Collective Focusing of a Neutralized Intense Ion Beam Propagating Along a Weak Solenodial Magnetic Field

Transcription

1 Havy Ion Fusion Scinc Vitual National Laoatoy Collctiv Focusing of a Nutalizd Intns Ion Bam Popagating Along a Wak Solnodial Magntic Fild M. Dof (LLNL) In collaoation with I. Kaganovich, E. Statsv, and R. C. Davidson (PPPL) DOE Plasma Scinc Cnt, Tlsmina, Apil 19, 01 This wok was pfomd und th auspics of th U.S. Dpatmnt of Engy y th Lawnc Livmo National Laoatoy und contact DE-AC5-07NA7344, and y th Pincton Plasma Physics Laoatoy und contact AC0-76CH-O3073 LLNL- PRES

2 Motivation: Contolld Fusion W. Shap t al,

3 Intial Confinmnt Fusion: Lass Vsus Ion Bams Psnt appoach Las Divn ICF National Ignition Facility (LLNL, Livmo, CA) Pomising altnativ Havy Ion Fusion Why ion ams? High poduction fficincy and ptition at High fficincy of ngy dlivy and dposition 3

4 Ion-Bam-Divn High Engy Dnsity Physics Havy Ion Fusion (Futu) Wam Dns Matt Physics (Psnt) D-T ρ~1000 g/cm 3 T~ 10 KV I total ~100 ka τ ~ 10 ns E ~ 10 GV Atomic mass ~ 00 I ~1-10 A τ ~ 1 ns E ~ MV Ions: K +, Li + foil Psntly accssil ρ-t gim ρ~1 g/cm 3, T~0.1 1 V cosponds to th intios of giant plants and low-mass stas Block schm of an ion div fo high ngy dnsity physics ion souc acclation and tanspot nutalizd compssion final focusing tagt 4

5 Nutalizd Dift Compssion Expimnt (NDCX) Havy ion div fo Wam Dns Matt Expimnts Built and opatd at th Lawnc Bkly National Laoatoy 5

6 Nutalizd Dift Compssion Expimnt (NDCX) Schmatic of th NDCX-I xpimntal stup (LBNL) Final Focus Solnoid Tagt 8T Fing magntic filds Bam paamts at th tagt plan K 300 kv (β =0.004) upgad I ~ A, < 5 mm (n ~10 11 cm -3 ) NDCX-II T tagt ~0.1 V Li 3MV (β =0.03) I ~30 A, ~1 mm (n ~ cm -3 ) T tagt ~1 V 6 Wak fing magntic filds (~100 G) pntat dply into th ackgound plasma

7 Outlin I. Enhancd slf-focusing of an ion am popagating though a ackgound plasma along a wak (~100 G) solnodial magntic fild plasma ion am B 0 v - impotant fo th dsign of a havy-ion div (.g. NDCX nutalizd dift sction) can utilizd in ion am slf-pinch tanspot applications (.g. HIF divs) II. Collctiv Focusing (Rotson) Lns nutalizd ion am -, i + magntic lns B 0 can usd fo th ion am final focus (.g. NDCX-I, II) phaps can utilizd fo collimation of las gnatd poton ams Collctiv focusing with B 0 ~ 1 kg is quivalnt to standad magntic focusing with B 0 ~10 T 7

8 I. Ion Bam Popagation though a Nutalizing Backgound Plasma Along a Solnoidal Magntic Fild plasma ion am v - B 0 8

9 Magntic Slf-Pinching (B 0 =0) Th ion am spac-chag is typically wll-nutalizd What aout ion am cunt? z B slf am B slf t Ez Inductiv fild acclats lctons λ=c/ω p collisionlss lcton skin dpth (n p ~10 11 cm -3 λ~1.7 cm) dfins th chaactistic lngth scal fo scning cunt (o magntic-fild) ptuations in a cold plasma ( inductiv analog of th Dy lngth) (a) <c/ω p j c/ω p j cunt is not-nutalizd (locally) maximum (j xb slf ) slf-pinching () >c/ω p j = j cunt is wll-nutalizd (locally) ngligil slf-pinching Elcton adial foc alanc V z E V E B slf V z c Cunt nutalization ~ Z n n 1 Magntic pinching is dominant B slf V c 9

