We derive explicit local transport relations for the global gyrokinetic formalism at arbitrary wavelength. This is an extension of the analysis in Scott et. al. 2010 where this was examined in the long-wavelength limit. Deriving a local expression for the fluxes requires that the gyroaveraging operator is symmetric, so that if point B is on the gyroring around A, point A is on the gyroring around B, for the same value of the magnetic moment. An algorithm for constructing a symmetric gyroring in a global code is described. Finally, using a simple 2D gyrokinetic code, we demonstrate the application of the momentum transport relation in a model problem with the full gyroaveraging operator without any long-wavelength approximation.
In the tokamak scrape-off layer (SOL) the magnetic field lines are open, channeling particles and heat onto plasma facing components, and constraining their lifetime. This is a critical issue for ITER and future devices -- safe operation of fusion devices will require a better understanding of the SOL plasma dynamics \cite{Loarte2007}. The steady-state heat load onto the tokamak plasma facing components depends on the SOL width, which results from a balance between plasma injection from the core region, turbulent transport, and losses to the divertor or limiter. Recently, we have gained deep insights into the tokamak SOL dynamics in the inner-wall limited configuration (like the ITER start-up plasmas), by means of massively-parallel fluid electromagnetic turbulence simulations. SOL turbulence, in fact, is characterized by the presence of large amplitude meso-scale turbulence, which requires the use of a global, flux-driven approach. In order to address this turbulent system, we have developed GBS, a flux-driven global turbulence code implementing the drift-reduced Braginskii equations. Our investigations have pointed out, among the others, the mechanisms regulating the turbulence level and therefore the SOL width, the turbulent regimes, and the mechanisms driving the rotation in this region. GBS simulations at realistic size and plasma parameters display features normally observed in the SOL of limited discharges, for instance, low frequency drift-wave or ballooning turbulence, fluctuations with an amplitude of the order of 30 percent and a poloidal width of about 10 ion sound larmor radii. Moreover, we have recovered strongly skewed fluctuation PDFs revealing the presence of intermittent transport events. In the present talk, we address, in particular, (a) the mechanisms establishing the SOL width, which regulates the steady-state heat load and (b) the physics of coherent filamentary plasma structures (blobs) that can travel across the SOL carrying heat and particles. The simulated non-linear dynamics have been compared with analytical estimates, that have highlighted the key physics mechanisms at play in the SOL, and with experimental measurements taken in a number of tokamak worldwide, showing good agreement.
The impact of plasma shaping on tokamak scrape-off layer (SOL) turbulence is investigated. The drift-reduced Braginskii equations are written for arbitrary magnetic geometries, and an analytical equilibrium model is used to introduce the dependence of turbulence equations on tokamak inverse aspect ratio (), Shafranov's shift (Δ), elongation (κ), and triangularity (δ). A linear study of plasma shaping effects on the growth rate of resistive ballooning modes (RBMs) and resistive drift waves (RDWs) reveals that RBMs are strongly stabilized by elongation and negative triangularity, while RDWs are only slightly stabilized in non-circular magnetic geometries. Assuming that the linear instabilities saturate due to nonlinear local flattening of the plasma gradient, the equilibrium gradient pressure length in the SOL is numerically computed and its dependence on , Δ, κ, and δ is analyzed, showing that stabilization of RBMs results in shorter Lp. An analytical estimate of Lp in the infinit aspect ratio limit and neglecting the Shafranov's shift is also derived. Nonlinear SOL turbulence simulations with non-circular magnetic geometries are carried out using the global, three-dimensional, flux-driven fluid code GBS (Ricci et al 2012 Plasma Phys. Control. Fusion 54 124047) and the results are compared with the findings obtained from the linear analysis of the SOL instabilities, showing good quantitative agreement.
