Fernow, R C

Fukui, Y

Gallardo, J C

Kaplan, D M

Kirk, H G

Lebrun, P

Moretti, A

Palmer, R B

Tollestrup, Alvin V

CERN Document Server

AN IONIZATION COOLING CHANNEL FOR MUON BEAMS BASED ONALTERNATING SOLENOIDSJuan C. Gallardo, Richard C. Fernow, Harold G. Kirk, Robert B. Palmer, BNL, Upton NYPaul Lebruny , Alfred Moretti, Alvin V. Tollestrup, FNAL, Batavia, IL.Daniel M. Kaplan, IIT, Chicago, IL.Yasuo Fukui, KEK, Tsukuba, JapanAbstractThe muon collider requires intense, cooled muon bunchesto reach the required luminosity. Due to the limited life-time of the muon, the cooling process must take place veryrapidly. Ionization cooling seems to be our only option,given the large emittances of the muon beam from piondecay. However, this ionization cooling method has beenfound quite difficult to implement in practice. We describea scheme based on the use of liquid hydrogen absorbers fol-lowed by r.f. cavities (“pillbox” or “open iris” type), em-bedded in a transport lattice based on high field solenoids.These solenoidal fields are reversed periodically in order tosuppress the growth of the canonical angular momentum.This channel has been simulated in detail with independentcodes, featuring conventional tracking in e.m. fields and de-tailed simulation of multiple scattering and straggling in thethe absorbers and windows. These calculations show thatthe 15 Tesla lattice cools in 6-D phase space by a factor 2over a distance of 20 m.1 INTRODUCTIONIonization cooling of intense muon beams ( 2: 1012 parti-cles per bunch) has been recognized as one of the most chal-lenging aspects of the design of a high energy, high inten-sity Muon Collider[1]. The principle of ionization coolingvia deceleration in an absorber followed by re-accelerationin a LINAC, proposed more than 20 years ago[2], is rel-atively straightforward[1]. However, due to the relativelyshort muon lifetime, such cooling channels must be very ef-ficient. This entails reaching low values for the ?func-tion rapidly, and therefore high focusing magnetic fields.The performance of such lattices needs to be verified withaccurate simulations, with complete field maps and de-tailed simulation of the straggling and multiple scatteringin the absorbers and foils. Three distinct computer codeswere used to study the performance of this channel: (i) aspecial version of PARMELA[3] in which multiple scat-tering was simulated using the Gaussian approximation;(ii) ICOOL[4]; (iii) an extended version of the GEANT3package[5], DPGeant, featuring higher numerical accuracyin tracking particles over large distances and full e.m. fieldWork supported by the U.S. Department of Energy.y Email: lebrun@fnal.govsimulation in the r.f. cavities. Although results presented inthis paper have been obtained with DPGeant, these varioussimulation agree within the expected code accuracy.2 DESCRIPTION OF THE 15 TESLAALTERNATING SOLENOID COOLINGCHANNELWe here consider one component of a single cooling stage,consisting of the transverse cooling channel. This muoncooler, sketched in figure 1 is based on the use of the lowestZ material, liquid hydrogen (LH2), embedded in a strong(15 T) solenoidal magnetic field. Linacs are inserted be-tween these absorbers, to compensate for the energy loss.This channel has been designed for a nominal momentumof 187 MeV/c ( = 0:87 ) and accepts a transverse normal-ized emittance of 1600: mm mRad, a momentum spreadof  3% and a bunch length of  1:5 cm. The linac r.f.frequency is 805 MHz.To provide the longitudinal focusing required to keepthis single bunch together these linacs must be separated byshort distances ( less than 50 to 75 cm). Thus one section(defined as one deceleration in the absorber followed byone LINAC) is approximately 2 m long, where the muonswill lose and gain  20 MeV, leaving the momentumunchanged after one section. Without the absorbers andlinacs, the beam would have a constant (0) value for thecanonical angular momentum, despite the large fluctuationof the ?function. However, the presence of the absorberscauses the canonical angular momentum to grow and wouldlead to severe transverse emittance growth at the end of achannel made of multiple sections. This growth is stoppedby reversing the direction of the solenoidal field each timethe beam goes though the high ?points in the lattice,which are located in the middle of the linacs.The transport in such a channel is far from isochronous:particles at large transverse amplitude have longer pathlengths, causing a longitudinal growth as they reach thelinac slightly out of phase. It is therefore necessary to startwith a bunch