Energy dynamics in a simulation of LAPD turbulence

Energy dynamics calculations in a 3D fluid simulation of drift wave turbulence in the linear Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] illuminate processes that drive and dissipate the turbulence. These calculations reveal that a nonlinear instability dominates the injection of energy into the turbulence by overtaking the linear drift wave instability that dominates when fluctuations about the equilibrium are small. The nonlinear instability drives flute-like ($k_\parallel = 0$) density fluctuations using free energy from the background density gradient. Through nonlinear axial wavenumber transfer to $k_\parallel \ne 0$ fluctuations, the nonlinear instability accesses the adiabatic response, which provides the requisite energy transfer channel from density to potential fluctuations as well as the phase shift that causes instability. The turbulence characteristics in the simulations agree remarkably well with experiment. When the nonlinear instability is artificially removed from the system through suppressing $k_\parallel=0$ modes, the turbulence develops a coherent frequency spectrum which is inconsistent with experimental data

Intrinsic suppression of turbulence in linear plasma devices

Plasma turbulence is the dominant transport mechanism for heat and particles in magnetized plasmas in linear devices and tokamaks, so the study of turbulence is important in limiting and controlling this transport. Linear devices provide an axial magnetic field that serves to confine a plasma in cylindrical geometry as it travels along the magnetic field from the source to the strike point. Due to perpendicular transport, the plasma density and temperature have a roughly Gaussian radial profile with gradients that drive instabilities, such as resistive drift-waves and Kelvin-Helmholtz. If unstable, these instabilities cause perturbations to grow resulting in saturated turbulence, increasing the cross-field transport of heat and particles. When the plasma emerges from the source, there is a time, τk, that describes the lifetime of the plasma based on parallel velocity and length of the device. As the plasma moves down the device, it also moves azimuthally according to E × B and diamagnetic velocities. There is a balance point in these parallel and perpendicular times that sets the stabilisation threshold. We simulate plasmas with a variety of parallel lengths and magnetic fields to vary the parallel and perpendicular lifetimes, respectively, and find that there is a clear correlation between the saturated RMS density perturbation level and the balance between these lifetimes. The threshold of marginal stability is seen to exist where τk ≈ 11τ⊥. This is also associated with the product τkγ∗, where γ∗ is the drift-wave linear growth rate, indicating that the instability must exist for roughly 100 times the growth time for the instability to enter the non-linear growth phase. We explore the root of this correlation and the implications for linear device design

Verification of BOUT++ by the method of manufactured solutions

BOUT++ is a software package designed for solving plasma fluid models. It has been used to simulate a wide range of plasma phenomena ranging from linear stability analysis to 3D plasma turbulence and is capable of simulating a wide range of drift-reduced plasma fluid and gyro-fluid models. A verification exercise has been performed as part of a EUROfusion Enabling Research project, to rigorously test the correctness of the algorithms implemented in BOUT++, by testing order-of-accuracy convergence rates using the Method of Manufactured Solutions (MMS). We present tests of individual components including time-integration and advection schemes, non-orthogonal toroidal field-aligned coordinate systems and the shifted metric procedure which is used to handle highly sheared grids. The flux coordinate independent approach to differencing along magnetic field-lines has been implemented in BOUT++ and is here verified using the MMS in a sheared slab configuration. Finally, we show tests of three complete models: 2-field Hasegawa-Wakatani in 2D slab, 3-field reduced magnetohydrodynamics (MHD) in 3D field-aligned toroidal coordinates, and 5-field reduced MHD in slab geometry

SOLPS-ITER predictive simulations of the impact of ion-molecule elastic collisions on strongly detached MAST-U Super-X divertor conditions

