Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is formally stable to small perturbations, but, given a large enough initial perturbation, it transitions to a turbulent state. A scenario for such a transition is proposed and supported by numerical results: close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Whereas this appears to represent a new scenario for transition to turbulence in tokamak plasmas, it is reminiscent of the behaviour of other subcritically turbulent systems, e.g. pipe flows and Keplerian magnetorotational accretion flows.Comment: 16 pages, 5 figures, accepted to Journal of Plasma Physic

Abstract. A procedure is presented to map from the spatial correlation parameters of a turbulent density field (the radial and binormal correlation lengths and wavenumbers, and the fluctuation amplitude) to correlation parameters that would be measured by a Beam Emission Spectroscopy (BES) diagnostic. The inverse mapping is also derived, which results in resolution criteria for recovering correct correlation parameters, depending on the spatial response of the instrument quantified in terms of Point-Spread Functions (PSFs). Thus, a procedure is presented that allows for a systematic comparison between theoretical predictions and experimental observations. This procedure is illustrated using the MAST BES system and the validity of the underlying assumptions is tested on fluctuating density fields generated by direct numerical simulations using the gyrokinetic code GS2. The measurement of the correlation time, by means of the cross-correlation time-delay (CCTD) method, is also investigated and is shown to be sensitive to the fluctuating radial component of velocity, as well as to small variations in the spatial properties of the PSFs.Keywords: Beam-emission spectroscopy, point-spread functions, synthetic diagnostics, plasma turbulence, plasma diagnostics, tokamaks. Inner Outer Figure 1. Example e −1 amplitude contours of PSFs [1] for five specific cases taken from MAST shots and described in Section 4.3. The dots mark the locations of the focal points of the detector channels. The characterisation of the PSFs is described in Section 4.2.

We investigate the effect of varying the ion temperature gradient (ITG) and toroidal equilibrium scale sheared flow on ion-scale turbulence in the outer core of MAST by means of local gyrokinetic simulations. We show that nonlinear simulations reproduce the experimental ion heat flux and that the experimentally measured values of the ITG and the flow shear lie close to the turbulence threshold. We demonstrate that the system is subcritical in the presence of flow shear, i.e., the system is formally stable to small perturbations, but transitions to a turbulent state given a large enough initial perturbation. We propose that the transition to subcritical turbulence occurs via an intermediate state dominated by low number of coherent long-lived structures, close to threshold, which increase in number as the system is taken away from the threshold into the more strongly turbulent regime, until they fill the domain and a more conventional turbulence emerges. We show that the properties of turbulence are effectively functions of the distance to threshold, as quantified by the ion heat flux. We make quantitative comparisons of correlation lengths, times, and amplitudes between our simulations and experimental measurements using the MAST BES diagnostic. We find reasonable agreement of the correlation properties, most notably of the correlation time, for which significant discrepancies were found in previous numerical studies of MAST turbulence. * ferdinand.vanwyk@physics.ox.ac.uk † highcock@chalmers.se ‡ alex.schekochihin@physics.ox.ac.uk arXiv:1704.02830v2 [physics.plasm-ph] 1 Aug 2017 2 V 0 dV B · ∇φ is the toroidal magnetic flux, V is the volume enclosed by the flux surface, B is the magnetic field, φ is the toroidal angle, and ψ tor,LCFS is the toroidal flux enclosed by the last closed flux surface [see figure 1(b)], ψ pol = (1/2π) 2 V 0 dV B · ∇θ is the poloidal magnetic flux, θ is the poloidal angle, and ψ pol,LCFS is the poloidal flux enclosed by the LCFS. 4 http://w3.pppl.gov/transp/ c , including two cases that match the experimental level of heat flux. This is a considerable improvement over previous nonlinear gyrokinetic simulations of this MAST discharge [51], which overpredicted τ SYNTH c by two orders of magnitude. Examining figure 24(d), we see that (δn i /n i ) SYNTH rms increases with increasing κ T or de-