Deflection of GeV particle beams by channeling in bent crystal planes of constant curvature

Nuclear Physxcs B318 (1989) 301-318 North-Holland, Amsterdam

DEFLECTION IN BENT

OF GeV PARTICLE

CRYSTAL

PLANES

BEAMS

BY CHANNELING

OF CONSTANT

CURVATURE

J S FORSTER, H HATTON and R J TOONE Atonu~ Lnergv of Canada Lmuted Research Company, Chalk Rwer ~udear Laboratmws, Chal~ Rwer, Ontarto, Canada KOJ IJO

G ESTE Advan(ed Technology Laboratory, Bell-Northern Re~ear~h, P 0 Bo~ 3511. Statton C, Ottawa, Ontarto, Canada K1 Y 4H7

S I BAKER and R A CARRIGAN, JR Ferret Natwnal Ac(elerator Laboratory*, P 0 Box 500, Bataem, IL 60510, {iS4

W M GIBSON and R L WIJAYAWARDANA** Depal tment of Physt~s, State Umversm' of New York at A lban~, Albam, N Y 12222, &SA

J A ELLISON* Department of Mathemattcs, Unwersztv of New Meatu), Albuquerque, NM 87131, liSA

L EMMAN-WORI Department of Mathematics, New Me_xtco lnstttute of Mmmg and TedTnolog), So~orro, NM 87131, USA

B O KOLBESEN Zentrale Fors~hung and Entwtcltlung Fors~hunglaboratorwn, Swmem' A G, Postfa~h 832720, D-8000 Munchen 83. Fed Rep Germany

Receaved 3 October 1988

* Operated by Umversxtles Research Association, Inc, under contract w~th the U S Department of Energy ** Now at Department of Physics, Faculty of Scmnce, Umverslty of Peradenlya, Parademya, Sn Lanka + This work was supported by the Nanonal Science Foundation undcr grants DMR-8214301 and DMR-8704348

302

J S Forster et al / Channehng The deflection of charged pamcle beams moving v, lthin the (110) planes of a 43 mm long silicon crystal has been observed for momenta from 60 to 200 GeV/~ The crystal was bent by a 10 8/~m thick coating of ZnO along the central 26 mm of the crystal Measurements were made with the crystal at room temperature, where a total deflection of 32 5 mrad was observed, and with the crystal cooled to 145°C, where a 30 9 mrad deflectmn was observed The ratio of the number of pamcles that dechannel upon entenng the bend to the number of mmally channeled particles compares well with calculations based on the continuum model

1. Introduction The deflection of a beam of charged particles moving within the planes of a bent crystal of silicon was first observed at D u b n a with 8.4 GeV protons [1] Subsequently, a C E R N - A a r h u s - S t r a s b o u r g collaboration [2, 3] demonstrated both axial and planar bending at 12 G e V / c . In more recent experiments at Fermllab [4 6], the intensity loss of channeled particles along the crystal bend was studied for particle m o m e n t a between 12 and 180 G e V / c . The success of these experiments has resulted in the application of such crystal septa to replace bending magnets at 200 G e V / c [7] and at 800 G e V / c [8]. In all of these experiments, the crystal was bent by a three- or four-pin mechanical bending device In refs. [4, 5] It was shown, for a three-point bender, that a peak in the middle of the angular distribution of emergent particles occurred because of local distortions in the crystal produced by the center pin of the bending device. The use of a four-point bending device revealed two peaks in the deflected particle angular distribution corresponding to local distortions caused by the center two bending pins. However, for a given angle of deflection, the overall efficiency of the four-point bender considerably exceeds that of the three-point bender. This occurs because for a fixed deflection angle and a fixed distance between outer pins the m a x i m u m curvature in the four-point bender is less than the maximum curvature in the three-point bender. Although some theoretical work has been done on these variable curvature cases with a "slowly varying curvature assumption" [6], the most complete work to date is on the constant curvature case [9,10]. Ideally, one would like a crystal which is bent In such a way as to produce constant curvature without the use of mechanical pins We have produced a crystal with constant curvature by coating a SI slab with a thin layer ( ~ 10 /~m) of ZnO; the residual stresses caused by the ZnO result in a convex, uniform, circular bend on the side to whmh the ZnO is applied This crystal allows comparison with detailed calculations such as those of Elllson [9], Kudo [10], and Taratin and Voroblev [11]. These calculations assume a uniform (i.e. constant radius of curvature) bend, and with this assumption earlier comparisons between experiment [5] and theory [9] proved difficult because of the variable curvature and the distortion caused by the pins In the bending device. In this work, we report results for the deflection of charged particle beams of protons and plons from 60 to 200 G e V / c through a bending angle of > 30 mrad in

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a c o n s t a n t curvature crystal. D a t a were collected for the bent silicon crystal operating at r o o m temperature and at = - 1 4 5 ° C In sect. 2 we gwe experimental details; sect. 3 presents results and analysis and sect. 4 gives a comparison of the results with calculations based on Elllson [9] A summary and conclusions are given in sect. 5.

