Federico David Halpern

Simulation of plasma turbulence in scrape-off layer conditions: the GBS code, simulation results and code validation

Based on the drift-reduced Braginskii equations, the Global Braginskii Solver, GBS, is able to model the scrape-off layer (SOL) plasma turbulence in terms of the interplay between the plasma outflow from the tokamak core, the turbulent transport, and the losses at the vessel. Model equations, the GBS numerical algorithm, and GBS simulation results are described. GBS has been first developed to model turbulence in basic plasma physics devices, such as linear and simple magnetized toroidal devices, which contain some of the main elements of SOL turbulence in a simplified setting. In this paper we summarize the findings obtained from the simulation carried out in these configurations and we report the first simulations of SOL turbulence. We also discuss the validation project that has been carried out together with the GBS development.

Boundary conditions for plasma fluid models at the magnetic presheath entrance

The proper boundary conditions at the magnetic presheath entrance for plasma fluid turbulence models based on the drift approximation are derived, focusing on a weakly collisional plasma sheath with Ti≪Te and a magnetic field oblique to a totally absorbing wall. First, the location of the magnetic presheath entrance is rigorously derived. Then boundary conditions at the magnetic presheath entrance are analytically deduced for v||i, v||e, n, ϕ, Te, and for the vorticity ω=∇⊥2ϕ. The effects of E × B and diamagnetic drifts on the boundary conditions are also investigated. Kinetic simulations are performed that confirm the analytical results. Finally, the new set of boundary conditions is implemented in a three-dimensional global fluid code for the simulation of plasma turbulence and, as an example, the results of a tokamak scrape-off layer simulation are discussed. The framework presented can be generalized to obtain boundary conditions at the magnetic presheath entrance in more complex scenarios.

Predictions of H-mode performance in ITER

Time-dependent integrated predictive modelling is carried out using the PTRANSP code to predict fusion power and parameters such as alpha particle density and pressure in ITER H-mode plasmas. Auxiliary heating by negative ion neutralbeaminjectionandion-cyclotronheatingofHe 3 minorityionsaremodelled,andtheGLF23transportmodelis used in the prediction of the evolution of plasma temperature profiles. Effects of beam steering, beam torque, plasma rotation, beam current drive, pedestal temperatures, sawtooth oscillations, magnetic diffusion and accumulation of He ash are treated self-consistently. Variations in assumptions associated with physics uncertainties for standard base-line DT H-mode plasmas (with Ip = 15MA, BTF = 5.3T and Greenwald fraction = 0.86) lead to a range of predictions for DT fusion power PDT and quasi-steady state fusion QDT (≡PDT/Paux). Typical predictions assuming Paux = 50‐53MW yield PDT = 250‐720MW and QDT = 5‐14. In some cases where Paux is ramped down or shut off after initial flat-top conditions, quasi-steady QDT can be considerably higher, even infinite. Adverse physics assumptions such as the existence of an inward pinch of the helium ash and an ash recycling coefficient approaching unity lead to very low values for PDT. Alternative scenarios with different heating and reduced performance regimes are also considered including plasmas with only H or D isotopes, DT plasmas with toroidal field reduced 10% or 20% and discharges with reduced beam voltage. In full-performance D-only discharges, tritium burn up is predicted to generate central tritium densities up to 10 16 m −3 and DT neutron rates up to 5 ×10 16 s −1 , compared with the DD neutron rates of 6 × 10 17 s −1 . Predictions with the toroidal field reduced 10% or 20% below the planned 5.3T and keeping the same q98, Greenwald fraction and βn indicate that the fusion yield PDT and QDT will be lower by about a factor of two (scaling as B 3.5 ).

Theory-based scaling of the SOL width in circular limited tokamak plasmas

A theory-based scaling for the characteristic length of a circular, limited tokamak scrape-off layer (SOL) is obtained by considering the balance between parallel losses and non-linearly saturated resistive ballooning mode turbulence driving anomalous perpendicular transport. The SOL size increases with plasma size, resistivity, and safety factor q. The scaling is verified against flux-driven non-linear turbulence simulations, which reveal good agreement within a wide range of dimensionless parameters, including parameters closely matching the TCV tokamak. An initial comparison of the theory against experimental data from several tokamaks also yields good agreement.

Turbulent regimes in the tokamak scrape-off layer

The non-linear turbulent regimes in the tokamak scrape-off layer (SOL) are identified according to the linear instability responsible for the perpendicular transport. Four regions of the SOL operational parameters are determined where turbulence is driven by the inertial or resistive branches of the ballooning mode or of drift waves. The analysis, based on the linear electrostatic drift-reduced Braginskii equations, evaluates the pressure scale length self-consistently from the balance between plasma losses at the vessel and perpendicular turbulent transport. The latter is estimated by assuming that turbulence saturation occurs due to a local flattening of the plasma gradients and associated removal of the linear instability drive; it is also shown that transport is led by the mode that maximizes the ratio of the linear growth to the poloidal wavenumber. The methodology used to identify the turbulent regimes is confirmed by the results of non-linear simulations of SOL turbulence. The identification of the turbulent regimes, the predicted pressure scale length, and the poloidal wavenumber of the leading mode are in reasonable agreement with non-linear simulation results.

