LH transitions driven by ion heating in scrapeoff layer turbulence (SOLT) model simulations


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1 LH transitions driven by ion heating in scrapeoff 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 DEFG097ER
2 Outline SOLT model equations selfconsistent evolution of ion pressure and ion diamagnetic drift Turbulent flow energetics generalized Reynolds work (T i > 0, nonboussinesq) Sourcedriven 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 timeindependent sources. Conclusions
3 SOLT Model Equations The SOLT code now includes the selfconsistent 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 driftordered, reducedbraginskii fluid equations derived by Simakov and Catto* and used in the BOUT code.** The electrostatic 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 (quasineutral) 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. Selfconsistent 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 nonboussinesq 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 zeromomentum 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 coreside boundary. This injection region is well removed from the separatrix (Dx = 0) in the simulations to observe LH 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 Hregimes decreasing, with negative bursts in the Aregime mean flow fluctuations L H A 8
9 S Pi ~ t a propagating meanflow production front In response to mounting ion pressure, the meanflow bloom detaches from the source region, initiating the LH 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 meanflow 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 meanflow 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 sweetspot for the location of this phalanx. 11
12 S Pi ~ t : local Reynolds production The nearsource 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 lowconfinement regimes, but L : P mf > 0 mean flow production by turbulence A : P mf < 0 turbulence production by mean flow (KH?) 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 highshear layer provides a transport barrier (circled) in the Hmode: v E > g mhd. This barrier is absent from the Lmode. 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 sourcedriven 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 KH 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
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