10 Enhancd Collctiv Slf-Focusing (B 0 ~100 G) P m V A A c B 0 const Radial displacmnt of ackgound lctons is accompanid y an azimuthal otation Stong adial lctic fild is poducd to alanc th magntic V B foc acting on th lctons This adial lctic fild povids nhancd ion focusing F sf fo Z m V V c 1 n p 1 dn d c p Th is a significant nhancmnt of th ion am slf-focusing ffct in th psnc of a wak solnoidal magntic fild (fo <<c/ω p ) 10 M. Dof t al, PRL 103, (009).

11 Enhancd Slf-Focusing is Dmonstatd in Simulations Gaussian am: =0.55c/ω p, L =3.4, β=0.05, n =0.14n p, n p =10 10 cm -3 Cntal am slic F /Z (V/cm) Radial focusing foc Bam dnsity pofil R (cm) Analytic LSP (PIC) Radial lctic fild B xt =300 G ω c /β ω p =9.35 LSP (PIC) B xt =0 Magntic slf-pinching B xt =300 G Collctiv slf-focusing Th nhancd focusing is povidd y a stong adial slf-lctic fild Influnc of th plasma-inducd collctiv focusing on th ion am dynamics in NDCX-I is ngligil NDCX-II is compaal to th final focusing of an 8 T shot solnoid 11

12 Local Plasma Rspons is Dastically Diffnt fo ω c >β ω p and ω c <β ω p Modat magntic fild (ω c >β ω p ) Wak magntic fild (ω c <β ω p ) -E - δ>0 F V B - δ<0 - - F V B V φ >0 ˆ ẑ B E V φ <0 ˆ ẑ B 0 Bam chag is ovcompnsatd Radial lctic fild is focusing Diamagntic plasma spons Bam chag is und-nutalizd Radial lctic fild is dfocusing Paamagntic plasma spons ω c =β ω p sonant xcitation of lag-amplitud whistl wavs n p =10 11 cm -3, β =0.05 B 0 =100G 1 M. Dof t al, PoP 19, (01).

13 Numical Simulations Dmonstat Qualitativly Diffnt Local Plasma Rsponss ω c >β ω p ω c <β ω p B 0 =300 G (ω c /β ω p =18.7) Radial lctic fild LSP (PIC) B 0 =5 G (ω c /β ω p =1.56) Radial lctic fild LSP (PIC) Focusing lctic fild Diamagntic spons (δb z <0) Dfocusing lctic fild Paamagntic spons (δb z >0) 13 =0.55c/ω p, l =3.4, β=0.05, n =0.14n p, n p =10 10 cm -3

14 Signal amplitud Whistl Wav Excitation Tansvs magntic fild PIC (LSP) Analytic Smi-analytic Magntic pick-up loop Analytical tatmnt of pols in th complx plan Numical intgation (FFT) assuming wak dissipation Schmatic of th dtctd signal Stong wav-fild xcitation β =0.33, l =10, =0.9 c/ω p, n =0.05n p, B xt =1600G, n p = cm -3 Analytic thoy is in vy good agmnt with th PIC simulations 1 Enhancd slf-focusing (local filds) ω c /β ω p Stong wav xcitation occus at ω c /β ω p (suppotd y PIC simulations) Wav-fild xcitations can usd fo diagnostic puposs am vlocity=phas vlocity=goup vlocity 14 M. Dof t al, PoP 17, (010).

