Transport in a field aligned magnetized. C.M. Cooper, W. Gekelman, P. Pribyl, J. Maggs, Z. Lucky

Transcription

1 Transort in a fild alignd magntizd lasma and nutral gas boundary: Th nd of th lasma C.M. Coor, W. Gklman, P. Pribyl, J. Maggs, Z. Lucky UnivrsityofCalifornia California, LosAngls Fbruary 15, 2013

2 Motivation Ovrviw Rlation to Auroral Physics, Divrtor Physics Summary of Enormous Toroidal Plasma Dvic Modl of ETPD lasma rgions Nutral Boundary Layr modl: Plasma Trmination 1. Occurs at lasma/nutral gas rssur quilibrium 2. Plasma trminats on currnt fr ambiolar shath dtrmind by a gnralizd Ohm s law 3. Hating, ionization occur in NBL Masurd scaling laws in ETPD

3 Motivation: Aurora Th auroral arccurrnt arc currnt loo associatd with a rndicular lctric fild imosd in th magntoshr [Borovsky 1993] Aurora ovr Jokulsarlon Lak, Icland Sthan Vttr, Nuits sacrs Fb Schmatic viw of aralll currnts j, lasma motions, v r, lctric filds, and otntial contours abov auroral arc, sktchd in grn [Harndl 1996] J. Borovsky, J. Go Rs 98, A (1993) G. Harndl, J. Atmos. Trr. Phys. 58, (1996)

4 Motivation: Gasous Divrtors Gasous divrtor dsign for DIII D Gasous divrtor dsign for JET Gasous divrtors dsignd to dissiat lasma articls, momntum, and nrgy on nutral gas bfor touching wall R. W. Conn, Fusion and Eng. Dsign (1991)

5 Diagram of th ETPD Toroidal Magnts Vrtical Magnts LaB 6 sourc ETPD Plasma (rd) rovid a 250 G confining fild (blu) rovid a 6 G vrtical fild to sac out rings injcts rimaris to form thn hat th lasma (ink) follows th hlical magntic fild u to 120 m C.M. Coor t al, Rv of Sci Inst (2010) R.J. Taylor t al, Nuclar Fusion (2002)

6 Pictur of a LaB 6 Cathod Fram and Shilding Hatr Anod Cathod

7 Primary lctrons boild off LaB 6 ar acclratd along th fild by anod. Primaris ioniz nutral gas to crat and hat lasma. Data takn whr lasma nds, 90% around machin. Exrimntal Stu

8 Nutral Boundary Layr Prob 400 V discharg 2 mtorr 300 V discharg 2.5 mtorr 2.2 ka 220 V discharg 3.6 mtorr

9 220 V HEAT Enrgy Balanc in ETPD Hlium Gas B <100 kv Ionoshr i i i i i HEAT Atmo shr Enrgy Balanc in Aurora

10 3 Zons in ETPD Plasma Hat Dnsity + Thrmalization Conduction/ Ohmic Hating of rimaris ionization and cooling + ionization > Radial diffusion Ionization and y losss Radial diffusion Tk Tak Data Enrgy inut lngth Enrgy loss lngth λ mf, rim ~ 15 m Γ / rγr ~ 15m ν Efild Trm. in / v ~ 1. 5 m

11 Ambiolar Trmination Shath in NBL! Plasma otntial in nutral gas boundary indicativ of larg fild alignd lctric fild Rlativ y coo ord (cm) Φ (V) Rlativ x coord (cm) Rlativ x coord (cm) Rlativ x coord (cm) Rlativ x coord (cm) Nutral fill of 3.6 mtorr H, a lasma discharg of 194 A 220 V, Btor=250 G, Bvr=6 G,

12 Gnrat Radial Profils Usd to study rat at which articls, momntum, and hat mov across th fild and out of th lasma Rlativ y coo ord (cm) Φ (V) Rlativ x coord (cm) Rlativ x coord (cm) Rlativ x coord (cm) Rlativ x coord (cm) Nutral fill of 3.6 mtorr H, a lasma discharg of 194 A 220 V, Btor=250 G, Bvr=6 G,

13 Gnrat Axial Profils in NBL A B C Plot data along th cntr of lasma coordinat s Thr zons! A B C Rlativ y coo ord (cm) Φ (V) Rlativ x coord (cm) Rlativ x coord (cm) Rlativ x coord (cm) Rlativ x coord (cm) Nutral fill of 3.6 mtorr H, a lasma discharg of 194 A 220 V, Btor=250 G, Bvr=6 G,

