L. Villard

On the definition of a kinetic equilibrium in global gyrokinetic simulations

Nonlinear electrostatic global gyrokinetic simulations of collisionless ion temperature gradient (ITG) turbulence and ExB zonal flows in axisymmetric toroidal plasmas are examined for different choices of the initial distribution function. Using a local Maxwellian leads to the generation of axisymmetric ExB flows that can be so strong as to prevent ITG mode growth. A method using a canonical Maxwellian is shown to avoid this spurious generation of ExB flows. In addition, a revised delta f scheme is introduced and compared to the standard delta f method. (c) 2006 American Institute of Physics.

Global Linear Gyrokinetic Simulations in Quasi-Symmetric Configurations

First global linear study of electrostatic drift waves in two realistic quasisymmetric configurations, namely the Quasi-Axially symmetric Stellarator with three fields periods (QAS3) [P. Garabian and L. P. Ku, Phys. Plasma 6, 645 (1999)] and the Helically Symmetric eXperiment (HSX) [F. S. B. Anderson , Trans. Fusion Technol. 27, 273 (1995)], are presented. Effects of the shape of the plasma on the growth rate and frequency of the ion temperature gradient (ITG) driven mode are investigated by varying the quasi-symmetric configurations to an equivalent symmetric system. The calculations have been performed using a three-dimensional (3D) global gyrokinetic code in the magnetic configurations provided by the magnetohydrodynamic (MHD) equilibrium code VMEC [S. P. Hirshman and D. K. Lee, Comput. Phys. Commun. 39, 161 (1986)]. The plasma is modeled by gyrokinetic ions and adiabatic electrons. In QAS3, results are very close to those obtained for a tokamak. The drift waves are only slightly affected by the shape of the plasma or the local magnetic shear. On the other hand, results for the HSX configuration show a clear 3D effect, namely a strong toroidal variation of the drift wave mode structure. This variation is a clear structure of the 3D plasma shape. However, first results show that the growth rate of the ITG driven mode is largely unaffected by this effect

Global-gyrokinetic study of finite β effects on linear microinstabilities

Electromagnetic microinstabilities in tokamak plasmas are studied by means of a linear global eigenvalue numerical code. Ion dynamics is described by the gyrokinetic equation, so that finite ion Larmor radius effects are taken into account to all orders. Nonadiabatic electrons are included in the model, with passing particles described by the drift-kinetic equation and trapped particles through the bounce averaged drift-kinetic equation. A large aspect ratio plasma with circular shifted surfaces is considered for the numerical implementation. The effects of an electromagnetic perturbation on toroidal ion temperature gradient driven modes are studied, confirming the stabilization of these modes with increasing beta (parameter identifying the ratio of the plasma pressure to the magnetic pressure). The threshold for the destabilization of an electromagnetic mode, the so-called kinetic ballooning mode or Alfvenic ion temperature gradient mode is identified. Moreover, owing to the global formulation, the radial structure of these electromagnetic modes is observed for the first time. Finally, the contributions of trapped electron dynamics and the effects of the Shafranov shift are addressed

Effect of E×B flows on global linear ion temperature gradient modes

Strong electric fields generate an E×B rotation of the equilibrium plasma. Experiments have shown that this effect could lower the anomalous transport in tokamaks. The study of the effect of these flows on the linear stability of ion temperature gradient (ITG) modes has therefore been undertaken. The question is addressed solving the spectrum of the gyrokinetic equation in the full two-dimensional poloidal plane for a large aspect ratio tokamak with concentric circular magnetic surfaces. Results show a strong stabilizing effect of E×B flows on the ITG modes. Study with respect to different profiles of the flow shows that the so-called curvature of flow (second derivative) has no effect, while the intensity of flow itself produces the strongest effect. Study with respect to different magnetic shears did not allow the discovery of any particular behavior of the negative magnetic shear cases. Eventually, an experimental comparison was conducted.

A full radius gyrokinetic stability analysis for large aspect ratio finite-β tokamaks

Linear, fully gyrokinetic, full radius (global), large aspect ratio studies of Alfven-ion temperature gradient mode (AITG) or kinetic ballooning modes or beta-induced Alfven eigenmodes considering only “passing” species is presented. Effects hitherto completely neglected in a full radius approach such as B∥-fluctuations and the ones which have been treated partly [Phys. Plasmas 10, 1424 (2003)] such as Shafranov shifts are included. To this end, an existing code EM-GLOGYSTO has been upgraded to incorporate these effects. Among others, the most interesting results include: (i) For relatively large positive magnetic shear ŝ [1.25<ŝ<4.25, ŝ=du200alnu200aqs/du200alnu200aρ, where qs(ρ) is safety factor and ρ minor radius], B∥ fluctuations have a benign effect on AITG growth rates and for positive but small shear (0.0<ŝ<2.7), B∥ fluctuations are too weak to play any crucial role. (ii) In the later case, inclusion of Shafranov shift leads to the following: (a) Growth rates without Shafranov shift effects are in general larger t...

