Engineering topics
Diamond, P. H.
Publications and source records attributed to Diamond, P. H..
Density fluctuation statistics and turbulence spreading at the edge of L–mode plasmas
Long-wavelength density fluctuations ($k{\rho _i}$ <1) are studied using beam emission spectroscopy (BES) at the edge of DIII-D L-mode plasmas (ρ = 0.88–1.1) in scenarios with electron cyclotron heating (ECH) power ramp (P ECH up to 1.5 MW), neutral beam injection (NBI) power ramp (P NBI up to 2.5 MW), and injected torque scan (-1 < T inj <0.6 Nm). We find that broadband turbulent density fluctuations (ƒ ~ 20–120 kHz) have a non-Gaussian distribution. The skewness of $\delta n/n$ changes sign from negative at ρ < 0.95–0.97 to positive at ρ > 0.97, indicating the prevalence of density 'voids' at inner radii and density 'blobs' at outer radii and outside of the separatrix. The turbulence intensity flux $\left\langle {{{\tilde v}_{\text{r}}}{{\tilde n}^2}} \right\rangle$ is calculated to characterize turbulence spreading at the plasma edge. During ECH/NBI power ramps and at counter-I p injected torque, $\left\langle {{{\tilde v}_{\text{r}}}{{\tilde n}^2}} \right\rangle$ is directed inward inside the separatrix, which is evidence of inward spreading of turbulence intensity from the edge gradient region caused by the inner propagation of density 'voids'. Significantly weaker $\left\langle {{{\tilde v}_{\text{r}}}{{\tilde n}^2}} \right\rangle$ is observed with co-I p torque. A correlation between co-I p torque, turbulence intensity $\delta n/n$ at ρ = 0.97, and increased srape-off layer (SOL) heat flux decay length ${\lambda _q}$ is found in the torque scan scenario, showing that edge turbulence plays a material role in determining the SOL conditions and heat flux width.
Turbulence spreading effects on the ELM size and SOL width
BOUT++ turbulence simulations were performed to investigate the impact of turbulence spreading on the edge localized mode (ELM) size and divertor heat flux width (λ q ) broadening in small ELM regimes. Here, this study is motivated by EAST experiments. BOUT++ linear simulations of a pedestal radial electric field (E r ) scan show that the dominant toroidal number mode (n) shifts from high-n to low-n, with a narrow mode spectrum, and the maximum linear growth rate increases as the pedestal E r well deepens. The nonlinear simulations show that as the net E × B pedestal flow increases, the pressure fluctuation level and its inward penetration beyond the top of the pedestal both increase. This leads to a transition from small ELMs to large ELMs. Both inward and outward turbulence spreading are sensitive to the scrape-off-layer (SOL) plasma profiles. The inward turbulence spreading increases for the steep SOL profiles, leading to increasing pedestal energy loss in the small ELM regime. The SOL width (λ q ) is significantly broadened progressing from the ELM-free to small ELM regime, due to the onset of strong radial turbulent transport. The extent of the SOL width (λ q ) broadening depends strongly on outward turbulence spreading. The fluctuation energy intensity flux Γ ε at the separatrix can be enhanced by increasing either pedestal E r flow shear or local SOL pressure gradient. The λ q is broadened as the fluctuation energy intensity flux Γ ε at the last close flux surface (LCFS) increases. Local SOL E × B flow shear will restrain outward turbulence spreading and the associated heat flux width broadening. Operating in H-mode with small ELMs has the potential to solve two critical problems: reducing the ELM size and broadening the SOL width.
