SScheme for a 50 TeV muon accumulator
O.R. Blanco-Garc´ıa ∗ INFN-LNF, Via E. Fermi 40, 00044 Frascati, Rome, Italy (Dated: September 8, 2020)Submitted as input for discussions on a possible low emittance muon accumulator at 50 TeV.I present a scheme to obtain high quality positive and negative muon beams in terms of lowemittance, high charge and high energy using an accumulator at 50 TeV (or tens of TeV) filled witha train of low charge and low emittance muon bunches to be injected in top-up mode on a singlebunch circulating in a storage/collider ring at the same energy, where damping from synchrotronradiation merges the bunches with minimal emittance degradation.
I. INTRODUCTION
The construction of a 100 TeV proton–proton col-lider (FCC–hh) is currently under study to continue ex-panding the energy frontier exploration in high energyphysics [1]. Two proton beams, at 50 TeV each, circu-late inside two intercepting rings.In this context, it is also worth studying in parallel thepossibility of a muon–muon collider in the tens of TeVscale because of the advantages in the kinematics analysisof point-like particle collisions given by leptons and pos-sible access to physics beyond the standard model [2, 3].The main difficulty in the realization of a muon colliderlies in the limited time (before muons decay) to obtain ahighly populated, small emittance and high energy bunchfor high luminosity collisions [4].I would like to present, as input for further discus-sion, a scheme to produce high quality muon beams (interms of high charge, high energy and low emittance) ob-tained from a muon accumulator at 50 TeV filled with alow emittance multi-bunch train to be injected in top-upmode into a single bunch of a main storage/collider ring.Given the intermediate mass of the muon at rest, i.e.207 times the electron mass and about 1/9 of the protonmass, a muon bunch at 50 TeV in the FCC–hh colliderring would experience total energy loss from synchrotronradiation in a relative small amount of time, which iscomparable to one beam life time τ and very close toone second. This energy loss can be recovered with radiofrequency (RF) cavities in the accelerator that in combi-nation produce a damping effect, well known in electronand positron rings [5]. Therefore, damping should bevisible for muons at 50 TeV in a 100 km ring like theFCC–hh design.Profiting from damping in a high energy main ring, wecan consider the known method of operation called top-up injection in electron storage rings [6]. It consists inthe increase of the bunch population by injecting a smalladditional amount of particles on top of the existing onesin the main ring. In electron rings, particles perform de-caying oscillations in the phase space over a time interval ∗ [email protected] of few units of τ after which they finally reach an equi-librium. The most convenient type of injection for ourmuon collider/storage ring seems to be on-axis longitudi-nal injection that consist in the injection of new particleswith an offset in time and/or energy with respect to thesynchronous bunch. It has the advantage to be twicefaster than the transverse damping due to the partitionnumbers of a typical storage ring.It might be possible that muons show longitudinaldamping even at 25 TeV in a ring with a circumferenceadapted to the reduced life time of muons, thus, loweringthe requirements on fast acceleration in previous stages.However, for the moment we leave this as a possibilityfor further study and concentrate in the 50 TeV schemeto obtain a high intensity bunch at high energy startingfrom a low charge 22 GeV small emittance muon traingiven by e + e − annihilation of a positron bunch train intofixed targets, studied by the Low EMittance Muon Ac-celerator (LEMMA) [7–11] team.The scheme presented in this article could increase thecharge of a single muon bunch while preserving or miti-gating the growth of the muon beam emittance profitingfrom synchrotron radiation in the main storage/colliderring. II. SCHEME
The scheme is shown in Fig. 1. It consist in four stages :a positron source, a positron to muon conversion andtransport line, a chain of low muon current fast accel-eration rings, and finally a muon accumulator rampingfrom few TeV to the desired energy (7 to 50 TeV in thescheme). I will describe the stages in the following.
