The energy loss of an unbunched beam circulating in the CERN-SPS has been obtained from the observed frequency change of a longitudinal Schottky signal. This experiment was carried out for protons at 14, 120 and 270 GeV/c and for lead ions PB82208 at Z .270 GeV/c momentum. The dominant effects which determine the energy loss are synchrotron radiation, ionization of the residual gas and parasitic mode loss in the resistive longitudinal impedance. Since all the protons in a lead nucleus radiate coherently the synchrotron radiation is proportional to Z2 like the other effects. The experimental results are analyzed and the contributions of the individual effects determined. Using an impedance of | Z/n | ~ 12 W gives the best fit through the experimental data

Arnold, J

Bohl, T

Burkhardt, H

Cornali, R

Cornelis, Karel

Engelmann, G

Giachino, R

Hofmann, A

Jonker, M

Linnecar, Trevor Paul R

Meddahi, Malika

Normann, L

Shaposhnikova, Elena

Wagner, A

Zotter, Bruno W

CERN Document Server

ENERGY LOSS OF PROTON AND LEAD BEAMS IN THE CERN-SPSJ. Arnold, T. Bohl, H. Burkhardt, R. Cornali, K. Cornelis, G. Engelmann,R. Giachino, A. Hofmann, M. Jonker, T. Linnecar, M. Meddahi, L. Normann,E. Shaposhnikova, A. Wagner and B. Zotter, CERN, 1211 Geneva 23, SwitzerlandAbstractThe energy loss of an unbunched beam circulating in theCERN-SPS has been obtained from the observed frequencychange of a longitudinal Schottky signal. This experimentwas carried out for protons at 14, 120 and 270 GeV/c andfor lead ions Pb82208at Z  270 GeV/c momentum. Thedominant effects which determine the energy loss are syn-chrotron radiation, ionization of the residual gas and par-asitic mode loss in the resistive longitudinal impedance.Since all the protons in a lead nucleus radiate coherentlythe synchrotron radiation is proportional to Z2 like the othereffects. The experimental results are analyzed and the con-tributions of the individual effects determined. Using animpedance of jZ=nj  12 gives the best fit through theexperimental data.1 INTRODUCTIONThis experiment was carried out to measure the energy lossdue to the synchrotron radiation emitted by protons andlead ions and due to the resistive wall impedance but alsothe energy loss due to ionization of the rest gas had to beconsidered.The synchrotron radiation of a radially acceleratedcharge in free space is well known. For the fully strippedlead ions Pb82208it has to be considered that the charge isq = Ze and all the 82 protons radiate coherently resultingin a emitted power being proportional to Z2. Furthermorethe shielding effect by the vacuum chamber has to be takeninto account. For the energy loss caused by the impedanceof the beam surroundings we have to consider that the un-bunched beam consists of point charges without any phaserelation between them. Each charge produces an electricfield concentrated in the transverse direction with an open-ing angle of about 1= which induces on the wall a shortcurrent pulse of length proportional to 1=. By measur-ing the loss for different beam energies some informationabout the resistive wall impedance can be obtained. In thefollowing we will discuss the different effects leading toan energy loss and calculate the expected magnitude forthe conditions used in the experiment. We make some es-timates of the impedance based on earlier measurementsdone in the SPS and similar machines and we will use theactual measured pressures of the residual gas to estimatethe loss due to ionization. The expected effects are pre-sented and compared with the experimental results.circumference 2R m 6912bending radius  m 741.3revolution freq. !0s 1 2 43400mom. compaction c0.0018chamber height hMBAmm 24” hMBBmm 41eff. chamber radius b mm 35Table 1: Relevant SPS parameters2 KINEMATICSA particle with charge q, rest mass m0and momentum pcirculates in a transverse magnetic field B on an orbit withradius of curvature  given by1=qBp=qBm0c: (1)Since the bending radius and the field are the same forprotons (q = e, m0= mp) and lead ions (q = Ze,m0= mPb) we have the relationpPb= mPbc PbPb= Z pp= Zmpc pp: (2)As approximations we take for the mass of the lead isotopePb82208ion mPb= Ampand set  = 1 except where itis subtracted from a quantity close