2. Experiment T h e experiment was carried out in the M - B o t t o m beam of the Meson Laboratory at Fermxlab. A plan view of the experimental layout is shown schematically m fig 1. The beam enters from the left through scintillator SC1 and drift chamber DC1. To reduce multiple scattering, the beam continues through a vacuum pipe = 18.5 m long and then passes through drift chamber DC2 and scintillator SC2. It then enters the c h a m b e r containing the crystal and passes on through a tube, = 10 m long, filled with helium gas at atmospheric pressure to reduce multiple scattering which would otherwise occur in air. Finally, the beam passes through drift chamber DC3 and scintillator SC3. Each drift chamber measures the beam p a m c l e ' s posttlon event-by-event, in both x and y directions. The middle scintillator, SC2, has a rectangular hole 1 m m wide by 5 m m high cut in the middle of it and acts as an anti-coincidence scintillator to ensure that only particles centered on the beam axis are counted. Fast timing signals are taken from

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the three scintillators and from the detector on the upstream end of the crystal and the coincidence requirement that SC1, SC3 and the crystal have fired, but not SC2, is made. If this is satisfied, then the energy-loss signals from the crystal and the timing reformation from the drift chambers are written onto magnetic tape. The crystal is mounted in a three-axis gonlometer which can be remotely stepped in angles 0x, 0 v or q~. The rotation angle, q,, has steps of 0.01 ° which is adequate for positioning the crystal in the beam. The crystal is aligned for planar or axial channeling by movement in 0x or 0 v and, because of the extremely small critical angles revolved, the step size m these two angles is 0.0005 °. The crystal used in the present experiment was a slab 43 m m long by 11 m m high and 0.72 m m thick. It was cut from 50 k~2 cm, n-type silicon with a (110) plane parallel to the 43 m m by 11 m m face to better than 0.1 ° as determined by backscattered X-ray analysis and channeling measurements with a 1.0 MeV 4He beam. An energy-loss detector was fabricated on each end of the crystal by implanting = 1015/cm 2 B on one side of the slab and = 1015/cm 2 P directly opposite over an area 3 m m along the slab by 8 m m high. One of the detectors was very noisy at room temperature but operated well when the crystal was cooled. The crystal was oriented to place this detector on the downstream end during the experiment so that the less noisy detector was used to select channeled particles based on lower energy loss. T o make a permanent bend on the crystal, ZnO was sputter coated onto one side of the slab over a 26 m m length centered on the crystal face. The ZnO coating was 10.8/~m thick, which resulted in ~ 30 mrad total bend angle. The crystal was mounted in the goniometer w~th the long face parallel to the b e a m and with the 12 m m side vertical i.e. the (110) plane vertical and parallel to the beam. Alignment of the (110) plane was achieved by moving the crystal in small increments In 0x and observing the energy-loss spectrum from the detector on the upstream end of the crystal. Fig. 2 shows energy-loss spectra for an 80 G e V / c incident beam, when the crystal is aligned (a) and for random incidence (b). The critical angle at this momentum for (110) planar channeling of protons in S1 is 17 /~rad. Consequently, about 10% of the beam is withm the critical angle and this is shown by the low-energy Landau peak in fig. 2. Once the crystal was aligned, beam deflection measurements were made for 60, 80, 100, 120, 150, and 200 G e V / c momenta with the crystal at room temperature. The crystal was clamped hghtly between the upstream detector and the ZnO coating. The detector holder was connected, via a copper braid, to a liquid nitrogen cold trap. An aluminum shroud, open at both ends m the beam direction, was m o u n t e d on the crystal holder to give radiative cooling as well as the direct cooling provided by the clamp. A thermocouple was mounted on the holder at the end furthest from the braid and, when the trap was filled with liquid nitrogen, recorded a temperature of - 1 4 5 ° C . With the crystal cooled, measurements were again made for the same m o m e n t a as at room temperature.

