During fixed target operations -- beam intensity is limited by coherent instabilities in both the Main Ring and Tevatron. The growth rates for instabilities are generally inversely proportional to the proton bunch length. Since fixed target operations are insensitive to the longitudinal emittance of the beams, bunch spreaders are employed to increase the emittance, and hence the bunch length. Emittance growth is stimulated by injecting noise onto either the RF phase or amplitude control voltages. Test results of the efficiency of various stimulation schemes are reported. The design of a bunch length monitor, used to measure the effect of the bunch spreader, is also presented. 12 refs., 5 figs

Ieiri, T.

Jackson, G.

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I)c. Fermi National Accelerator Laboratory FERMILAB-Conf-89/87 Stimulated Longitudinal Emittance Growth in the Main Ring * G. Jackson Fermi National Accelerator Laboratory P.O. Box 500, Batavia, Illinois 60510 U.S.A. and T. Ieiri KEK Tsukuba Ibmki 305 Japan March 1989 * Presented by G. Jackson at the 1989 IEEE Particle Accelerator Conference, Chicago, Illinois,Mmh20-23, 1989. *p 0 erated by Universities Research Association, Inc., under contract with the United States Department of Energy STIMULATED LONGITUDINAL EMITTANCE GROYCA IN TBE MAIN RING C. Jackson and T. Ieiril Fermi National Accelerator Laboratory2, Box 500, Batavia, IL 60510 Abstract During fixed target operations -beam intensity is limited by coherent instabilities in both the Main Ring and Tevatron. The growth rates for instabilities are generally inversely proportional to the proton bunch length. Since fixed target operations are insensitive to the longitudinal emittance of the beams, bunch spreaders are employed to increase the emittance, and hence the bunch length. Emittance growth is stimulated by injecting noise onto either the RF phase or amplitude control voltages. Test results of the efficiency of various stimulation schemes are reported. The design of a bunch length monitor, used to measure the effect of the bunch spreader, is also presented. Motivation During fixed target physics operations the Fermilab accelerators are expected to transmit as many protons as possible to 800 GeV. The maximum proton intensity, which in the last 1%37/1986 fixed target run was around 1.8 x 1013 protons/pulse, or about 1.8 x 1010 protons/bunch. This limit was imposed by the simultaneous onset of instabilities in the Main Ring and the Tevatron. The Main Ring problem is quite erratic, and has not been identified. It strikes at the peak Main Ring energy of 150 CeV, just before the beam is transferred into the Tevatron. The Tevatron suffers from a slow head-tail instability [3] which begins soon after the beam energy has exceeded 600 GeV. The threshold intensity of this instability was a function of longitudinal emittance [4]. The peak intensity of 1.8 x 1010 protons/bunch coincided with a BOX invariant longitudinal bun&area (A) of 5 eY-sec. At M area of 1.5 eV-set the peak intensity w.s 1.4 x 10'0 protons/bunch. The larger bunch area of 5 eV-set was stimulated by devices called bunch spresdere. Instead of spending time eliminating the instability, it nas decided to increase the threshold instability intensity by increasing the bunch length by a proportional amount. The Yain Ring bunch spreader wae used both to increase the Yain Ring instability threshold intensity, and to help the Tevatron bunch spreaders attain a final longitudinal emittance of 5 eV-sec. This document describes efforts to upgrade the bunch spreaders in anticipation of even greater intensity requirements (2-3 x 1010 protons/bunch) in the coming fixed target run. In order to better snalyse their performance, a 10 kEe bandwidth bunch length monitor has been built, and is also described below. The discussion will center around the new. recently tested Main Ring bunch spreader and bun& length monitor. Bunch Length Monitor A bunch length monitor is needed in order to measure the performance of a bunch spreader. Variation of the bunch length must be easily and clearly read from the monitor. The previous method of measuring ,the bunch length is to photograph the beam profile on a ride band resistive wall monitor. This method is too imprecise and to cumbersome. Instead, a real time monitor which outputs a voltage proportional to bunch length has been proposed [5] and developed. Assuming a train bunches with Gaussian longitudinal density distributions of rms width (r, the Fourier transform of the response of a resistive mall monitor is vm = 2 v. exp - - q Wrf 0 [ 12 22 I (1) 2 where m>O and Vm is the voltage per unit bandwidth at the mth harmonic of the RF angular frequency urf. Available is a stripline detector, and not a resistive wall monitor. Its length is such that the m=2 line is missing, so therefore the m=l and q =3 voltages are detected. Basically, the monitor performs the analog calculation o=pqpJ , (2) where k is an empirically determined number whose theoretical value should be 2 urf. In fact, the 85% interval of the beam distribution, referred to as the -I I.0 Figure 1: Keasured Main Ring bunch le.&b ~8 a function of time. Se curve marked with circles is the current in the dipole bus. Ths scales are 3 nsec and 0.4 seconds per division. I:, :a :” ‘ pi I. si 2: I! :. .