ARDB Technical Note -Draft-11/4/97 µµ Pion Collection from an Intense Proton Beam in a Plasma

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1 ARDB Tchnical Not -Daft-//97 µµ Pion Collction fom an ntns Poton Bam in a Plasma B. Shadwick, D. Whittum, and J. Wutl Th µµ collid conct quis an intns oton am smashing into a tagt to mak ions that susquntly dcay into muons. As dscid in th litatu, th conct quis a high-fild solnoid to nhanc th ffctiv final muon yild. Givn th difficulty of maintaining th muon am in th snc of muon dcay, it sms intsting to consid concts that sv fist th intgity of th ion am, and maintain a low ion am mittanc. n this not w lay out th considations fo alication of a lasma cham togth with th tagt to this nd. Th conct quis -modulation of th oton am; this w suggst could accomlishd y mans of a lasma -unch, with wakfilds divn y a Ku-Band o W-Band modulatd lcton am, with aamts in th ang of thos dmonstatd at LLNL. Poton Bam Paamts Th oton am to mloyd fo th µµ collid souc has not n oducd, so th aamts a somwhat in flux. W will us aamts as in Tal, and th figu of 8 GV fo th oton kintic ngy. Tal. Poton am aamts usd fo xamls. aticls in th unch N unch lngth (ms) z 3 cm ms nomalizd mittanc ε n mad initial ms am siz,. 5cm x y Using m = MV, on ss that th Lontz facto is γ Th am chag is Q 3 µc, and th ak cunt, assuming a Gaussian longitudinal ofil is, Qc /. 8 ka. π = ( ) z Th Aflvn constant fo a oton am is 3 = 3. 3 MA, and th Budk aamt is ν =.. Th asic scalings fo lasma focusing can st down in tms of this constant, th am cunt and th nomalizd mittanc. Fo th lasma, w will f to th lasma wavnum k = π n, "µ+µ- Collid: A Fasiility Study", (July, 996) BNL-553. W mloy fo mittanc figus th quotd as "95%" mittanc; no dout visions will in od lat.

2 3 wh (in cgs units) = / mc 8. cm is th classical lcton adius, - is th lcton chag, and m is th lcton mass. Th angula lasma fquncy is ω = kc. Whn saking of th injctd am, w will ictuing a long Gaussian unch with x = y =. "Long" mans k z >>. Finally, fo thos of us usd to woking with lctons, it is hlful to not m m 836, 5 and in this connction w not that = / m c 5. cm. Slf-Focusing in a Plasma A lativistic am injctd into a lasma will tu lasma lctons y mans of its lctostatic fild. An lcton am xls lasma lctons, whil a oton am will attact thm. Whn th am cunt vaiation is adiaatic on th tim-scal of a lasma iod, on may ictu a quasinutal stady-stat, wh a sufit of lctons sids within th am volum, canclling th lin chag dnsity of th am. n this limit, th only fild comonnt maining is th magntic fild du to th am. This w may comut fom Am's Law, B n V = π θ c x, with am dift sd V c. Th solution is B θ V = πn x, c and th nt foc on a am oton is givn y F V E c B n = θ π x k x, wh w intoduc th oton am wavnum, =( ) = / / c k n = ν π π π / / / = ( ). Fo = 5. cm, and z = 3 cm, and 3 otons, n 7. cm cm, scaling in invs ootion to th am siz. Paaxially, k d dt = Fˆ k, d γ k. dz and

3 This may xssd in vaious convntional foms as K = γ k ν o kβ = k =. (magntically slf-focusd gim), γ γ Th atio ν / γ will cognizd as th atio of am cunt to Alfvn cunt. Th slfinchd taton iod fo = 5. cm is λβ = π / kβ =. 8 cm. Lt us not th quiliium slf-inchd am-siz, fo an initially matchd am, asnt scatting and oth soucs of incohnc. Nomalizd mittanc is constant, ν εn = γ kβ = γ γ so that / / ν γ, (MFR quiliium) =( ) q εn /, k νγ = ( ) β = ν γ / νγ ( ) / ν = / εn γ ν =. (MFR quiliium) ε n Fo ou assumd mittanc, this cosonds to λ β 5. cm in quiliium, with q 6. cm. Howv, this assums a lasma dnsity on th od of (o lag than) th cosonding am dnsity n / c ν = =. π π This cosonds to n 7. 3 cm 3. A -m tank with lasma dnsity n 7. 3 cm 3 dos not challng th stat-of-th-at; such a tank with -5 high dnsity has n oosd fo SLAC E-57, and is cuntly ing tstd. Th cosonding lasma wavnum is k 76. cm ; sinc k q., lasma comnsation ffcts affod a small coction to th filds. Th lasma fquncy is f = ck/π 36GHz. At th still-modst dnsity of n. cm 3 on has f 9 GHz. Catu in a Poton-Bam Divn Wakfild Th fogoing considations suggst that th oton am could handld y mans of slf-focusing in a lasma, and focusd to a small sot. W can ask that th lasma accomlish still mo, howv. Pions oducd fom th tagt slas intssd in th lasma will also focusd. n addition, howv, if w -modulat th oton am, an acclating wakfild can dvlod in th lasma, assisting ion catu and am fomation. Th fquncy of th acclating wav will th lasma fquncy, in th Ku-Band o W-Band ang, and this could quit aoiat fo downstam acclation, ovidd th small atu diamt is acctal th, and dnding on T. Katsoulas, t al., "A oosal fo a GV lasma-wakfild acclation ximnt at SLAC", Pocdings of th 997 Paticl Acclato Confnc (EEE, Nw Yok, to ulishd); R. Assmann, t al., "Poosal fo a On GV Plasma Wakfild Acclation Eximnt at SLAC", SLAC-E57. 3

