1、Comment s1: Page: 1D:/Nov98MD/01decMD.docCERN/PS/RF/Note 98-? (MD)Calibration of BTFM by high-harmonic phase space displacement and study of energy spectrum versus injected intensity of un-bunched beam in PS BoosterA. Blas, S. Koscielniak, F. Pedersen and H. SchonauerAbstractA subsidiary purpose of
2、the December 1998 Machine Development periods was to calibrate the Beam Transfer Function Measurement system and then use this system to measure the kinetic energy spread of the PS Booster proton beam versus number of injected turns; and to compare this with measurements using the MEBT spectrometer.
3、 The BTFM was calibrated by introducing notches into the energy spectrum by sweeping high-harmonic empty buckets into the particle beam.GENEVA1 IntroductionThe efficiency of capture and bunching of a particle beam into RF buckets depends on the width of the initial beam energy distribution. Creating
4、 hollow bunches by introducing high-harmonic empty buckets in to the core of a coasting beam will increase the energy width. Consequently, for practical reasons and to facilitate more accurate computer simulations it is useful to have an accurate measure of the beam energy spread. Historically, ther
5、e had been a long standing discrepancy between measurements made in the MEBT transfer line and those in the Booster ring. The transfer line measure is taken with a spectrometer and harp; and is considered reliable. The Booster measure is taken from a Beam Transfer Function (BTF). The intention of th
6、e MDs was to calibrate the BTF and then use it measure energy spread of the circulating beam.2 Emittance of Linac BeamThe jitter of the mean energy of the linac beam and the instantaneous energy width of that beam has some effect on the reproducibility and outcome of the high-harmonic empty bucket d
7、eposition scheme. After the October 1998 MDs, it was suspected that these energy characteristics vary according to the timing of injection into the Booster. Consequently we decided to quantify this variation using the LEBT spectrometer which consists of an analyzing dipole magnet and harps. Measurem
8、ents were made on 26 November 1998.2.1 Distribution of the meanThe table below summarizes variation of the “distribution of the mean” linac energy based on 8 samples for each of six injection timings (LX.AGEN)LX.AGEN Range of mean centre of mean Width of mean(ms) (keV) (keV) (keV)2000 7593 84 182020
9、 7895 86.5 172040 83101 93 182060 85103 94 182080 85103 94 18Column three of this table of data implies a slow change of the mean energy during the linac pulse; but the variation during the time to inject, say, 10 turns into any one of the 4 Booster rings is probably negligible. What is not obvious
10、from these statistics is that the jitter in the mean energy is not gaussian distributed rather it appears to follow some kind of limit cycle hunting between two possible values.2.2 Distribution of the widthWe also attempted to quantify the variation of beam energy width versus injection timing. The
11、data recorded below are for single beam samples.LX.AGEN Mean energy r.m.s. width full width B-field H-emittance(ms) (keV) (keV) 15 keV Tesla mm.mrad2000 72.7 82.7 375 .35252000 86.2 70.85 330 .3385 6.02020 85.8 76.4 285 .3495 5.72040 99.58 72.3 330 .3356 5.92060 84.6 68.8 285 .3341 6.02080 103.2 70.
