The understanding and prediction of transport due to plasma microturbulence is a key open problem in modern plasma physics, and a Grand Challenge for fusion energy research. Ab initio simulations of such small-scale, low-frequency turbulence are to be based on the gyrokinetic equations, a set of nonlinear integro-differential equations in reduced (five-dimensional) phase space. In the present paper, the extension of the well-established and widely used gyrokinetic code Gene [F. Jenko et al., Phys. Plasmas 7, 1904] from a radially local to a radially global (nonlocal) version is described. The necessary modifications of both the basic equations and the employed numerical methods are detailed, including, e.g., the change from spectral methods to finite difference and interpolation techniques in the radial direction and the implementation of sources and sinks. In addition, code verification studies and benchmarks are presented.

Nonlinear electromagnetic stabilization by suprathermal pressure gradients found in specific regimes is shown to be a key factor in reducing tokamak microturbulence, augmenting significantly the thermal pressure electromagnetic stabilization. Based on nonlinear gyrokinetic simulations investigating a set of ion heat transport experiments on the JET tokamak, described by Mantica et al. [Phys. Rev. Lett. 107, 135004 (2011)], this result explains the experimentally observed ion heat flux and stiffness reduction. These findings are expected to improve the extrapolation of advanced tokamak scenarios to reactor relevant regimes.

Gyrokinetic simulations identify microtearing modes (MTM) to be the dominant microinstabilities in the JET-ILW (ITER like wall) pedestal. Nonlinear simulations show that MTM-driven turbulence produces the bulk of the transport in the steep gradient region, demonstrating that MTM may be the principal mechanism limiting JET-ILW pedestal evolution. The combination of MTM, electron temperature gradient (ETG), and neoclassical transport reproduces experimental power balance across most of the pedestal. Kinetic ballooning modes are significant only in the local limit and only at low β, far below the experimental operating point. PACS numbers:The tokamak H-mode [1] is defined by a narrow insulating region-the pedestal-at the plasma edge, where turbulence is suppressed and sharp pressure gradients develop. The pedestal is at the center of the most pressing issues facing fusion energy. ITER, for example, must reach a sufficient temperature at the pedestal's inner boundary in order to achieve its fusion power targets [2]. This work reports the results of, perhaps, the very first, first-principles simulations of the H-mode pedestal dynamics that reproduce experimentally observed transport levels. In addition to providing unprecedented insight into the dynamics of the existing H-mode pedestals, such simulations are likely to advance our capabilities towards predictive modeling of future burning plasma devices.This study targets the JET-ILW (ITER-like wall) pedestal [4][5][6], which approaches ITER conditions in two important ways: 1) as the largest tokamak in operation, it most-closely approximates plasma parameters that are dependent on machine size (like ρ * , the ratio of the gyroradius to minor radius), 2) to approximate ITER conditions even better, JET has recently installed an ITERlike wall (ILW) (composed of a tungsten divertor and beryllium chamber). This modification decreases the global performance of discharges by 20-30%, attributable largely to changes in pedestal structure. In addition to the performance loss, certain observed key properties of the ILW pedestal are inconsistent with predictions of the leading pedestal model (EPED [7,8]).In this work, we elucidate possible mechanisms limiting profile evolution in the JET-ILW discharges. We demonstrate, through simulations using the gyrokinetic code Gene [9,10], that the microtearing mode (MTM) [11][12][13][14] is the dominant instability in the pedestal. Interestingly, the simulations do not find the kinetic ballooning mode (KBM), a basic component of the EPED model, except locally in a narrow region near the separatrix. Most importantly, we determine via nonlinear gyrokinetic simulations that a combination of MTM and electron temperature gradient (ETG) [9,[15][16][17][18] driven turbulence plus the neoclassical flux, produces transport levels closely matching experimental power balance across most of the pedestal, demonstrating the capacity of these mechanisms to limit JET-ILW pedestal evolution.The JET-ILW Pedestal-JET pulse 82585 (described in Ref. [4]) is pa...

The impact of electromagnetic stabilization and flow shear stabilization on ITG turbulence is investigated. Analysis of a low-β JET L-mode discharge illustrates the relation between ITG stabilization, and proximity to the electromagnetic instability threshold. This threshold is reduced by suprathermal pressure gradients, highlighting the effectiveness of fast ions in ITG stabilization. Extensive linear and nonlinear gyrokinetic simulations are then carried out for the high-β JET hybrid discharge 75225, at two separate locations at inner and outer radii. It is found that at the inner radius, nonlinear electromagnetic stabilization is dominant, and is critical for achieving simulated heat fluxes in agreement with the experiment. The enhancement of this effect by suprathermal pressure also remains significant. It is also found that flow shear stabilization is not effective at the inner radii. However, at outer radii the situation is reversed. Electromagnetic stabilization is negligible while the flow shear stabilization is significant. These results constitute the high-β generalization of comparable observations found at low-β at JET. This is encouraging for the extrapolation of electromagnetic ITG stabilization to future devices. An estimation of the impact of this effect on the ITER hybrid scenario leads to a 20% fusion power improvement.