Staircase resiliency in a fluctuating cellular array
Inhomogeneous mixing by stationary convective cells set in a fixed array is a particularly simple route to layering. Layered profile structures, or staircases, have been observed in many systems, including drift-wave turbulence in magnetic confinement devices. The simplest type of staircase occurs in passive-scalar advection, due to the existence and interplay of two disparate timescales, the cell turn-over (τ H ), and the cell diffusion (τ D ) time. In this simple system, we study the resiliency of the staircase structure in the presence of global transverse shear and weak vortex scattering. The fixed cellular array is then generalized to a fluctuating vortex array in a series of numerical experiments. The focus is on regimes of low-modest effective Reynolds numbers, as found in magnetic fusion devices. By systematically perturbing the elements of the vortex array, we learn that staircases form and are resilient (although steps become less regular, due to cell mergers) over a broad range of Reynolds numbers. The criteria for resiliency are (a) τ D >>τ H and (b) a sufficiently high profile curvature (κ ≥ 1.5). We learn that scalar concentration travels along regions of shear, thus staircase barriers form first, and scalar concentration "homogenizes" in vortices later. The scattering of vortices induces a lower effective speed of scalar concentration front propagation. The paths are those of the least time. We observe that if background diffusion is kept fixed, the cell geometric properties can be used to derive an approximation for the effective diffusivity of the scalar. Furthermore, the effective diffusivity of the fluctuating vortex array does not deviate significantly from that of the fixed cellular array.
How turbulent transport broadens the heat flux width: local SOL production or edge turbulence spreading?
This paper uses data from limited HL-2A Ohmic-plasma to answer the question of how turbulent transport broadens the heat flux width. A key issue in this study is the determination of the origin of scrape-off layer (SOL) turbulence. We develop the concept of the energy production ratio ${R_a}$, which compares the flux of turbulence energy across the last closed flux surface (LCFS) to the net, integrated energy production in the SOL. The flux of turbulence energy (i.e. spreading) is measured directly, using Langmuir probes. Experimental data is used to evaluate ${R_a}$. Results show that usually ${R_a} > 1$, indicating that SOL turbulence is energized primarily by edge turbulence spreading. The exceptions—cases where ${R_a} < 1$—are those with relatively stronger ${\mathbf{E}} \times {\mathbf{B}}$ shear near the LCFS. The latter inhibits both turbulence spreading and local SOL production, but has greater effects on spreading. High blob fraction in the turbulence correlates with large values of ${R_a}$. The implications for heat flux width physics are discussed.
Further rotation reversal studies in C-Mod L-mode plasmas
Studies of core toroidal rotation reversal phenomenology in C-Mod deuterium L-mode plasmas have been expanded to include details of the dependences on plasma current and toroidal magnetic field. Rotation reversal occurs at a critical density, and universal scaling indicates that the product of ncritq95R ∼ BT/2, with ncrit in 1020/m3, R in m, and BT in T. Measurements in H and He plasmas exhibit similar behavior, including a connection with the linear Ohmic confinement/saturated Ohmic confinement transition and the cutoff for non-diffusive heat transport. Electron density and ion cyclotron range of frequencies power modulation experiments suggest that the collisionality ν* is a unifying parameter. Strong impurity puffing causes the critical density to increase, indicating that the situation is more complicated than only collisionality, perhaps involving the details of the effects of dilution on ion temperature gradient mode stability.
Characterization of mesoscopic turbulent transport events with long-radial-range correlation in DIII-D H-mode plasmas
A dimensionless collisionality scan has been performed in H-mode plasmas on DIII-D tokamak, with detailed measurements of intermediate-to-high wavenumber turbulence using Doppler backscattering systems. Furthermore, it is found that the shorter wavelength turbulence develops into spatially asymmetric turbulent structures with a long-radial-range correlation (LRRC) in the mid-radius region of high collisionality discharges. Linear cgyro simulations indicate that the underlying turbulence is likely driven by the electron-temperature-gradient mode.
Generation of momentum transport in weakly turbulent β -plane magnetohydrodynamics
Magnetohydrodynamic turbulence on a β plane with an in-plane mean field, a system which serves as a simple model for the solar tachocline, is investigated analytically and computationally. We first derive two useful analytic constraints: We express the mean turbulent cross-helicity in terms of the mean turbulent magnetic energy, and then show that (for weak turbulence) the time-averaged momentum transport in the system can be expressed in terms of the cross-helicity spectrum. Here, we then complete a closure of the system using weak turbulence theory, appropriately extended to a system with multiple interacting eigenmodes. We use this closure to perturbatively solve for the spectra at lowest order in the Rossby parameter β and thereby show that the momentum transport in the system is O (β 2 ), thus quantifying the transition away from Alfvénized turbulence. Finally, we verify our theoretical results by performing direct numerical simulations of the system over a broad range of β.