12、 330 .3488The first 2 rows of the table indicate how changes in steering to the analyzing slit (different B-field) lead to sampling different transverse parts of the beam which may have slightly different momentum distribution.2.3 ConclusionBased on the data above, one must conclude that: the full w
13、idth energy spread of the linac beam is some 330 keV the jitter of the linac beam central energy is less than 20 keV full width.3 Calibration of the BTFMWhereas previously in the 29th October MD, we had relied upon the gain-calibrations of several pieces of hardware, here we used an HP 53310A freque
14、ncy analyzer to make a direct determination of the frequency synthesized as input to the C16 RF cavity. As before, narrow empty buckets (C16=0.5kV) were swept into the coasting beam so as to cleave a notch in the energy spectrum whose position could be correlated against the stop-value of the C16 fr
15、equency.3.1 Machine Development 30 November 1998A beam of 1.1 turns was injected into the MEFLAT cycle with C02 off and shorted. The C16 frequency was swept from high to low during 8 ms and then the voltage reduced to a few volts. Figure 1 below shows the frequency sweeping directly. After allowing
16、5 ms for the h=15 structure to disappear, the C04 cavity was used to make a BTFM during 20 ms. C04 was turned on (with RF feedback) to allow the BTFM but the base C04 voltage was set to a few volts to avoid any h=4 bunching.Comment s2: Page: 4Nov98Md/01decam/fsweep.pcx made from 01decam/tek0001 left
17、 fig. = 1 ms/div, right fig. = .2 ms/division.The BTFM is made at the 4th harmonic of the revolution frequency, whereas frequency measurements were made at the 15th harmonic. In order to compare to the former, one must multiply the latter by 4/15.GFA frequency meter BTFM(V) (MHz) h=4 (MHz)2.5 2.4018
18、72.0 2.400411.0 2.39771 2.3980.5 2.39625 2.3960.0 2.39479 2.395-0.5 2.39344 2.393-1.5 2.39052 2.391Linear regression of the data in the table above gives the following fit:FreqHP(MHz) = 1.0104*FreqBTF(MHz) -2.4988E-2In some sense, because it is much more accurately known, the HP frequency can be con
19、sidered the independent variable, leading to the fit:FreqBTF(MHz) = 0.97034*FreqBTF(MHz) +7.1083E-2The sum of the variances (X2) per degree of freedom () is 2E-7, and this can be used to estimate the measurement error of the BTFM, from the formula . Hence 450 /2XHz h=4. From the linear fit and error
20、 estimate, it is clear that the BTFM calculates the frequency correctly and quite precisely. The calibration between GFA voltage and absolute frequency at the fundamental is:Comment s3: Page: 5Nov98MD/01decam/calib1.pcx made from nov98md/01decam/btfm3 left fig.= notch at 538 keV; right fig=notch at
21、130 keV.Nine sample points were taken; and the end points are given below.GFA Volts 4.5 1.5 -1.5HPfreq MHz h=15 9.02188 8.99023 8.95820BTFM keV - -130 -537Absolute keV - 66.9 -341.4Linear regression gives the following fits:Comment s4: Page: 6Nov98MD/01decpm/calib7.pcx made from 01decpm/btfm9d FreqH
22、P(kHz h=1) = 5.20135E-3*BTFM(keV) + 600.025Using the relation below we can make an absolute conversion from frequency to kinetic energy:where .fT121tValues are as follows. T=50 MeV, f=0.599 MHz, =1.0533, , =0.8433. Hence 54.)(84.92)(kHzfeVkAbsolute T(keV) = 1.00305*BTFM T(keV) + 197.253.2.2 4.1 turn
23、s injectedFigure 3: notch deposition to calibrate BTFM for 4.1 turns injected. Left fig. = GFA= -3.0 (-720 keV), right fig.= GFA=+1.5 (-100 keV)Seven sample points were taken; and the end points are given below.GFA Volts 1.5 -1.5 -3.0HPfreq MHz h=15 8.99023 8.95820 8.94195BTFM keV -100 -505.5 -721Ab
24、solute keV 66.9 -341.4Linear regression gives the following fits:FreqHP(kHz h=1) = 0.7118*GFA(volts) + 598.28;FreqHP(kHz h=1) = 5.2173E-3*BTFM(keV) + 599.8Absolute T(keV) = 1.006*BTFM T(keV) + 161.93.3 ConclusionEvidently, the BTFM energy calibration for relative measurements is very accurate.Commen