Stability of global drift-kinetic Alfven eigenmodes in DIII-D

Global Alfven eigenmodes are studied using two different models for the plasma and the results compared with the instability threshold measured experimentally. Fluid-resistive models predict that continuum damped toroidicity induced Alfven modes (TAE) are formed in the frequency range of the experimental instabilities, but using realistic values of the resistivity makes a stability analysis impossible for computational reasons. The kinetic plasma model solves this problem by taking into account the ion Larmor radius and the resonant Landau interactions between the particles and the wavefield. As a consequence drift-kinetic Alfven eigenmodes (DKAE) are created by toroidal coupling between the global TAE wavefield, the mode converted kinetic Alfven, ion-acoustic and drift waves. The power transfers between the wave and the particles show that the drift character of the wavefield in the core destabilizes DKAE modes through resonant interactions with the fast beam ions. The predicted beam pressure instability threshold is in agreement with the one measured experimentally

Radial electric fields and global electrostatic microinstabilities in tokamaks and stellarators

The effects of applied radial electric fields on the stability of ion temperature gradient (ITG) modes and trapped particle modes are investigated with a full radius gyrokinetic formulation in both axisymmetric and helically symmetric configurations. The validity of a simplified stabilization criterion often applied to experimental analysis (the shearing rate larger than the linear growth rate) is examined for various profiles of E×B flows using an expression for the shearing rate derived for arbitrary quasisymmetric geometries [T. S. Hahm, Phys. Plasmas 4, 4074 (1997)]. The results show that the criterion holds for profiles with finite shearing rate and for toroidal, helical, and slab-like ITG modes. However, it is not always applicable for trapped particle instabilities: a case is shown for which E×B flows are destabilizing. For profiles with zero shearing rate, another stabilizing mechanism is found for toroidal and helical ITG modes but not for slab-like modes.

Ion and Electron Dynamics in Nonlinear PIC Simulations

ITG and ETG turbulence is investigated with the nonlinear global PIC code ORB5. The large variety of numerical schemes and simulations domains used has sometimes lead to important discrepancies in the transport predictions. In order to discuss these disagreements, emphasis must be put on ways to check the numerical accuracy, such as energy conservation and numerical noise measurement. This paper therefore presents benchmarks, new algorithms and a noise diagnostic. After having demonstrated the numerical quality of our simulations, 2 topics are visited: the unclear role of the parallel nonlinearity and the transport level in ETG turbulence, for which predictions differing by one order of magnitude had been made elsewhere.

Applicability of the ballooning transform to trapped ion modes

In the scope of the study of low-frequency electrostatic microinstabilities in tokamak plasmas, attention has been focused on the effect of trapped ions. The ballooning transform has been applied to the gyrokinetic equation, for the case of a large aspect ratio plasma with circular magnetic surfaces. A new eigenvalue code has been developed to solve the resulting integral equation, for the case of adiabatic electrons and full ion dynamics, thus taking into account both circulating and trapped ions. The goal has been to assess the validity of the ballooning transform for trapped ion modes. A scan over the parameter k(theta)rho(L) has been carried out to determine a lower threshold for applicability of the ballooning representation. Illustrative results of trapped ion modes (TIM) are presented, together with the comparison with the ones obtained using a global gyrokinetic code, for low toroidal wave numbers, and a local kinetic dispersion relation

Turbulence and zonal flow structures in the core and L-mode pedestal of tokamak plasmas

Zonal flows (ZF) play a crucial role in regulating ion temperature gradient (ITG) turbulence. In previous global gyrokinetic simulations [1] using the ORB5 code with the adiabatic electron model, it was observed that long-lived ZF structures, leading to a corrugated transport and temperature gradient pattern, could develop in shaped tokamak plasmas much more than in circular shaped plasmas, resulting in reduced transport. These studies are extended to a hybrid electron model in which trapped electrons are kinetic while passing electrons are assumed to have a Boltzmann response for a case dominated by ITG modes. These confirm the results of the fully adiabatic electron model. Simulations done in x93gradient-drivenx94 mode, with a Krook-like relaxation towards a given profile, result in non-realistic corrugated heat source/sink profiles. However, after switching off completely the heat source/sink, it is shown that the ZF and transport corrugation remains. Thus the heat source corrugation is merely a consequence, not a cause, of the zonal structures and related radial transport pattern. Considering then core profiles with constant logarithmic gradients and pedestal profiles with linear gradients for L-mode plasmas, as in Ref.[2], we analyze how ITG transport and zonal structures react by independently varying the logarithmic gradients in the core and the linear gradients in the pedestal, using the adiabatic electron model. Results show the presence of large radial zones straddling the core-pedestal transition region. Avalanche-like events propagate over the radial zone at constant speed and repeat with a well defined frequency somewhat below the local geodesic acoustic mode (GAM) frequency. These avalanches are observed on the E × B ZFs, effective heat diffusivity and heat flux, thus a change of gradient in the core affects transport in the pedestal and vice versa. In spite of these non-local effects, attempt is made to characterize transport, and in particular its stiffness, quasi-locally. Global simulation results show that with increased input power the logarithmic gradient in the core is only slightly increased while the linear gradient in the pedestal is substantially enhanced.