to unity. With this weget for the two particles circulating on the same orbit in thesame magnetic fieldPbpZA=82208= 0:394: (3)In the experiment the energy loss has been determinedby observing the change of the frequency !s=2fs=k!0of a Schottky signal being a harmonic of the revolution fre-quency !0which depends on the momentumd!0!0=  dpp  dEEwith  = c 12(4)where cis the momentum compaction. The relative en-ergy loss per unit time or the energy loss U per turn isobtained from the observed time variation of the Schottkysignal frequency1EdEdt=  1fSdfSdtand U =Ef0fSdfSdt: (5)Table 1 lists the relevant parameters of the SPS.3 SYNCHROTRON RADIATIONFor the calculation of the energy loss due to synchrotronradiation we use the equationUs=q23430q2430: (6)Here q is the charge of the circulating particle. For theproton it is just the elementary charge q = e. However, forthe lead ion we have q = Ze since the nucleus containingZprotons can be considered as a point charge within the scaleof the wavelength of the emitted radiation, in other words,all the protons of the lead nucleus radiate coherently. Usingthe ratio between the Lorentz factors for protons and thelead ions (3) we get for the energy loss ratioUPbUP=PbP4Z2Pb=Z6PbA4Pb=8262084= 162:4: (7)The relative energy loss per unit time 1EdEdt= f0UsE=e2Z2f0330AmPc2=121rad; (8)is half the total radiation damping rate 1=radand has theratio 1EdEdtPb 1EdEdtP=Z5A4= 1:98: (9)We arrive at this somewhat surprising result that the leadions have a larger damping rate and move faster to the in-side than the protons. But this is true only in free spaceand the radiation from lead, being at lower frequencies, isreduced by the vacuum chamber more than the one fromprotons. The spectrum of the emitted radiation is charac-terized by the critical frequency!cof wavelength cwhichdivides it into two parts of equal power!crit=3c32; c=43: (10)So far the synchrotron radiation has been calculated forthe case of free space. The presence of the conducting vac-uum chamber may reduce the emitted radiation because thelower frequencies cannot propagate. The calculation of thissuppression is quite complicated. We use here an equationfrom [1, 2] which gives the frequency !thabove which ra-diation is possible!th!0=r23h3=2: (11)Here, h is the full height of the chamber listed in table 1.The emitted power is calculated for the two types of magnetchambers using the simplifying assumption that the syn-chrotron radiation spectrum lying above!this not changedwhile the part below is completely suppressed.4 IONIZATION OF THE RESIDUAL GASThe energy loss due to ionization of the residual is [3]dEdX=  KZ22ZA12ln2mec222TI2  2 2(12)with T =2mec2221 + 2me=M + (me=M)2: (13)Here, X is the mass per unit cross section (usually given in[gr/cm2]), A and Z are atomic weight and number of theresidual gas, K = 4NAremec2= 0:307 g 1 cm2 and Mthe mass of the nucleus. For our application we can neglectthe density effect =2 and set  = 1. The quantity I is themean excitation energy which is about 19.2 eV for H2, 82eV for N2and 95.1 eV for O2, [3].Based on earlier measurements the relative partial pres-sures of the residual gas were estimated to be about 52%H2, 30% H2O and 18% N2. For our calculation we splitthe water molecule and get for the partitions of the par-tial densities 11% for H, 66% for N and 23% for O. Thepressure has been measured with about 70 gauges aroundthe ring and averaged taking the distance between the mea-surement points and the pressure bumps in between intoaccount. These values are listed in table 2. For three ofthe experiments a lower pressure was obtained by using thesublimation pumps.5 PARASITIC MODE LOSSThe resistive impedance of the vacuum chamber leads toan energy loss of the particles in the coasting (unbunched)beam. Each charge produces an electric field which is bythe relativistic contraction concentrated in the transversedirection with a typical opening angle of 1=. It induceson the conducting wall surface a current pulse of rms length[4] t= b=(p2c) where b is the radius of a circular cylin-der which approximates the different cross sections of thevacuum chamber. The energy loss is proportional to anintegral over the product of resistive impedance times theFourier