- - .I T t T . . . - !fs I.. I. Figure 2: Expected Main Ring bunch length PS a function of time. The beam momentum is also displayed. The scales are identical to figure 1. -2- full bunch length, is the quantity of interest and the result given by the monitor. Calibration is accomplished through detailed comparison with bunch profile photographs. The output of the stripline detector is split and sent to two parallel circuits, one to detect the 53 MEz component of the bcem and the other to detect the 1.58 Mile component of the beau. Using matched 1 MEe bandwidth bandpees filters centered about these two frequencies, the monitor output is insensitive to the number of bunches in the accelerator. Beterodyne receivers then convert the RF amplitudes into 10 kBe bandwidth signals which are manipulated according to equation (2). The dynamic range of the system is 30 db, which means it can handle intensity fluctuations over a factor of 30 range. Figure 1 shows the measured response of the Main Ring bunch length monitor, along with the dipole current, as a function of time in an antiproton production acceleration cycle. Injection of 81 bunches, with an intensity of approximately 1.8 x 1010 protons/bunch, takes place at 0.3 seconds. Transition [7], the point at which the bunch length attains its minimum value, occurs just before 0.6 seconds into the cycle. Flattop is reached at 1.6 seconds, where the beam undergoes bunch rotation [a] just prior to extraction into the antiproton target. Figure 2 contains the expected full bunch length assuming B constant bunch area of 0.22 eV-sec. The agreement with the measured curve in figure 1 is very good. The noise in the measured bunch length is dominated by real beam hunch length fluctuations. Bunch Spreader Physics The invariant longitudinal emittsnce of e bunch can be changed through the introduction of random energy kicks to the beam [8]. Since narrow bunch lengths are to be avoided, and adinbstic bunch narrowing is taking place up the ramp, bunch spreading must occur while the beams are accelerating. The bunch spreader can be connected to an RP phase shifter (as was the case in en old bunch spreader) or to the RF peak voltage control. The problem with phase modulation is the need to decrease the radial offset feedback gain, which determines the RF frequency during acceleration. In the case of RF voltage modulation and full radial position gain the beam energy increment per turn is conserved and the synchronous phase is modulated. As the voltage is decreased, the synchronous phase is increased toward 900. Therefore, the small amplitude voltage gradient is reduced by both voltage decrease and the cc+ dependence of the gradient on synchronous pheee. Voltage modulation eeeme to be the theoretically best channel for introducing B bunch lengthening signal into the Main Ring IW system. The dependence of the amplitude growth rate on the frequency content of the bunch spreader signal is very important. First, there is no growth in the amplitude of a proton by this mechanism unless come fraction of the spreader power spectrum is at twice the natural particle frequency. Second, there is B spread in the natural proton synchrotron frequencies for L finite length bunch. The functional dependence of the synchrotron period on oscillation amplitude ia quite complicated, requiring avrluotion of integrals [8]. elliptic For phase oscillation amplitudes # about the synchronous phase angle #s which are at most half of the distance between the unstable fixed point end synchronous phases, this functional dependence can be approximated by the relationship "(6) = "(0) (1 - a2(#,) #"] where # and #. are in degrees, , (3) .?(#J = PO + Bz(f + P&Z I (4) and where pO=O.l84 x IO-', p2=0.194 x 10-8, and /J4=0.603 x 10-11 [Q]. This approximation is beet at uero synchronous angle [lo], getting progressively worse as #s=800 is approached. The limit to the amplitude of bunch spreading noise in the old bunch spreaders we.8 determined by the onset of beam lose from the RF bucket, end hence from the accelerator. This loss was minimised by applying random noise on the Rp voltage control at frequencies at twice the small emplitude synchrotron frequency. By constructing e sharp S-pole active filter network, the noise amplitude at half this frequency was reduced by 30db. The idea is that only protons e.t smell amplitudes are spread, and protons new the saparatrix in longitudinal phase space are unmolested. New Bunch Spreader Design Since at transition energy the momentum aperture of the Main Ring is at its minimum, bunch spreading can only occur after transition. The synchrotron frequency, as well as the RF voltage, are plotted in figure 3. Note that after transition the synchrotron frequency varies substantially, and twice the synchrotron frequency ranges from 300 to 500 BE. Since beam losses must be minimised, e narrow bend variable frequency noise source xae required. The noise is generated by amplifying and filtering the Johnson noise across a resistor. By mixing the noise and e voltage controlled reference frequency. a variable frequency noise band is crested. After additional filtering, this noise signal is gated end amplitude modulated using AD532 analog multipliers. The resultant signal is summed with the RF amplitude control voltage and sent on to the RF emplifiers. A control voltage of 10 volts corresponds to ;irimately 4.W of pee RF voltage samplek~~ :k: The no180 bandrldth is 100 Es. amplitude and frequency of the noise voltage are functions of time in the ecceleration cycle through the use of remp generators connected to the RF control system. Gating is accomplished through timing pulses also generated by the RF control system. . . .L :: .a -i! = :i 3; .I .I Figure 3: Predicted RF voltage .ud syncbrotron frequency during a Main Ring ac~elsration cycle. The sceles are 1 W end 200 8s per iirision. As expected, the synchrotron frequency dips dam to Nero at transition. Measured Performance The new Yain Ring bunch spreader has been tested under the same conditions shorn in figure 1. Figure 4 shows the measured bunch length, BP voltage, and total -3- beam intensity in 81 bunches during the acceleration cycle with the bunch spreader activated. The bunch length curve should be compared with figure 1, where the spreader was turned off. :a I.