using global gyrokinetic particle simulations. The linear eigenmode of the ion temperature gradient ͑ITG͒ instability exhibits a mode gap around the minimum safety factor ͑q min ͒ region, particularly when q min is an integer, due to the rarefaction of rational surfaces. The collisionless trapped electron mode ͑CTEM͒ instability is suppressed in the negative-shear region due to the reversal of the toroidal precessional drift of trapped electrons. However, after nonlinear saturation, the ITG gap is filled up by the turbulence spreading and the CTEM fluctuation propagates into the stable negative-shear region. The steady state turbulence occupies the whole volume without any identifiable gap or coherent structures of the heat conductivity, perturbed temperature, or zonal flows in the q min location or the reversed shear region. Our finding indicates that the electrostatic drift wave turbulence itself does not support either linear or nonlinear mechanism for the formation of internal transport barriers in the reversed magnetic shear when q min crossing an integer.

2010

We present recent results on turbulence measurements in TCV L-mode plasmas. It has been shown that the heat transport is reduced by a factor of two for a plasma at negative triangularity compared with a plasma at positive triangularity. This transport reduction is reflected in the reduction of the temperature fluctuation level, in the low frequency part of the spectrum (20-150 kHz), measured by correlation ECE in the outer equatorial plane. Moreover, the radial correlation length of the turbulence is typically reduced by a factor of two at negative triangularity compared with positive triangularity. Nonlinear gyrokinetic simulations predict that the TEM turbulence might be dominant for these TCV plasmas. The TEM induced transport is shown to decrease with decreasing triangularity and increasing collisionality. Both dependences are in fairly good agreement with experimental observations. We also report on an innovative divertor magnetic configuration: the snowflake (SF) divertor whose properties are expected to affect the local heat load to the divertor plates in particular during ELMs when compared with the classical single-null (SN) divertor. In L-mode plasmas, the intermittent particle and heat transport in the SOL is associated with the presence of "blobs" propagating in the radial direction. Intermittency is compared between SN and SF configurations by looking at the statistical properties of the ion saturation current J sat measured with Langmuir probes (LPs) in the LFS scrape-off layer. For ELMy H-mode SF plasmas, the time evolution of J sat during ELMs is estimated with LPs covering the strikepoints target zones.

Physics of Plasmas, 2005

The dynamical behavior of the global, two-fluid, electromagnetic model of a tokamak plasma is explored under conditions corresponding to the Rijnhuizen tokamak project ͓A. J. H. Donné, Plasma Phys. Rep. 20, 192 ͑1994͔͒ using the CUTIE code ͓A. Thyagaraja, Plasma Phys. Controlled Fusion 42, B255 ͑2000͔͒. Simulations of an off-axis electron-cyclotron-heated ͑350 kW͒ hydrogen discharge and a purely Ohmic one over several resistive evolution times ͑ res Ӎ 15− 20 ms͒ are described. The results illustrate profile-turbulence interactions and the spectral transfer processes implicated in the spontaneous generation and maintenance of mesoscale zonal flows and dynamo currents. Relaxation phenomena, including off-and on-axis sawteeth and periodically repeating edge ballooning instabilities mediated by these mechanisms, are presented. The CUTIE model reproduces many observed features of the experiment qualitatively and suggests that global electromagnetic simulations may play an essential role in understanding tokamak turbulence and transport.

Plasma Physics and Controlled Fusion, 1999

Spontaneous improvements of plasma confinement during auxiliary heating have been observed in many tokamaks when the q profile has been modified from its normal resistive equilibrium so that q > 1 and the magnetic shear is reduced or reversed in a region near the magnetic axis. The effects on the overall plasma confinement result from the formation in the plasma interior of transport barriers, regions where the thermal and particle transport coefficients are substantially reduced. These internal barriers are sometimes tied to unique magnetic surfaces, such as the surface where the shear reverses. The reduction in transport appears to result from the suppression of turbulence by sheared plasma flow, which has now been measured in TFTR. Extensions of the theory for turbulence suppression show that this underlying paradigm may also explain other regimes of improved core confinement. The excitement generated by these discoveries must be tempered by the realization that transport and stability to pressure-driven MHD instabilities are intimately linked in these plasmas through the bootstrap current and the effect of the resulting current profile on the transport. Thus the development of control tools and strategies is essential if these improved regimes of confinement are to be exploited to improve the prospects for fusion energy production.

Progress in understanding turbulence and related cross-field transport of fusion relevance is achieved in the simple magnetized plasmas of the TORPEX toroidal device, which provides an ideal test bed for code benchmarking and theory validation. In TORPEX (R = 1 m, a = 0.2 m), a small vertical magnetic field B z < 4 mT is superposed on a toroidal magnetic field B t < 100 mT, resulting in open helical magnetic field lines. Similarly to the Scrape-Off Layer of fusion devices, ∇B and magnetic field curvature are at play. Here, Hydrogen plasmas are produced by microwaves (2.45 GHz, P<10 kW) with electron temperatures ~5 eV and densities ~1x10 16 m -3 . Drift and interchange instabilities are observed and characterized in terms of dispersion relation, driving mechanisms and non-linear development into turbulence and blobs. Density fluctuations associated with driftinterchange waves exhibit universal statistical properties. Their probability density functions (PDFs) are best fitted by a Beta distribution, with a unique quadratic polynomial relation linking their skewness and flatness. At large vertical fields, PDFs with positive skewness are associated with blobs, which form from radially elongated structures that are sheared off by the ExB flow. These structures are in turn generated by interchange waves that increase in amplitude and extend radially following an increase of the radial pressure gradient. The transport of heat and particles associated with the interchange wave and the blobs is investigated, revealing that fundamentally different mechanisms are involved. Initial fluid simulations of the interchange-dominated regime show intermittent transport in the presence of plasma blobs.

Physical Review Letters, 2003

Effects of externally imposed and self-generated poloidal flows on turbulent transport in the edge region of a tokamak are investigated using 3D nonlinear global simulations of resistive pressuregradient-driven turbulence. Transport reduction is found to be due to synergetic changes in the fluctuation amplitude and in the dephasing of the fluctuations. A scaling of the fluctuation level and turbulent diffusivity with EB flow shear strength is deduced from these simulations. These scalings agree with recent experimental observations on edge biasing as well as with analytical models.

Brazilian Journal of Physics, 2014

Plasma turbulence at the edge of tokamaks is an issue of major importance in the study of the anomalous transport of particles and energy. Although the behavior of a turbulent plasma seems intractable, it turns out that many of its aspects can be described by low-dimensional nonintegrable dynamical models. In this paper, we consider a number of dynamical effects occurring in tokamak plasma edge-in particular the role of internal transport barriers. Furthermore, we present experimental results on turbulentdriven transport for two machines-the Brazilian TCABR tokamak and University of Texas' Helimak-that can be explained by those theoretical models. Dedicated to Professor Wendell Horton for his outstanding contributions to the nonlinear dynamics approach to plasma turbulence.

2022

In a previous work we provided the explicit form of the nonlinear PDEs, subjected to the appropriate boundary conditions, which have to be satisfied by transport coefficients for systems out of Onsager's region. Since the proposed PDEs are obtained without neglecting any term present in the balance equations (i.e., the mass, momentum, and energy balance equations), we propose