Zonal flow screening in negative triangularity tokamaks
Here, this paper presents a comparative study of zonal flow screening in positive and negative triangularity tokamaks. Neoclassical screening sets the strength of zonal flow shear for fixed drive and damping. Orbit calculations show that the radial excursions of trapped particles are reduced in negative triangularity tokamaks, as compared to positive triangularity. Yet surprisingly, the neoclassical dielectric susceptibility actually increases with decreasing triangularity, such that the susceptibility is higher for negative triangularity than for positive triangularity. This is because the reduction in neoclassical polarization by shrinking the banana width is offset by the increase in neoclassical polarization by the enhancement of trapped fraction for negative triangularity. As a result, the zonal flow screening length is actually enhanced for negative triangularity, as compared to positive triangularity. Hence, the zonal flow residual is smaller for negative triangularity than for positive triangularity. Results from gyrokinetic simulations support the analytic calculations.
Zonal shear layer collapse and the power scaling of the density limit: old L-H wine in new bottles
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. Furthermore, the dynamical hysteresis here is fundamentally different from the hysteresis associated with the existence of bi-stable states.
Electrode biasing maintains the edge shear layer at high density in the J-TEXT tokamak
Collapse of the edge flow shear as the line-averaged density approaches the Greenwald density limit has been observed as a precursor to the enhanced edge particle flux characteristic of proximity to the density limit regime. Here, we report the use of a biased electrode to sustain the edge shear layer in high density discharges, in which the shear layer would otherwise collapse. A stable increase in line-averaged density is observed along with a strong increase in edge density. These experiments were carried out on the J-TEXT tokamak. The Reynolds stress at the edge is enhanced, and the zonal flow sustained, while density perturbation levels, the flux of turbulence internal energy (i.e., turbulence spreading), and particle and heat flux all decrease significantly. Electron adiabaticity increases, and bias voltage modulation experiments show that an increase in the edge shear leads the increase in adiabaticity. Furthermore, these results suggest that external edge E × B flow shear drive may be of interest for sustaining edge plasma states at high density, and support the hypothesis that collapse of the edge shear layer triggers the onset of the strong transport and turbulence characteristic of the density limit regime.
SOL width broadening by spreading of pedestal turbulence
The pedestal turbulence intensity required to convert the thin, laminar H-mode scrape-off layer (SOL) to a broad turbulent SOL is calculated using the theory of turbulence spreading. A lower bound on the pedestal turbulence level to exceed the neoclassical heuristic drift (HD) width is derived. A reduced model of SOL turbulence spreading is used to determine the SOL width as a function of intensity flux from the pedestal to the SOL. The cross-over value for exceeding the HD model width is then calculated. We determine the pedestal turbulence levels—and the critical scalings thereof—required to achieve this level of broadening. Both drift wave and ballooning mode turbulence are considered. Here, a sensitivity analysis reveals that the key competition is that between spreading and linear E × B shear damping. The required pedestal turbulence levels scale with ρ/R.
Enhanced particle transport events approaching the density limit of the J-TEXT tokamak
Enhanced particle transport events are discovered and analyzed as the density limit of the J-TEXT tokamak is approached. Edge shear layer collapse is observed and the ratio of Reynolds power to turbulence production decreases. Simultaneously, the divergence of turbulence internal energy flux (i.e. turbulence spreading) increases, indicating that shear layer collapse triggers an outward spreading event. Studies of correlations show that the enhanced particle transport events are quasi-coherent, and manifested primarily in density fluctuations which exhibit positive skewness. Furthermore, electron adiabaticity emerges as the critical parameter which signals transport event onset. For α < 0.35 as density approaches the Greenwald density, both turbulence spreading and density fluctuations rise rapidly. Taken together, these results elucidate the connections between edge shear layer, density fluctuations, particle transport events, turbulence spreading and plasma edge cooling as the density limit is approached.
