We consider the radiation of particles of one bunch in the collective field
of the oncoming bunch, called coherent bremsstrahlung (CBS). The main
characteristics of CBS for LHC (in the Pb-Pb mode) and for RHIC are calculated.
At LHC about $3.9 10^8 dE_\gamma/E_\gamma$ photons per second are expected for
photon energies $E_\gamma \stackrel{<} {\sim} E_c= 93 $ eV. It seems that CBS
can be a potential tool for optimizing collisions and for measuring beam
parameters. The bunch length can be found from the critical energy of the CBS
spectrum; the transverse bunch size is related to the photon rate. A specific
dependence of photon rate on the impact parameter between the beams allows for
a fast control over the beam displacement.Comment: 9 pages + 4 figures, latex with poscript figures uuencode

Engel, R.

Schiller, A.

Serbo, V. G.

English

arXiv

We consider the radiation of particles of one bunch in the collective field of the oncoming bunch, called coherent bremsstrahlung (CBS). The main characteristics of CBS for LHC (in the Pb-Pb mode) and for RHIC are calculated. At LHC about 3.9 10^8 dE_\gamma/E_\gamma photons per second are expected for photon energies E_\gamma \stackrel{<} {\sim} E_c= 93 eV. It seems that CBS can be a potential tool for optimizing collisions and for measuring beam parameters. The bunch length can be found from the critical energy of the CBS spectrum; the transverse bunch size is related to the photon rate. A specific dependence of photon rate on the impact parameter between the beams allows for a fast control over the beam displacement

