The conceptual design of a compact source of GeV-class muons is presented,
based on a plasma based electron-gamma collider. Evaluations of muon flux,
spectra and brilliance are presented, carried out with ad-hoc montecarlo
simulations of the electron-gamma collisions. These are analyzed in the context
of a large spread of the invariant mass in the e-gamma interaction, due to the
typical characteristics of plasma self-injected GeV electron beams, carrying
large bunch charges with huge energy spread. The availability of a compact
point-like muon source, triggerable at nsec level, may open a completely new
scenario in the muon radiography application field

Bacci, A.

Broggi, F.

Conti, M. Rossetti

Curatolo, C.

Drebot, I.

Marocchino, A.

Panzeri, N.

Petrillo, V.

Rossi, A.

Serafini, L.

English

arXiv

The conceptual design of a compact source of GeV-class muons is presented, based on a plasma based electrongamma collider. Evaluations of muon flux, spectra and brilliance are presented, carried out with ad-hoc Monte Carlo simulations of the electron-gamma collisions. These are analyzed in the context of a large spread of the invariant mass in the e-gamma interaction, due to the typical characteristics of plasma self-injected GeV electron beams, carrying large bunch charges with huge energy spread. The availability of a compact point-like muon source, triggerable at nsec level, may open a completely new scenario in the muon radiography application field

