Overview of edge modeling efforts for advanced divertor configurations in NSTX-U with magnetic perturbation fields

Transcription

1 Overview of edge modeling efforts for advanced divertor configurations in NSTX-U with magnetic perturbation fields H. Frerichs, O. Schmitz, I. Waters, G. P. Canal, T. E. Evans, Y. Feng and V. Soukhanovskii University of Wisconsin - Madison ISTW - November 3-6, 2015 H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U

2 Motivation: control of divertor head loads Control of divertor heat loads (both steady state and transient) remains one of the key challenges for a fusion based reactor and for a compact fusion nuclear science development facility (FSNF) Resonant magnetic perturbations (RMPs) are a promising method for ELM control breaking of axisymmetry Advanced divertors (specialized divertor geometry): Snowflake, X-divertor) for steady state heat flux reduction Likely, both concepts will have to work together, and NSTX-U is a well suited device to study this: What is the impact on neutral fueling and exhaust (density control), and how does this affect high recycling and transition to detachment? H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 1

3 1 Introduction to magnetic perturbations 2 The snowflake divertor configuration 3 Edge transport modeling Introduction to EMC3-EIRENE First simulation results H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 2

4 Perturbation of the magnetic separatrix lobes The separatrix associated with X has 2 branches (set of field line trajectories): W + = W = { } p lim F p (l) X l { } p lim F p(l) X l W W + X point F p (l): field line through p Both branches overlap in the unperturbed configuration (arrows indicate field direction) H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 3

5 Perturbation of the magnetic separatrix lobes The separatrix associated with X has 2 branches (set of field line trajectories): W + = W = { } p lim F p (l) X l { } p lim F p(l) X l + W W (arrows indicate field direction) F p (l): field line through p Both branches overlap in the unperturbed configuration Magnetic perturbations result in a splitting, and both branches may intersect each other transversely This opens up a connection between the plasma interior and the divertor targets H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 3

6 Lobe density increases with lower aspect ratio n = n = 3 Vertical position [cm] A = 1.7 NSTX U Vertical position [cm] A = 2.8 DIII D Major radius [cm] Major radius [cm] Lobes become smaller and more frequent towards the X-point lobe density: 1 L n B tor 2π R B pol n B 0 2π R 0 B pol ( 1 δ ) 2 X A Higher density may facilitate heat flux spreading between lobes Radial extension of lobes depends on perturbation strength H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 4

7 Radial size of lobes defines poloidal extend of the magnetic footprint, lobe density not affected by I c NSTX U: ISP I c [ka] = Vertical Position [cm] Toroidal Angle [deg] H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 5

8 1 Introduction to magnetic perturbations 2 The snowflake divertor configuration 3 Edge transport modeling Introduction to EMC3-EIRENE First simulation results H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 6

9 The snowflake divertor configuration Second order null of the poloidal magnetic field the separatrix acquires a characteristic hexagonal form This results in a flux expansion near the null-point, and while B (snowflake) pol r 2 (standard divertor) B pol r: distance from the null-point r SF facilitates longer connection lengths and two additional strike points Generalization: two first order nulls in (close) proximity D. Ryutov et al, Phys. Plasmas 15, (2008) H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 7

10 The snowflake configuration allows for a variety of magnetic topologies at NSTX-U Nearly exact Snowflake (SF0) Normalized poloidal flux Nearly exact snowflake : approximation to classical snowflake H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 8

11 The snowflake configuration allows for a variety of magnetic topologies at NSTX-U Nearly exact Snowflake (SF0) Normalized poloidal flux Nearly exact snowflake : approximation to classical snowflake Here SF0 is actually snowflake minus, which is topologically equivalent to connected double null (CDN) H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 8