Engel, R

Schiller, A

Serbo, V G

CERN Document Server

Particle Accelerators, 1996, Vol. 56, pp. 1-12Reprints available directly from the publisherPhotocopying permitted by license only© 1996 OPA (Overseas Publishers Association)Amsterdam B.Y. Published in The Netherlands underlicense by Gordon and Breach Science Publishers SAPrinted in MalaysiaA NEW POSSIBILITY TO MONITORCOLLISIONS OF RELATIVISTICHEAVY IONS AT LHC AND RHICR. ENGEL,l,* A. SCHILLER1,t and V.G. SERB02,+1Institut fiir Theoretische Physik, Universitiit Leipzig, Germany2Novosibirsk State University, 630090 Novosibirsk, Russia(Received 8 January 1996; in final form 24 April 1996)We consider the radiation of particles of one bunch in the collective field of the oncomingbunch, called coherent bremsstrahlung (CBS). The main characteristics of CBS for LHC (inthe Pb-Pb mode) and for RHIC are calculated. At LHC about 3.9 . l08dEy / E y photons persecond are expected for photon energies E y ~ E c = 93 eV. It seems that CBS can be a potentialtool for optimising collisions and for measuring beam parameters. The bunch length O'z can befound from the critical energy of the CBS spectrum Ec ex: 1/O'z; the transverse bunch size 0'1- isrelated to the photon rate d Ny ex: 1/0'1-2• A specific dependence ofd Ny on the impact parameterbetween the beams allows for a fast control over the beam displacement.Keywords: Coherent bremsstrahlung; heavy-ion collisions; photon spectrum; azimuthal asym-metry; bunch length; transverse bunch sizes.1 INTRODUCTIONIn this paper a new type ofradiation at colliders - the coherentbremsstrahl~ng(CBS) - is considered. The CBS is the radiation of one bunch particles in theshort collective electro-magnetic field of the oncoming bunch.For definiteness, let us consider the photon emission by a single ion witha charge Zle moving through a bunch of ions with the charge Z2e. Theordinary (incoherent) bremsstrahlung of ions at colliders has a relativelysmall cross section. On the other hand, at small enough photon energies E y ,*E-mail: eng@tph200.physik.uni-Ieipzig.det E-mail: schiller@tph200.physik.uni-leipzig.de+E-mail: serbo@adm.cnit.nsk.su2 R. ENGEL et al.the radiation due to interaction of the Zl ion with the second bunch becomescoherent resulting in large number of emitted photons. This increase arisesfrom an extra factor N2 where N2 is the second bunch population. Therefore,the number of the emitted photons dNy is already proportional to N22(1)The CBS occurs when a coherence length rv 4Y1 2 tu:/ Ey becomescomparable or larger to the length of the second bunch a2z (here YlEl/(mlc2) is the Lorentz factor of the Zl ion). At photon energies(2)the radiation arises from the interaction of the Zl ion with the second bunchwhich looks like a "particle" with the huge charge Z2eN2.A classical approach to CBS was given in Ref. 1, a quantum treatment ofCBS and applications to some working and planned colliders can be found inRefs. 2--4. Recently we have developed a new simple and transparent methodto calculate this radiation.5 For the application of CBS to relativistic heavyion colliders we collect the needed formulae from Refs. 3 and 5.The method of calculation is valid if the ion deflection angle Od in thefield of the oncoming bunch is small compared with the typical radiationangle Or rv I/Yl. The ratio of these angles is easily estimated knowing theelectric and magnetic fields of the second bunch which are approximatelyequal in magnitude, lEI ~ IBlrv 2Z2eN2/(a2za2J.J (for LHC the effectivefield lEI + IBI rv O.IT)Od Z2 rlN2- rv1]= ---Or Zl a2l-(3)where a2l- is the transverse size of the second bunch and rl = Z 12e2f(rnt c2)is the classical ion radius.For LHC (in the mode Pb-Pb) and for RHIC the parameter 1] is of the order(4)so the above mentioned method is valid.MONITOR COLLISIONS OF RELATIVISTIC HEAVY IONSTABLE I Parameters of some eollidersN Y == E/(mc2 ) crz (em) cr-t (JLm)Ph (LHC) 0.9 . 108 2980 7.5 15Au (RHIC) 109 108 11.9 150P (RHIC) 1011 268 7.2 1103It is worthwhile to notice that for the majority of the colliders rJ is eithermuch smaller than one (all pp, pp, some e+e- colliders and B-factories) orrJ f".J 1 (e.g., LEP, TRISTAN) and only the linear e+e- colliders have rJ » 1.Therefore, the CBS has a very wide region of applicability.In calculating the CBS effect we have assumed that the densities of thebunches do not change during the collisions and that the bunches in theinteracting region have Gaussian particle distributions with mean-squaredtransverse CYj..l and longitudinal CYjz radii, j = 1, 2. All parameters which arenecessary for the calculation are given in Table I, for LHC they are takenfrom Ref. 6 and for RIDC from Ref. 7. For collisions of identical beams weassume Nl = N2 = N.2 SPECTRUM OF CBS PHOTONSThe number of CBS photons for a single collision of the beams is equal todEydNy = No (Ey/Ec)-.EyHere for the round Gaussian bunches withthe constant No is equal to(5)(6)(7)(8)4 R. ENGEL et ai.TABLE II Parameters of CBSPh-Ph (LHC) Au-Au (RHIC) p-Au/Au-p (RHIC) p-p (RHIC)No 49 590 49/1800 170Ee (eV) 93 0.077 0.48/0.13 0.79Ae (J,tm) 0.013 16 2.6/9.7 1.6the formula (7) simplifiesNo = ~ In ~ ; Nl (Z2~~N2) 2 = 8.91 . 