25、t s5: Page: 7Nov98MD/03decpm/btfms2.pcx4 Beam energy spreadUsing these calibrations as basis, we next acquired the energy spectrum with C16 off and shorted, so as to find the energy width of the injected beam. It is appropriate to repeat the cautions of the 29th October MD. Results depend strongly o
26、n how much of the tails are included. Moreover, there is the problem that a drooping baseline can turn what is really a tail into appearing like the core density. We shall give three measures of width. When tails/artifacts are included, we call this the 100%FW. When tails are excluded we call this s
27、imply the full width (FW). Full width at half height (FWHH) is less ambiguous.4.1 0.1 turns injectedMachine Development 03 December 1998In an attempt to explore the dependence of beam energy width on intensity, “the sieve” was introduced into the linac beam so as to reduce the intensity transported
28、through the MEBT. 1.1 turns was injected into the Booster MEFLAT cycle resulting in a beam intensity of 1.6E11 ppp. Without the sieve, 1.1 turns injected corresponds to about 1.2E12 ppp. An example of the energy profile is given below, Figure 4. The BTFM is performed in 20 ms with C16 and C02 off an
29、d shorted, C04 on at few volts with rf feedback enabled.Figure 4: Energy profile of 1.1 turns injected with sieve placed in MEBT to reduce intensity to 1.6E10 ppp.100%FW FW FWHH440 406 257460 416 259440 418 283480 440 269Comment s6: Page: 8Nov98MD/01decam/calib2.pcx made from nov98md/01decam/btfm4a
30、FW = 420 14 keV; FWHH = 267 12 keV.The stated variances do not include the measurement error due to quantization. If we add this value ( 8keV) in quadrature, then we obtain the distribution characteristics:100%FW = 455 20 keVFW = 420 16 keVFWHH = 267 14 keV.4.2 1.1 turns injectedMachine Development
31、1st December 1998.BTF Measurements were made on the 50 MeV MEFLAT cycle with C16 and C02 off.Figure 5: Measurement of beam energy spectra for 1.1 injected turns; C16 off.Raw data is given below from 01 December MD.100%FW FW (keV) FWHH543 520 307.7543 538 307.7548 509 301.4536 490 327537 509 327We fo
32、rm the means of these data and convert between BTFM and absolute keV, to find the beam energy width for 1.1 injected turns (1E12 ppp):100% FW = 543 6 keV; FW = 514 18 keV; FWHH = 315 12 keV.The stated variances are purely from the data, and do not include quantization errors of the cross-hairs. If t
33、his measurement error is added in quadrtaure, we obatin100% FW = 543 11 keVComment s7: Page: 9Nov98MD/dump1/calib.pcx made from dump1/btfm3y see Figure 6. The small blip at the foot of the right hand tail is present in all the data and is probably best interpreted as a systematic artifact.Figure 6:
34、Energy width measurement for 1.1 turns injected (1E12 pp). Left fig. = BTFM; right fig. = harp and spectrometer.100%FW FW FWHH620 546 340627 565 330620 546 362Mean values of this raw data (3 samples) gives:100%FW = 622 4 keV; FW = 552 11 keV; FWHH = 344 16 keV.If we add the measurement error due res
35、olution/quantization in quadrature we obtain:100%FW = 622 10 keVFW = 552 14 keVFWHH = 344 18 keVBy contrast, the MEBT Figure 6-right gives a full width of 360 keV.4.4 2.1 turns injectedRaw data is given below from 01 December MD.100%FW FW FWHH571 571 375567 544 375Comment s8: Page: 10Nov98MD/01decpm
36、/calib5.pcx made from nov98md/01decpm/btfm3c FW = 556 13 keV; FWHH = 375 6 keV.To these distribution variances one should add the quantization errors, to give:100% FW = 569 10keVFW = 556 15 keVFWHH = 375 10 keV.Figure 7: BTFM of energy distribution 01 Dec 98; C16 off; left figure =2.1 turns injected
37、; right figure = 4.1 turns injected.4.5 2.1 turns injectedMachine Development 02 December 1998We took extra data to complement the meager set taken on 01 December for 2.1 turns injected. MEFLAT at 50 MeV. Injection at 315 ms. C02 and C16 off. Eight more measurements were taken. The error in a single BTF measurement is a quantization error of about 10 keV.
