Pedersen, F

Rasmussen, N

Schönauer, Horst Otto

Schönauer, H

CERN Document Server

Fast capture of heavy ions in the CERN PS booster

22/7/94 OCR OutputGeneva, SwitzerlandLondon, United KingdomEPAC94, 4th European Particle Accelerator Conference, 27.6. — 1.7.94,method of evaluating the capture efficiency is employed.well as for injection and capture later, at higher values of dB/ dt. A novelthe capture efficiency at the beginning of the magnetic cycle (dB/ dt = 0) asThe paper describes computer and machine studies performed to optimiseacceleration.very fast rising magnetic field tends to reduce capture efficiency at earlyoverall transmission. However the rapidly shrinking area of the bucket at theto accelerate as quickly as possible, in particular at low energies, pays off ingive rise to substantial loss with the vacuum conditions achievable. An effortthe cross-sections of charge exchange with the residual gas are very large andPS Booster will accelerate Pb53* ions from 4.2 to 95.4 MeV/ u. For these ionsIn the context of the CERN Lead Ion Facility now near to completion, theAbstractF. Pedersen, N. Rasmussen, H. SchonauerFAST CAPTURE OF HEAVY IONS IN THE CERN PS BOOSTERCERN-PS-94-28 i- BO YIlllllllUlIlllllllllllllllllllllllllllll CERN/PS 94-28 QIM ICERN LIBRARIES, GENEVACERN - PS DIVISIONCERNEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHf L;limited to 100 V/ms. OCR Outputhigher the losses are such that it is worthwhile to capture and rise of the magnet voltage (dV,,,/dt), which in turn islf the pressure of N2 or equivalent gases is l()" torr or voltage. The value of dB/dtis proportional to the rate of2zdB/dtup to the maximum value of the magnet supply2zenergy in the PS Booster. value of dB/dt and accelerated with a high value ofFigure l. Life—time of Pbversus kinetic of the low energy regime, they are captured at a high53+ln order that the particles are accelerated quickly outKinetic Energy [MeV/ti]0 20 40 so ao 1oo0.0 4.2 lss I 207.948 I 17 I 2.4 I 2 I 1000.2 T/S I v/msi I tM<=V/¤ I I a.m.u.Fi 0.4T IQI Al I *· I ka IGB/dtl Idvm/d,1; 0.s5 o.aParameter values for ionsE 1.o Table 1J2. 1.2in terms of the synchrotron period.144 p(N2) .-= 9.E-10 Torr the relative increase of the bucket area divided by the time1.6 in table 1. The constant of adiabaticity k, is defined asparameters which represents a near optimum and is listedBelow is given a set of calculated values forimportance of the low energy phase.the nominal Pb ions versus of their energy, illustrates the3.1 Generallow energy phase. Figure l showing the computed lifetime of3 CALCULATIONSOne remedy is to accelerate as fast as possible, at least during thetransmission losses is out of reach with the existing machine.but achieving a low pressure such as to guarantee negligibleofthe slope at injection is the object of this investigation.at low energies I1}. The obvious cure is to improve the vacuumhigher than the value for protons. This optimum valueexchange processes between circulating ions and the residual gasvalue of the slope of the field which is about 5 to 6 timessignificant enects are due to the large cross—s¤:tions of chargemaximum value. In addition we inject the beam at aimpossible without substantial modifications. The mostvoltage is allowed to rise with this slope, up to itsaccelerating highly but not completely ionised hwvy ions isfunctioning of the main quadrupole supplies, and theAlthough the PS Booster has amleratw light ions,V/ms, which is the maximum value for a proper1 uvrtzooucriow For the ions we increase the rate of voltage rise to 100cycle.generation of the field parabola in the beginning of thecapture etiiciency is employed. the capture of protons in the PSB is about 43V/ms for thehigher values of dB/dt. A novel method of evaluating the The usual rate of rise of the magnet supply voltage forcycle (dB/dt = 0) as well as for injection and capture later, atoptimise the capture ethciency at the beginning of the magnetic2 GENERAL PROCEDUREpaper describes computer and