J S Forster et al / Channehng

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For each measurement approximately 100,000 events were recorded. For the 80 G e V / c measurement with the crystal cooled, an additional 300,000 events were collected to give data with lower statistical uncertainty in the region between the unbent and fully bent peaks in the angular distribution of emergent particles. Also, at 80 G e V / c with the crystal cooled, approximately 100,000 events were recorded with the crystal rotated --- 1 mrad m 0x away from the aligned position, to obtain data for r a n d o m incidence (cf. fig. 2).

3. Results and analysis The event-by-event data were analyzed on the Concurrent Corporation 3230 minicomputer at Chalk River. To reconstruct the particle trajectories, event by event, the T D C ' s on all the drift chamber wires were cahbrated with the beam by requiring a fast coincidence between SC1 and SC3 (see fig. 1); in this way we determined the time delay caused by the cables from the experimental area to the data collection area. With the known drift velocity, each particle's coordinates in x and y in the drift chambers, can then be determined. To calculate trajectories, the relative positions of the three drift chambers must be known. We chose to define the center of the undeflected beam in each drift chamber as the "zero" posmon. During analysis at each m o m e n t u m and crystal temperature, a window was set on the low energy portion of the energy-loss spectrum (see fig. 2) and the emergent angular distribution of particles determined. A two-dimensional intensity plot of the

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EMERfiENT PARTICLE DISTRIBUTION p = 80 ISeVlc, SI (110), COOLED CRYSTAL

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outgoing angular distribution, 0x vs. 0~, for the 80 G e V / c cooled crystal data is shown in fig. 3. It can be seen that the darkest regions in the plot (highest intensity) occur (a) at 0x = 0 mrad corresponding to undeflected particles that dechannel because of multiple scattering between the energy-loss detector and the beginning of the bend, and that dechannel because of the bend, and (b) at 0, ~ 30 m r a d c o r r e s p o n d i n g to fully deflected particles. Most of the intensity is contained m these two regions with fewer particles in between that dechannel m the bend region. A projection of the data onto the 0x direction (henceforward referred to as 0~ou,) results in the spectra shown in figs. 4 and 5. Intensity vs. 0~ ts shown for 60, 100, 150, and 200 G e V / c with the crystal at r o o m temperatures (fig. 4) and with the crystal cooled (fig. 5). These figures show clearly the two separated peaks corresponding to undeflected and fully deflected particles. It is obvious that, for a given radius of curvature of the crystal, the n u m b e r of particles that are fully deflected decreases as the m o m e n t u m increases because of the higher centrifugal force experienced at the higher m o m e n t a .

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3 1 MULTIPLE SCATTERING DECHANNELING IN THE BENT REGION The distribution of particles between the undeflected and fully deflected regions shows httle structure as would be expected for uniform curvature of the crystal In Ellison's model [9] all particles that are lost because of bending, dechannel within a short distance after entering the bend region. Therefore, the particles that appear between = 2 mrad and = 30 mrad m figs. 4 and 5 result from multiple scattering dechanneling. To investigate this dechannehng, we plot the number of channeled particles I ( 0 ) versus 0 where I ( 0 ) = fd°Y(O)dO and Y(O) is the number of counts per 0.5 mrad bin. Results for 150 G e V / c are shown in fig. 6 both for the crystal cooled and at room temperature and the data show an exponential dependence on angle. Since the curvature is constant in the bent region of the crystal, it as straightforward to convert the angle, 0, to distance, z, along the crystal length by

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TABLE1 Dechannehng lengths for GeV/~ protons and pxons m the (110) plane of the bent $1 crystal

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the data, it is possible to extract a d e c h a n n e h n g length, l d (the 1 / e value). Results for our twelve sets of data are s u m m a r i z e d m table 1 a n d are shown in fig. 7 where we have p l o t t e d the d e c h a n n e h n g length versus b e a m m o m e n t u m , p; the u n c e r t a m ues are statistical only. All of the data points for the cooled crystal lie above the r o o m t e m p e r a t u r e data as one would expect because of the lower thermal vtbrat l o n a l a m p h t u d e of the Si atoms b r o u g h t a b o u t b y the cooling. F r o m table 1, it can