In the tokamak scrape-off layer (SOL) the magnetic field lines are open, channeling particles and heat onto plasma facing components, and constraining their lifetime. Therefore, safe operation of future fusion reactors requires an understanding of SOL plasma dynamics. Recently, we have gained deep insights into the tokamak SOL dynamics by means of massively-parallel fluid electromagnetic turbulence simulations carried out with the Global Braginskii Solver (GBS) code. GBS is currently capable of performing full-size SOL simulations of medium-size tokamaks such as TCV or Alcator C-Mod. In the present paper, we emphasize recent numerical developments aimed towards (a) more realistic description of the plasma geometry and (b) simulating larger, reactor-class machines. First, we address the numerical implementation of parallel advection and diffusion operators in finite difference representation. This is a crucial aspect of our computation, as the cost of the simulation can be drastically reduced if the parallel dynamics are discretized adequately taking advantage of the strong anisotropy of the turbulent modes that are aligned to the magnetic field lines. Second, we address the development and implementation of a matrix-free, parallel multigrid solver for the Poisson operator in the vorticity equation. Using this new solver, it is now possible to further parallelize GBS without breaking parallel scalability, an important step towards the realm of 10^4 CPUs. Finally, we summarize the understanding of SOL turbulence obtained through GBS simulations - for instance, the mechanisms regulating the turbulence level and therefore the SOL width, the turbulent regimes, and the mechanisms driving plasma rotation in this region. The simulated non-linear dynamics have been compared with analytical estimates, which have highlighted the key physics mechanisms at play in the SOL, and with experimental measurements taken in a number of tokamak worldwide, showing good agreement.
The influence of plasma size on global ion temperature gradient turbulence is studied with the full- f Eulerian code GT5D (Idomura et al 2009 Nucl. Fusion 49 065029 ). The gyrokinetic model includes a consistent neoclassical electric field as well as a fixed-power source operator, enabling long-time simulations with self-consistent turbulent transport and equilibrium profiles. The effects of plasma size (from ρ * = 1/100 to ρ * = 1/225) are studied by scaling the minor radius a and the input power. For the first time, worse-than-Bohm scaling is observed under experimentally realistic conditions. For all plasma sizes, avalanches propagate over significant radii but their propagation depends on the radial electric shear. It is found that this quantity does not scale with ρ * due to the building up of intrinsic momentum. Such a dependence can be inferred from a force balance relation, which remains approximately valid in nonlinear simulations. An adaptive parallel momentum source has been implemented in GT5D to damp the parallel momentum profile. The new scan then reveals that the radial electric shear scales with ρ * while the transport is globally higher. These simulations therefore suggest that intrinsic momentum reduces heat transport. This work also addresses another important issue in gyrokinetics: it is shown that for fixed initial physical parameters the turbulent quasi-steady-state is statistically independent of the initial conditions.
Global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence in an ideal MHD ITER equilibrium plasma are performed with the ORB5 code. The noise control and field-aligned Fourier filtering procedures implemented in ORB5 are essential in obtaining numerically healthy results with a reasonable amount of computational effort: typical simulations require 109 grid points, 109 particles and, despite a particle per cell ratio of unity, achieve a signal to noise ratio larger than 50. As compared with a circular concentric configuration with otherwise similar parameters (same ρ* = 1/720), the effective heat diffusivity is considerably reduced for the ITER MHD equilibrium. A self-organized radial structure appears, with long-lived zonal flows (ZF), modulating turbulence heat transport and resulting in a corrugated temperature gradient profile. The ratio of long-lived ZF to the fluctuating ZF is markedly higher for the ITER MHD equilibrium as compared with circular configurations, thereby producing a more effective ITG turbulence suppression, in spite of a higher linear growth rate. As a result, the nonlinear critical temperature gradient, R/LTcrit,NL, is about twice the linear critical temperature gradient, R/LTcrit,lin. Moreover, the heat transport stiffness above the nonlinear threshold is considerably reduced as compared with circular cases. Plasma elongation is probably one of the essential causes of this behaviour: indeed, undamped ZF residual levels and geodesic acoustic mode damping are both increasing with elongation. Other possible causes of the difference, such as magnetic shear profile effects, are also investigated.
Reference EPFL-CONF-169387 URL: http://www-pub.iaea.org/MTCD/Meetings/Announcements.asp?ConfID=38091 URL: http://crpplocal.epfl.ch/pinboard/papers/107801912.pdf Record created on 2011-10-14, modified on 2017-05-12
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