12 The snowflake configuration allows for a variety of magnetic topologies at NSTX-U Nearly exact Snowflake (SF0) Tilted Snowflake Minus (SF ) Snowflake Plus (SF+) Njw_ NfHz0+Qf NfHz0+Qg Normalized poloidal flux Nearly exact snowflake : approximation to classical snowflake Here SF0 is actually snowflake minus, which is topologically equivalent to connected double null (CDN) The secondary X-points in the (tilted) SF- and SF+ configurations here are outside the divertor targets topology is lower single null (LSN) H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 8

13 SF0 has increased connection length, but flux compression on target (with respect to SD) Connection Length [ m] PFR Outer Strike Point SOL SD SF- SF+ SF0 Distance from OSP [cm] Flux surface connection SD SF- SF+ SF Distance from Separatrix [cm] Distance from Separatrix (LFS midplane) [cm] Both SF0 and SF- feature longer connection lengths then SD at the outer strike point: may result in lower divertor temperatures SF0 features flux compression while SF- features flux expansion with respect to standard divertor (SD) configuration: can impact heat flux spreading H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 9

14 SF0 has increased connection length, but flux compression on target (with respect to SD) Connection Length [ m] PFR Outer Strike Point SOL SD SF- SF+ SF0 SF0 (div. adjust) Distance from OSP [cm] Flux surface connection SD SF- SF+ SF0 SF0 (div. adjust) Distance from Separatrix [cm] Distance from Separatrix (LFS midplane) [cm] Both SF0 and SF- feature longer connection lengths then SD at the outer strike point: may result in lower divertor temperatures SF0 features flux compression while SF- features flux expansion with respect to standard divertor (SD) configuration: can impact heat flux spreading H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 9

15 Lobe size and extension depends on equilibrium Vertical Position [cm] BT = 1T -160 IP = 2 MA SD Vertical Position [cm] BT = 1T IP = 1 MA Major Radius [cm] Major Radius [cm] SF0 Lobe density is much higher in SF0, i.e. lobe size is smaller (I p = 1 MA) Lobe size scales with r 2 near the X-point 4 3 in SF0, because B pol does 2 very small change in size between 1 neighboring lobes 0 Lobe spacing [cm] SD SF- SF+ SF Distance from X-point along separatrix [cm] H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 10

16 1 Introduction to magnetic perturbations 2 The snowflake divertor configuration 3 Edge transport modeling Introduction to EMC3-EIRENE First simulation results H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 11

17 A 3D steady state transport model for the edge plasma Field lines are reconstructed from a 3D block-structured grid which can be adapted to the topology at hand H. Frerichs et al., Comp. Phys. Commun. 181 (2010) 61 Classical transport (Braginskii) along field lines Self-consistent solution by iterative application Magnetic field structure FLARE: 3D field line grid Plasma Transport EMC3: Fluid model Monte Carlo method Plasma Background n, u, Te, Ti Sources/Sinks Sp, Sm, See, Sei Transport coefficients Neutral Gas Transport EIRENE: Kinetic Model Monte Carlo method The following simulations are based on: Particle in-flux Γ in = s 1 (50 A) Recycling coefficient c rec = 0.99 Edge input power P in = 2 MW Anomalous cross-field transport: (particles) D = 0.3 m 2 s 1 (energy) χ e = χ i = 2.0 m 2 s 1 Impurity transport and radiation is neglected at this point H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 12

18 No RMPs: SF0 operates at higher divertor density H. Frerichs 3D edge modeling for NTSX-U 13

19 RMPs: Lobes at the LFS, diffusion to strong at HFS H. Frerichs 3D edge modeling for NTSX-U 14

20 Heat load analysis favours SF- configuration Target Heat Load [MW m -2 ] Heat load in axisymmetric configuration Distance from Separatrix [cm] SD SF- SF+ SF0 Small reduction of peak heat load in SF+ Moderate reduction of peak heat load in SF-, peak is found at cm distance from the separatrix Significant increase of peak heat load in SF0 due to compression of flux surfaces at the divertor target. H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 15

