M. J. Pueschel

Characterizing electron temperature gradient turbulence via numerical simulation

Numerical simulations of electron temperature gradient (ETG) turbulence are presented that characterize the ETG fluctuation spectrum, establish limits to the validity of the adiabatic ion model often employed in studying ETG turbulence, and support the tentative conclusion that plasma-operating regimes exist in which ETG turbulence produces sufficient electron heat transport to be experimentally relevant. We resolve prior controversies regarding simulation techniques and convergence by benchmarking simulations of ETG turbulence from four microturbulence codes, demonstrating agreement on the electron heat flux, correlation functions, fluctuation intensity, and rms flow shear at fixed simulation cross section and resolution in the plane perpendicular to the magnetic field. Excellent convergence of both continuum and particle-in-cell codes with time step and velocity-space resolution is demonstrated, while numerical issues relating to perpendicular (to the magnetic field) simulation dimensions and resolution are discussed. A parameter scan in the magnetic shear, s, demonstrates that the adiabatic ion model is valid at small values of s (s < 0.4 for the parameters used in this scan) but breaks down at higher magnetic shear. A proper treatment employing gyrokinetic ions reveals a steady increase in the electron heat transport with increasing magnetic shear, reaching electron heat transport rates consistent with analyses of experimental tokamak discharges. (c) 2006 American Institute of Physics.

Gyrokinetic turbulence simulations at high plasma beta

Electromagnetic gyrokinetic turbulence simulations employing Cyclone Base Case parameters are presented for β values up to and beyond the kinetic ballooning threshold. The β scaling of the turbulent transport is found to be linked to a complex interplay of linear and nonlinear effects. Linear investigation of the kinetic ballooning mode is performed in detail, while nonlinearly, it is found to dominate the turbulence only in a fairly narrow range of β values just below the respective ideal limit. The magnetic transport scales like β2 and is well described by a Rechester–Rosenbluth-type ansatz.Electromagnetic gyrokinetic turbulence simulations employing Cyclone Base Case parameters are presented for β values up to and beyond the kinetic ballooning threshold. The β scaling of the turbulent transport is found to be linked to a complex interplay of linear and nonlinear effects. Linear investigation of the kinetic ballooning mode is performed in detail, while nonlinearly, it is found to dominate the turbulence only in a fairly narrow range of β values just below the respective ideal limit. The magnetic transport scales like β2 and is well described by a Rechester–Rosenbluth-type ansatz.

Nonlinear stabilization of tokamak microturbulence by fast ions.

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.

Transport properties of finite-β microturbulence

Via nonlinear gyrokinetic simulations, microturbulent transport is investigated for electromagnetic trapped electron mode (TEM) and ion temperature gradient (ITG) tokamak core turbulence with β up to and beyond the kinetic ballooning mode threshold. Deviations from linear expectations are explained by zonal flow activity in the TEM case. For the ITG scenario, β-induced changes are observed in the nonlinear critical gradient upshift—from a certain β, a strong increase is observed in the Dimits shift. Additionally, a Rechester–Rosenbluth-type model for magnetic transport is applied, and the amplitudes of magnetic field fluctuations are quantified for different types of turbulence.

The European turbulence code benchmarking effort: turbulence driven by thermal gradients in magnetically confined plasmas

A cross-comparison and verification of state-of-the-art European codes describing gradient-driven plasma turbulence in the core and edge regions of tokamaks, carried out within the EFDA Task Force on Integrated Tokamak Modelling, is presented. In the case of core ion temperature gradient (ITG) driven turbulence with adiabatic electrons (neglecting trapped particles), good/reasonable agreement is found between various gyrokinetic/gyrofluid codes. The main physical reasons for some deviations observed in nonlocal simulations are discussed. The edge simulations agree very well on collisionality scaling and acceptably well on beta scaling (below the MHD boundary) for cold-ion cases, also in terms of the non-linear mode structure.

