Large solid angle mode for a broad range magnetic spectrograph

Nuclear Instruments and Methods 204 (1982) 85-90 North-Holland Publishing Company

LARGE SOLID ANGLE MODE A.A. ROLLEFSON

85

FOR A BROAD RANGE MAGNETIC

**, J . D . Z U M B R O

SPECTROGRAPH

+, J . W . K A I S E R + +, R . W . T A R A R A ,

*

a n d C.P. B R O W N E

University of Notre Dame, Indiana 46556. U.S.A. Received 3 March 1982

The design and testing of a specially designed magnetic quadrupole doublet to increase the solid angle of a broad-range magnetic spectrograph is described. Solid angle enhancements of over a factor of 13 are observed. This is accomplished without compromising the capabilities of the spectrograph for accurate energy measurements. Problems with alignment and sensitivity to beam spot position are described and resolutions of these problems are given. 1. Introduction

At the time of the design and construction of the 100 cm broad range magnetic spectrograph [1] at Notre Dame, two modes of operation were envisioned. In the first, or high-accuracy mode, only the main dipole with its uniform field is used and all focussing comes from the field boundaries. The second, or high-solid-angle mode, called for a pair of specially designed magnetic quadrupoles to be placed between the target and the entrance of the main dipole. The operating philosophy for the implementation of this second mode was that nothing be done to disturb the calibration of the instrument in the high accuracy mode. The use of a single quadrupole ahead of a Browne-Buechner broad-range magnetic spectrograph to increase solid angle was first proposed by Enge [2]. Although providing a useful device this approach would violate the condition that the high accuracy mode remain undisturbed since the use of a quadrupole singlet changes the effective object position for the dipole and requires moving the focal surface to keep the groups in focus. The use of a quadrupole doublet permits an increase in solid angle without requiring motion of the focal surface. The first quadrupole converges in the reaction plane, thereby increasing the solid angle, while the second quadrupole converges in the vertical plane (the focussing direction of the main dipole) until the apparent position of the object for the main dipole is the same as with the

* Work supported by the National Science Foundation under Grant PHY 80-08234. ** On leave from University of Arkansas at Little Rock, Little Rock, Arkansas, U.S.A. + Present address: Physics Department, Princeton University, Princeton, NJ 08450, USA. + + Present address: Department of Chemistry and Physics, St. Mary's College, Notre Dame, Indiana, USA. 0167-5087/82/0000

0000/$02.75 © 1982 North-Holland

quadrupole removed. This is shown in more detail in fig. 1. Fig. 1 shows trajectories for a magnetic rigidity of 1.13 Bpo where Boo is the rigidity for which the quadrupole fields are set. (Normally the main dipole field would then have the value B.) The lower part of the figure shows the vertical plane (plane in which the main dipole focuses) and the upper part shows the horizontal plane. The heavy horizontal lines show the effective length and diameter of the quadrupole fields. The points labeled H and the dashed vertical lines represent principal points and principal planes, respectively. The subscripts i and o signify image and object, and d and c signify diverging and converging fields. The target is located at o~ which is thus the object point for the spectrograph without quadrupoles. The first field diverges the particles and produces a virtual image of the target at i l, which is then the object point o 2 for the second quadrupole. This second field converges the particles to produce a virtual image at i 2. This is then the object for the main dipole field. For rigidity BOo the image point i 2 coincides with o~, so the dipole focuses particles which passed through the quadrupole at the same point as it focuses particles from the target with no quadrupole. It is seen that the points i 2 and i'z (Bp = 0.98 Bpo) lie close to o I so final images lie close to the focal surface of the spectrograph without quadrupoles. The "depth of focus" of the spectrograph is large enough so that the small displacement of object points has only a small effect on the aberration. The point P2 marks the effective entrance point and the arc through it, the effective entrance edge of the dipole field. The arrows show movable slit jaws, referred to as the alpha slits, which limit the divergence angle in the vertical direction.

86

A.A. Rollers'on et all /" Broad range magnetic ~spectrograph i I I I

ii II Ii ii HodT~Hid

p I I I

Ii ii

mira2=0.6

0

12

-

tip

=

1"13BPo

H T"

q'

:-~L~g..~

nt

,

II

i

P2

/~p' = 0.98/~,"o Fig. 1. Focussing by a pair of quadrupoles placed between the target and main dipole field of a modified broad range spectrograph. The heavy horizontal lines show the positions of the effective fields of the 7.62 cm and 15.24 cm diameter quadrupoles. The target is at o~ and the arc through P2 marks the entrance edge of the main dipole field. The upper part of the figure shows the horizontal plane and the lower part the vertical plane. The main dipole focuses only in the vertical plane. For magnetic rigidity BOo the vertical image of the the target spot formed by the quadrupole pair in the vertical plane lies at o I whereas for the values of BO above and below BO,, the vertical image lies at i 2 and i'2 respectively (still close to o~ ).