15 II. Th Us of Wak Magntic Filds fo Final Bam Focusing Schmatic of th psnt NDCX-I final focus sction dift sction FFS Challngs: Opat 8 T final focus solnoid Fill 8 T solnoid with a ackgound plasma (8 Tsla) Can a wak magntic lns usd fo tight final am focusing? 15

16 Magntic Lns chagd paticl am magntic lns q, v B 0 B v -v φ v B povids azimuthal otation (v φ ) v φ B 0 povids adial focusing Consvation of canonical azimutal (angula) momntum P m v q A c A B 0 const c v Cycloton fquncy c qb0 mc Equation of motion d m dt v m v q c B 0 F F m 4 c 16 cntifugal foc V B Lontz foc

17 Collctiv Focusing Concpt* Collctiv Focusing Lns Elcton am focusing i Ion am focusing L ~0.01 mm L i ~ 10 m L c =(L L i ) 1/ ~ 1 cm i+ β=0.01 β=0.01 β=0.01 Nutalizd am focusing B=500 G L=10 cm B=500 G L=10 cm B=500 G L=10 cm Collctiv Focusing Lns nutalizd ion am -, i + magntic lns B 0 Th us of a collctiv focusing lns ducs th quid magntic fild y (m i /m ) 1/ 17 *S. Rotson, PRL 48, 149 (198)

18 Collctiv Focusing Lns (Cont d) Elctons tavsing th gion of magntic fing filds acqui an azimuthal vlocity of V B0 m c Stong amipola lctic fild is poducd to alanc th magntic V B foc acting on th co-moving lctons E Elctic foc c V B 0 V B magntic foc m V Cntifugal foc E m 4 Conditions fo collctiv focusing 1. Quasi-nutality. Small magntic fild ptuations 18 p c p 3. No p-fomd plasma insid th lns

19 Collctiv Focusing Lns fo a Havy Ion Div Final Focus Schmatic of th psnt NDCX-I final focus sction dift sction FFS (FFS) Th ion am can xtact nutalizing lctons fom th dift sction filld with plasma. Th collctiv focusing concpt can utilizd fo final ion am focusing in NDCX. 19 No nd to fill th final focus solnoid (FFS) with a nutalizing plasma Magntic fild of th FFS can dcasd fom 8 T to ~700 G

20 (cm) Numical Simulations Dmonstat Tight Collctiv Final Focus fo NDCX-I kintic cm E (kv/cm) I (A) Schmatic of th NDCX-I simulation R-Z PIC (LSP) am Tilt gap z= Plasma Conductivity modl Final Focus Solnoid (700 G) I simulation II simulation z (cm) Bam injction paamts: K 30 kv, =1.6 cm, I =7 ma T =0.094 V, Plasma paamts (fo th simulation II) n p =10 11 cm -3, T =3 V Bam focal plan cm z (cm) n (cm -3 ) Radial lctic fild insid th solnoid (cm) LSP (PIC) Analytic Bam focal plan tim (ns) M. Dof t al, PoP 18, (011)

21 Conclusions Evn a wak magntic fild (sval hundd gauss) can hav a significant influnc on nutalizd ion am tanspot. plasma ion am - nutalizd ion am -, i + magntic lns B 0 B 0 Slf-focusing foc can significantly nhancd y application of a wak magntic fild (~100 G) fo <<c/ω p. Fo a givn focal lngth th magntic fild quid fo a nutalizd am is small y a facto of (m /m i ) 1/. Can impotant fo th dsign of a havy-ion div (.g. NDCX) Can utilizd fo slf-pinch ion am tanspot applications Can utilizd fo th ion am final focus (.g. NDCX-I, II) Phaps could utilizd fo collimation of las gnatd poton ams

22 Enhancd Slf-Focusing VS Collctiv Lns Enhancd slf-focusing Collctiv Lns plasma ion am - nutalizd ion am -, i + magntic lns B 0 B 0 dn F Z m V n d ω c >>β ω p 1 slf Non-lina foc can ffctivly alanc p~t n (impotant fo slf-pinch tanspot) Conditions: g V c 1 c p n p =10 11 cm -3, β =0.05 B 0 >100 G >1 cm Conditions: F m 4 col i i Lina foc (impotant fo am focusing) p c p no plasma insid th lns In th limit of ~ g and Z n ~n F slf ~F col