D. A. D Ippolito, J. R. Myra, and D. A. Russell Lodestar Research Corporation

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1 D. A. D Ippolito, J. R. Myra, ad D. A. Russell Research Corporatio Preseted at the 33rd EPS Coferece o Plasma Physics, Rome, Italy, Jue 9-3, 6

2 Coheret structures ( blobs ) created by edge turbulece covective trasport of particles ad heat across the SOL Experimets, simulatios ad theory show that the trasport rate icreases with collisioality. q q icreased collisioality Λ (ad resistivity η ) strog ballooig (discoectio from sheaths) faster ExB drift ew -regio D code ecapsulates the essetial physics reduced coectio to sheaths, larger turbulet flux at high Λ A correspodece rule (γ v x /a b ) has bee exploited to uderstad ew regimes of blob trasport q icludes collisioality ad geometry depedece q valid i ear SOL ad edge regio (blob birth zoe) q blob trasport ~ mixig legth trasport i edge plasma at high Λ

3 -regio thermal equilibrium model gives good agreemet with C-Mod experimets q covective desity limit (CDL) due to thermal istability q CDL correspods to q > q i edge plasma q occurs at high collisioality The geeral picture from all of this work is that: q q the distictio betwee edge ad SOL disappears at high collisioality because of shorter L ~ λ ei edge trasport icreases dramatically ad ca be estimated usig collisioal blob models with packig fractio ~

4 BOUT simulatio with δ/ ~ by X. Xu (3); Blob aalysis by D. Russell (4) 3D structure is importat! desity ad collisioality Λ icrease with time (gas puffig) blobs discoect from divertor regio ad move faster as η ad Λ icrease Φ eφ (ev) coected outboard midplae OM D divertor.5..5 t (ms) t (ms) discoected Russell et al, Phys. Rev. Lett 4

5 !" η ν e Λ Curvature drift curret source η J sheath Effective circuit resistace R eff potetial Φ R eff J κ L growth rate γ (liear) E B speed v x (blob) J η J pol divertor J κ + X-poit midplae large η Λ discoectio

6 # I the edge plasma, the blob ad mixig legth trasport estimates agree i order of magitude provided that the blob packig fractio ~ (skewess ~ ) ad we use the blob correspodece rule (see ext page). Mixig legth estimate: v~ x ~ ~ ~ i k ~ Φ, / ~ k Φ /( ωl Use saturatio coditio: Blob estimate: ω ), ~ ~ k Φ ~ ω/ k v~ ~ ~ Γ ~ Re[ v x ] ~ γ /(k L ) Γ ~ bvx where b ~ ad vx ~ γ a b (correspodece rule) Usig the correspodece rule, both estimates agree.

7 As oted by Edler et al. (NF 995) for sheathiterchage modes, there is a correspodece betwee the liear istability ad the resultig turbulece. For all istabilities that saturate by wave breakig ( ω ~ k v~ ) we postulate the followig correspodece rule betwee the istability ad the blob velocity: γ v a x b, k a b, L a b growth rate waveumber desity scale legth blob radius

8 $ %! Notes: similar eqs. for T j, but T = cost. here Bohm uits (dimesioless) charge d dt J Φ pol = : J J / L : β y curvature d Φ = (J3 J dt J pol : J sh : J ) / L desity d dt + Γ / L =, Γ = c s, d dt = ( Γ Γ3 ) / L, Γ3 = c s, d dt = + v t J σ ( Φ Φ), J3 = α Φ = L

9 $ " % &'$( Field lies from midplae regio (x, y) are mapped to stretched / squeezed coordiates i X-poit regio (x, y) by faig factor f <<. At preset the model eglects magetic shear. y Outboard Midplae = f, = x x y f y. x X-Poit y x charge is coserved betwee regios ad sheath boudary coditios are applied at the ed of regio J = ecs e ( e( Φ Φ ) ) / T e 3T e

10 ) " φ λφ, t λ σ λ ( ρ s 5 4µ / R, L σ, µ 3 / R) λ t, 5 3µ x ( ρ λ s µ / R, L x for arbitrary λ, µ / R) ivariat scalig method: Coor & Taylor, Phys. Fluids 984 the followig ivariat combiatios characterize the dimesioless parameter space (Λ = collisioality, Ω = scale size) Λ = ω ω η s ω a = ν Ω e e L ρ s, ω Ω = γ s mhd = L R L dispersio relatio ca be writte as ω = ω Λ, Ω(k), ε] ˆ mhd / same dispersio relatio applies to blobs usig the correspodece rule: ω v x /a b ad L, /k a b γ ω k ˆ[ ρ s,

11 Y (Poloidal) %$ & *( +, N Time = 4 a σ =. Λ = X (Radial) b σ =. Λ = c σ =. Λ = d σ =. Λ =.5... Vx.5.. Ω = Blob Dispersio Relatio with VxIm 5 Ω = 36 blobs speed up with icreasig collisioality Λ ( resistivity) for low Λ, small blobs move fastest (b: Ω = (a b /a * ) 5/ blob size)

12 collisioality Λ discoected RB ω Λ = ε / Ω IC ω ε / Λ = Ω ω Λ/Ω RX CR CR s ω /Ω coected electrostatic -regio model Ω = (a b /a * ) 5/ a* = ρ s 4/5 L /5 / R /5 ε ε x = f = X-pt faig factor /ε / scale size Ω

13 $ The two-regio fluid turbulece code predicts a icrease i turbulet particle flux with collisioality, as see i experimets. Figure: Time history of the turbulet (blob) particle flux Γ for two values of the collisioality parameter Λ with f = /4. Γ is averaged over poloidal directio y for a fixed radial poit i the SOL. Note the earlier oset of the oliear turbulet phase ad the much larger particle flux for large Λ. ~ ~ v x y collisioality parameter Λ = Λ at top of pedestal Λ = Λ = t D. Russell (6)

14 -. (x,y) φ (x,y), t.max PHI_, t.max.344 f = /4, β =, σ 3 =, t = Λ = y y, t.max PHI_, t.max.74 Note: more blobs ad faster v x as Λ icreases Λ = y y x D. Russell (6) blobs x

15 Λ Σ3 Σ a b c ix Red: midplae Blue: X-poit Λ = Λ φ (t), φ (t) x,y at x = b Φ x, Ly t max (l ) at x = b f = /4, β =, σ 3 = Λ = Λ Φ x, Ly t partially discoected: φ (t) > φ (t) D. Russell (6)

16 I this work, we iclude heat trasport i a aalytic -regio model for (Φ, T e ) with, = cost. SOL thermal equilibrium limit desity limit higher desity higher collisioality faster radial heat trasport lower T thermal istability thermal collapse of SOL C-Mod observes covective desity limit (CDL) with q > q our model CDL whe q icreases as X-poit cools (thermal istability aalogous to MARFE with radiative coolig radial covectio) (D Ippolito ad Myra, Phys. Plasmas, Jue, 6)

17 . T H H H T warm X-pt. cold X-pt. T T = midplae, T = X-pt T T H C C heat covectio warm X-pt root (solid) is thermally stable cold X-pt root (dashed) is ustable thermal istability of SOL.8.6 Q.4. Q Q Q Q C fixed root coalescece = CDL C

18 %$ ))" $/ # Model C-Mod data.8 Q Q.6.4 Q Q. Q heat covectio C α d Λ / C / LaBombard et al, NF 5

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