Special Issue on L-H Transition Physics

This paper presents an overview of results from L–H transition experiments that were performed at ASDEX Upgrade (AUG) with the aim of identifying the underlying mechanisms leading to H-mode confinement. With a broad variety of experiments and new diagnostic techniques, as well as modeling efforts, AUG has contributed substantially to improving our understanding of the L–H transition over the past years. In this review, the important roles of the ion heat channel and the edge radial electric field (E_r) in the L–H transition physics are brought into context with known dependencies of the H-mode power threshold ($P_\mathrm{LH}$), such as the impact of wall material, magnetic perturbations, and the magnetic configuration. Furthermore, experimental and theoretical results obtained at AUG on the L-mode edge turbulence are connected to the mean-field E_r and its related shear flow. This led to a deeper understanding of the I-phase plasma regime, has resolved the so-called isotope effect of $P_\mathrm{LH}$, and led to the development of a semi-analytical model that can describe AUG's experimental observations of the L–H transition together with the L- and H-mode density limits.

The mean E $\times$ B shear in a stochastic magnetic field is calculated, using the radial force balance relation and transport equations. This analysis is relevant to the L → H transition with resonant magnetic perturbations, and special focus is placed upon the physics of non-ambipolar transport and radial current. The key physical process is the flow of fluctuating currents along wandering magnetic fields. The increments in poloidal and toroidal rotation, density and ion pressure are calculated. The radial envelope of the magnetic perturbations inside the plasma defines a new scale ${\ell _{{\text{env}}}}$, which is the characteristic scale of the magnetic fluctuation intensity profile. The net particle outflow due to stochastic magnetic fields is calculated and is determined by the net radial current through the separatrix. Implications for the L → H transition are discussed.

The understanding of the physics underlying the L-H transition has strong implications for ITER experimental reactor and demonstration power plant (DEMO). In many tokamaks, including JET, it has been observed that, at a particular plasma density, n_e,min, the power necessary to access H-mode P_L-H is minimum. In the present work, L-H transitions of JET deuterium plasmas heated by neutral beam injection (NBI) are studied for the first time by means of a power balance analysis to characterize the main contributions in the transition, through integrated transport modelling. In the pulses analysed, we do observe a minimum of the L-H power threshold in density, indicating the presence of density branches and of n_e,min. Electron and ion heat fluxes at the transition are estimated separately. The electron/ion equipartition power results in favour of the ions, as shown by QuaLiKiz quasilinear gyrokinetic simulations, which predict a larger ion transport that causes T_e > T_i. The resulting edge ion heat flux also shows a clear change of slope below n_e,min, similarly to ASDEX-Upgrade (AUG) NBI pulses (Ryter et al 2014 Nucl. Fusion 54 083003). JET NBI data are compared to radio-frequency heated AUG and Alcator C-mod pulses (Schmidtmayr et al 2018 Nucl. Fusion 58 056003), showing a different trend of the power, coupled to ions at the L-H transition with respect to the linearity observed in the radio-frequency heated plasmas. The presence of n_e,min and the role of the ion heat flux is discussed in the paper, although it seems it is not possible to explain the presence of a P_L-H minimum in density by a critical ion heat flux and by the equipartition power for the JET NBI-heated plasmas analysed.

In this paper, a phenomenology of competing behavior between the geodesic acoustic mode (GAM) and the limit-cycle oscillation (LCO) is presented. Before the LCO occurs, the GAM can grow to the observable amplitude via the turbulent Reynolds stress force. Approaching the L-H transition, the LCO is excited and the GAM decays. In the LCO phase, the GAM driving force is possibly suppressed by the nonlocal turbulence amplitude modulation by the LCO.

Edge shear layer collapse causes edge cooling and aggravates radiative effects. This paper details on the microscopic dynamics of the emergence of power (Q) scaling of density limit (DL) from the shear layer collapse transport bifurcation scenario. The analysis is based on a novel 4-field model, which evolves turbulence energy, zonal flow energy, temperature gradient and density, including the neoclassical screening of zonal flow response. Bifurcation analysis yields power scaling of critical density for shear layer collapse as $n_{crit}\sim Q^{1/3}$. The favorable Q scaling of the DL emerges from the fact that the shear layer strength increases with Q, thus preventing shear layer collapse. This in turn reduces particle transport and improves particle confinement. RMP induced ambient stochastic fields degrade the shear layer by inducing decoherence in the Reynolds stress. As a result the particle transport increases and particle confinement degrades. This leads to the emergence of unfavorable stochastic field intensity ($b_{st}^{2}$) scaling of the critical density as $n_{crit}\sim(1+b_{st}^{2})^{-5/3}$. All fields, including zonal flow shear, exhibit hysteresis when the power (Q) is ramped cyclically across the bifurcation point. The hysteresis is due to dynamical delay in bifurcation on account of critical slowing down. Thus, the dynamical hysteresis here is fundamentally different from the hysteresis associated with the existence of bi-stable states.

In this paper, we present an analysis of the conservation of currents in a full-F electromagnetic gyro-kinetic model in the long-wavelength limit. This equation corresponds to what is usually called the 'vorticity equation', which is not strictly correct as it cannot be formulated as the curl of a velocity equation. In the paper, we will therefore use the term 'current conservation equation' instead. Our results are relevant to reduced plasma descriptions like gyro-kinetic, drift-kinetic, gyro-fluid and drift-fluid models for tokamaks and stellarators. The equation describes the change of the polarization charge density (often called 'vorticity') in terms of the polarization stress due to the $\boldsymbol{E}\times\boldsymbol{B}\$ flow, external sources and three currents: the parallel current, the curvature current and a current related to the magnetic field fluctuations. We compare this equation with previous drift- and gyro-fluid equations and find general agreement, except in the vorticity source terms where previous drift-fluid models fail to capture the heating and density sources. We discuss the role of currents in the dynamics of diamagnetic and $\boldsymbol{E}\times\boldsymbol{B}\$ flow shear. The possible connection between these currents with phenomena observed in experiments that influence the radial electric field in the edge of tokamak plasmas, like resonant magnetic perturbations, and different magnetic field configurations and shapes, is presented.