L . Serafini

I. Drebot

A. Bacci

F. Broggi

C. Curatolo

A. Marocchino

N. Panzeri

V. Petrillo

A. R. Rossi

M. R. Conti

AIR Universita degli studi di Milano

Nuclear Inst. and Methods in Physics Research, A 909 (2018) 309–313Contents lists available at ScienceDirectNuclear Inst. and Methods in Physics Research, Ajournal homepage: www.elsevier.com/locate/nimaA muon source based on plasma acceleratorsL. Serafini a, I. Drebot a,*, A. Bacci a, F. Broggi a, C. Curatolo a, A. Marocchino b, N. Panzeri c,V. Petrillo a,c, A.R. Rossi a, M. Rossetti Conti a,ca INFN - Sezione di Milano, via Celoria 16, 20133 Milano, Italyb INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Frascati, Italyc Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italya r t i c l e i n f oKeywords:MuonComptonPlasmaSourcea b s t r a c tThe conceptual design of a compact source of GeV-class muons is presented, based on a plasma based electron–gamma collider. Evaluations of muon flux, spectra and brilliance are presented, carried out with ad-hoc MonteCarlo simulations of the electron–gamma collisions. These are analyzed in the context of a large spread of theinvariant mass in the e–gamma interaction, due to the typical characteristics of plasma self-injected GeV electronbeams, carrying large bunch charges with huge energy spread. The availability of a compact point-like muonsource, triggerable at nsec level, may open a completely new scenario in the muon radiography application field.1. IntroductionMuons presence on the Earth is due to the interaction betweencosmic rays and the atmosphere: they are produced from pion 𝜋± andkaon 𝐾± decay in the high atmosphere (15 000 m), and they reach ourplanet surface with a medium kinetic energy of 4 GeV. Atmosphericmuons flux is spread all over the solid angle 𝛺, and it is measured tobe [1,2] 𝑑𝑁𝑑𝛺𝑑𝑡 = 0.66 cos2 (𝜃𝑧)sr−1.cm−2.min−1, i.e. integrating overthe upper hemisphere solid angle and considering only muons withmomentum 𝑝𝜇 > 1 GeV.c−1,𝑑𝑁𝑑𝐴𝑑𝑡 ≃ 1 cm−2.min−1. Roughly, we couldsay that a human hand, anyway orientated, is crossed by a muon everyminute.GeV-class muons are keys to several strategic applications, in par-ticular radiography of very thick objects (Volcanoes, Nuclear PowerPlants, National Security) thanks to their high penetration/low stoppingpower (compared to photons/electrons. . . ). A compact muon sourcebased on the most advanced technologies could deliver a muon beamwith 1–100 muons/s at GeV energy, collimated within hundreds/tensmrads. A Plasma Accelerator could guarantee the needed compactnessof a GeV muon source (order of magnitude cheaper and shorter thanGeV-class muon section of a typical muon collider). The combination ofadvancement in plasma accelerators (high charge GeV electron bunches)and in Compton Sources (high intensity tens MeV-class photon beamsas in ELI-NP-GBS) allows to conceive such a source possible in the nearfuture. The challenge consists in running a 1031 cm−2 s−1 luminosity(Lorentz Boosted) 𝑒 − 𝛾 collider at 𝐸𝑐𝑚 = 400 MeV to make a point-like,GeV-class, ns synchronized, muon source at 1 μ+,−∕s with collimated* Corresponding author.E-mail address: illya.drebot@mi.infn.it (I. Drebot).emission (200 mrad) compact Muon Photo-Cathode producing 𝜇-pairswith GeV-scale energy.The basic ingredients of a plasma based muon source are: a laserdriven self-injected plasma accelerator generating low-quality (largeenergy spread, large emittance) high charge (10 nC) electron bunchat 𝐸 > 1.5 GeV (compare state of the art: 100 pC at 5 GeV, 1 nC at500 MeV); a high-power interaction laser ELI-NP-GBS (Yb:Yag 1 J @ 1kHz, state of the art 1 J @ 100 Hz). Control, reproduce, stabilize the𝑒−𝛾 collisions at IP with μm-size beam spots within the gas jet of plasmaaccelerator. Embed the whole accelerator (3–5 m in size) into a thickradio-protection bunker absorbing all beams but the muons (escapingthrough bunker walls). Additional filtering of surviving 𝑒−, 𝛾 ′ s w.r.t.positive muons through magnetic fan-out spectrometer. A proof-of-principle experiment can be proposed: 0.1 − 1 𝜇-pair per second gatedin 10 ns time frame covering a 4 m2 detector located 3 m far from thepoint-like source (compare 400×10−8×100 = 4×10−4 atmospheric muons⇒ SNR > 250).2. Muon photoproductionFor the muon source we consider the process:𝑒− + 𝛾 → 𝜇+ + 𝜇− + 𝑒−where the muon flux scales with the total cross section [3]:𝜎𝑀𝑃𝑃 (𝑠) ≃2𝛼3𝑚2𝜇ln(2) ln(𝑠𝑚2𝑒)(1)https://doi.org/10.1016/j.nima.2018.02.003Received 15 November 2017; Received in revised form 20 December 2017; Accepted 1 February 2018Available online 5 February 20180168-9002/© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).L. Serafini, I. Drebot, A. Bacci et al. Nuclear Inst. and Methods in Physics Research, A 909 (2018) 309–313Fig. 1. 