Stump, R

Waldman, B

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1lillilMIIIII o 1160 003a6a4 1 FREQUENCY MEASUREMENTS AND RESONANCE SURVEY IN THE ELECTRON MODEL SPffiAL SECTOR FFAG ACCELERATOR R. Stump and B. Waldman REPORT NUMBER ~3.=.:::61:.--_ · MURA-361 MIDWESTERN UNIVERSITIES. RESEARCH ASSOCIATION* 2203 University Avenue. Madison. Wisconsin FREQUENCY MEASUREMENTS AND RESONANCE SURVEY IN THE ELECTRON MODEL SPIRAL SECTOR FFAG ACCELERATOR R. Stump** and B. Waldman*** August 30. 1957 ABSTRACT Beam intensities, vertical and radial betatron oscillation frequencies. and stop bands in the tuning range of the spiral sector FFAG accelerator were measured. The machine is tunable from '\fz = o. 46 to 1. 76 and --V x = 1. 12 to 1. 71. In this tuning region the resonances V =1. V =0.5. V =1. 5.z z z V x = 1. 5. "'Vx + \J z = 2 and 2 V x + 2 V z = 6 are observed to destroy the beam. Of these only....v z = 1, 'If z = 0.5 and 2)J x + 2 V z = 6 cause com~ plete loss of beam at all points in the available tuning range. The Walkinshaw resonance (2.tJ z - V x = 0) appears as a minimum of beam intensity. *	 Supported by Contract AEC No. AT(l1-1)~384 r"'	 ** Summer participant at MURA from University of Kansas *** Summer participant at MURA from Notre Dame University MURA-361 Introduction This report describes a series of measurements which were made on the electron model spiral sector FFAG accelerator, to determine the tuning characteristics of this machine. Beam intensities, vertical and radial betatron oscillation frequencies, and stop bands in the tuning range available were found. Experimental Arrangement 1) Detector A cylindrical plastic scintillator of 1 cm diameter and 1 cm length was mounted at the end of a light pipe inside the vacuum donut. A thin ~	 layer of aluminum was evaporated over the scintillation to make it light tight and still allow the electrons to enter. The photomultiplier was outside of the magnetic field. The presence of an electron beam was detected by observing a pulse on an oscilloscope at the proper time after injection. 2)	 RF Probe Betatron frequencies were determined by the rf. knock-out method described by Cole et al (RSI, 28, 403 (1957». The probe consisted of two parallel plates inserted approximately at the beam position in the donut. One plate was grounded, the other had an rf. voltage of approximately 50 volts. Resonance with the radial betatron frequency was identified by the shift of the time of arrival of the beam. Vertical betatron frequency was identified by a I"'"" decrease of intensity. Resonances identified were usually of the form: - 2 ­MURA-361 jav-n/ where fo is the frequency of revolution of the electron, is the applied/rf. rf. frequency. a is 1 or 2. and n is zero or any integer. Radio frequencies were measured with a grid dip meter and could be reproduced to about 1%. 3) Tuning Parameters The current through the flutter ( D. F) coils could be varied from zero to ± 1. 5 amperes. Likewise the current in the A' coils could be varied from zero to ± 1. 33 amperes. With the data of Fig. 1 and Fig. 2 a cross plot of Fig. 3 was made. r- This is shown in Fig. 4. Certain resonances are entered on this plot. - 3 ­MURA-361 Intensities were estimated by the amplitude of the pulse from the photo­multiplier. Where no beam is indicated the intensity was less than 10-3 times the intensity found in neighboring regions. Where minima are indicated (Fig. 4), the intensity dropped to 10-1 to 10-2 times the normal beam intensity. Examination of Fig. 4 shows that the integral resonance -1J z = 1, the half-integral resonances 'ITz =0.5, V z = 1. 5, V x =1. 5 and the linear sum resonances -V-x + 11 z = 2 and 2 '"\.Ix + 2V = 6 (which is also a cubicz resonance 2 cr x + 2 o-z = 2 'iT) all destroy the beam completely at some tuning. Of these only ifz =1, "'11'z ~ 0.5 and 21/"x + 2 V =6 cause completez loss of the beam at all points in the tuning region. Beam was found in some regions of half-integral resonance. In these regions there was however a marked decrease of intensity. These regions were carefully examined to determine both that the beam existed and that the frequencies actually crossed the resonances. The Walkinshaw resonance ('\fx - 2 -Vz = 0) appeared as a minimum, but did not destroy the beam completely. The 2"\/x + 21/ = 6 z resonance appears to have the wrong slope. This is possibly due to the lack of scaling in the machine, together with the possibility that this resonance is serious only near injection. APPENDIX Parameters of the Electron Model Spiral Sector FFAG Accelerator N = 6 Ro = 55 cm. (Outer radius) :r = 6.25 E,~. = 25 kev (Injection Energy) i. =0.7 Design Flutter = 1. 08 Ri =30.5 cm. (Inner radius) Measured Flutter = 1. 02 -4­RADIAL TUNING 1.8 o 6. F=+/. 3S" ex"" l1 F=+().15' AF=O A~: -0. 7S" 1.4 /.0 ~ - 1.4 ,­1.2 1.0 .8 .6 .4 ----L. .2 0 .2 .4 fj K (QrTJPS) .6 .8 -+-­1.0 1.2 1.4 + ______ fl',. J l1 K. current VERTICAL TUNING -U1 (amps) 1.8 1.6 1.4 It} 1.2 1.0 .B .6 .4 .2 I"" a L.....-_~----:-'~~----'::--~.....a..:-----':::--:~--=-~-~---'::-----'-~~......a..-_---.J - 1.4 1.2 1.0 .8 .6 .4 .2 a .2 t4 .6 .8 1.0 1.2 1.4 + fjF(amps) Cross - hatched teg,ons are r eg,ons where no beam is obtained 1/'1. =1.5 1.6 -Vx.= /25//././ / / /,~./ / / ./ /, / /, /,././ / /,./ / \'> '\. 1/I 4· v \ V I 2 )1' " ~ -"-~ .;' " / /\.. v - 1.6 ~ "\ f / / / / / 1" vI =0.5, I / / / /1/ / / / / / / / . / ~ - Iii­ 1.2 1.0 .8 .6 1)6. ~ .4 .2 0 Li K .2 .4 .6 (a m ps) .8 1.0 1.2 1.4 + Tuni g Tuning limif 1.5 1----- --+---+-~--==" 1.0 I--------.,;*"'_----,. 0.51------~.....,.olI " " _ Region of no beam (;) Region of minimum beam found on ~ F sweep 1.0 1.5 2.0 llllllillllll\1 o 11bO 0036b6S & THE V -= t IY NON-LINEAR RESONANCE OF A FIXED FIELD ACCELERATOR G. Parzen NUMBER :t62.REPORT MURA-362 MIDWESTERN UNIVERSITIES RESEARCH ASSOCIATION* 2203 University Avenue, Madison, Wisconsin THE V -= ...L. N NON- LINEAR RESONANCE OF A3 FIXED FIELD ACCELERATOR G. Parzen** June 8, 1957 ABSTRACT This paper is a continuation of the reports MURA-258, and MURA-273. This paper treats the problem of finding the stability limits. due to the )) -::: t IV non-linear resonance in the radial motion. of an accelerator having an arbitrary magnetic field. The general spiral sector machine is treated in detail. The results of the theory are compared with numerically computed results. Supported by Contract AEC No. AT(11-l)-384* ** On leave from the University of Notre Dame 

Frequency measurements and resonance survey in the electron model spiral sector FFAG accelerator

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