Study of Plasma Detachment in a Simplified 2D Geometry using UEDGE

Study of Plasma Detachment in a Simplified 2D Geometry using UEDGE M. Groth 1, M.A. Mahdavi 2, G.D. Porter 1, T.D. Rognlien 1 1 Lawrence Livermore National Laboratory, Livermore, CA 9455, USA 2 General Atomics, P.O.Box 8568, San Diego, CA 92186, USA

Plasma detachment in fusion devices: How / Can we control the degree of detachment? Heat fluxes predicted for next-step fusion devices will cause ablation of divertor target plates reduction needed Detached plasma» Cold (1eV) and dense (n div >1 2 m -3 ) divertor plasma» Formation of an ionisation front, hot plasma well-separated from material surface» Momentum and heat losses (plasma flow and temperature) synergetically linked advantageous operational regime Experimentally well-achievable regime; but, lack of detailed analytic description allowing active control

Detachment in experiment: formation of ionisation and recombination-dominated zones.8 Attached (a).8 Detached (c) DIII-D shot: 93993 (Fenstermacher, PSI1998) Z (m) 1. 1.2 1.4 Z (m) 1. 1.2 1.4 Dalpha radiation from ionisation (ionisation front).8 (b).8 (d) 1. 1. Z (m) 1.2 1.4 1. 1.2 1.4 1.6 1.8 Major Radius R (m) Z (m) 1.2 1.4 1. 1.2 1.4 1.6 1.8 Major Radius R (m) Dalpha radiation from recombination (recombining plasma) 1 2 4 a.u. 1 2 3 4 a.u.

Use UEDGE to simulate detached plasmas in 2D slab geometry to...... determine and describe the main processes that cause and affect plasma detachment... study n core and P heat - dependence of the position of ionisation front (ionisation of hydrogen ~ 5eV), i.e. what is L Te=5eV n x core Py heat? Active control of detachment in current and future fusion devices... study sensitivity of boundary conditions on UEDGE solutions» How significant is wall pumping?» What is the effect of the assumption for the ion speed at the target on the location of the ionisation front?

Highlights UEDGE simulations of plasma detachment in 2D geometry reveal... Location of ionisation front is chiefly determined by» parallel heat flux into divertor SOL» radial heat transport from SOL into PFR below x-point» radiation losses due to ionisation of recycling neutrals Highest separation of plasma - wall at high n core (ionisation front close to x-point) High heating power permits highest degree of volumetric recombination and momentum flow reduction No further reduction of peak heat flux density once plasma detached

Computational domain: 2D slab geometry Hydrogenic plasma - no impurities!.4 x outer wall y Separatrix scrape-off layer plasma -.1 core plasma private flux region..75 1. upstream core boundary x-point target D =.5 m 2 /s, χ =.7 m 2 /s, spatially constant Ion removal at target (2%), neutral pumping outer wall (1%) n core and P heat defined at core boundary

Braginskii Equations for momentum and power flow in UEDGE 2D slab geometry Momentum equation (plasma): η η x mnu u i Bx Pp i i i ix ix ux B x y mnu i i i u i + iy iy + uy = S i mom Energy equation (electrons): x 5 2 nu e exte kex T x e + y nu e eyte key P u e P u e u B x Pp = ix iy i + K ( T T )+ S x y B x 5 2 T y e q e i Ee

Base case results (energy equation) Power Density (W/m 3 ) Variation of Power Density along Separatrix ionisation front 1 1 7 25 Te 2 5 1 6 Eqp 15 q_pol q_rad 1-5 1 6 5 SeE -1 1 7 x-point.2.4.6.8 1 Poloidal Distance (m) Electron Temperature (ev) Significant outflow of heat from SOL into PFR due to geometry plasma cooling spreading of heat over larger area Inside ionisation front: plasma cooling due to radiation, but also electron heating due to i-e temperature equipartition Recombining plasma zone: T e ~ 1eV, but still significant radiation losses due to recombination / ionisation

Base case results (momentum equation) Momentum Density (N/m 3 ) Variation of Momentum Density along Separatrix 2 15 1 5-5 -1-15 Ion Parallel Velocity dp/dx MomLoss du/dy d(mnu 2 )/dx 1 1 4 5 1 3-5 1 3-2 -1 1 4.2.4.6.8 1 Parallel Ion Velocity (m/s) Significant pressure drop along SOL:» x-point: due to viscosity» target region: CX momentum losses Ion speed responds to decrease in plasma temperature shear around x-point CX momentum losses reduces ion speed onto target plate Poloidal Distance (m)

Ionisation zone moves toward x-point and spreads radially in strongly detached plasmas Attached plasma: ionisation occurs nearby strikepoint Detached plasma: ionisation front moves to x-point core radial wall SOL Core XPT PFR nen<σ ion v> upstream poloidal target

Recombination zone expands both poloidally and radially in strongly detached plasmas Detachment onset: recombination zone adjacent to target (also in PFR?) Strongly Detached plasma: cold plasma fills space between ion.front and plate core radial wall SOL Core XPT PFR neni<σ rec v> upstream poloidal target