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be seen that the dechanneling length increases by = 14% at 60 G e V / c to ~ 70% at 200 G e V / c b y cooling the crystal. Also, in fig. 7, we observe that, for a given temperature, the dechannehng length increases with beam m o m e n t u m and then decreases Thzs contrasts w~th a straight crystal in which the dechanneling length increases roughly hnearly with beam energy or m o m e n t u m . The reason for this is as follows. In the constant curvature case, the channeled particles oscillate about an equilibrium position, x c, which is displaced by the centrifugal force from midway between the planes (as in an unbent crystal); x e increases with increasing m o m e n t u m going from zero, midway between the planes, to d p / 2 . Thus for x e small, the dechannehng length should be approximately the straight crystal value. However, as x~ increases, the effective crmcal angle decreases (see fig 1 of ref. [9]) and the channeled particles interact with a larger electron density. Each of these causes a decrease in the slope of l d vs. p, eventually causing I d to decrease with increasing p. Thus we expect l d as a f u n c n o n of xe to reach a maximum and then decrease as x e approaches d p / 2 . This behaviour ~s shown in fig. 8 where ~t is seen that the dechannehng length begins to decrease at x J ( d p / 2 ) : 0.3. Electron multiple scattering calculations with a diffusion equation approach are in progress [12] in order to quantify this m o m e n t u m d e p e n d e n c e and compare with the present experimental data.

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3 2 EFFECTS OF ZnO COATING

In the earlier experiments [1-5] with mechanical bending devices, the silicon crystal was bent only in one direction (along the length of the crystal). In our case, using a ZnO coating to produce the bend, we do not only have bending along the length of the crystal, which gxves the deflected beam, but also bending perpendicular

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to the beam direction. Over the vertical 12 mm face of the crystal, assuming the same Young's modules in both x and y-directions, we expect a total bending of = 13.9 mrad. However, as pointed out in sect. 2, the anti-coincidence scintillator, SC2, selects the center 5 mm of the crystal which would give a maximum bending in the y-direcnon of --- 5.8 mrad. The result of such bending is shown in fig. 9 where we show the angular distribution of particles entering the crystal as a function of vertical position on the crystal. Fig. 9a shows the envelope of beam parncles incident on the crystal in the x direction i.e across the (110) plane Figs 9b-91 show the same incident angular distribution but for a window set on low energy-loss particles (cf. fig. 2) and as a function of vertical position; fig. 9b corresponds to the top of the crystal while fig. 91 corresponds to the bottom It is evxdent that the ZnO coating causes a distortion of the crystal resulting in the observed poslnon of the (110) plane changing by = 200/~rad from top to bottom. This is considerably less than 5.8 mrad estimated above and is probably a result of the channeled particles being defined by the energy-loss detector which is centered 5 m m upstream of the beginning of the ZnO coating. The width of each dlstrlbunon however, is approximately 35-40/~rad F W H M as expected since 2~pp = 34 #tad for 80 G e V / c particles in the SI (110) plane. The other result of the ZnO coating is reflected m the outgoing angular distribution of particles. In figs. 4 and 5, the data were plotted in 0.5 mrad bins. However, with higher resolution, we fred structure in the dlstribunons as shown m fig. 10. Fig.

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10a is the outgoing angular distribution m the x-direction (bend dlrectton) for random incidence. Fig. 10b is the corresponding case for the crystal aligned and fig. 10c is the same as fig. 10b but for a window on low energy-loss. Both figs. 10b and 10c show a peak to the left of the main beam indicating a deflection in the direction opposite to the bend direction! This second peak is obviously a result of steering by the crystal since it disappears when the crystal is rotated ~ 1 mrad from alignment of the (110) plane, as shown m fig. 10a. We have investigated this effect by looking at the region about the beam direction, centered on 0 mrad in fig. 10, by setting a window on low energy-loss i.e. channeled particles, and looking at the outgoing angular distribution of particles in the x-direction for windows on the position of the incident beam on the entrance end of the crystal. Three windows in x (0.25 mm wide) and four windows in y (1.25 mm wide) were set on the crystal, as seen by the beam, and the resulting outgoing angular distributions in the x-direction are shown In fig. 11. The results for the incoming particles (fig. 9) showed an effect in going vertically along the crystal but the outgoing distributions show a left-right asymmetry. Most of the initially channeled particles which dechannel In the left side of the crystal result in the peak to the left of the main beam i.e. figs. 11a, d, g and j while those that dechannel m the right side of the crystal result in the peak centered on the beam direction. This effect occurred at all beam momenta and at both crystal temperatures. We have no explanation for this except that it appears to be associated with the ZnO coating The deviation from a straight line due to the bending caused by the 26 mm long ZnO coating is 0.4 ram. This means that channeled particles entering the crystal on the left hand 0.4 mm of the 0 72 mm thick crystal, which become