14 Nutral Boundary Layr Modl Thr fluid, currnt fr Continuity quation: ionization and losss ( ) Γ =,, s S v n s Momntum quation rssur quilibration Continuity quation: ionization and losss ( ) Γ =, n, s n n S v n s A Momntum quation: rssur quilibration ( ) ( ) 0,,,, Γ + Γ = + n s n s i n v v m s A ( ) ( ) n s n s B n s v v m n T k n t E ν,, = Momntum quation: gnralizd Ohms Law s B s s,, T 3 Hat quation: ionization and Ohmic hating C ionz s s B s S E E v n s T k v n =,, 2 3 C

15 For Zon A: Prssur Equilibration Diffusivity argumnt: Nutral dnsity convctd out along fild by lasma, diffuss across fild Drag forc limitd to cross fild nutral diffusion rat Axial nutral flow dvlos from forc balanc Momntum gaind from lasma Momntum lost to stationary nutrals

16 Elctron Tmratur in Zon A Φ (V) T T = 2. 2 V Constant T Ionization ~ 0 λ = m m i ΔT λn ~ 100 m (V) Distanc from anod (cm)

17 Plasma Vlocity in Zon A Φ (V) vcr, s = 2 10 cm / s Γ ~ D 0.4 v, a, Γn, ~ Dn, a (10 5 cm/s) Distanc from anod (cm) asma mach at 2.2 V 0.5Pl Plasma vlocity is flat Momntum balanc = miv, s rγ, r + s m n v v 0. 5ν + ν i ( )( ), s n, s Sts a critical vlocity v q = c, s s Γ, Γ, + Γ in n, cx

18 Φ (V) Plasma Dnsity in Zon A v Plasma dnsity is droing from radial losss, s n s = r Γ, r = D r n λ 2 n 0.8 (10 12 /cm 3 ) 0.4 D a, D r D Bohm D r λ ~ 4Da, ~ ~ 10 cm 1 2 D Bohm Distanc from anod (cm)

19 Zon B: Ambiolar Elctric Fild Currnt fr lasma ss nutral gas at nd Elctrons sto, ion currnt ntrats Elctric fild dvlos, drivs lctron currnt Elctric fild maintains Currnt tfr trm.

20 Potntial Structur in NBL Plasma isoil form nstd otntials V s Whit arrows show lctric fild, aralll l fild 10x Quasinutral λ n λ i Colorma of lasma otntial from Colorma of lasma otntial from 1,300 oints introlatd onto toroidal coordinats λ D

21 Φ (V) Elctron Tmratur in Zon B Φ Elctron tmratur riss with otntial For m λ n < L ΔΦ < λ m Φ T ΔT~ΔΦ ~ (V) V m i n Distanc from anod (cm)

22 Plasma Vlocity in Zon B Φ (V) v (10 5 cm/s) Distanc from anod (cm) asma mach at 2.2 V 0.5Pl Plasma vlocity dros du to drag on nutrals

23 Th diffrnc btwn momntum Elctrons and tmratur loss Ions Momntum loss: Momntum loss: ν n fastr. 5ν + ν slowr Enrgy loss: m ν n mi slowr in cx Enrgy loss:.5ν in+ ν cx fastr In lctric fild, lctrons In lctric fild, ions

24 Plasma Dnsity in Zon B Φ (V) n (10 12 /cm 3 ) 0.4 Plasma dnsity is droing from radial losss Balanc btwn Flux consrvation v n, s Adiabatic hating T n Distanc from anod (cm)

25 Plasma Trmination Us gnralizd Ohms law to solv for lctric fild 0 E = s T s 0 n E ( t n ) n E m v, sν n 0.19 ~ 2 V / m for t n = 0.1 m n v, s ν n E J Ji = =, Jtot = 0 ασ ασ n n

26 Zon C: Additional Ionization T =2. 2V R. K. Janv, Elmntary Procsss in Hydrogn and Hlium Plasmas (1987)

27 Elctron Tmratur in Zon C Φ (V) Prdiction: Elctron tmratur continus to ris raidly with otntial ti T (V) Distanc from anod (cm)

28 Elctron Tmratur in Zon C 1 Φ (V) 2 3 ΔΦ ~2. 5V T 3 (V) 2 < σv> < σv> 4.7V 2.2V ~ Distanc from anod (cm)

29 Φ (V) Plasma Dnsity in Zon C Prdiction: Plasma dnsity continus to dro n 0.8 (10 12 /cm 3 ) Distanc from anod (cm)