10-4 Nl (Z2~~N2 ) 2 (9)The function (x) is defined as follows(10)(x) = 1 at x« 1; (x) = (0.75jx 2 ). e -x2 at x» 1 (11)(some values of this function are: (x) = 0.80, 0.65, 0.36, 0.10, 0.0023 forx = 0.1, 0.2, 0.5, 1,2).The calculated constants No, the critical energies Ec and wave lengthsAc = 2n nc/Ec are presented in Table II.Note the following features of the CBS spectrum. The constant No isproportional to 1ja..l2 and the shape of the spectrum strongly depends on thebunch length a2z via Equations (2) and (5). Therefore, measuring the photonrate and the shape of the spectrum one can obtain informations about thebeam sizes.It may be convenient for LHC to use the CBS photons in the range ofvisible light E y rv 2 - 3 eV « Ec = 93 eV. In this region the rate of photonsis expected to bedN dE--y ~ 3.9 . 108 --y photons per second (12)r Ey(here r = 0.125 JLs 8 is the time between bunch collisions at a giveninteraction point). Furthermore, for visible light the photon polarisationshould be easily measurable.MONITOR COLLISIONS OF RELATIVISTIC HEAVY IONS 5(14)(15)Let us discuss the question of a possible background due to synchrotronradiation (SR) on the external magnetic field of the collider B ext. A completetreatment of this background can be done only knowing the details ofthe collider magnetic layout. Nevertheless, for all the discussed heavy ioncolliders we expect this background to be small.A rough estimation of the SR rate can be performed as follows. The firstbunch moving through the uniform field B ext emits dN~R photons in thetime ~tHere d I is the classical synchrotron radiation intensity per unit time, E~Rthe critical SR energyESR = n3Z1eBext Y1 2 = n 3Y1 3Ce 2mlC 2RBwith the circular orbit of radius RB. The normalised function F (y) is definedas an integral over the modified Bessel function KS/3(X)600F(y) = ~ V3 y ! KS/3(X) dx .8nySince the CBS radiation is confined to angles.;5 1/YI . Only those SR photonsshould be considered which are emitted in the same angular interval. Usingthis condition one can estimate ~t~t t".J RB = mlCYIC ZleB extwhich allows to write Equation (13) in the form(16)(17)4 dEdN SR t".J - a N Z 2 F(E /E SR ) _YY 9 I lYe E·YIn Figure 1 we compare the rate for the CBS and SR photons usingEquations (5), (17) and the parameters of LHC assuming an external fieldB ext = 1T, for definiteness. The critical SR energy for this field strength is0.35 eV (remember Ee = 93 eV for CBS). The ratio of the CBS rate to the SRrate changes drastically with the photon energy. It is equal to 1, 10, and 10006 R. ENGEL et al.I ICBS-SR····1012dN1By dE,dt(8-1) 10810010(eV)1E11~----'---L----'--L.~L....L...L..-_..L...-.J.--,.J...~-'-'-'-'-------'---L-......L-.J..................~0.1FIGURE 1 Number of photons emitted due to CBS and SR (B ext = IT) at LHC (Pb-Pb) asfunction of the photon energy.for E y = 6.5,7.5, and 9.8 eV. So we conclude that for photon energiesabove 10 eV the synchrotron radiation can be neglected. It may be useful toconsider the case E y = Ee » E~R where the signal to background ratio canbe estimated as follows(18)Let us stress that the CBS spectrum is completely different to that ofthe synchrotron radiation in a uniform magnetic field. Both are classicalradiations in the considered cases, but CBS is an emission in a shortelectro-magnetic field at the length scale of the bunch while SR correspondsto photon emission in a static magnetic field with a much larger characteristiclength scale. In particular, the critical energy Ee of CBS (2) does not dependneither on the charge nor on the mass of the radiating ion contrary to E~R .MONITOR COLLISIONS OF RELATIVISTIC HEAVY IONS 714p-Au ....Pb-Pb -Au--:-p-6 8 10 12R/aLl420~---'--------'---------'--_...L..--_--'--_-.1-_----L----'o1.41.21~dN,(R) 0.8dN,(O)0.60.40.2FIGURE 2 Normalised number of CBS photons as function of the impact parameter R.It should be mentioned that for the application CBS to the RHIC colliderthe background from the thermal radiation in the detector region canplay essential role. Therefore, the corresponding cooling of the detector isnecessary.9If the first bunch axis is transversely shifted by a distance R from thesecond bunch axis, the luminosity L(R) (as well as the number of events forthe ordinary reactions) decreases very quicklyL(R) = L(O) exp (- 2 R22 ).2(O"L1 + 0"2J)(19)On the contrary, for the discussed colliders the number of CBS photonsdecreases slowly and for small values of R this number even increases. For thecollision ofidentical round beams the maximum ofthe ratio d Ny (R) / d Ny (0)8 R. ENGEL et al.is equal to 1.06 at R ~ 1.3 a1- (see Figure 2) whereas the luminosity alreadydecreases significantly. At large displacements R » a1- this ratio is(20)Additionally, two cases of non-identical beams (p-Au and Au-p collisions atRHIC) are also shown in Figure 2. The dependence of CBS on the beam axisdisplacement can be used for a fast control over the collision impact parameterbetween beams at the interaction point (especially during the beginning ofevery run) and over the transverse beam size. For the case of another type ofradiation (beamsstrahlung), such an experimenthas already been successfullyperformed at SLC. IO3 AZIMUTHAL ASYMMETRY AND POLARISATIONThe angular distribution for central head-on collisions of round beams hasno azimuthal asymmetry, it is given by the expression3 dEy l+z2 [( E y )2]dNy = -No -.