where particles at large amplitude have highermomentum, by up to  20MeV=c for a particle at  3.For a fixed maximum field (15 T), the transverse coolingrate decreases as the beam goes though these sections, be-cause this rate is proportional to the transverse emittance.0-7803-5573-3/99/$10.00@1999 IEEE. 3032Proceedings of the 1999 Particle Accelerator Conference, New York, 1999The longitudinal emittance grows because of the stochasticprocesses in the absorbers (energy loss and multiple scatter-ing). In addition, there are higher order effects in the beamoptics and the longitudinal/transverse coupling induce lon-gitudinal motions that are are difficult to compensate for.Thus, the length of such a channel has to be limited to ap-proximately 20 m, after which one must go though an emit-tance exchange section.The performance of such a channel has been studied fortwo different lengths of a section: the 2 m (1.5 m) sectionhas a 64 cm (42. cm) liquid hydrogen absorber and 1.3 m(0.98 m) r.f. cavity, respectively. For the short section case,two different configurations of the linac have been simu-lated:1. A “pillbox” type cell, =2, with a peak field on axisof 36 MV/m. and 12 identical cells. The beams goesthough the walls of each cell, traversing 13 125: mberyllium foil2. A more conventional open cell cavity runs in  mode,where the iris aperture matches the transverse size ofthe beam (radius  4:5 cm at the entrance and exitpoints of the cavity, and 8 cm at ?max). The peakfield on axis is 60 MV/m, implying maximum field of 90MV=m on the iris wall.The lengths of these cavities as well as the phase for thesynchronous, on axis particle were kept identical. This syn-chronous phase[6] was set to 30 degrees, so only approx-imately one half of the voltage is used for acceleration, thelinac acts as much as a buncher as an accelerator. Finally,the liquid hydrogen must be contained in a vessel thermallyinsulated from the linac, this is achieved using thin ( 1:5mil) stainless steel window(s).3 PERFORMANCE AND ISSUESThe transverse and longitudinal emittances as function ofthe distance along the channel are shown in figure 2, for the1.5 m long section and for the open-iris cavity. Over a dis-tance of 25. meters, the channel achieves a cooling of abouta factor 2.3 in transverse emittance and a significant longi-tudinal reheating of about 2.1. Therefore, the overall 6-Demittance is reduced from 2:2 109 (mmmRad)3 down to0:86 (mmmRad)3. Correspondignly, the r.m.s. beamsize (radius) in the channel decreases from 1.09 cm downto 0.7 cm.Over 20 m, the non-decay loss is found to be less than1 %. For longer channels, this beam loss increases rapidlyas the bunch length grows; at the end of the channel, thebucket develops an “alpha” shape, signaling the need tostop cooling transversely and recover control of the longitu-dinal emittance. Very similar results were obtained with thepillbox cavity. Provided the average net acceleration acrossthe cavity is matched to the energy loss in the absorber andsufficient voltage is applied to ensure re-bunching, the netcooling merit factor of such a channel does not depend onL = 2 m.R.F. (TM010) R.F. (TM010)Hydrogen vessel Hydrogen vesselR = 15 cm.L = 2 m. ( or 1.5 m.)0 50 100 150 200 250 300 350 400 450-1000100200Bz PFigure 1: The Alternate Solenoidal muon cooling channel(top). The hashed lines are actual traces of muons obtainedvia the DPGeant package. Also shown (bottom), with ap-proximately the same horizontal scale, are the longitudinalcomponent of the magnetic field in KG., and the momentumfor the synchronous particle (MeV/c).the details of the acceleration system. However, the multi-ple scattering occurring at relatively high ?in the latticemust remain small, i.e., thin ( 125: m ) beryllium win-dows must be used. The tolerance on the phase (3 degreesis not particularly stringent. The difference in peak field issimply due to the different transit time factors for the twomodes ( vs =2:).The 2 m long section was found to be slightly worse thanthe 1.5 m one. The ratio of 6D emittances initial over fi-nal is about 10% smaller than for the 1.5 m long section.In principle, a longer cell period could give us faster trans-verse cooling time because less longitudinalspace is wastedin providing access cooling/shielding equipment betweenthe absorber and the r.f. Longer section section also min-imizes multiple scattering in the windows of the LH2ves-sels. However, the non-relativistic bucket would drift for alonger time in the absorber, resulting in a faster increase ofthe longitudinal emittance.3033Proceedings of the 1999 Particle