21 Heat load analysis favours SF- configuration Target Heat Load [MW m -2 ] Heat load in axisymmetric configuration Distance from Separatrix [cm] SD SF- SF+ SF0 Target Heat Load [MW m -2 ] Heat load in RMP configuration Distance from Separatrix [cm] SD SF- SF+ SF0 Small reduction of peak heat load in SF+ Moderate reduction of peak heat load in SF-, peak is found at cm distance from the separatrix Significant increase of peak heat load in SF0 due to compression of flux surfaces at the divertor target. No significant impact of RMPs on toroidally averaged heat loads H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 15

22 Summary and conclusions Application of RMPs results in the formation of helical lobes which have a higher frequency at lower aspect ratio The snowflake family of divertor configurations allows a variety of magnetic topologies ranging from flux compression to flux expansion at the divertor targets First transport simulations favour the SF- configuration for heat load reduction Outlook: How do RMPs and advanced divertor configurations impact neutral fueling and exhaust, and how does this affect high recycling and transition to detachment? What is the impact of plasma response effects (use NIMROD, M3D-C1) H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 16

23 2w h R 0 w aspect ratio: A = R 0 /w elongation: κ = h/w triangularity: δ = /w 2h X H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 17

24 Radial lobe size depends on perturbation strength in relation to equilibrium field Vertical Position [cm] Vertical Position [cm] SD -125 SF Ψ = B T = 1T B T = 1T IP = 2 MA Ψ = IP = 2 MA Major Radius [cm] Major Radius [cm] SF SF Ψ = Ψ = Ψ = B -155 T = 1T B T = 1T -155 I P = 2 MA IP = 1 MA Major Radius [cm] Vertical Position [cm] Vertical Position [cm] Major Radius [cm] H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 18

25 Field lines can connect through the lobes from inside the separatrix to the divertor targets H. Frerichs 3D edge modeling for NTSX-U 19

26 Moiré pattern caused by small, similar sized lobes Lobe frequency is much higher in SF0, i.e. lobe size is smaller (I p = 1 MA) Lobe size scales with r 2 near the X-point 4 3 in SF0, because B pol does 2 very small change in size between 1 neighboring lobes 0 Lobe spacing [cm] SD SF- SF+ SF Distance from X-point along separatrix [cm] H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 20

27 A 3D steady state fluid model for the edge plasma Particle balance (n: plasma density) [nu e D e e n ] = S p D : anomalous cross-field diffusion, S p: ionization of neutral particles Momentum balance (u : fluid velocity parallel to magnetic field lines) [ m i nu 2 e η e e u D e e ( m i nu ) ] = e n (T e + T i ) + S m η T 5/2 i : parallel viscosity, η = m i nd : cross-field viscosity, S m: interaction (CX) with neutral particles Energy balance (T e, T i : electron and ion temperature) [ 5 ( 2 Te nu e D e e n ) ( ] ) κ ee e + χ en e e Te [ 5 2 T ( i nu e D e e n ) ( ] ) κ i e e + χ i n e e Ti = +k (T i T e) + S ee = k (T i T e) + S ei κ e,i T 5/2 e,i : classical parallel heat conductivity, χ e, χ i : anomalous cross-field transport, k n 2 T 3/2 e : energy exchange between el. and ions, S ee, S ei : interaction with neutral particles and impurities (radiation) H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 21

28 Field lines are reconstructed from a finite flux-tube grid The 3D grid is generated by field lines tracing starting from 2D base grids Grid nodes Pre calculated field lines > 3D finite flux tube grid Reconstructed field line ϕ base EMC3: bilinear interpolation within flux-tubes (4 pre-calculated field lines) Separatrix LCFS LSN 0 DDN 0 CDN Inner sepx. Outer sepx. LCFS Separatrix LCFS Discretization in the cross-field direction can be adapted to the magnetic configuration at hand. Unlike grids for 2D transport modeling, the actual information about the magnetic configuration is not stored in the 2D base grid(s) but in the 3D grid. H. Frerichs (hfrerichs@wisc.edu) 3D edge modeling for NTSX-U 22