A. Positron source
LEMMA has put forward the idea of a low emittancemuon source where muons are produced as secondariesfrom e + e − annihilation of a high energy positron beam,above the energy threshold at 43.7 GeV for muon pairproduction, impinging on a fixed target.It is convenient to set the positron beam energy to44 GeV because the energy spread of the produced muon a r X i v : . [ phy s i c s . acc - ph ] S e p beam will match the acceptance of the next stage. Fur-ther details are discussed in Subsection II B.The positron bunch population has been fixed to5 × , which is a relatively high charge in order toproduce as many muons as possible given the small prob-ability of muon pair production, also further discussed inSubsection II B.I fix the positron source requirement to a train of 1000bunches in order to increase the muon population by afactor 1000 when combining all separate muon bunchesinto one, and also to be compatible with the positronsource requirement studied in [11–13].The required positron rate has been estimated to beabout 1 . × e + /s given a separation of 100 m amongneighboring bunches. Notice that the positron bunch sep-aration will be the same muon bunch separation in thetrain inside the muon accumulator ring.The transverse emittance and beam size is set to be7 π nm and 60 µ m respectively to match the input pa-rameters of the positron to muon conversion stage, dis-cussed in Subsection II B.The energy spread and bunch length are 0.1% and3 mm respectively, taken from previous studies of a 6or 27 km positron ring [13].Finally, I remark that all numbers have been usedto clarify and discuss an initial scheme and they couldchange as required. B. Positron to muon conversion
The purpose of the positron to muon conversion stageis to produce a low charge and low emittance muon bunchper positron bunch passage.The three particles species ( e + at 44 GeV, and µ + µ − or simply µ pairs at 22 GeV) are transported to the finalend of the transport line without significative emittancegrowth of the muon beam, and a small deterioration ofpositron bunch in terms of emittance and particle popu-lation.A detailed description of materials and accelerator op-tics studies dedicated to this stage can be found in [14].In this article I have chosen to use a line consistingof 25 liquid Lithium (LLi) targets of 1% of a radiationlength X connected by a series of quadrupoles for a totallength of 323 m. This design is able to produce 0 . × − muon pairs per impinging positron, which is factor 10above a single thin target of 1% X and also distributesthe target power deposition.Using the parameters of the positron source shown inSubsection II A, we will obtain a bunch population of3 × muon pairs at 22 GeV per positron bunch, withan energy spread of ±
5% in a flat distribution, and with avery small transverse emittance of about 25 π nm (equiv-alent to 5 π µ m normalized emittance).The longitudinal emittance will be product of thebunch length of the incoming positron beam by the en-ergy spread from the kinematics of the collision, therefore 3 × π mm GeV (3 mm × . ×
22 GeV).For a 22 GeV muon beam the length of the transportline is very short and no significative muon losses areexpected.Each one of the 1000 positron bunches will pass one atthe time and produce muon pairs that are transportedto the acceleration stage. The remaining positrons in thebunch could be spilled or redirected to the previous stage.
C. Low Muon Current Fast Acceleration
Fortunately in the LEMMA scheme the kinematics ofthe collision boosts the lifetime by a factor 208 with re-spect to that of muons at rest, giving an initial time-frame of 0.46 ms of lifetime to accelerate the beam.Muons are already relativistic and therefore I expectacceleration would influence minimally the timing amongbunches at different energies.The positive and negative muon beams at 22 GeV willhave to be separated and passed through a chain of fastaccelerating cavities with the highest possible gradient.I have done an estimation of 500 m of RF cavities at20 MV/m in order to gain 10 GeV per passage. Althoughthis number could appear high, it is required in order toreduce the number of muon losses due to decay alongthe acceleration chain. Even higher gradients would bebeneficial.There is no definitive structure for the accelerationchain. I have considered three stages as an initial pro-posal :1. from 22 to 200 GeV, which is a factor ten in energygain obtained in ten passages over an RF configura-tion providing 20 GeV per passage, or twenty turnsover an RF configuration at 10 GeV per turn;2. from 200 GeV to 1 TeV, which is a factor five inenergy gain obtained over approximately 