Nonlinear energy transfer and dissipation in Alfvén wave turbulence are analyzed in the first gyrokinetic simulation spanning all scales from the tail of the MHD range to the electron gyroradius scale. For typical solar wind parameters at 1 AU, about 30% of the nonlinear energy transfer close to the electron gyroradius scale is mediated by modes in the tail of the MHD cascade. Collisional dissipation occurs across the entire kinetic range k ⊥ ρi 1. Both mechanisms thus act on multiple coupled scales, which have to be retained for a comprehensive picture of the dissipation range in Alfvénic turbulence.Introduction. Spacecraft measurements find a radial temperature profile of the solar wind which can only be explained by the presence of heating throughout the heliosphere [1]. The key mechanism of heating in the inner heliosphere up to ∼20 AU is thought to be the dissipation of turbulent fluctuation energy, and its understanding and description is one of the outstanding open issues in space physics [2]. Over the past decade, numerous studies, both observational [3][4][5][6][7] and theoretical/computational [8][9][10][11][12][13][14], have focused on this topic, extracting ever more sophisticated measurements of solar wind fluctuation properties, and accomplishing increasingly detailed turbulence simulations.As the solar wind plasma is only weakly collisional, a variety of kinetic effects such as cyclotron damping, Landau and transit time damping, finite Larmor radius effects, stochastic heating, or particle acceleration at reconnection sites can contribute to the conversion of field energy to particle energy, and thus determine how collisional dissipation will ultimately set in. A kinetic description is crucial in order to judge the relative importance of each of those effects. Due to the complexity of a nonlinear kinetic system, numerical simulations are essential to interpret observations and provide guidance for analytical theory.In the present Letter, we employ an approach based on gyrokinetic (GK) theory [15], which is a rigorous limit of kinetic theory in strongly magnetized plasmas. Due to the assumptions of low frequencies (compared to the ion cyclotron frequency) and small fluctuation levels, the gyrokinetic model excludes cyclotron resonances and stochastic heating. In absence of these effects, we focus on the energetic properties of kinetic Alfvén wave (KAW)

Turbulence is widely expected to limit the confinement, and thus the overall performance, of modern neoclassically-optimized stellarators. We employ novel petaflop-scale gyrokinetic simulations to predict the distribution of turbulence fluctuations and the related transport scaling on entire stellarator magnetic surfaces, and reveal striking differences to tokamaks. Using a stochastic global-search optimization method, we derive the first turbulence-optimized stellarator configuration stemming from an existing quasi-omnigenous design.Throughout the history of magnetic fusion, a recurrent theme has been the surprising sensitivity of plasma performance to the details of the magnetic field. For instance, it has long been known that the confinement of alpha particles can be spoiled by small ripples in the magnetic field. More recently, magnetic perturbations have been found to dramatically influence instabilities of the plasma edge [1]. In both stellarators and tokamaks, experiments show that the level of turbulence may be reduced by modifying the magnetic field. As notable examples, the confinement time in the TCV tokamak is doubled by reversing the triangularity of the poloidal cross section of the flux surfaces [2], and in the LHD stellarator the turbulent transport can be reduced significantly by adjusting the coil currents so as to shrink the circumference of the torus by pushing it radially inwards [3].Stellarators typically possess 40-50 degrees of freedom in the shaping of the magnetic field, an order of magnitude more than for tokamaks [4]. This enhanced flexibility can be used to optimize various plasma properties [5], and the latest demonstration of the power of such optimization is expected to be realized in the superconducting stellarator experiment Wendelstein 7-X (W7-X), in Greifswald, Germany [6]. A tantalizing possibility for fusion researchers is to try to exploit any leeway in the magnetic geometry to design configurations with better confinement. In W7-X, this has already been done for the collisional (so-called "neoclassical") transport, but no device built so far is optimized with respect to turbulence.In order to understand how energy transport depends on the magnetic-field geometry, it is helpful to numerically simulate the turbulence in a large portion of the plasma. In tokamaks, thanks to axisymmetry, restricting the computational domain to a "flux tube", a slender volume encompassing a magnetic-field line [7], suffices to calculate the transport at a radial location. In a stellarator, however, different flux tubes on a magnetic surface are not geometrically equivalent, thus it appears necessary to simulate the entire magnetic surface. Much has been learned from the flux-tube approach which, except for inspiring efforts [8], has characterized stellarator turbulence simulations to date [9][10][11][12] . Nevertheless, all these simulations have a major inherent drawback: the transport cannot be reliably determined, as the turbulence strength generally varies between different flux tubes on th...

First global gyrokinetic simulations of microtearing instabilities in ASDEX Upgrade geometry provide increasing evidence for the existence of these modes in standard tokamaks. It is found that even in only moderately large devices, nonlocal effects like profile shearing are negligible, supporting the use of an efficient flux-tube approach. Nonlinear gyrokinetic simulations show that the resulting level of magnetic electron heat flux can be experimentally relevant.

Tokamak scenario development requires understanding of the properties that determine the kinetic profiles in non-steady plasma phases, and of self-consistent evolution of the magnetic equilibrium. Current ramps are of particular interest since many transport-relevant parameters explore a large range of values and their impact on transport mechanisms has to be assessed. To this purpose a novel full-discharge modeling tool has been developed, which couples the transport code ASTRA [1] and the free boundary equilibrium code SPIDER [2], utilizing a specifically designed coupling scheme. The current ramp-up phase can be accurately and reliably simulated using this scheme, where a plasma shape, position, and current controller is applied, which mimics the one of ASDEX Upgrade. Transport of energy is provided by theory-based models (e.g. TGLF [3]). A recipe based on edge-relevant parameters [4] is proposed to resolve the low current phase of the current ramps, where the impact of the safety factor on microinstabilities could make quasi-linear approaches questionable in the plasma outer region. Current ramp scenarios, selected from ASDEX Upgrade discharges, are then simulated to validate both the coupling with the free-boundary evolution and the prediction of profiles. Analysis of the underlying transport mechanisms is presented, to clarify the possible physics origin of the observed L-mode empirical energy confinement scaling. The role of toroidal micro-instabilities (ITG, TEM) and of non-linear effects is discussed.