𝜎𝑀𝑃𝑃 as function of square of center-of-mass energy 𝑠 (in unit of 𝑚2𝜇).as function of the invariant mass 𝑠 = 𝐸2𝑐𝑚∕𝑚2𝜇 , where 𝑚𝜇,𝑒 is muons andelectrons rest mass, 𝛼 ≈ 1∕137 is fine structure constant, 𝐸𝑐𝑚 = 2√𝛾𝑚𝑒ℎ𝜈is deduced from the kinematics of the system, where ℎ𝜈 is energy of laserphoton. Since the cross section has a cut-off at 2𝑚𝜇 , to exceed this energycut-off we need to have an energy in the center of mass of the systembigger than about 200 MeV. The cross-section of 𝑒− + 𝛾 → 𝜇+ + 𝜇− + 𝑒−scattering is reported in Fig. 1.A possible implementation of the muon source is shown in Fig. 2.Two high power, counter propagating laser pulses generate (counterpropagating) high charge, low quality, electron bunches: one of thosewill collide with a third laser pulse in order to generate gamma photonsby Compton back-scattering (CBS). Then, those photons collide with theother electron bunch to produce muon pairs. Notice that the third laseris not mandatory: its presence would allow to tune gamma rays energyTable 1Electron beam parameters.Electrons energy (GeV) 1.6Energy spread (%) 10𝜎𝑥,𝑦 (μm) 1𝜎𝑃𝑥,𝑃 𝑦 (MeV) 5𝜎𝑧 (μm) 5Table 2Laser parameters.Pulse energy (J) 1wavelength (nm) 1030𝜎𝑙 (μm) 5𝜎𝑡 (ps) 1.5so that both muon production cross section and system center of massenergy can also be tuned. Giving up this possible flexibility, allows toimplement an easier set-up where gammas are produced by CBS withdriving laser pulses.If we consider an electron beam whose energy is around 1.5 GeV, thephotons should be the gamma rays with tens MeV of energy. Thereforethe gamma rays are foreseen to be produced by a Compton sourcethat can either use the same electron beam of the muon production,or another beam produced ad-hoc for the Compton interaction.It is important to notice that in this proposed scheme of 𝑒−, 𝛾collision, the center of mass reference system moves relatively to thelaboratory system with 𝛾𝑐𝑚 =𝐸𝐿𝐴𝐵𝐸𝐶𝑀≅ 12(√𝛾𝑚𝑒ℎ𝜈), in the direction of theelectron. Due to this fact, the muons created in center of mass systemwith energy close to rest mass energy will move with a 𝛾𝐶𝑀 in thelaboratory system. As a consequence, the proposed scheme provides abeam of muon that has a 𝛾𝜇 ≥ 𝛾𝐶𝑀 .We constructed an ideal electron beam, with parameters similar tothe state of the art of plasma accelerated beams [4,5], see Table 1.The phase spaces are in Fig. 3.The Compton source exploits the same electron beam and a Yb:Yaglaser with parameters shown in Table 2.The simulations of Compton 𝛾−rays have been done with the MonteCarlo code CAIN [6]. Fig. 4 shows the gamma spectrum, with a totalnumber of photon of about 1.7 ⋅ 1011 and energy 𝐸𝑝ℎ = 4𝛾2𝐸 laserranging from 0 up to 70 MeV. However only photons with energy biggerthan 25 MeV participate in the muon production. The propagation ofthe beams has been done with the code ROSE [7]. The code ROSE(Rate Of Scattering Events) has been implemented for studying theFig. 2. Scheme of source.310L. Serafini, I. Drebot, A. Bacci et al. Nuclear Inst. and Methods in Physics Research, A 909 (2018) 309–313Fig. 3. Electron beam phase-space.Fig. 4. Propagation of particle in ROSE code at various instance.photon–photon scattering and then applied to other particle collisionsand decays, as Breit–Wheeler, TPP, Compton scattering [8–11]. Startingfrom two colliding beams of massive particles or photons (say beam 1and beam 2) defined through the phase spaces of an appropriate number𝑁1;2 of macroparticles of weight respectively 𝑞1;2, the procedure requiresthe definition of a common space grid where the kinematics takes place.The tracking of both beams during their overlapping up to the end ofthe scattering process permits to dimension the total space window. Theinitial time 𝑡0 is the instant when the first collisions occur, the timeevolution being discretized over a total of NT steps. Fig. 4 shows few311L. Serafini, I. Drebot, A. Bacci et al. Nuclear Inst. and Methods in Physics Research, A 909 (2018) 309–313Fig. 5. Energy distributions of muons.Fig. 6. Energy-Angular distribution of muons.Fig. 8. The spectrum of emerging muon per primary incident muon for the caseof 1 m concrete wall.temporal snapshot of the interaction (upper line) and the number ofinteractions as function of the energy of the center of mass at the relativeshot given by the convolution of the energy distribution of the possibleevents with the cross section. The final output of muons is presented inFig. 