100 turnsin a dedicated ring;3. from 1 TeV to 7 TeV, which is a factor seven inenergy gain obtained over more than 500 turns.The exact configuration of these acceleration stages needsto be further studied, but, I would like to avoid ramp-ing magnets because of the short lifetime of the muonbeam when compared to technological ramping capabil-ities. Better said, I would prefer to avoid ramping mag-nets in the KHz range.Several proposals point to technology based in multi-pass Energy Recovery Linacs (ERL) [15] and/or FixedField Alternating Gradient (FFA) [16, 17] ring designs,in particular, vertical FFA (vFFA) [18] to profit fromthe zero momentum compaction factor and large energyacceptance that could accelerate the beam without thedilution of the longitudinal emittance.Due to the total number of cycles in the accelerationchain, it is expected to produce a significative muon pop-ulation loss that has been estimated to be half of theinitial bunch, leaving 1.5 × muons per bunch. D. Accumulator Ring
The last section is the Accumulator Ring. It is includedlast in the scheme because further acceleration in theTeV scale of single muon bunches would require severalkilometers of RF cavities and it would be preferable touse a single ring. The ramping frequency is expected tobe in the order of few hundreds of Hz, which is a factor10 above the muon beam life time of 140 ms at 7 TeVthat grows up to one second at 50 TeV.The muon life time of 140 ms at 7 TeV also allowsfor enough time to allocate 1000 individual bunches intoseparated buckets inside the accumulator with negligiblelosses due to decay.Once the muon bunch train is in the accumulator, itcan be ramped from low to high energy (7 TeV to 50 TeVin the scheme). Then, it could be possible to extract oneby one the individual low charge bunches into a singlebunch provided the synchronization of the two machines.The most simple case that I can foresee is to have a smalldifference in circumferences between the accumulator andthe main storage/collider ring in order to make coincideonce cycle of the bunch in the storage/collider ring witha different bucket of the accumulator every time.We could expect muon losses due to decay given thelarge number of passages to accelerate (ramp up) themuon beam train. I have estimated a reduction of theindividual bunch to 1.0 × muons.Injecting a thousand of these bunches into a stor-age/collider ring will bring the final bunch charge toabout 10 muons with a normalized transverse emittanceclose to 5 π µ m, and bunch length and energy spread de-pendent on the realization of the acceleration stages. III. CONCLUSION
I have presented a scheme to produce a high qualitymuon beam in terms of high particle population, lowemittance and energy of 50 TeV (or tens of TeV), us-ing an accumulator ring at the same energy to ramp alow charge, low emittance and low energy train of muonbunches to be injected in top-up mode into a main stor-age/collider ring.This scheme uses a positron source and a short trans-port line to produce muon pairs as secondaries from e + e − annihilation of a high energy positron beam on fixed tar-gets.Muon pairs are produced at 22 GeV and acceleratedin a chain of Fixed Field Accelerator Gradient (FFA)rings or alternatively Energy Recovery Linacs (ERL).The number of acceleration stages has been set to threeconsidering the possibility to gain a factor 10 in energy per stage, and the availability of radio-frequency cavi-ties to provide at least 10 GeV per passage to the muonbeam.I believe several of the parameters here mentioned (e.g.the RF cavity gradient and the positron to muon conver-sion efficiency) can be pushed by a factor two or 4, ormaybe more, so that the final possible outcome of fur-ther studies of this scheme could be very positive. IV. ACKNOWLEDGMENTS
This work has been financially supported by the Isti-tuto Nazionale di Fisica Nucleare (INFN), Italy, Com-missione Scientifica Nazionale 5, Ricerca Tecnologica –Bando n. 20069, 2019. T e V , bun c h A cc u m u l a t o r A nd t o T e V R a m p i n g R i n g C i r c u m f e r e n c e : k m bun c h e s o f . x µ E m i tt n o r m . ~ µ m W h e n bun c h e s a r e a cc u m . W e R a m p i n ~ t u r n s → R F c a v i ti e s : G e V = k m k m x M V / m M u li f e ti m e ( a t T e V ) m s → k m M u li f e ti m e ( a t T e V ) s → x k m A t T e V t h e m u o n b e a m d a m p s w e p e r f o r m T O P - U P I n j e c ti o n ( v ) FF A f a s t a cc . G e V → T e V ~ t u r n s ( v ) FF A f a s t a cc . o r E R L a r m s G e V → G e V ~ t u r n s T e V . x µ / bun c h L o w M u o n C u rr e n t F a s t A cc e l e r a ti o n ( G e V / t u r n ) m x M V / m = G V N o m a g n e t r a