- 4 dz exp - (1 +z)-2 Ey (1 + z) Ec(21)where z = (YI ())2, () is the polar angle of the emitted photons. In Figure 3we present the normalised angular distribution for different photon energiesas function of YI (). For small photon energies (Ey « Ec ) it almost coincideswith that of the ordinary bremsstrahlung. At photon energies of the order ofEc the distribution shrinks considerably.It may be useful to note that in the energy region(22)the angular distributions of CBS and SR photons are quite different.According to (21) the characteristic emission angle () char of CBS in thisregion is1()ehar ~ - .YI(23)MONITOR COLLISIONS OF RELATIVISTIC HEAVY IONS 9520.21==----r----.----.-------.-------,0.10.0010.0001 '--_---'-__-1...__--1.-_------'-__--'---'0.1r(B) 0.01FIGURE 3 Angular distribution of the CBS photons for two typical energies, normalised at8 = 0, r(8) = dNy(8, Ey)jdNy(O, E y).For photon energies (22) the distribution of SR photons over an angle tJ(defined as the angle between the photon momentum and the orbit plane) canbe obtained from Ref. 11 (see §74) as followsdN~R 1 + 2zSR (Ey SR 3/2) SR 2dEydzSR ex: .Jl + ZSR exp - EfR (1 +z) , z = (YII?-) .(24)From this expression one can see that the SR photon rate is stronglysuppressed for angles tJ larger thanI?- char ~ ..!..-.j2Ef R . (25)Yl 3EyThe characteristic angle of SR is considerably smaller than that of CBS. Thisfact can be used to suppress the SR background even stronger.10 R. ENGEL et al.10.80.6I(R)0.40.22 4p-Au····Pb-Pb -Au-p-6 8 10 12 14R/aLlFIGURE 4 Average degree of linear polarisation as function of the impact parameter R.If the impact parameter R between beams is non-zero, the angulardistribution over () (or z) is unchanged, but an azimuthal asymmetry ofthe CBS photons appears which can also be used for an operative beamcontrol. For example, if R increases in the vertical direction, the first bunchis shifted to the region where the electric field of the second bunch is directedalmost vertically. This moving field of the second bunch can be representedas a flux of equivalent photons.5 These photons are linearly polarised in thevertical direction. The average degree ofsuch a polarisation 1for the discussedcolliders with identical and non-identical beams as function of R is shownin Figure 4.Let us define the azimuthal asymmetry of the emitted photons by therelationdNy(q; = 0) - dNy(q; = rr/2)A= . ,dNy(q; = 0) +dNy (q; = 1f/2) (26)MONITOR COLLISIONS OF RELATIVISTIC HEAVY IONS 11where the azimuthal angle cp is measured with respect to the horizontal plane.This quantity does not depend on the photon energy and is equal to2( (})2A == Yl I(R) .1 + (Yl(})4 (27)Increasing R in the vertical direction (see Figure 4), the fraction of photonsemitted horizontally becomes larger than the fraction of photons emittedvertically.Finally, let us briefly discuss the polarisation of CBS photons. For linearlypolarised equivalent photons the CBS photons also get a linear polarisationin the same direction. Denoting by ICBS the average degree of CBS photonpolarisation, the ratio ICBS / I varies as function of E y in the interval from0.5 to 1 4 (see Table III).TABLE ill Degree of the linear polarisation of the CBS photonso 0.2 0.4 0.6 0.8 1.5 2[CBS / [ 0.5 0.7 0.81 0.86 0.89 0.94 0.96 0.974 CONCLUSIONSWe have calculated the main characteristics of CBS photons for heavy ioncolliders, the photon rate, the energy and angular distributions as well asthe polarisation. It seems that CBS can be a potential tool for optimisingcollisions and for measuring beam parameters directly at the interactionpoint. Obtaining the critical energy Ec from the CBS spectrum, the bunchlength O'z can be found since Ec is proportional to IjO'z. The transversebunch size O'...L. is related to the rate of photons dNy (X IjO'...L. 2. Thepossible background due to synchrotron radiation on the external magneticfield of the collider is estimated. Furthermore, CBS may be very usefulfor a fast control over the impact parameter between the colliding bunchaxes because the photon rate dNy depends on this parameter in a veryspecific way.12AcknowledgementsR. ENGEL et al.We are grateful to P. Cameron and K. Eggert for useful discussions and toS. Peggs for providing us the RHIC parameters. V.G. Serbo acknowledgessupport of the Sachsisches Staatsministerium fiir Wissenschaft und Kunst, ofthe Naturwissenschaftlich-Theoretisches Zentrum of the Leipzig Universityand of the Russian Fond of Fundamental Research. R. Engel is supported bythe Deutsche Forschungsgemeinschaft under grant Schi 422/1-2.References[1] Bassetti, M., Bosser, J., Gygi-Hanney, M., Hofmann, A., Keil, E. and Coisson, R. (1983),IEEE Trans. Nucl. Sci., NS·30, 2182.[2] Ginzburg, I.P., Kotkin, G.L., Polityko, S.I. and Serbo, V.G. (1992). Phys. Rev. Lett., 68,788; Phys. Lett., B286 (1992) 392; Z. Phys., C60 (1993) 737.[3] Ginzburg, I.P., Kotkin, G.L., Polityko, S.1. and Serbo, V.G. (1992). Yad. Fiz. (in Russian),55,3310 and 3324.[4] Polityko, S.I. and Serbo, V.G. (1995). Phys. Rev., E51, 2493.[5] Engel, R., Schiller, A. and Serbo, V.G. (1995). Leipzig preprint UL-NTZ 29-95 (1995),hep-ph/9511262.[6] Review of Particle Properties, The Particle Data Group (1994). Phys. Rev., D50, 1197.[7] RHIC Design Manual and S. Peggs, private communication.[8] Eggert, K., private communication.[9] Cameron, P., private communication.[10] Bonvicini, G., et al. (1989). Phys. Rev. Lett., 62, 2381.[11] Landau, L.D. and Lifshitz, E.M. (1988). The Classical Theory of Fields (Nauka, Moscow).

A new possibility to monitor collisions of relativistic heavy ions at LHC and RHIC

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