machine studies performed totends to reduce capture eEciency at wly acceleration. Theefficient.shrinking arm of the bucket at the very fast rising magnetic Heldbe short. Hence the capture is less adiabatic and lessenugies, pays 0E in ovaall Uansrnission. However the rapidlytransverse losses, the duration of the capture process musteH0rt to accelerate as quickly as possible, in particular at lowspiralise very fast, and in order to reduce the ensuingsubstantial loss with the vacuum conditions achievable. Anstable phase angle of zero for maximum bucket area,exchange with the residual gas are very large and give rise torising bending field; the particles which are captured at a95.4 MeV/u. For these ions the cross-sections of chargeThe longitudinal losses arise because of the very fastcompletion, the PS Booster will accelerate Pbions from 4.2 to53+ have prepared ourselves for this eventuality.In the context of the CERN Lead Ion Facility now nw tolongitudinal and transverse losses which arise, and weAbstract accelerate the beam very rapidly and accept someF. Pedersen, N. Rasmussen, H. Schonauer, CERNFast Capture of I-lcavy Ions in the CERN PS Boosterconstant adiabaticity during CapIl1I`€. OCR Outputexcursion is influenced as well by the duration of capture.function i.e., the function which ensuresradial excursion and the uansversal acceptance. The radialFigure 5. The Iso-adiabatic gap voltageacceptance at t = tk, the second is a function of the maximumtime, msadiabaticity of the capture process and of the longitudinal17.6 17.8 18 18.2The first mentioned is a function of the duration andcompromise between the longitudinal and transversal losses.The optimum value of the slope dB/dt is determined by ato the programmed frequency until the error becomes zero. S |....,.,..........•~.....%....e............,.....,.§decreases approximately linearly and thereafter increases duewhere capture takes place, the mean radius of the beamcapture is shown in figure 4. In the time interval (t, to ti,)10} ................ ]...The evolution of the radial error which appears duringangle (os,) corresponding to a correct orbitfrequency fp, is shown in Hg. 3 together with the stable phase15phase loop. The stable phase (qt,) calculated [4] for the gap voltage, kVthe stable phase angle as well as the frequency input to thebut rapidly to a phase program, it is advantageous to program voltage rises adiabatically up to a value (3 kV) which is necessaryphase loop, by nature, reacts very slowly to a frequency input shrinks due to the fast acceleration. During capture the gapfrequency and f, is the field derived frequency. Since the only a Baction of the voltage nwded later on, when the bucketThis is illustrated in fig. 2 where fp is the programmed approximately 5 keV so the gap voltage riwded for capture isfield derived frequency i.e., the one for which AR = O. The energy spread (20) of the injected bmm is small,subsequently has to increase more rapidly in order to join thereturn to a correct orbit again the acceleration frequency 3.3 Capture Ejiciencytheir revolution frequencies increase, but very slightly. Tospirals approaching the centre of the accelerator and hence, stationary bucket.constraint means that the trajectories of the particles are Figure 4. Radial excursion during capture into aDue to the increasing bending field, the above mentioned14 18 20 22 24*10Capture takes place in the interval Ig to tig.and programmed frequency (fp) versus time."8]*··‘·‘*··‘··"···‘·‘Z··£·Fig.2. Acceleration frequency (fa) for AR = Otime, ms-‘| ................... ‘..z.0s·i¤" iv is is zu zi 22-3r........"3-1»l0" ,.,. aura. .... ,...,...`,.s,.2l ................... *1.;.fVl/fp —1|———-·~-·‘i-l*¤—3_u.l°' ...... .........,3.,,, the time scale is different from that in fig. 2...t ........... ..... ,,£.t..Figure 3. Stable phase angle versus time. Nmtlnij m’I¤l'I‘Sx,zs·i¤ 15 tia2O 25 30 35 40frequency, Hzefficiency then experienced.the gain of time obtained does not outweigh the low captureIf, on the contrary, the beam is accelerated during capture, ¢l OJ ....... .... Y.stationary bucket, that is, when the stable phase angle is zero. 0.2 I ..... :..;|.The best capture efficiency [3] is obtained with a03 t ....... E ...... ....... .......3.1 Capture 0f I0ns? * t / `k —— `Mathcad and QuickBasic [2]. 