Attainment of a stable, fully detached plasma state in innovative divertor configurations

Attainment of a stable, fully detached plasma state in innovative divertor configurations M.V. Umansky, Lawrence, Livermore National Laboratory, Livermore, CA 94550, USA O. Izacard, M.E. Rensink, T.D. Rognlien (LLNL) D. Brunner, B. LaBombard, J.L. Terry, D.G. Whyte (MIT) Presented at 58th Annual Meeting of the APS Division of Plasma Physics October 31 - November 4, 016 San Jose, California This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore Na?onal Security, LLC, Lawrence Livermore Na?onal Laboratory under Contract DE-AC5-07NA7344. LLNL-PRES-707418

Outline Introduction: Tokamak divertor challenge & innovative divertors Modeling innovative divertors with long legs and secondary X-points Simulation model and setup Robust fully detached regimes Analysis of fully detached divertor Summary & conclusions Long-legged divertor performance much beyond standard divertor Promise of stable fully-detached high-power divertor

Traditional tokamak divertor configuration is formed by two toroidal currents: plasma and divertor coil Toroidal plasma current I p Divertor coil current I d Ip Id Magnetic flux surfaces are formed X-point (B p =0 null point) Magnetic separatrix between ü core plasma ü scrape-off layer (SOL) ü private-flux (PF) region Divertor plates intercept most of heat exhausted from the core 3

Divertor heat exhaust is going to be a major challenge for next generation tokamaks SOL width λ SOL small (~1 mm) => divertor heat flux large For constant λ SOL a figure of merit is P/R 00 MW/m 150 MW/m Exhaust power [MW] Major radius [m] q div = P A w = P π Rλ SOL P R 100 MW/m 50 MW/m Near-term facilities ITER NHTX (PPPL) CTF (PPPL) FDF (GA) ARIES-ST 4

Divertor heat exhaust is going to be a major challenge for next generation tokamaks SOL width λ SOL small (~1 mm) => divertor heat flux large For constant λ SOL a figure of merit is P/R 00 MW/m 150 MW/m Exhaust power [MW] Major radius [m] q div = P A w = P π Rλ SOL P R Recently found scaling* λ SOL ~ 1/B p and independent of machine size unfavorable for large tokamaks (if it holds) Innovative divertor solutions are needed for next generation tokamaks 100 MW/m 50 MW/m Near-term facilities ITER NHTX (PPPL) CTF (PPPL) FDF (GA) ARIES-ST *T. Eich et al., 013 Nucl. Fusion 53 093031 5

Divertor parameters are constrained by overall tokamak design but there are some degrees of freedom for divertor R a λ For given tokamak design one cannot change: Exhaust power Major radius Minor radius SOL width L max L d But (within some limits) one can change: Divertor plate tilt/shaping Divertor leg length Divertor poloidal flux expansion Divertor magnetic field topology 6

Increasing plasma-wetted area A w geometrically is limited for given target major radius R t α A w can be increased by plate tilting and poloidal flux expansion For either method, grazing angle γ between surface and total B becomes small For γ<γ 0 1 ο hot-spot formation due to surface roughness At minimum angle γ=γ 0 A w πr t [(λ mid /γ 0 ) (B p /B t ) mid ] For further increase of A w larger R t needed* γ q Purely geometric solutions for innovative divertor are limited Can we make plasma and/or atomic physics play in our favor? * P. Valanju et al., Phys. Plasmas 16, 056110, 009 7

