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.

We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a localisation problem belonging to one of a set of non-standard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalisation transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width M is proportional to M 3 , and not exponential in M as with conventional algorithms. We show how the approach may be used to calculate for the RBIM: the free energy; typical correlation lengths in quasi-one dimension for both the spin and the disorder operators; even powers of spin-spin correlation functions and their disorder-averages. We examine in detail the square-lattice, nearest-neighbour ±J RBIM, in which bonds are independently antiferromagnetic with probability p, and ferromagnetic with probability 1 − p. Studying temperatures T ≥ 0.4J, we obtain precise coordinates in the p − T plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small p, and determine critical exponents at the multicritical point. i i+1 i+2 J (n,i) J (n+1,i) J (n,i+1) v J (n,i-1) J (n,i)

In the context of gyrokinetic flux-tube simulations of microturbulence in magnetized toroidal plasmas, different treatments of the magnetic equilibrium are examined. Considering the Cyclone DIII-D base case parameter set ͓Dimits et al., Phys. Plasmas 7, 969 ͑2000͔͒, significant differences in the linear growth rates, the linear and nonlinear critical temperature gradients, and the nonlinear ion heat diffusivities are observed between results obtained using either an s-␣ or a magnetohydrodynamic ͑MHD͒ equilibrium. Similar disagreements have been reported previously ͓Redd et al., Phys. Plasmas 6, 1162 ͑1999͔͒. In this paper it is shown that these differences result primarily from the approximation made in the standard implementation of the s-␣ model, in which the straight field line angle is identified to the poloidal angle, leading to inconsistencies of order ͑ = a / R is the inverse aspect ratio, a the minor radius and R the major radius͒. An equilibrium model with concentric, circular flux surfaces and a correct treatment of the straight field line angle gives results very close to those using a finite , low ␤ MHD equilibrium. Such detailed investigation of the equilibrium implementation is of particular interest when comparing flux tube and global codes. It is indeed shown here that previously reported agreements between local and global simulations in fact result from the order inconsistencies in the s-␣ model, coincidentally compensating finite ‫ء‬ effects in the global calculations, where ‫ء‬ = s / a with s the ion sound Larmor radius. True convergence between local and global simulations is finally obtained by correct treatment of the geometry in both cases, and considering the appropriate ‫ء‬ → 0 limit in the latter case.

We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green’s functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0.

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In the context of toroidal gyrokinetic simulations, it is shown that a hierarchy of damped modes is excited in the nonlinear turbulent state. These modes exist at the same spatial scales as the unstable eigenmodes that drive the turbulence. The larger amplitude subdominant modes are weakly damped and exhibit smooth, large-scale structure in velocity space and in the direction parallel to the magnetic field. Modes with increasingly fine-scale structure are excited to decreasing amplitudes. In aggregate, damped modes define a potent energy sink. This leads to an overlap of the spatial scales of energy injection and peak dissipation, a feature that is in contrast with more traditional turbulent systems.

The Eulerian gyrokinetic turbulence code GENE has recently been extended to a full torus code. Moreover, it now provides Krook-type sources for gradient-driven simulations where the profiles are maintained on average as well as localized heat sources for a flux-driven type of operation. Careful verification studies and benchmarks are performed successfully. This setup is applied to address three related transport issues concerning nonlocal effects. First, it is confirmed that in gradient-driven simulations, the local limit can be reproduced -provided that finite aspect ratio effects in the geometry are treated carefully. In this context, it also becomes clear that the profile widths (not the device width) may constitute a more appropriate measure for finite size effects. Second, the nature and role of heat flux avalanches are discussed in the framework of both local and global, flux-and gradient-driven simulations. Third, simulations dedicated to discharges with electron internal barriers are addressed.

The dominant source of anomalous transport in fusion plasmas on ion scales is turbulence driven by trapped electron modes (TEMs) and ion temperature gradient (ITG) modes. While the individual properties of each of these two instabilities and the corresponding microturbulence have been examined in detail in the past, the effects of a coexistence of the two modes and the phenomena of transitions between the TEM and ITG dominated regimes are not well studied. In many experimental situations, the temperature and density gradients support both microinstabilities simultaneously, so that transitional regimes are important for a detailed understanding of fusion plasmas. In this paper, this issue is addressed, using the gyrokinetic code GENE for a detailed investigation of the dominant and subdominant linear instabilities and the corresponding nonlinear system. A simple quasilinear model based on eigenvalue computations is presented which is shown to reproduce important features of the nonlinear TEM–ITG transition.