The role of ion-molecule ( D+ − D2 ) elastic collisions in strongly detached divertor conditions has been studied in the MAST-U Super-X configuration using SOLPS-ITER. Two strongly detached steady state solutions were compared, one obtained through a main-ion fuelling scan and the other through a nitrogen seeding scan at fixed fuelling rate. A significant difference in the electron-ion recombination (EIR) levels was observed; significant EIR in strongly detached conditions in the fuelling scan and negligible EIR throughout the seeding scan. This is partly because the fuelling scan achieves electron temperatures ( Te ) as low as 0.2 eV near the divertor target, compared to 0.8 eV in the seeding scan (EIR increases strongly below Te ≈ 1 eV), and partly due to higher divertor plasma densities achieved in fuelling scan. Features of the strongly detached seeded cases, i.e. higher temperatures and negligible EIR, are recovered in the fuelling scan by turning off D+ − D2 elastic collisions. Analysis suggests that dissipation mechanisms like line radiation and charge exchange (important for detachment initiation) become weak when Te falls below 1 eV, and that D+ − D2 elastic collisions are necessary for further heat dissipation and access to strongly recombining conditions in the fuelling scan. In the seeding scan, heat dissipation through D+ − D2 elastic collisions is weak. This could be because our nitrogen seeding simulations do not include interactions between nitrogen ions and neutrals, and the strongly detached cases contain high levels of N+ in the divertor. As a result, the N+ acts like a reservoir of energy and momentum which appears to weaken the impact of D+ − D2 elastic collisions on the divertor plasma energy and momentum balance, making it more difficult to access recombining conditions. This suggests that some of the differences between seeding and fuelling scans could be because energy and momentum exchange between impurities and neutrals is not sufficiently captured in our simulations

Predictive SOLPS-ITER simulations to study the role of divertor magnetic geometry in detachment control in the MAST-U Super-X configuration

The SOLPS-ITER code has been utilised to study the movement of the detachment front location from target towards the X-point for MAST-U Super-X plasmas. Two sets of detached steady state solutions are obtained by either varying the deuterium (D 2) fuelling rate or the nitrogen (N) seeding rate to scan the corresponding ‘control’ parameters of outboard midplane density, n u , and the divertor impurity concentration, f I . At seeding and fuelling rates ∼10× and ∼5× that required to start detachment at the divertor target, the detachment front only reaches ∼50% of the poloidal distance to the X-point, l p o l , corresponding to a region of strong parallel gradients in the total magnetic field B. The region of strong total field gradients correlates with where the detachment front location becomes less sensitive to control parameter variation. This result is qualitatively consistent with the predictions of a simple, analytic detachment location sensitivity (DLS) model (Lipschultz et al 2016 Nucl. Fusion 56 056007) which is based in a scaled parallel-to-B space, z. While the DLS model predictions are in agreement with SOLPS-ITER results in terms of where the front location becomes less sensitive to controls (i.e. in the region of strong parallel gradients in B), the DLS model predicts a higher sensitivity in the region of weak parallel gradients in B downstream as compared to the simulation results. Potential sources of differences between the SOLPS-ITER and DLS model predictions were explored: The DLS model does not include energy sinks beyond radiation from a single impurity nor cross-field energy transport. Momentum and particle balance are also not included in the DLS model. The tight opening into the divertor for flux surfaces could lead to variations in plasma-neutral pressure balance as the detachment front reaches that region, exactly how this affects the front movement needs further investigation

Experimental validation of coil phase parametrisation on ASDEX Upgrade, and extension to ITER

It has been previously demonstrated in (Li et al 2016 Nuclear Fusion 56 126007) that the optimum upper/lower coil phase shift ∆Φopt for alignment of RMP coils for ELM mitigation depends sensitively on q95, and other equilibrium plasma parameters. Therefore, ∆Φopt is expected to vary widely during the current ramp of ITER plasmas, with negative implications for ELM mitigation during this period. A previously derived and numerically benchmarked parametrisation of the coil phase for optimal ELM mitigation on ASDEX Upgrade (Ryan et al 2017 Plas. Phys. Cont. Fus. 59 024005) is validated against experimental measurements of ∆Φopt, made by observing the changes to the ELM frequency as the coil phase is scanned. It is shown that the parametrisation may predict the optimal coil phase to within 32 degrees of the experimental measurement for n = 2 applied perturbations. It is explained that this agreement is sufficient to ensure that the ELM mitigation is not compromised by poor coil alignment. It is also found that the phase which maximises ELM mitigation is shifted from the phase which maximizes density pump-out, in contrast to theoretical expectations that ELM mitigation and density pump out have the same ∆Φul dependence. A time lag between the ELM frequency response and density response to the RMP is suggested as the cause. The method for numerically deriving the parametrisation is repeated for the ITER coil set, using the baseline scenario as a reference equilibrium, and the parametrisation coefficients given for future use in a feedback coil alignment system. The relative merits of square or sinusoidal toroidal current waveforms for ELM mitigation are briefly discussed