Detached regime: Plasma stays away from PFC, cushioned by neutral gas potentially attractive solution for divertor Experimental features of divertor detachment: Low plasma temperature, density, power on target; T e ~1 ev Radiation moves away from plates Modeling: Semi-quantitatively reproduces many experimental features of detachment Problem with detachment for standard divertor: Sensitive to divertor plasma parameters Det. front tends to move to main X-point => MARFE, bad for core plasma Small (if any) parameter window for stable fully detached operation T e from divertor Thomson A. McLean et al., APS DPP 015 8

collisional mean free path, #d = mean free path, ρi =ion Larmor identical to those of a reactor. and divertor leg length could b any case, the overall message i reactor divertor parameters (B, q study reactor-relevant physics re multi-machine empirical scaling the parallel heat flux scales a means that B, n and PSOL B/R similar to that in a reactor. Fr a compact, high-field tokamak ADX it is the way to perform m divertor prototypes without cons it removes the uncertainty and divertor performance from extre computational models, develope are far from those expected in a r Configurations with a secondary X-point in divertor considered by several groups in recent years 06450- Phys. Plasmas 14, 06450!007" D. D. Ryutov Cusp divertor [1] Snowflake divertor [] X-divertor Very similar to the cusp divertor:! FIG. 1. A snowflake divertor. The separatrix near the null point forms a characteristic hexagonal structure "an inset# reminiscent of a snowflake. The distances are measured in units of a "which is the distance between the null point and the conductor imitating the plasma current#. The thick line represents the separatrix; the thin lines outside and inside the separatrix represent flux surfaces whose distance is 0.00a from the separatrix in the equatorial plane "i.e., 1 cm for the device with a = 5 m#. At the scale of the figure, the 1 cm of distance in the main SOL is too small to be resolved, whereas the distance of the outer flux surface from the null point is approximately 80 cm. In other words, the broadening of the scrape-off layer near the null point is very large. This extra downstream X-point can be created with an extra pair of poloidal coils Each divertor leg (inside divertor andnearoutside) needs the null point,!, will scale as! /! #, whereas in a usual X-point divertor one such a pair!would of! "bcoils. The distant have!!! "b /! #. According to Eq. "#, the affected coils are situated at the dismain plasma is hardly tance b$a / "a b# from the null point. In a reactor, the dicoils should be placed outside the radiation shield, i.e., because thevertor line flaring happens they cannot be situated too close to the plasma. As a representative value of b, we take b = 0.3a; then the coils will be only near the extra coils. situated at a distance!0.5a %.5 m from the null point. X-divertor [3] 0 0 /3 0 [1] [] 0 1/ FIG.. The shape of the separatrix for the case in which the divertor current is five percent higher "a# and five percent lower "b# than the current Id0, Eq. "3#. We call the first of them snowflake-plus and the second snowflakeminus. Shown by the light line in "a# is the separatrix of a standard X-point divertor with the upper part of the separatrix not much different from that of the snowflake-plus divertor with $ = 0.05. We compare these two configurations in terms of the flux expansion properties in Fig. 4. The opposite possibility, namely running the divertor at the current that is somewhat smaller than optimum, also provides the robustness to the configuration and significant flux expansion. However, as one can see from Fig. "b#, in this case the divertor region contacts the plasma core not in one point but rather along a line &CD, Fig. "b#'. Although the possible effect of the line contact is at present not quite clear, we prefer to stay within a more customary geometry of Fig. "a#. One obvious concern regarding the configuration of Fig. "b# is that the line contact may have an adverse effect on impurity penetration from divertor to the plasma core. We will call the configuration of Fig. "a# "with the divertor current somewhat higher than Id0# snowflake-plus, and the configuration of Fig. "b# snowflake-minus. For a more detailed analysis of the magnetic field structure in the divertor region, one can use a Taylor expansion of the magnetic field near the point x = z = 0. Some rather lengthy algebra leads to the following result for the normalized magnetic field &B = "ac / I#B, the CGS system is used': X-point 5. Motivation: low-pmi RF ac target current drive, heating neede divertor [4] 5.1. Challenges It is recognized that RF current dr must evolve into primary act replacing the roles that neutral bea As stated in a 007 US DoE [1] on page 190): The auxiliary syst Figure 7. RF antennas can take advantage of the low-pmi, I 4ab z I a "4b d # 1 + 1 + 4 d "4b + d in # double-null plasmas and I 4b +on athe IHFS quiescent SOL thatb =forms experiments, while extremely us # z x I a "4b det H. Takase, J. Phys. Soc. Japan, 70, 609, 001. [3] Kotschenreuther al., 004 IAEA FEC, paper IC/P6-43. the M. dominant power exhaust 1 4through,the low-field + "4# side (LFS) SOL suitable for a reactor. RF scheme a I "4b + d # (represented by red arrows). 9 require signifi D.D. Ryutov. Phys. Plasmas, 14, 06450, 007. [4] B. LaBombard Nucl. 55, 05300,to015. 4 a "4b al., d # xz 3d # x Iet I a "4b Fusion be used and will + 1 4. "5# B = 1 + 4 a I "4b + d # a I "4b + d # levels of reliability and predicta This seems to be sufficiently far, given that the shield thickness isp.!1m. m "e.g., Ref. 6#. S. The Mahajan, current per divertor coil, M. Kotschenreuther, Valanju, according to Eq. "3#, will be!0.45i, with the total current J. Wiley. On heat loading, novel divertors, and!0.9i. For nonradioactive experimental facilities, one can, fusion reactors. Phys. (007) of course,plas. consider14, much0750 more compact snowflake divertors, with a smaller ratio b / a. A disadvantage of a snowflake configuration is its topological instability: if the plasma "or divertor# current do not exactly satisfy Eq. "3#, the configuration becomes either an X-point configuration &Fig. "a#' if Id " Id0, or a double-xpoint configuration &Fig. "b#' if Id # Id0. The position of the strike point and the overall structure of the divertor plasma change substantially for a small variation of a plasma current if the initial current is exactly Id0. We suggest making the configuration more robust by operating at a divertor current somewhat higher than Eq. "3#. d x d d z d d