‘ :.. I.,” 7;:: I., ., i Figure 4: Measured performance of the new Main Ring bunch spreader. Plotted are the RF voltage, the bunch length, and the total beam intensity in 81 bunches. The scales mre 1 W, 3 usec, and 9 x 10'1 protons/beam per division, respectively. By looking at the modulation on the measured RF voltage, it is clear that bunch spreading started just after transition and continued through the msjority of the acceleration interval. The growth in the bunch length during this period is uneven, but with a sum total growth in bunch 1.6 msec, or SW. length of approximately On the other hand,I~even though the losses mre dominated by the poor Main Ring lifetime at low momentum and the step loss through transition, some beam losses does occur due to the bunch spreader. With a total loss due to bunch spreading of around 1X, a great improvement has been made wer the performance of the old bunch spreader [Q]. It should be pointed out that the frequency and amplitude curves used in this test have not been extensively optimized. During lrormal operations a considerable amount of real time fine tuning will be possible. Tevatron Design In the near future a Tevatron version of the bunch spreader will be constructed and installed. There will be two major differences between the Main Ring and Tevstron systems. the First, synchratron frequency es shorn in figure 6, during the Tevatron acceleration cycle is much lower than that in the Main Ring. Second, since the Tevatrun RF system does nut employ beam driven fre pency or phase feedback systems, phase noise will be introduced at the synchrotrcn frequency, rather than RF voltage noise at twice the synchrotron frequency. The reason for tryinq phase noise at the synchrotron frequency is related to theoretical questions concerning the Sidgh proton response to the two types of RF noise. In the case of phase noise the response of the longitudinal emittance cau be readily calculated via a harmonic oscillator solution, ms xa8 done in the Tevatron in the case of transverse emittmnce growth [ll]. The grorth rate of large amplitude particles, and hence their loss rate from the bucket, can be calculated. These calculations *- TF TE I I 0. I? II.. VI.. ..t . ? I.. I.. . . .t L Figure 5: Calculated value of the small amplitude synchrotron frequency during Tevatran acceleration. The scales are 5 seconds and 40 Bz per division. provide guidance as to the sharpness of the edges of the noise band in frequency space. For RF voltage noise the dominant response of a proton is described by the differential equation x + oo2 [l + I: a cos(2wmt)] x = 0 . (8) In the case of a single modulation frequency the solutions of this differential equation are called Ymthieu functions [12]. These functions mre quite nonlinear, and more work is needed to understand the relationships between noise frequency and mmplitude and beam loss for large amplitude protona. Conclusions In order to avoid intensity limits during fixed target operations, bunch spreaders are used to stimulate longitudinal emittance growth. In order to avoid beam loss, narrow band rmndom noise is applied near a multiple of the small amplitude syncbrotron frequency during accelerstion. A new Main Ring bunch spreader has been tested which sllors time dependent noise frequency and amplitude. Tests show that 50% bunch length growths are possible with tolerable beam loss, Theoretical work aimed at trying to understand the difference batneen waltage md phase noise is underway. While the Usin Ring bunch spreaders use I@ voltage noise at twice the synchrotron frequsncy, the uev Tevatron system will attempt to use phmme noise at the synchrotron frequency itself. References 1. Address is KEK, Tsukuba, Ibarski, 305, Japan 2. Operated by the Universities Research Association under contract with the U.S. Department of Energy. 3. S.A. Bogaca, Y. Barrison, and K.Y. Ng, Fermilnb note FN-486 (1088). 4. S.A. Bogacs, Permilrb note FN-498 (1988). 5. R. Siemmnn. Private communication. 6. J. Griffin, et. ml., 2630 (1883). IBEE Trans. Nucl. Sci. Ns-30, 7. 8. E. Courmnt and B. Snyder, Ann. Phys. 2, 1 (1958). 9. G. Dome, CERN 84-15, 216 (1984). G. Jackson, Fermilab note TM-1672 (1989). 10. S. Ohnuma, Fermilab note n-1381 (1988). 11. S.R. Mane and G. Jackson, Nucl. In&. mud Yeth. A, in ores8 f1QSQL 12. Y. ibra&t;-bnd I. Stegun, Bandbook of pfah;a;tical Functions, Dover Publications, Inc., k 1072 , pg.721. 

Stimulated longitudinal emittance growth in the Main Ring

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Stimulated longitudinal emittance growth in the Main Ring

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