-87. Flower Power and the Energy Doubler/Saver. Val L. Fitch. Princeton University Princeton, New Jersey

Transcription

1 -87 Flower Power and the Energy Doubler/Saver Val L. Fitch Princeton University Princeton, New Jersey The following considerations of focusing differential Cerenkov counters were originally stimulated by the needs of Fermilab Experiment #302 and Brookhaven National Laboratory Experiment #661. The results of these considerations would appear to have broad applicability at Fermilab especially in meeting the requirements of experiments using the Energy Doubler/Saver. The scheme presented here results in substantial increases in the velocity resolution and/or the angular acceptance of focusing differential counters. Consider the pattern in Figure 1 to lie in the focal plane of a conventional focusing differential counter. distribution of photons from the focused The circle of dots represents the Cerenkov radiation. A measurement of the di~eter of the ring of dots determinea the r.crenkc. angle and hence the velocity of the radiating particles. In the usual counter the Cerenkov ring of light is allowed to fallon an annular slit covering a phototube. Particles which radiate into an angular band corresponding to the width of l the slit are thereby detected. Meunier and collaborators in their elegant DISC have obtained a velocity resolu~ion of 6B 1.5 x 10-7 For a rms Cerenkov angle of 15 mr this corresponds to a 68 of 10-5 radian. We note

2 -88 a substantial disadvantage. The angular spread in the beam traversing the counter must be less than the angular resolution of the counter. Non-parallel beam particles with the same velocity result in rings of light with the same diameter but with their centers displaced. For a fixed annular slit only a fraction of the light from such particles is received at the phototube (and in the DISC counter is deliberately discriminated against - hence the selfcollimating in the acronym DISC). Obviously what is needed is a measurement of the diameter of the ring of light from each particle as it traverses the counter independent of the exact center of the ring. This is where the power of the flower pattern in Figure 1 enters. With reference to Figure I, it is clear, if the light which strikes the petals of the flower and the light which misses the petals is measured independently, a comparison of the two light outputs results in a diameter measurement of the ring of light. A convenient parameter is where L I is the light which strikes the petal and L is the light which I I falls outside. It turns out, for a variety of petal shapes, that ~ is remarkably insensitive to the offset of the circle of light from concentricity. Implementation of flower power is easily accomplished at Fermilab energies. Figure 2 shows the essentials. lhe Cerenkov light is focused by mirror 1 on phototube 81. A quartz plate on which the flower pattern has been aluminized is placed on the face of PT #1. Light which strikes the petals is reflected, collected by mirror #2 and focused on PT #2. (In the arrangement shown, mirror 2 should have half the focal length of mirror 1). Light which

3 -89 misses the petals is transmitted through the quartz plate to Pr #1. The outputs of Pr's #1 and 2 are digitized and recorded for later analysis. Alternatively, the arithdetic associated with computing ~ can be done in a fast analog fashion and the particle selection done in real time. The shape of the petals can be determined to meet any desired condition (daisy, aspen, black-eyed susan?). Two convenient shapes are the following. If the edge of the petal is chosen to be a section of an Archimedes spiral the radius is a linear function of ~, i.e., where R and R O l r = + are the inner and outer liinits of the petal radii. We assume the errors in L and L (and therefore ~) to be normally I I I distributed and equal to the square root of the number of photoelectrons in the phototubes covering each area. The error in r is ISr where N is the total number of photoelectrons. We have found little advantage in preserving the linearity between ~ and r. Rather we have found it desirable to make the error in r independent of~. The petal shape which does this is the one shown in Figure 1. In this case the petal edge is proportional to the arcsine of the azimuthal angle and yields with the error in r given by r = + arcsin ~

4 -90 A bit of mathematical elegance surfaces here. M. Witherell has shown that this petal shape gives a smaller average error in r than any other. How many petals? In general, the larger the number of petals the smaller the sensitivity of ~ to the circle of light originating from nonparallel particles and being offset. We have been using 4 and 8 petals. R l - R 2 With 8 petals and R + R =.05 the change in ~ at maximum offset is no more 1 2 than.016. How much does one gain in angular acceptance and/or velocity resolution. The Meunier design 'c in reference l(a) separates w's from K's to 380 MeV. Using the relation that the number of photoelectrons 100 ~sin2e where c ~ is the length of the counter in centimeters, we find N 32 photoelectrons in design C. Using flower power in this counter the error in the radius measurement would be ~ 6% of the interval covered. The flower pattern covering the angular interval in this DISC-counter would increase the precision in Bby 16 or increase the angular acceptance by 16 for the same velocity resolution. The separation in Bfor two different masses goes inversely as the momentum squared. The energy doubler operation with beams of twice the old momentum requires, therefore, four times as much velocity resolution in the Cerenkov counter, other factors remaining the same. With 32 photoelectrons one has, therefore, with flower power, all the additional velocity resolution needed to compensate for the higher momenta and, in addition, four times the angular acceptance. The technique has other niceties associated with it. R. Cester observes that the error in the diameter of the circle of light due to dispersion in the gas decreases as l/in. This fact, in many cases, obviates the need for chromatic correctors. She has observed further that coma, a distortion while arises in the case of off-axis particles and which leads to a non

5 -91 circular pattern is largely averaged out by flower power. References 1. (a) R. Meunier, 1970 l~ Summer Study Report, p.bs. (b) J. Litt, R. Meunier, and S. Ecklund, NALREP (Dec. 1974) p. 12. (c) J. Litt and R. Meunier. Ann. Rev. Nuc1. Sci (1973).

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