Accelerator Conference, New York, 1999At injection, and during the cooling process, there isa strong coupling between the longitudinal and transversemotion in this channel. Particles at a large transverse ampli-tude tend to have large synchrotron motions because path-lengths depend on the betatron motion or the transverse am-plitude. The synchrotron oscillation tune in such channel isill-defined: as the stochastic processes (energy loss strag-gling while loosing energy in the absorber and, more im-portantly, scattering in the absorber or the foils) move theparticles suddenly in a slightly different location in phasespace. As a result, one can only quote a broad range for thesynchrotron wave length, of about 5 to 15 m This is also thescale at which the correlation between the transverse am-plitude and the momentum fades away, concurrent with thelongitudinal emittance growth. The loss of this correlationitself implies a emittance growth, which has not been takeninto account quoting the emittance at injection.The result presented in figure 1 has been obtained for50m thick stainless steel LH2windows. This is a ratherconservative design. We have studied the cooling perfor-mance of the channel varying the thickness and materialfor these window, and observed a degradation of 5 to 10% in the ratio the initial/final 6D emittance per additional25m of stainless steel. Titanium or Aluminium could alsobe used, but does not provide significantly better perfor-mance, because such window must be slightly thicker. Notethat these windows can be made hemispherical, which givesenhanced mechanical strength without compromising thebeam dynamics.Another uncertainty in this calculation is due to the im-perfect simulation of multiple scattering in Geant, (or sim-ilar packages), via the Moliere formalism [7]. The Molieretheory has been verified in numerous situation. However,for light materials, the uncertainty in the effective atomicscreening angle could lead to uncertainties of a few %. But,more relevant to our application, the Moliere formalism nolonger holds for very thin absorbers where the “effectivenumber of collisions” is small [8]. The LH2vessel mustbe divided into such thin layers while tracking, because ofthe betatron motion of the particles. The average scatter-ing angle in small steps becomes comparable to the angledue to the Larmor precession in the high magnetic field. InLH2, such steps are of the order of a few microns, with an-gle of tens of rad. A detailed simulation, (few m steps!) indicates that the Moliere approximation overestimatesthe radial displacement of the muon track in the absorber,leading to an over estimate of the beam reheating process.Based on a preliminary result, the ratio on the initial to final2-D emittance could be 30% to 50% larger than estimatedvia the Moliere formalism.Finally, if this channel remains a single-pass device (i.e.,not embedded in a cooling ring), one could consider slightlyincreasing (few % per section) the magnetic field in order tokeep the cooling rate optimal.0 2 4 6 8 10 12 14 16 18 20 22 24 26 2805001000150020002500E2D(mm.mRad.) ELong(mm.mRad.)0 2 4 6 8 10 12 14 16 18 20 22 24 26 280.9850.990.99511.005Z(m.)Trasm.Figure 2: Top: the 2-dim. transverse emittance (squares)and the longitudinal emittance (dots) versus the distancealong the channel, showing a net 6-dim. cooling. Alsoshown (bottom) is the transmission, (The decay loss ofabout 2:% is not included).4 REFERENCES[1] Status of the Muon Collider Research and Development andFuture Plans submitted to Phys. Rev., BNL-65-623, Fermilab-PUB-98/179, LBNL-41935.[2] G. I. Budker and A. N. Skrinsky, Electron cooling and newpossibilities in elementary particle physics, Sov. Phys. Usp.21 277 (1978)[3] H. Kirk, Parmela Modeling of Alternate Solenoids, presentedat the mini-workshop on Ionization Cooling (BNL, 1998).[4] R. C. Fernow, ICOOL: A Simulation Code for IonizationCooling of Muon Beams , these proceedings, THP31.[5] Geant Manual, V3.2.2.1, CERN Program LibraryW5013 (cern 1994).http://wwwinfo.cern.ch/asdoc/geant html3/geantall.html[6] Convention taken from An introduction to the physics of highenergy accelerators, John Wiley & Sons, 1993, by D.A. Ed-wards and M.J. Syphers, p. 33.[7] See for instance C. Caso et al Eur. Phys. J. C 3 1-794 (1998),page 146.[8] H. A. Bethe Phys. Rev. 89 1256 (1953)3034Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

An ionization cooling channel for muon beams based on alternating solenoids

An ionization cooling channel for muon beams based on alternating solenoids

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