Recent upgrades made in UEDGE make it possible to include a secondary X-point in divertor θ = angle between X-point bisector & horizontal axis 3 mesh regimes 0 < θ < 30 o 30 o < θ < 60 o 60 o < θ < 90 o x SF - x Unique indexing rules for each regime x [1] T. D. Rognlien et al., J. Nucl. Mater. 196 198, 347 (199) [] M.E. Rensink et al. (in prepara)on) 11 x SF +

UEDGE capability for modeling configurations with secondary X-points is now applied to NSTX-U* Illustracve grids for domain w/ two X-pts Illustracve UEDGE solucons 400 ElectrRn 7emperature [ev] 350 1. 3 300 Z [m] 1. 4 1. 5 50 00 150 1. 6 100 1. 7 0. 30 0. 45 0. 60 0. 75 5 [m] 50 Z [m] 1. 3 1. 4 1. 5 1. 6 Density deuterium1+ [m -3 ] 10 0 4. 0 3. 5 3. 0. 5. 0 1. 5 1. 0 1. 7 0. 30 0. 45 0. 60 0. 75 5 [m] 0. 5 *O. Izacard et al., poster NP10.00031 on Wednesday 1

UEDGE applied to four tokamak divertor arrangements based on same (or similar) magnetic configurations Z [m] symmetry plane 1 SVPD R [m] SXD XPTD 4 symmetry plane LVLD R [m] SVPD Standard Verccal Plate Divertor SXD Super-X Divertor XPTD X-point Target Divertor LVLD Long Verccal Leg Divertor 3 Z [m] Tokamak edge transport code UEDGE [1] finds a steady state solution of plasma fluid equations in edge domain Using newly added capabilities in UEDGE for including a secondary X-point in the divertor Analyzing several divertor configurations based on ADX tokamak design [] [1] T. D. Rognlien et al., J. Nucl. Mater. 196 198, 347 (199) [] B. LaBombard et al., Nucl. Fusion 55, 05300 (015) 13