Physics of turbulence spreading and explicit nonlocality
In this paper, we systematically derive a model for turbulence spreading from the basic kinetic equation. The model contains explicit nonlocal nonlinear diffusion and nonlocal growth. When the nonlocality scale parameter δ b (banana width) vanishes, this model reduces to the usual turbulence spreading model. We elucidate the mechanisms of nonlinear saturation and nonlocal growth. Results show that nonlocal effects, especially the nonlocal growth, thicken the turbulence spreading front and increase the speed of front propagation. More turbulence intensity penetrates the stable region when δ b increases. The penetration depth Δ p is proportional to $ \delta_b/L_T $, therefore the fraction of turbulence in the unstable region scales as 1 – δ b* . Lastly, the transport scales the same way.
Bounds on edge shear layer persistence while approaching the density limit
This paper details the theory of edge shear layer collapse as the density approaches the Greenwald density limit. It significantly extends earlier work, which was restricted in applicability. The zonal shear flow screening length is calculated for banana, plateau and Pfirsch–Schluter regimes. Poloidal field scaling persists in the plateau regime. Neoclassical screening and drift wave–zonal flow dynamics are combined in a theory, which is then reduced to a predator–prey model. Zonal noise, due to incoherent mode coupling, is retained. The threshold condition for edge shear layer collapse is computed, and linked to a critical value of the dimensionless parameter ${\rho }_{\mathrm{s}}/\sqrt{{\rho }_{\mathrm{s}\mathrm{c}}{L}_{n}}$. Here ${\rho }_{s}$ is the ion sound radius, ${\rho }_{sc}$ is the zonal flow screening length and ${L}_{n}$ is the equilibrium density scale length. The limiting initial edge density for shear layer collapse is derived and shown to scale favorably with the plasma current. Here, the results are discussed in light of the density limit and Ohmic phenomenology.
Anisotropic E × B shearing rate in a magnetic island
We derive the E × B shearing rate associated with vortex flow inside a macroscopic magnetic island (MI) in axisymmetric toroidal geometry. Due to the elongation of the MI and incompressibility of the E × B flow, the shearing rate near X-points is much lower than that near the mid-plane (x-axis of the local Cartesian coordinate) of the MI on the same flux surface. Furthermore, the rate formally vanishes at the X-points where the local poloidal magnetic field associated with the MI stagnates. Here, this calculation of E × B shearing profile and, in particular, minimal E × B shear near the X-points is consistent with the recent experimental finding that turbulence tends to spread into an MI through regions around the X-points and can contribute to more thorough quantitative interpretation of the results from experiments and simulations.
A unified theory of zonal flow shears and density corrugations in drift wave turbulence
A unified theory of zonal flow shears and density corrugations in drift wave turbulence is presented. Polarization and density advection beat excitation are studied in combination with modulational response. Noise is driven by two-time flux correlation. While the effective zonal flow eddy viscosity can go negative, the zonal diffusivity is positive definite. There is no inverse cascade of density corrugation. The connection between avalanches and corrugations is discussed. Here, the zonal cross-correlation is identified and calculated. Conditions for alignment of zonal shears and corrugation gradients are determined, and the implications for staircase structure are discussed. We show that the synergy of beat noise and modulational effects is stronger than either alone. Strong zonal flows can be excited well below the modulational instability threshold. In the context of L–H transition, zonal noise quenches turbulence overshoot by eliminating the threshold for zonal flow excitation. The power threshold for L–H transition is lowered.
Curvature of Radial Electric Field Aggravates Edge Magnetohydrodynamics Mode in Toroidally Confined Plasmas
We show that the radial electric field (E r ) plays a dual role in edge magnetohydrodynamics (MHD) activity. While E r shear (first spatial derivative of E r ) dephases radial velocity and displacement, and so is stabilizing, a new finding here is that E r curvature (second spatial derivative of E r ) tends to synchronize the radial velocity and displacement, and so destabilizes MHD. As a highlighted result, we analytically demonstrate that E r curvature can destabilize an otherwise stable kink mode, and so form a joint vortexkink mode. The synergetic effects of E r shear and E r curvature in edge MHD extend the familiar E × B shearing paradigm. This theory thus explains the experimental findings that a deeper E × B well may aggravate edge MHD, and so trigger the formation of the edge harmonic oscillation. Here, a simple criterion linking E r structure and the edge MHD activity is derived.