5.To get the distributions of muons, simulations by event generatorWHIZARD [12] were done. The energy of the produced muons rangesbetween 105.65 MeV (the muon is produced at rest, i.e. backward inCM) and about 2 GeV (all of the electron energy is transferred to themuon). The energy distribution of the produced muons is peaked around150 MeV. The almost totality of the muons is emitted in a cone ofaperture 𝜃 of 1 radiant, the most part of them within a angle 1∕𝛾𝑐𝑚 ≃ 350milliradiants with the peak of emission around 100 millirads. Noticethat, for the sake of simplicity, in this work we do not take intoconsideration effects of plasma fields on produced muons. The Energy-Angular distribution of generated muons is presented in Fig. 6.Fig. 7. The number of emerging muon per primary incident muon for the case of 1 m concrete wall.312L. Serafini, I. Drebot, A. Bacci et al. Nuclear Inst. and Methods in Physics Research, A 909 (2018) 309–313Fig. 9. The beam spot of the muon beam at the exit of the concrete.The produced muons are then driven to a concrete wall. Thedynamics (or the interactions) of the muons inside the concrete wallhas been evaluated by the FLUKA [13,14] code Two thicknesses havebeen considered 1 m concrete. The results of the FLUKA evaluation,obtained with 20 different runs of the roughly 106 primary muons areshown in the following plots. The cut off used in the simulations was100 keV. The number of emerging muons per primary incident muonis ≈ 0.244 ± 0.007% and ≈ 0.005 ± 0.15% for the case of 1 m and 3 mconcrete wall respectively presented on Fig. 7.The spectrum of the emitted muons (integrated over angle) is shownin Fig. 8 in case of 1 m.The beam spot of the muon beam at the exit of the concrete is shownon Fig. 9.3. ConclusionAdvancement in fiber-lasers, expected to meet laser–plasma basedTeV collider requirements at 10–100 kHz rep rate, offers the opportunityto develop a Compact Muon Source delivering the muon beam with 1–100 muons/s at GeV energy, collimated within hundreds/tens mrads,synchronized at nsec level, based on a compact O(10 m) and cheap O(10Me) system.References[1] E.V. Bugaec, A. Misaki, V.A. Naumov, et al., Atmospheric muon flux at sea level,underground, and underwater, Phys. Rev. Lett. D 58 (1998) 054001.[2] C.L. Morris, J. Bacon, K. Borozdin, et al., Horizontal cosmic ray muon radiographyfor imaging nuclear threats, Nucl. Instrum. Methods Phys. Res. 330 (2014).[3] H. Athar, Muon pair production by electron-photon scatterings, Phys. Rev. D 64(2001) 071302.[4] R. Hu, B. Liu, H. Lu, et al., Dense helical electron bunch generation in near-criticaldensity plasmas with ultrarelativistic laser intensities, Sci. Rep. 5 (2015) 15499.[5] S.Y. Kalmykov, S.A. Yi, A. Beck, et al., Numerical modelling of a 10- cm-long multi-Gev laser wakefield accelerator driven by a self-guided petawatt pulse, New J. Phys.12 (2010) 045019.[6] K. Yokoya, 1985. http://www-acc-theory.kek.jp/members/cainS/.[7] I. Drebot, D. Micieli, V. Petrillo, et al., ROSE: a numerical tool for the study ofscattering events between photons and charged particles, Nucl. Instrum. MethodsPhys. Res. (2017).[8] D. Micieli, I. Drebot, et al., Compton sources for the observation of elastic photon–photon scattering events, Phys. Rev. Accel. Beams 19 (2016) 093401.[9] I. Drebot, A. Bacci, et al., Study of photon–photon scattering events, Nucl. Instrum.Methods Phys. Res. A (ISSN: 0168-9002) (2016). http://dx.doi.org/10.1016/j.nima.2016.07.039.[10] I. Drebot, et al., Matter from light-light scattering via Breit-Wheeler events producedby two interacting compton sources, Phys. Rev. Accel. Beams 20 (2017) 043402.[11] I. Drebot, V. Petrillo, et al., Breit-Wheeler Scattering Events Produced by Two Inter-acting Compton Sources. Proc. of IPAC 2017, 14–19 May, Copenhagen, Denmark,2017.[12] W. Kilian, T. Ohl, J. Reuter, Eur. Phys. J. C 71 (2011) 1742. http://dx.doi.org/10.1140/epjc/s10052-011-1742-y.[13] A. Fasso, A. Ferrari, J. Ranft, P.R. Sala, FLUKA: a multi-particle transport code,CERN-2005-10, 2005, INFN/TC_05/11, SLAC-R-773.[14] G. Battistoni, S. Muraro, P.R. Sala, F. Cerutti, A. Ferrari, S. Roesler, A. Fasso, J. Ranft,The FLUKA code: Description and benchmarking, in: Proceedings of the HadronicShower Simulation Workshop 2006, Fermilab 6–8 September 2006, AIP Conf. Proc.896 (2007) 31–49.313

A muon source based on plasma accelerators

L. Serafini

A.R. Rossi

M. Rossetti Conti

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A muon source based on plasma accelerators

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