Ionisation front moves toward x-point at higher core plasma density Density (m -3 ) 6 1 2 5 1 2 4 1 2 3 1 2 2 1 2 1 1 2 n core =7.5x1 19 m -3 n core =2x1 2 m -3 Te Ionisation Fronts n plasma n neutral.75.8.85.9.95 1 x-point Poloidal Distance (m) 25 2 15 1 5 Electron Temperature (ev) Higher core plasma densities at constant heating power give rise to... Lower T e in upstream SOL Lower influxes of heat into divertor Heat is convected rather than conducted Lower divertor plasma densities, but higher divertor neutral densities Shallower temperature gradients inside ionisation front

Ionisation front moves closer to the target at higher input power 1.5 1 21 Pin=1x1 4 W Pin=2x1 4 W Ionisation Fronts 25 Higher input power at constant core plasma density give rise to... Density (m -3 ) 1 1 21 5 1 2 Te n plasma 2 15 1 5 Electron Temperature (ev) Higher T e in upstream SOL Higher influxes of heat into divertor Larger divertor plasma and neutral densities.75.8.85.9.95 1 x-point Poloidal Distance (m) n neutral Steeper temperature gradients inside ionisation front

Ionisation front moves closer to target at lower wall pumping rates Density (m -3 ) 6 1 2 5 1 2 4 1 2 3 1 2 2 1 2 1 1 2 P wall =1% P wall =.5% Te Ionisation Fronts n neutral n plasma.75.8.85.9.95 1 x-point Poloidal Distance (m) 2 15 1 5 Electron Temperature (ev) Decreasing the wall pumping rate gives rise to... Higher divertor neutral densities Similar divertor plasma densities Modest drop in upstream T e at x-point Similar T e gradients inside ionisation front

Location of ionisation front insensitive to ion speed setting at the target Ion Velocity (Mach Number) 1.8.6.4.2 Mach(target)=1 Ionisation Front Mach(target)=.1.75.8.85.9.95 1 25 2 15 1 5 Electron Temperature (ev) Reducing the Mach number at the target plate for detached plasmas gives rise to... Identical temperature profile no changes to ionisation front location However, varying Mach number for attached plasmas slight changes to temperature and density profiles Poloidal Distance (m)

Result I: Location of the ionisation front in core density - heating power space Contours of constant distance between ionisation front (T e =5eV) and target plate Core Plasma Density (m -3 ) 2.5 1 2 2 1 2 1.5 1 2 1 1 2 5 1 19.2m.15m.1m.5m Significant separation of plasma from wall require high core plasma densities Increasing heating drives plasma closer to target even higher core densities needed Non-linear relationship between location of ionisation front and core density / heating power 5 1 1 4 1.5 1 4 2 1 4 2.5 1 4 Heating Power (W)

Result II: Roll-over of ionisation current with n div, threshold for vol. recombination at high P heat? Density (m -3 ) 1.5 1 21 1 1 21 5 1 2 Divertor Density 2E4W 1.5E4 1E4W 7E3W 5E3W 1 2 3 4 5 Normalised Core Density Iion ni,div Recombination Current 1 2E4W 8 Ionisation Current (Part/s) 1 8 6 4 2 Ionisation Current 1 2 3 4 5 Normalised Core Density 2E4W 1.5E4 1E4W 7E3W 5E3W Irec n 2 i,div VRDR I rec (Part/s) 6 4 2 1.5E4 1E4W 7E3W 5E3W 1 2 3 4 5 Normalised Core Density

UEDGE density normalised to predicted upstream density by 2-Point Model Use Two-Point Model (1D Model) to predict upstream SOL density (detachment onset, T t = 1eV) : nup 2PM = m 2 i e q 2 4/ 7 7 ql 2 κ e γ 2 e 2 T t Estimate width of parallel heat flux density: q P in λ q BT BP

Result III: Fractions of plasma momentum lost to neutrals larger at high heating power.6 CX Momentum Losses Smom ni,rdr n,rdr VRDR CX Momentum Losses.5.4.3.2.1 2E4W 1.5E4 1E4W 7E3W 5E3W 1 2 3 4 5 Normalised Core Density Plasma momentum integrated over PRF and SOL domain in divertor, over SOL upstream Higher heating power higher ion densities in divertor larger momentum removal Drop in ion density as ionisation front moves off target compensated by increase in neutral density and RDR width

Result IV: Peak heat flux is reduced and shifted radially outward in transition to detachment Electron + ion heat flux density measured at divertor entrance (xpoint) and target attached plasma plasma at detachment onset 1.2 1 6 1.2 1 6 1 1 6 q div 1 1 6 q div q par,e +q par,i (W/m 2 ) 8 1 5 6 1 5 4 1 5 2 1 5 q target q t /q div ~.3 q par,e +q par,i (W/m 2 ) 8 1 5 6 1 5 4 1 5 2 1 5 q t /q div ~.3 q target -.1.1.2.3.4 Radial Distance (m) -.1.1.2.3.4 Radial Distance (m)

Peak heat flux is reduced until onset of detachment, no further reduction once detached P Rad,SOL / P heat 1.8.6.4.2 Radiation Heat Losses 2E4W 1.5E4 1E4W 7E3W 5E3W 1 2 3 4 5 Normalised Core Density q,rdr q,up Prad n 2 div Radiated power integrated over PRF and divertor SOL domain Sharp increase in power losses when plasma is attached (.1 n 1.5) core,norm P rad approaches unity and then decreases as entire SOL plasma becomes cold (T e ~5-1eV) High fraction of P rad are sustained at high heating power