Model parameters are set to match projected ADX characteristics Modeled cases are based on geometry & parameters from ADX tokamak design MHD equilibrium Power P 1/ into lower half-domain, 0.1-4 MW Density at separatrix ~0.5e0 m -3 SOL profiles width, λ T,N 3-5 mm Reactor-relevant q up to 5 GW/m^ 10 0 [m -3 ] Mid-plane profiles 1.0 0.5 0 5.0 Te Ne 300 00 100 0 [ev] Fully recycling wall B.C. on all material surfaces (unless stated otherwise) Radially growing density diffusion coefficient D Spatially constant heat diffusion coefficient χ e,i Fixed fraction impurity model, 1% C [m/s] 4.0 3.0.0 1.0 0 D χ e,i -4-0 4 6 8 10 1 R-Rsep [mm] 14

Results for XPTD, power P 1/ = 3.0 MW 16

Results for XPTD, power P 1/ = 1.6 MW 17

Results for XPTD, power P 1/ = 0.6 MW 18

Results for SXD, power P 1/ = 1. MW 19

Results for SXD, power P 1/ = 0.8 MW 0

Results for SXD, power P 1/ = 0.6 MW 1

Results for LVLD, power P 1/ = 1. MW

Results for LVLD, power P 1/ = 0.8 MW 3

Results for LVLD, power P 1/ = 0.6 MW 4

Varying input power into SOL shows how transition to detachment depends on divertor configuration Identically same physics model, B.C., etc. Large parameter window with detached divertor found for all three long-legged configurations For SVPD, detached plasma may exist only at low input power Radially or vertically extended outer leg good for detached operation Long vertical leg (LVLD) enters detachment at about same power as radially extended leg (SXD) Secondary X-point in outer leg (XPTD) significantly extends detached operation window 5

Varying input power into SOL shows how transition to detachment depends on divertor configuration C-Mod Identically same physics model, B.C., etc. Large parameter window with detached divertor found for all three long-legged configurations For SVPD, detached plasma may exist only at low input power Radially or vertically extended outer leg good for detached operation Long vertical leg (LVLD) enters detachment at about same power as radially extended leg (SXD) Secondary X-point in outer leg (XPTD) significantly extends detached operation window 6

Analysis needed to address important questions for these numerical solutions What is interplay of model physics terms in these detached regimes? What is going on with plasma & neutral density, momentum, energy flux? What sets position of detachment front? What are limits of power handling capability? How sensitive is this equilibrium to model details (impurity, neutrals)? Can this regime be scaled to reactor parameters? 8

Analysis of plasma & neutral density fluxes in divertor leg show stagnant poloidal flow picture Analyzing a representative case: SXD, P 1/ =0.6 MW Γ=6.5x10 0 [1/s] On each surface bounding the leg domain ion flux is matched by opposing neutral flux Γ=3x10 0 [1/s] Γ=180x10 0 [1/s] Poloidal fluxes entering/ leaving domain are tiny compared to radial fluxes SOL flow is stagnant why? Γ=0.6x10 0 [1/s] Need to analyze parallel momentum balance 9

Plasma pressure conservation relation is helpful for understanding plasma parallel force balance t F in! ( m i n i u i ) + ( m i n i ui u i η u! i ) = p ei m i n i n n K cx ( u i u n ) m i S r u i + m i S i u n Integration along field line leads to conservation law Thermal pressure Ram pressure Radial transport u p ei + m i n i u iθ i B p B + R ψ + R η + R in = const p ei + m i n i u i const Plasma viscosity Neutral force Reduced version similar to Bernoulli equation 30

Parallel plasma pressure drop in the leg is mainly balanced by CX interaction with neutrals Analyzing a representative case: SXD, P 1/ =0.6 MW A B Prad [W m-3] 1e1 1e3 1e5 1e7 Te [ev] 1 5 0 Ni [m-3] 1e19 3e19 1e0 3e0 Ng [m-3] 1.0e19 1.5e19.0e19 3.0e19 Plasma par. momentum balanced by In radiating zone: neutrals, viscosity, and convection Below radiating zone: neutrals Pressure [Pa] P+ρv...+R in...+r η...+r ψ A P B Target plate Poloidal index 31