0.4 r'*"***"E istable phase angle, radiansThe calculations arc madc with a combination ofconstant (ki,). Phase Plane", CERN, PS/Hi Note 94-07, 1994. OCR Outputl5j N. Rasmussen, "Tracking Particle Trajectories in theFigure 7. Longitudinal capture efficiency versus adiabaticitykvaliatxatidtyaxtsartte 1 2 :2 4 5 5 7 5 PS/Hl—Note 94-06, 1994.···•·i··»··¤•i·i»60·i···•»··in¤·····¤··iii»»·•»·¤i··¤··Longitudinal Beam Transfer Function", CERN,[4] N Rasmussen, "A Complete Expression for the70:75: PS/HI Note 92-09, 1992.Capture Efficiency. Low Intensity St11dies", CERN,[3] N. Rasmussen, "The Influence of Voltage Function onPS Booster", CERN, PS/HI—Note 94-05, 1994.[2] N. Rasmussen, "Calculations for PbInjection into thesk109t"‘ "'"'1"\Report", p. 4, CERN 93-01.@[X1I€ q’,% 1251lt] D. Wamer, editor, "CERN Heavy-lott Facility Designthe end of capture (3) att: 1,, are shown. 6 REFERENCESAdditionally one final bunch at t = tk (2), and one bunch atlongitudinal and transversal losses.Figure 6. Capture regions (1) for two adjacent buckets.result is a compromise betweeen charge exchange. andstable phase angle, radians-20 -15 -1e -5 e 5 ie 15 ze optimisation of the uansmission through the PS Booster. The'393ITl\'l1'1\'fi'f\TlTUTI';lT1TH'!ITlTIT|1'l\`f1TIYI\'H‘l'\YiTl\'!\‘f\'fI'fI\'f\‘fl'f|1'iI'i1‘flTI\'Ii of the capture process of lead ions have been calculated fcr the-25g..To minimise losses due to charge exchanges, parameter values-2e€5 CONCLUSIONS...... ...., ..... .. .... a .... .. ¢,,.; JE; .... . . .... 4_Ei ........... ............. .....`.,. lifetime of at least 60 ms .advisable. Indeed the vacuum must be improved to have atime constant of 20ms so it looks as if fast acceleration will be,0; ............. injection energy in one ring. The intensity is demying with a‘5.....€ ......... . ....... ...... .*. .... ' .... .*.Q.... .4.* = Hm = maximum. We have also had a coasting bwm of Pb imts atprotons of 63% has been mmsured but this is not yet the25: this case was found to be about 70%. A capture emciency forenergy deviation, keV tested without the charge exchange losses. The emciency forjust described has been calculated for protons so that it may befigures 7 and 8 respectively.ln order to check the calculations an analogical case to the onebeen plotted versus the adiabaticity coefficient in theefficiency and the maximum radial excursion have 4 MACHINE STUDIESTo facilitate the search for an optimum, the capturecapture efficiency can easily be calculated. figure 3).captured parts have shapes of parallellograms and the intmval during which the stable phase rim linwly (seekeV symmetrically around zero energy deviation so the mtcursim vums adiamticity wtaant. 'I`he time & is theThe injected ion beam lies in a ribbon of the width 10 Figure 8. Family of curves fm the maximum radialoutside the capture regions are lost.k., iso-adiabatic constantfollowing called a capture region. Particles lying0 1 rruvw\’¤ *•v•\‘\‘•\‘•w\‘•1vii 2 3 4 5 6 79'h•vi·r·rt·u‘t·iare captured in the bucket at t = tk. This area is in the- amt-onincludes all the particles of the injected beam whichofthe trajectories encloses an area (see fig. 6) which \§16very beginning ofthe capture. The locus of the endsseparatrix of the final moving bucket at t = tk to the.....1Sthe particle trajectories are tracked backwards from theefficiency a program has been developed [5]. By this,For calculation of the longitudinal capture s:Wd`°°"’“’25kV). This is illustrated in fig. 5.adiabatically up to thc maximum possible value (12 39max. radial excursion, mmfor a good efficiency, and afterwards we lei it continue

Fast capture of heavy ions in the CERN PS Booster

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