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J S Forster et al / Channehng

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dechanneled, exit through the ZnO coating while those particles on the remaining 0.32 mm which dechannel do not encounter ZnO; this assumes dechannellng to be a gradual increase in transverse energy such that the angle to the plane becomes a few times the critical angle, i.e. no violent collisions. Th~s picture is consistent with what is observed in fig. 11. We note that these effects on the incoming and outgoing distributions, caused by the ZnO coating should have no effect on the analysis described in the next section.

4. Comparison with calculations The inset in fig. 1 shows a schematic of the beam and crystal. The beam enters the crystal at the left end and a channeled beam is selected at the energy-loss detector. This channeled beam moves through the straight portion with some dechannehng due to multiple scattering, enters the bend which causes bending dechannehng as discussed in ref. [9], moves through the constant curvature region with further dechannehng due to multiple scattering, enters the straight region with no bending dechannehng and continues in the downstream straight portion with the usual multiple scattering dechanneling. The particles that are dechanneled leave the crystal at roughly the angle at which they were dechanneled. The particles channeled all the way through the crystal exit at the full crystal deflection angle. This picture ignores feeding-in [13]. In ref. [9], a framework for calculating the dechanneled fraction, F, due to bending, as a function of pyre, where t¢ = 1 / R is the constant curvature, was presented. The main assumptions used are that (1) the channeled particles are in statistical equilibrium when they reach the bend, (2) a particle dechannels if it penetrates too close to a plane, (3) the particle wavelength m the bend is shorter than the length of the bend, and (4) the bent planes can be modeled with a planar continuum potential. As a consequence of (2) and (3), bending dechanneling takes place in the first wavelength of particle motion after the particles enter the bend. In the present experiment, the incident beam has a large angular spread with respect to the channeling critical angle. Hence, the incident channeled beam is roughly uniformly distributed in both angle and space Since a uniform distribution in phase space is a statistical equilibrium distribution, we assume, consistent with ref. [9], that the distribution upon entering the bend is uniform in phase space. Thus the dechanneled fraction is simply F = ( A o - A , ) / A o where A 0 IS the phase space area of the channeled particles just before entering the bend and A, is the phase space area of the particles which remain channeled after the onset of the bend (see fig. 1, ref [9]). In fig. 12, the values of F are plotted versus the d~mensionless parameter, K defined as F = pvx./2rrZiZ2e2n,

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0

RE

I

I

I

I

t

I

05

10

15

20

25

30

pVK F=

2-rr Z 1 Z 2 e2n

Fig I2 The dechanneled fracnon, F, as a function of the &menslonless momentum parameter, I', for the room temperature and cooled crystal data

Z 2 are the atomic number of the projectde and target, respectwely, e is the electronic charge and n is the areal density of each plane. The results for the (110) planes of $1 for dechanneling at 2.5 0 1 ( T ) from the planes for our two temperatures are shown; also shown is the result for dechannehng at the planes (dp/2). Here, o t ( T ) is the one-&menslonal root mean square lattxce vibrational amphtude, T is the temperature and 01 = 0.057 A and 0.075 A for T = 128 K and 293 K, respectively. This dechanneling criterion was chosen as a consequence of a recent study [14] of scattering from crystal planes where the authors find a rapid transmon from conservation to non-conservatmn of transverse energy at an ~mpact parameter of -- 2.501 F r o m the data m figs. 4 and 5, it ~s possible to extract the dechanneled fraction due to bending for comparison with fig. 12. If we let N 1 denote the total number of p a m c l e s in the peak at 0 mrad, N 2 denote the number in the peak at 0 mrad due to muluple scattering dechannehng between the energy-loss detector and the bend and N denote the total number of particles, then the dechanneled fractton due to bending is F = ( N 1 - N 2 ) / ( N N2). These values are gwen m table 2 and shown in fig. 12 for the room temperature case (crosses) and the cooled case (open mangles) where the uncertainties shown are due to statisucs only. N 2 has been calculated with results from a separate experiment [13]. The uncorrected F values ( F = N1/N) are

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TABLE2 Measured dechanneled fraction, F, as a funcUon of momentum p (GeV/c)

F (room temp )

F (cooled)