m p i n g P r o fi ti n g t h e l a r g e FF A / v FF A e n e r g y a cc e p t a n c e , t h e b e a m c i r c u l a t e s f r o m l o w t o h i g h e n e r g y m o v i n g r a d i a ll y - o u t w a r d s / v e r ti c a ll y . P a r t o f t h i s a cc e l e r a ti o n c o u l d b e a l s o a c h i e v e d w i t h a n E n e r g y R e c o v e r y L i n a c ( E R L ) . C h o i c e d e p e nd i n g o n e ffi c i e n c y x µ / bun c h ± % e n e r g y s p r e a d G e V ε n = x n m = µ m P o s i t r o n t o M u o n C o n v e r s i o n T o t a l l e n g t h : m E ffi c i e n c y : . x - µ / e + % X * LL i t a r g e t s T r a n s p o r t li n e m p t . m β * µ = . m β * e + = . m L * = c m M u A p o c h r o m ( ± % e . s p r e a d ) T a r g e t p o w e r r e du c e d b y µ bun c h l e n g t h e qu a l t o e + bun c h l e n g t h , f e w mm e + s o u r c e . G e V bun c h e s x e + / bun c h ( m A / bun c h F r o m bun c h t o bun c h d i s t a n c e , m ) . x e + / s E m i tt a n c e ~ n m B e a m s i z e ~ µ m ( v ) FF A f a s t a cc . T e V → T e V ~ t u r n s T e V x µ / bun c h T o p - up i n j e c ti o n FIG. 1. Production and acceleration scheme of a low emittance muon beam for a 50 TeV collider. [1] A. Abada, M. Abbrescia, S.S. AbdusSalam, et al. “FCC-hh: The Hadron Collider”, Eur. Phys. J. Spec.Top. , 775-1107 (2019) https://doi.org/10.1140/epjst/e2019-900087-0 [2] J.P. Delahaye et al. , “Muon Colliders”, Input to theEuropean Particle Physics Strategy Update, January18, 2019. arXiv:1901.06150v1 https://arxiv.org/abs/1901.06150 [3] F. Zimmermann. MOPMF065, Proceedings on IPAC18,Vancouver, BC, Canada (2018) https://accelconf.web.cern.ch/IPAC2018/papers/mopmf065.pdf [4] M. Boscolo, J.P. Delahaye, M. Palmer. “The fu-ture prospects of muon colliders and neutrino fac-tories”. arXiv:1808.01858v2 https://arxiv.org/abs/1808.01858 [5] S. Turner. “Fifth General Accelerator Physics Course”.The CERN Accelerator School, University of Jyvaskyla,Finland, September 7–18, 1992. CERN Yellow Proceed-ings Volume 1/1994. CERN 94-01. http://dx.doi.org/10.5170/CERN-1994-001 [6] B. Holzer. “Beam Injection, Extraction and Transfer”.The CERN Accelerator School, Erice, Italy, March 10–19, 2017. CERN Yellow Reports: School Proceedings Vol-ume 5/2018. CERN-2018-008-SP. http://dx.doi.org/10.23730/CYRSP-2018-005 [7] M. Antonelli, M. Boscolo, R. Di Nardo and P. Rai-mondi, “Novel proposal for a low emittance muon beamusing positron beam on target,” Nucl. Instrum. Meth.A (2016) 101 https://doi.org/10.1016/j.nima.2015.10.097 [8] M. Antonelli et al. , “Very Low Emittance MuonBeam using Positron Beam on Target”, in
Proc.7th Int. Particle Accelerator Conf. (IPAC’16) , Bu-san, Korea, May 2016, pp. 1536–1538. doi:10.18429/JACoW-IPAC2016-TUPMY001 [9] M. Boscolo et al. , “Studies of a Scheme for LowEmittance Muon Beam Production From Positrons onTarget”, in
Proc. 8th Int. Particle Accelerator Conf.(IPAC’17) , Copenhagen, Denmark, May 2017, pp. 2486– 2489. doi:10.18429/JACoW-IPAC2017-WEOBA3 [10] M. Boscolo, e t. al. “Low emittance muon acceleratorstudies with production from positrons on target”, Phys.Rev. Accel. Beams 21, 061005 (2018), DOI: https://doi.org/10.1103/PhysRevAccelBeams.21.061005 [11] M. Biagini, e t. al., “Positron Driven Muon Sourcefor a Muon Collider: Recent Developments”, pre-sented at the 10th International Particle AcceleratorConf. (IPAC’19), Melbourne, Australia, May. 2019,paper MOZZPLS2. https://accelconf.web.cern.ch/IPAC2019/papers/mozzpls2.pdf [12] D. Alesini, e t. al., “Positron driven muon source for amuon collider”, 2019, arxiv 1905.05747. https://arxiv.org/abs/1905.05747 [13] S. Liuzzo. “Lemma e+ ring”. Presentation at the LowEmittance Muon Collider Workshop, Padova, Italy. July1-3, 2018. https://indico.cern.ch/event/719240/ [14] O.R. Blanco-Garcia and A. Ciarma. “Nanometric muonbeam emittance from e+ annihilation on multiple thintargets.” Phys. Rev. Accel. Beams Accepted for publica-tion, August 31, 2020.[15] A. Bartnik, N. Banerjee, D. Burke, e t al. “CBETA:First Multipass Superconducting Linear Accelera-tor with Energy Recovery.” Phys. Rev. Lett. https://link.aps.org/doi/10.1103/PhysRevLett.125.044803 [16] D. Trbojevic et al. FFAG lattice for muon accelerationwith distributed RF, Proceedings of the 2003 ParticleAccelerator Conference. https://accelconf.web.cern.ch/p03/PAPERS/TPPG003.PDF [17] J. B. Lagrange. THPMB053 et al.
NUSTORM FFAGdecay ring. Proceedings of IPAC2016, Busan, Korea. https://accelconf.web.cern.ch/IPAC2016/papers/thpmb053.pdf [18] S. Brooks. Vertical orbit excursion fixed field al-ternating gradient accelerators. Physical Review Spe-cial Topics – Accelerators and Beams , 084001(2013), 084001(2013)