4 dvlomnt of acclato tchnology in th CLC o W-Band fquncy angs. Th maximum acclating gadint oducd y a modulatd oton am sonantly diving th lasma cosonds to wav-aking in th lasma and is givn y E w k. This is 3 MV/m fo ou xaml at n 7. 3 cm 3, with f 36 GHz (Ku and). (At n. cm 3, with f 9 GHz---W-Band---on has 9. GV/m.) To aciat th ffct on th ion am, call that th ion mass is m = π+ π m =, " π" MV, and th liftim is τ = π+ π τ, " π" 6. ns. Thus a -m lasma cll would sult in tyical ion ngis of GV, and γ π 5, with liftims in th la fam τl γ πτ π. µ s ( ft). On would xct th ffct of focusing and acclation to a low mittanc ion am, with a high catu faction. (Things would go somwhat tt at W-Band, wh th intaction lngth could ducd y a facto of 3 and th yild imovd du to th high gadint.) Slf-modulation of th oton am in th lasma will ocd at a gowth at scaling with th longitudinal oton am lasma fquncy and this is quit low. Thus som mans of modulating th oton am io to th tagt cham is quid. P-Bunch Givn th fquncy ang, a micowav unch would hav a ath small atu (o qui lag ak ows fom soucs that don't xist). n addition, th oton am avag ow is 8MW at 3 Hz uls tition fquncy, and stuctu damag du to halo would a majo concn. On could mloy su-hamonic unching. Howv, lt us consid instad unching at th fundamntal fquncy (Ku o W-Band), in a scond lasma tank. Such a lasma -unch would qui a div. On thought fo a div is an intns las mloyd in th las wakfild configuation. Th gadint oducd y a las with dimnsionlss vcto otntial amlitud a is givn y E lwfa k a. Th las ak ow is thn P l π 5 ω w c a, 5 wh / 87. GW, w is th las waist, and ω is th las fquncy. Taking a (th wav-aking limit), mloying th sam lasma fquncy as fo th tagt cham n 7. 3 cm 3, w q. 3cm, and µm las wavlngth w otain a ak las ow of P l 3. PW. Th Rayligh ang is quit long L R 3 3 cm, so diffaction of th uls is not an issu fo a unch tank lss than a fw mts in lngth. This uls must last fo 3 ns, and cosonds thn to.8 GJ of las uls ngy. This would quit a las, somthing on th scal of NF. Th siml xlanation fo ths discouaging nums is that th las wakfild xcitation mchanism is nonsonant. Givn that th las figus a xtaodinay, on is intstd to consid oth

5 mans of diving th lasma to wav-aking. A natual altnativ div is an lcton-am mloyd in th mod of a lasmawakfild acclato div. Such a am would itslf qui modulation; howv, at Kuand and W-Band, modulation of th quid ka, - ns ams has n accomlishd mloying an induction linac with a f-lcton las. 3 With 3 MV/m wavaking gadint, th actual lasma tank lngth could quit shot, has. m, dnding on th dift lngth to mloyd (fo unching) twn th unch tank and th tagt tank. (At W-Band, th tank could still shot). Th ictu of th ion souc on aivs at is that of Fig.. nduction njcto (.8 MV) nduction Linac (5 MV) ELF Wiggl Elcton Analysis & Dumlin Poton Bamlin Plasma Punch Tank Dift Plasma & Tagt Cham π + π FGURE. Conctual layout of comonnts fo lasma-asd ion am oduction with an an intns oton am. A ka lcton am with ns uls lngth is oducd in an induction linac on th scal of th LLNL Eximntal Tst Acclato (ETA). Th am is modulatd at Ku and, as in th ELF ximnt, and divs a lasma. Th sulting lasma wakfild modulats th oton am ngy. Th oton am unchs in th dift, and divs an acclating wakfild in th lasma and tagt cham. Wok To Do Th a many intsting issus to xamin futh h, concning th diffnt havios of th ositiv and ngativ ions, am-loading and stoing of th oton am y th lasma. This olm is most asily simulatd in two ics. Th fist simulation would fo th oton div, aiving at an accuat assssmnt of th amlitud of th sonantly xcitd wakfild, with tansvs gadints and has-mixing. Th scond simulation would saml th ion has-sac, in Mont Calo fashion, and xamin ion catu and yild, with a alistic atu. Oth fatus of concn a: H- fomation, tagt sla layout and damag, ion 3 A. L. Thoo, t. al., Eximntal Rsults of a High-Gain Micowav FEL Oating at GHz, Nuc. nst. & Mthods in Phys. Rs. A7, 5 (988), S. L. Alln, t. al., Gnation of High Pow GHz Micowavs with an FEL fo th MTX Eximnt, Pocdings of th 993 Paticl Acclato Confnc (Washington, D.C., 993), 55. 5

6 ost-acclation. Natually on is intstd too in lcton am modulation y mans of a lativistic klyston. n addition, th downstam acclato comlx should visitd taking account of th imovd ion am chaactistics. n aticula, it sms likly that a visd collid ing conct could mloy a dual-ing dsign, consisting of a ion stoag & dcay ing, with filds dsignd to automatically channl dcayd ions into th collid ing o. Fo that matt, on could contmlat just a π-stoag ing, functioning as a ππcollid, with µµ and µπ hysics functioning as ackgound, o as aasitic o standy ximnts. 6

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

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