On the role of numerical dissipation in gyrokinetic Vlasov simulations of plasma microturbulence

Abstract Non-physical effects of discretization schemes on simulations of plasma microturbulence are investigated, and different types of hyperdiffusion terms in the gyrokinetic Vlasov equation are employed to cancel or mitigate these effects. Widely applicable rules on how to operate parallel spatial and velocity space diffusion – to avoid numerically excited high- k ∥ modes and recurrence phenomena, respectively – are presented. The impact of diffusion terms on and the applicability of these findings to results obtained in the context of a benchmark scenario are demonstrated.

Magnetic stochasticity and transport due to nonlinearly excited subdominant microtearing modes

Subdominant, linearly stable microtearing modes are identified as the main mechanism for the development of magnetic stochasticity and transport in gyrokinetic simulations of electromagnetic ion temperature gradient driven plasma microturbulence. The linear eigenmode spectrum is examined in order to identify and characterize modes with tearing parity. Connections are demonstrated between microtearing modes and the nonlinear fluctuations that are responsible for the magnetic stochasticity and electromagnetic transport, and nonlinear coupling with zonal modes is identified as the salient nonlinear excitation mechanism. A simple model is presented, which relates the electromagnetic transport to the electrostatic transport. These results may provide a paradigm for the mechanisms responsible for electromagnetic stochasticity and transport, which can be examined in a broader range of scenarios and parameter regimes.

Ion temperature profile stiffness: non-linear gyrokinetic simulations and comparison with experiment

Recent experimental observations at JET show evidence of reduced ion temperature profile stiffness. An extensive set of nonlinear gyrokinetic simulations are performed based on the experimental discharges, investigating the physical mechanism behind the observations. The impact on the ion heat flux of various parameters that differ within the data-set are explored. These parameters include the safety factor, magnetic shear, toroidal flow shear, effect of rotation on the magnetohydrodynamic equilibrium, R/L-n, beta(e), Z(eff), T-e/T-i, and the fast-particle content. While previously hypothesized to be an important factor in the stiffness reduction, the combined effect of toroidal flow shear and low magnetic shear is not predicted by the simulations to lead to a significant reduction in ion heat flux, due both to an insufficient magnitude of flow shear and significant parallel velocity gradient destabilization. It is however found that nonlinear electromagnetic effects due to both thermal and fast-particle pressure gradients, even at low beta(e), can significantly reduce the ion heat flux, and is a key factor in explaining the experimental observations. A total of four discharges are examined, at both inner and outer radii. For all cases studied, the simulated and experimental ion heat flux values agree within reasonable variations of input parameters around the experimental uncertainties.

Gyrokinetic simulations of magnetic reconnection

Fast magnetic reconnection, believed to be a mechanism for rearranging the magnetic topology and creating energetic particles in many astrophysical and laboratory plasmas, is investigated with the nonlinear gyrokinetic code Gene. After some code-code benchmarking, extensive linear studies are presented, covering all relevant parameter dependencies of two-dimensional slab reconnection. The results are used to ascertain the validity of a fluid model and understand for which parameters it fails to describe the physics correctly. The nonlinear phase is studied for two scenarios: decaying and driven turbulence. In the former case, the initially injected energy is cascading towards the largest scales of the system, whereas a fully turbulent, quasi-stationary state develops if the system is driven through a Krook-type term in the gyrokinetic Vlasov equation.

On secondary and tertiary instability in electromagnetic plasma microturbulence

Zonal flows, widely accepted to be the secondary instability process leading to the nonlinear saturation of ion temperature gradient modes, are shown to grow at higher rates relative to the linear mode amplitude as the plasma pressure β is increased—thus, confirming that zonal flows become increasingly important in the turbulent dynamics at higher β. At the next level of nonlinear excitation, radial corrugations of the distribution function (zonal flow, zonal density, and zonal temperature) are demonstrated to modify linear growth rates moderately through perturbed-field, self-consistent gradients: on smaller scales, growth rates are reduced below the linear rate. In particular, excitation of kinetic ballooning modes well below their usual threshold is not to be expected under normal conditions. These findings strengthen the theory of the non-zonal transition [M. J. Pueschel et al., Phys. Rev. Lett. 110, 155005 (2013)].