transformation of wall pulse. By measuring thisloss for different energies and hence, for different pulselengths t, we get some information about the impedance.At high frequencies the impedance is mainly due to diffrac-tion on the aperture changes which decreases like 1=p!and, to a lesser extent, due to the smooth resistive wallwhich increases likep!. For the diffraction contributionwe assume that the impedance has a maximum around 1.3GHz similar to the PS and ISR rings. Based on various SPSmeasurements we take for the characteristic impedance atlow frequencies jZ=nj = 10. The resistive wall effect iscalculated for a stainless steel chamber with radius b. Theestimated parasitic mode loss factor kpmare listed in ta-ble 2 for both contributions. This quantity is related to theenergy loss by U = q2kpm.parameters particle proton proton proton leadp=Z GeV/c 14 120 270 270 14.96 127.9 287.8 113.4 -0.00267 0.00174 0.00179 0.00172Synch. rad. crit:mm 94 1.5 0.13 2.1(free space) Us=Z2 m eV 0.0 2.2 55.8 1.3reduced Us=Z2 m eV 0.0 0.3 50.3 0.1Impedance  mm 1.65 0.194 0.086 0.217kpm=-diff. V/pC 3560 10 470 15 610 9 826kpm-res. w. V/pC 40 940 3 200 800Upm=Z2 m eV 0.6 1.8 3.0 1.7Ionization P nTorr 4.6 9.35 4.6 9.35 4.6 7.7density g/m3 0.031 0.063 0.031 0.063 0.031 0.052Ui=Z2 m eV 5.1 13.7 6.8 14.9 7.3 12.1Total estimated U m eV 5.7 15.8 8.9 68.2 60.6 13.9U   Usm eV 5.7 15.5 8.6 17.9 10.3 13.8Measured U=Z2 m eV 9.7 20.7 16.3 74.7 62.5 16.3(U   Us)=Z2 m eV 9.1 20.4 16.0 20.4 12.2 16.2Table 2: Top:Estimated energy losses of protons and Pb82208due to synchrotron radiation, due to parasitic modes (usingjZ=nj = 10) and due to ionization (taking for the partial pressures 52% H2, 30% H2O and 18% N2). Bottom: Resultsof the measurements and their correction for synchrotron radiation.6 EXPERIMENTS AND RESULTSIn the experiments a beam was accelerated to the desiredenergy where it was debunched and left coasting. A lon-gitudinal Schottky signal around !S= 2 109s 1 was ob-served and its central frequency measured as a function oftime for about 3 hours. From this the energy lossU per turnwas obtained using (5). For the case of 14 GeV protons thelife time was only about an hour which made the measure-ment less accurate. All other cases had a long life time.The variation of the dipole magnet field was checked andfound to be negligible. The results are listed at the lowerpart of table 2.The measured energy losses are corrected for syn-chrotron radiation U   Usand listed in table 2. In orderto determine the contributions of the impedance and of theionization to the energy loss we use the calculated valuesof the corresponding energy losses and calculate the factorsby which they have to be multiplied in order to get the bestagreement with the measurements. This procedure was car-ried out for all proton measurements and for the case whichalso included the lead measurements. The two approachesresulted in differences of about 30% for the impedance and10% for the pressure. Taking both with the appropriateweight we find for the impedance and the ionization losswhich give the best fit through the measured dataZn 12 4 and Ui(meas:)  1:4Ui(exp:): (14)The result for the impedance is good agreement with othermeasurements done at the SPS [5]. The obtained ioniza-tion loss could be explained by a slightly higher pressure ora different gas composition. In fact a distribution of 52%H2, 30% H2O, 4% N2, 10% CO and 4% of other gases likeArgon could be more realistic. In any case the measure-ments have errors large enough to explain differences withexpectations.7 ACKNOWLEDGEMENTSWe thank the LEP-SPS operation group for setting up thecoasting beams for this experiments. We also thank U.Wehrle for his help to obtain the Schottky signal and H.Jacob for measuring the beam life time.8 REFERENCES[1] S. Heifets, A. Michailichenko: Poc. of the 1991 Part. Accel.Conference, p. 458.[2] S.A. Kheifets, B. Zotter; CERN SL-95/92 (AP), 1995.[3] Review of Part. Phy.; Phys. Rev. D, Vol 54, 1996.[4] A. Hofmann, T. Risselada; IEEE-NS 30 (1983), p. 2400.[5] L. Vos; CERN SPS/86-21(MS), 1996.

Energy loss of proton and lead beams in the CERN-SPS

Energy loss of proton and lead beams in the CERN-SPS

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