Analysis of energy fluxes in divertor leg shows that most entering energy ends up on outer wall Analyzing a representative case: SXD, P 1/ =0.6 MW About 30% of input power P 1/ enters outer leg* q pol =187 kw Radiation: C - 4 kw, H - 34 kw About 1/ of power entering outer leg goes to outer wall with plasma and neutral energy flux q ei =10 kw q bind =5 kw q ei =54 kw q bind =39 kw q pol =3 kw The rest of power entering outer leg is lost with impurity and hydrogen radiation * the rest goes to outer walls above X-point and inner leg 3

Neutral particles confinement controls position of detachment front Analyzing a representative case: SXD, P 1/ =0.6 MW Plasma recycling coef: 100% Prad [W m-3] 1e1 1e3 1e5 1e7 Ni [m-3] 1e19 3e19 1e0 3e0 Neutral albedo: 99.5% Te [ev] 1 5 0 Ng [m-3] 1.0e19 1.5e19.0e19 3.0e19 Similar results if reducing plasma recycling coefficient Neutral particles confinement in the leg appears to control detachment front location 35

Summary Capability to model divertors with a secondary X-point is developed in UEDGE, enables analysis of novel configurations Several divertor configurations are studied computationally (long/short leg, with or without secondary X-points), for parameters matching design of ADX tokamak Steady-state fully-detached divertor regimes found for long-legged tightly baffled divertors, for a broad range of parameters Entering detached state at high input power Detachment front stays far away from main plasma Secondary X-point in divertor leg extends detached operation window - factor of 10 improvement compared to standard divertor! Neutral confinement in divertor controls detachment front position Promise of stable fully-detached operation for high-power tokamak 36

Backups 37

UEDGE (Unified EDGE code) solves a system of fluid equations in axisymmetric tokamak geometry plasma density ion momentum electron thermal energy ion thermal energy neutral density ad-hoc radial transport neutral momentum charge conservation sheath bound. cond. t (n i) +! (n i ui ) = S r + S i t (mn u ) + (mn u! i i i iu i η i u i ) = P i + mn N n i K cx (u N u i )+ ms r u N ms i u N t (3 / n et e ) + ( 5 n! et e ue + q! e ) = u! e (3 / n e T e ) Π e u! e +Q e t (3 / n it i ) + ( 5 n! it i ui + q! i ) = u! i (3 / n i T i ) Π i u! i +Q i t (n ) + (n! N Nu N ) = S r S i n N u N = D N n N q = n χ T; n i u = D i n i t (mn Nu N ) +! (mn N u N un η N u N ) = P N mn N n i K cx (u N u i ) ms r u N + ms i u N J(φ) = 0 J = en B x 0.51mν B 1 n P e x e φ J r = σ E r φ = Te e ln π J enu i env te x + 0.71 T e x UEDGE finds steady-state and transient solutions, mainly used for interpretation of edge plasma experiments T. D. Rognlien et al., J. Nucl. Mater. 196 198, 347 (199) 38

X-point target divertor study is motivated by the ADX tokamak concept discussed at MIT PSFC *B. LaBombard et al., Nucl. Fusion 55, 05300, 015 ADX = Advanced Divertor and RF tokamak experiment* Designed to address critical gaps on pathway to next-step devices Advanced divertors Advanced RF actuators Reactor-prototypical core plasma conditions 39

X-point target divertor is a component of ADX tokamak concept discussed at MIT *B. LaBombard et al., Nucl. Fusion 55, 05300, 015 XPT starts with the SXD idea, but places an X-point in the confined plasma Similar to SXD exploits 1/R geometric reduction of divertor heat flux May produce stable X-point MARFE localized to the divertor chamber 40