60 80 100 120 150 200

0 432 + 0 027 (0 506)~ 0 494 _+0 030 (0 563) 0 600 + 0 030 (0 636) 0 670 + 0 034 (0 696) 0 766 _+0 043 (0 780) 0 919 + 0 042 (0 923)

0 372 + 0 031 (0 454) 0 425 _+0 015 (0 488) 0 512 + 0 026 (0 556) 0 529 + 0 030 (0 567) 0 688 _+0 037 (0 707) 0 836 + 0 048 (0 844)

aThe numbers shown m parentheses are the F values before correction for multiple scattering dechannehng m the strmght pomon of the crystal between the energy-loss detector and the begmmng of the bent region See text for detmls

s h o w n in b r a c k e t s and show the m a g n i t u d e of the correction to F for m u l t i p l e s c a t t e r i n g d e c h a n n e l i n g between the energy-loss d e t e c t o r a n d the b e g i n n i n g of the b e n t region. Since the d a t a for d e c h a n n e l i n g in a straight crystal [13] were only m e a s u r e d at r o o m temperature, the correction to the d a t a for the cooled crystal c o u l d b e an overestimate, i.e. N 2 is larger than it should be which results m F being slightly s m a l l e r than it should be. However, low energy p l a n a r d e c h a n n e l i n g e x p e r i m e n t s , for the (110) p l a n e in S1, for 0.5 to 1.5 M e V p r o t o n s [15] a n d for 3 0 M e V p r o t o n s [16] show a t e m p e r a t u r e d e p e n d e n c e of ~ 10% for the t e m p e r a t u r e r a n g e of this experiment. Therefore, the use of r o o m t e m p e r a t u r e m u l t i p l e scattering d e c h a n n e h n g d a t a to correct the cooled crystal results should not be significant. F r o m fig. 12, It can be seen that there is g o o d a g r e e m e n t between theory a n d e x p e r i m e n t b o t h for F vs. F a n d for the t e m p e r a t u r e d e p e n d e n c e . In particular, it i n d i c a t e s that the d e c h a n n e h n g criterion of 2.501 is r e a s o n a b l e (it should be n o t e d that 2.501, at r o o m temperature, is a p p r o x i m a t e l y equal to the T h o m a s F e r m i s c r e e n i n g distance, aT).

5. Summary and conclusions A silicon crystal c o a t e d with Z n O , has been used to deflect high-energy b e a m s of p r o t o n s a n d p i o n s through angles as great as 32.5 mrad. T h e Z n O coating results in a r e g i o n of c o n s t a n t curvature where the Z n O is a p p h e d , which m a k e s it straightforw a r d to c o m p a r e the d e c h a n n e l e d fraction of initially c h a n n e l e d particles, as a f u n c t i o n o f m o m e n t u m , with calculations b a s e d on the c o n t i n u u m model. M e a s u r e m e n t s were m a d e at r o o m temperature, where a total deflection of 32.5 m r a d was observed, a n d at - 1 4 5 ° C , where a total deflection of 30.9 m r a d was o b s e r v e d . T h e d a t a agree very well with calculations b a s e d on d e c h a n n e h n g occurr i n g at a d i s t a n c e of 2.5pl from the planes.

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D e c h a n n e l i n g lengths in the b e n t crystal were f o u n d to increase m m a l l y with i n c r e a s i n g m o m e n t u m a n d then decrease. The p o i n t at which the length begins to decrease occurs at an e q u i l i b r i u m poslUon away from the center of the channel, xe/(dp/2),

of 0.3.

F i n a l l y , we note that the Z n O coating causes a deflection of the d e c h a n n e l e d f r a c t i o n of the b e a m in the opposite d~rection to that of the bend. The particles which are associated w~th this "negative angle" deflectxon are ones that are originally c h a n n e l e d b u t dechannel a n d exit through the Z n O coating. T h e results o b t a i n e d in this work make it possible to predict accurately the d e c h a n n e l e d fraction of initially channeled particles for a particular application. Since ~t is b e h e v e d that the Z n O coating is of piezo-electnc grade material, it may be possible to " f i n e t u n e " the deflection angle b y a d.c. voltage applied between the u n c o a t e d side of the S1 crystal a n d a metal electrode evaporated onto the Z n O . W e wxsh to t h a n k I.V. Mitchell for his interest in this work a n d J.U A n d e r s e n for m a n y s t i m u l a t i n g discussions regarding p l a n a r d e c h a n n e h n g

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