L-H transitions driven by ion heating in scrape-off layer turbulence (SOLT) model simulations

Transcription

1 L-H transitions driven by ion heating in scrape-off layer turbulence (SOLT) model simulations D.A. Russell, D.A. D Ippolito and J.R. Myra Research Corporation, Boulder, CO, USA Presented at the 015 Joint US/EU Transport Task Force Workshop Salem MA April 8 - May Work supported by the U.S. Department of Energy Office of Science, Office of Fusion Energy Sciences, under Award Number DE-FG0-97ER

2 Outline SOLT model equations self-consistent evolution of ion pressure and ion diamagnetic drift Turbulent flow energetics generalized Reynolds work (T i > 0, non-boussinesq) Source-driven turbulence Configurations of density and pressure sources L, H and Avalanche (A) regimes visited with increasing S pi (x,t) ~ t L, H and A regimes of stationary turbulence for time-independent sources. Conclusions

3 SOLT Model Equations The SOLT code now includes the self-consistent evolution of ion pressure and ion diamagnetic drift. Generalized vorticity is evolved; the Boussinesq approximation has been dropped. The new equations of evolution are consistent with the drift-ordered, reduced-braginskii fluid equations derived by Simakov and Catto* and used in the BOUT code.** The electro-static potential is extracted from the vorticity by different algorithms depending on the problem: relaxation on Poisson***, conjugate gradient and multigrid. Generalized Vorticity () (n p ) 0 i ( v ) b (p p ) J Bohm units t E e i D (OM) y x B B, nv v ( p ) (v p ) b n v di E i E i E p nt, v b, and v bp / n is the ion diamagnetic drift e,i e,i E di i *A.N. Simakov and P.J. Catto, Phys. Plasmas 10, 4744 (003). **M.V. Umansky et al., Comp. Phys. Comm. 180, 887 (009). ***J.R. Angus and M.V. Umansky, Phys. Plasmas 1, (014). 3

4 SOLT Model Equations (cont.) Density (quasi-neutral) Electron Temperature Ion Temperature ( v )n J D n S t E //,n n n ( v )T q / n D T S t E e //,e Te e Te ( v )T q / n D T S t E i //,i Ti i Ti d v ˆ ˆ E, ve b (b v E ), dt t J models // electron drift waves on the closed field lines and sheath physics, through closure relations, in the SOL. q models heat flux in the SOL. [8 * ] // All fields are turbulent: n = n(x,y,t), etc. We do not expand about ambient profiles in SOLT. Self-consistent O(1) fluctuations are supported. * [8] J.R. Myra et al., Phys. Plasmas 18, (011). 4

5 Turbulent Flow Energetics Mean Flow production by Reynolds work generalized for Ti > 0 and non-boussinesq dynamics g n ( v v ) n u : momentum density E di (1) tg ( veg) 0 vorticity equation (conservative form). Combine this equation with the density continuity equation to find () tu ve u us n / n, where S n is a source of zero-momentum particles. 1 Mean Flow Energy ε mf u g, u y - average( u) tεmf xqmf P mf Smf 1 qmf vx v x : Mean Flow Energy Flux u g g u 1 P S S n mf u g : Energy Loss n mf vxu x g v xg x u : Mean Flow Production Reynolds work : P mf xq mf 5

6 1 Fluctuation Energy : εfl u g εmf ε εmf tεfl xqfl P mf S fl, where 1 S q v n fl xu g qmf q q mf and S fl u g n Smf S S mf. The total energy is conserved: tε xq S P 0 energy transfer from fluctuations to mean flow mf P 0 turbulence production mf Turbulent Flow Energetics (cont.) T i = 0 and Boussinesq approximation ( n = P n x v v v mf Ey Ex Ey q n v v v mf Ey Ex Ey 0) In the present simulations, these limiting forms are poor approximations to the full expressions. 6

7 Source Configuration Particle and energy fluxes are driven by diffused (D) Gaussian sources (S) localized near the core-side boundary. This injection region is well removed from the separatrix (Dx = 0) in the simulations to observe L-H transition phenomena free from SOL physics. S Pi D P i (t 1,t ) Stationary Sources or S Pi ~ t Confinement Times n P dx n / dx Sn Dx0 Dx0 dx P / dx S P Dx0 Dx0 7

8 S Pi ~ t : visiting three confinement regimes L : low confinement times and mean field energy H : rising confinement times and a broad peak in the history of mean flow energy A (avalanche) : diminished mean flow energy and bursts in the fluctuation energy L H A n P e P i Reynolds Work global picture positive in the L- and H-regimes decreasing, with negative bursts in the A-regime mean flow fluctuations L H A 8

9 S Pi ~ t a propagating mean-flow production front In response to mounting ion pressure, the mean-flow bloom detaches from the source region, initiating the L-H transition. At the moving front, the mean flow production rate (P mf ) balances the turbulence injection rate (g mhd e fl ) : a moving Reynolds trigger. A H L 9

10 S Pi ~ t a propagating mean-flow production front (cont.) The front (a) drives a shear layer (b) and leaves a wake of increasing pressure gradient (c) and reduced fluctuation energy. a c b Avalanches curtail the pressure rise in the wake. L H A 10

11 S Pi ~ t a propagating mean-flow production front (cont.) A poloidal array of coherent structures underlies the production front. L H A Radial correlation lengths inside the separatrix are long in L and reduced in H. Coherent structures are broken up in the A regime. The H regime represents a sweet-spot for the location of this phalanx. 11

12 S Pi ~ t : local Reynolds production The near-source picture supports changes in transport seen near the separatrix. L H A H : e fl and particle flux are reduced. L and A are both low-confinement regimes, but L : P mf > 0 mean flow production by turbulence A : P mf < 0 turbulence production by mean flow (K-H?) 1

13 Fixed Sources L, H and A regimes of stationary turbulence Confinement times reveal distinct regimes similar to those seen in the S Pi ~ t study. n Pe Pi L H A S Pi x 100 S Pi x 100 S Pi x 100 H : confinement times increase with increasing ion heating (S Pi ). L, A : confinement times decrease with increasing ion heating. 13

14 Fixed Sources equilibrium shear layers A high-shear layer provides a transport barrier (circled) in the H-mode: v E > g mhd. This barrier is absent from the L-mode. H time averages v' E γ mhd v' di Local diagnosis can misguide global prediction. What you see depends on where you look. Global nonlinear analysis (P mf, e mf ) is in progress. 14

15 Conclusions We find 3 different confinement regimes with increasing ion heating (S Pi ) in a D source-driven fluid turbulence model that retains the ion diamagnetic and gyroviscous effects. The regimes L, H and A are reminiscent of tokamak L, H, and ELMy- H mode regimes. Enhanced confinement in the H regime is associated with the movement of a shear layer to just inside the separatrix; v E > g mhd in the layer. Our model does not have sufficient physics to describe peelingballooning ELMs, but rather A likely involves the K-H instability. The relationships between v E, v di and pressure gradient (g mhd ) depend strongly on radial location, making local diagnosis ambiguous. A global energetics model, taking into account ExB and diamagnetic flows, has been developed and is being applied to the simulations. 15

16 Extra 1 L H A 16

17 Extra L H A 17