30 Plasma Dnsity in Zon C 1 Φ (V) n 0.8 (10 12 /cm 3 ) 10% Distanc from anod (cm)

31 Plasma Production in Boundary If all nrgy gaind wnt into lasma roduction how much could you mak? For T = T, v = v Δn n = Ε ΔΦ + T ionz QΔΦ = Q ionz 2.5 V 24.6V + 2.2V What s th man fr ath of ionization? i i n = v z ~ 10 cm < <σ v> n > 4. 7V b a ~ 10% Any nrgy gaind by lctric fild is quickly absorbd by ionization b a

32 Φ 1 2 Plasma Vlocity in Zon C Prdiction: Plasma vlocity will dro to 0 (V) v (10 5 cm/s) Distanc from anod (cm) asma mach at 2.2 V 0.5Pl

33 Plasma Vlocity in Zon C 1 Φ (V) v (10 5 cm/s) Distanc from anod (cm) asma mach at 2.2 V 0.5Pl Additional flux is gnratd tdby th ionization at th nd of th lasma Still slowing down aftr ionization nds

34 P =(n (T i +T )/(n n T n )) NBL Consrvd Quatitis Normalizd Plasma Prssur: =n v,s Γ,s 4 2 Axial Plasma Flux: Distanc from anod (cm) Distanc from anod (cm) 0 Normalizd Plasma Prssur: End of th lasma occurs whr = n Droing rssur intrrutd by trmination ti E fild Plasma flux: Masur of axial articl flux Only loss of axial flux is radial flux Filling in of rofil Kintic ffcts (trad articls)

35 Scaling of Ambiolar Elctric Fild Th otntial marks a footrint for th boundary of th lasma 49 kw 43 kw 39 kw Th location and magnitud of Elctric fild trminating i th lasma chang as a function of inut owr Masur lasma aramtrs

36 Scald Plasma Paramtrs r NBL (a) T is flat at V (b) Extra owr raiss dnsity Axial flow dros (c)

37 Scaling Study = n s q,m =s q,t E s,m =E s,t Masurd lctric fild, E s,m, Masurd trmination oint, scals lik th thortical ti s q,m, coincids id with location of ambiolar valu rssur quilibration E s, t 2 m v, sν v n, sr ( T + Ti ) n ( s0) s = q, t ln 0.19 Dr Tnnn

38 Modifid Ambiolar Flow in ETPD Elctron currnt Ion currnt Elctron currnt Ion currnt Elctron currnt Ion currnt

39 Ambiolar Flow in NBL Magntic fild data from rob indicats axial currnt Ngativ currnt carrid by lctrons moving in ositiv dirction Data takn at s = 2870 cm, halfway through NBL

40 Non Zro Currnt in NBL NBL not currnt fr Currnt trnds to zro J = B T, mas mas Driftsd associatd with currnt << bulk flow

41 Tys of Currnt Not: Stady stat so J olz = 0 Som currnts ar associatd with articl drifts and transort Transor rt Causing Non Trans ort Causing Som currnts divrg and nd to b closd to maintain J=0 Divrgnc Fr Poloidal Hall (i n) Currnt (+) Poloidal Diamagntic Currnt ( ) Non Divrgnc Fr Paralll ( n) Currnt RdilPd Radial Pdrson (i n) Currnt Vrtical/ B Currnts

42 Estimation of J r J r Axial currnt tid to Radial currnt J S A r J So+DS = J So + J r A S Kirchoff s Junction Rul E * r = E r J ir r n = σ r = E * in, r m i v ir ν in

43 Futur Work on NBL Obsrvational Masur lasma otntial and flows in Aurora Exrimntal Study NBL for diffrnt rssurs and/or gass Simulation Modl in DEGAS (nutral gas collisional cod)* Modl in UEDGE (transort cod)* Rung Kutta solvr for fluid modl**

44 Futur work: 1.5 D Simulation Masurd 5 things: Modl nutral gas n, T, v, φ, Solv 5 quations + nutral gas transort: i J v n z z z n + v z = S n n v z v z z = T n z + Ξ T z + n φ + z Σ v v z n z iz n + viz = S in n v iz v z iz = T i n z n φ + z Σ iv 3 T q v z Gnralizd Sourc/Sink n vz = n T + ST 2 z z z calibratd by data

45 Conclusions Plasma trminats on ambiolar lctric fild Elctric fild occurs whr diminishing lasma rssur and nutral rssur quilibrat NBL dominatd by trmination fild through Ohmic hating and ionization NBL has a small modifid ambiolar diffusion du to diffrncs in dirctional articl motilitis

46 Thanks!