Low-frequency linear-mode regimes in the tokamak scrape-off layer

Motivated by the wide range of physical parameters characterizing the scrape-off layer (SOL) of existing tokamaks, the regimes of low-frequency linear instabilities in the SOL are identified by numerical and analytical calculations based on the linear, drift-reduced Braginskii equations, with cold ions. The focus is put on ballooning modes and drift wave instabilities, i.e., their resistive, inertial, and ideal branches. A systematic study of each instability is performed, and the parameter space region where they dominate is identified. It is found that the drift waves dominate at high R/Ln, while the ballooning modes at low R/Ln; the relative influence of resistive and inertial effects is discussed. Electromagnetic effects suppress the drift waves and, when the threshold for ideal stability is overcome, the ideal ballooning mode develops. Our analysis is a first stage tool for the understanding of turbulence in the tokamak SOL, necessary to interpret the results of non-linear simulations.

Ideal ballooning modes in the tokamak scrape-off layer

A drift-reduced Braginskii fluid model is used to carry out a linear and non-linear study of ideal ballooning modes in the tokamak scrape-off layer. First, it is shown that the scrape-off layer finite connection length and boundary conditions modify the ideal stability limit with respect to the closed flux-surface result. Then, in a two-fluid description, it is found that magnetic induction effects can destabilize long wavelength resistive ballooning modes below marginal ideal stability. Non-linear simulations confirm a gradual transition from small scale quasi-electrostatic interchange turbulence to longer wavelength modes as the plasma beta is increased. The transition to global ideal ballooning modes occurs, roughly, at the linearly obtained stability threshold. The transport levels and the pressure gradient as a function of plasma beta obtained in non-linear simulations can be predicted using the non-linear flattening of the pressure profile from the linear modes as a turbulent saturation mechanism.

Predictive simulations of ITER including neutral beam driven toroidal rotation

Predictive simulations of ITER [R. Aymar et al., Plasma Phys. Control. Fusion 44, 519 (2002)], discharges are carried out for the 15MA high confinement mode (H-mode) scenario using PTRANSP, the predictive version of the TRANSP code. The thermal and toroidal momentum transport equations are evolved using turbulent and neoclassical transport models. A predictive model is used to compute the temperature and width of the H-mode pedestal. The ITER simulations are carried out for neutral beam injection (NBI) heated plasmas, for ion cyclotron resonant frequency (ICRF) heated plasmas, and for plasmas heated with a mix of NBI and ICRF. It is shown that neutral beam injection drives toroidal rotation that improves the confinement and fusion power production in ITER. The scaling of fusion power with respect to the input power and to the pedestal temperature is studied. It is observed that, in simulations carried out using the momentum transport diffusivity computed using the GLF23 model [R. Waltz et al., Phys. Plasm...

Theory of the scrape-off layer width in inner-wall limited tokamak plasmas

We develop a predictive theory applicable to the scrape-off layer (SOL) of inner-wall limited plasmas. Using the non-linear flattening of the pressure profile as a saturation mechanism for resistive ballooning modes, we are able to demonstrate and quantify the increase of the SOL width with plasma size, connection length, plasma β, and collisionality. Individual aspects of the theory, such as saturation physics, parallel dynamics, and system size scaling, are tested and verified using non-linear, 3D flux-driven SOL turbulence simulations. Altogether, very good agreement between theory and simulation is found.

The GBS code for tokamak scrape-off layer simulations

We describe a new version of GBS, a 3D global, flux-driven plasma turbulence code to simulate the turbulent dynamics in the tokamak scrape-off layer (SOL), superseding the code presented by Ricci et al. (2012) 14. The present work is driven by the objective of studying SOL turbulent dynamics in medium size tokamaks and beyond with a high-fidelity physics model. We emphasize an intertwining framework of improved physics models and the computational improvements that allow them. The model extensions include neutral atom physics, finite ion temperature, the addition of a closed field line region, and a non-Boussinesq treatment of the polarization drift. GBS has been completely refactored with the introduction of a 3-D Cartesian communicator and a scalable parallel multigrid solver. We report dramatically enhanced parallel scalability, with the possibility of treating electromagnetic fluctuations very efficiently. The method of manufactured solutions as a verification process has been carried out for this new code version, demonstrating the correct implementation of the physical model.