2. Description of inslrument The first quadrupole has an aperture of 7.62 cm and a m a x i m u m field of 4.10 k G at a current of 210A. The second quadrupole has an aperture of 15.24 cm and a m a x i m u m field of 1.86 k G at a current of 210A. Power supplies for the quadrupoles were designed to track the m a i n spectrograph field so that the currents through each " q u a d " would be a fixed multiple of the current through the main dipole. Trim pots were provided for each quad so that different focussing conditions could be obtained. Tracking of the spectrograph is achieved by generating a signal proportional to that from the spectrograph power supply's shunt resistor. Trimpots are provided to adjust the proportionality constant for each quad. For the 7.62 cm quad, pot settings from 0 to 10 result in currents 1.36 to 1.68 times the spectrograph current, respectively. For the 15.24 cm quad, the range is from 1.00 to 1.32. The two signals generated are then used to control their respective supplies. The supplies themselves are constructed a r o u n d high current d.c. power sources powered from motor-driven three phase variacs. A control circuit raises or lowers the variac output to m a i n t a i n constant average voltage across the final pass transistors. The transistors themselves are on a large air cooled heat sink. The supplies use no water for cooling and no SCR switching circuitry, two sources of possible trouble. The supplies have been essentially trouble-free.

For use in the high-accuracy mode the quadrupoles were made removable as shown in fig. 2. The two quadrupoles are m o u n t e d on a c o m m o n base plate with provision made for adjusting the two elements relative to the base plate. The position of the base plate relative to the spectrograph is defined by three spherical balls which fit into sets of pads attached to the b o t t o m of the quad base plate and to a plate fixed to the spectrograph. This provides accurate reproducibility of the quadrupole position. A telescoping pipe with sliding Ooring seals is used to make the vacuum connection between the target c h a m b e r and main vacuum box.

3. Alignment and testing The quadrupoles were originally aligned optically using alignment holes provided by the manufacturer. In initial tests using p r o t o n scattering from a heavy metal target it appeared that turning the quads on steered the particles. The quadrupoles were than realigned by a technique based on the C o t t o n M o u t o n effect [3,4]. A cell containing a colloidal suspension of iron [5] was placed inside the quadrupole a n d observed between crossed polaroids. W h e n the field is turned on a dark cross appears centered on the center of the quadrupole field in the solution. At the same time that the quads were realigned the exit port from the scattering c h a m b e r was realigned. Measurements of elastic scattering of protons from a gold target then indicated that turning

A.A. Rollefson et al. / Broad range magnetic spectrograph

87

Fig. 2. The upper photograph shows the quadrupole doublet in place between target chamber and spectrograph, for running in the high solid angle mode. The lower photograph shows the quadrupole moved aside and the vacuum pipe replaced. Before running in the broad-range high accuracy mode, the quadrupoles are placed far away from the spectrograph.

88

A.A. Rollefson et a L / Broad range magneto" spectrograph I000

on the quads no longer appreciably steered the reaction products. Even after realignment, however, there remained some inconsistency in the results obtained using elastic scattering for the ratio of counting rate with quads on to that with quads off. It was suspected that this inconsistency might arise from the sensitivity of the results to motion of the beam spot in the horizontal direction. There was a clear need for more detailed calculations to provide a two dimensional distribution of events on the focal surface in order to determine the sensitivity of the c o u n t i n g rate to various experimental parameters. Direct measurements with a particle b e a m would take an inordinate a m o u n t of b e a m time and give confusing results because of the difficulty of holding all but one p a r a m e t e r constant throughout a test. A c o m p u t e r program was written by one of the authors (JDZ) which traces individual rays through the system and determines where they will strike the focal surface. After one ray has been traced with the quads off the program calculates the path of the ray with the quads on. The program then returns and randomly selects a ray from a different place within the designated b e a m spot and randomly selects the angle at which the ray leaves that position within a specified angular range. Tests are performed at various aperatures in the system to determine whether a ray will pass through. Provision has been made to include a weighting factor of 1 / s i n 4 ( 0 / 2 ) for the case where elastic scattering is used to test the quads. The ray tracing continues until a predetermined n u m b e r of events (usually 1000) fall within a 1.27 cm wide strip on the focal surface with the quads off. This corresponds to the width of the position-sensitive-proportional counter used to detect the particles. The ratio of the n u m b e r of events in the proportional counter with quads on to the n u m b e r with quads off may then be calculated. Since the complete two dimensional distribution on the focal surface is obtained the events may be sorted in strips of any desired width, usually 2 cm and 4 c m corresponding to c o m m o n settings of zone defining slits when using photographic plates as detectors. The results of these calculations indicated that elastic scattering was not a particularly good way to test performance of the quadrupoles because of the large variation in differential cross section over the relatively large acceptance angle (up to + 3 °) in the reaction plane with the quads on. This results in a large variation in distribution of events across the focal surface. Small horizontal motions of the b e a m spot are magnified by a b o u t a factor of 10 at the focal surface. If a proportional counter of 1.27 cm is used at the center of the focal surface to detect the particles, then small variations in b e a m spot position can produce large variations in the c o u n t i n g rate when the quads are on. For example, for protons scattered from gold at 50 ° a variation in beam

i

(A)

(B)

2001

80O

1501

600

iooo

! '~1

500

I

400 i

Z

z

200]:

z 'J 13._

0

~

I000

'

i

i

i

i

(c) z

800 -

tO

" w

600

400

-

-

~

200

400

600 CHANNEL

80

90

DISTANCE

t IO0

I10

ALONG

200

400

600

NUMBER | h .__~L_ 150 160 170 FOCAL

SURFACE

8O0

t 180

(cm)

Fig. 3. Typical spectra for the w6Yb(d, p)~VvYb reaction for quads on, (A) and (B), and quads off, (C) and (D). For both spectra with quads on the trim pots for the 15.24 cm and 7.62 cm quads were set at 10 and 3 respectively. The bombarding energy was 14.0 MeV and the lab. angle was 60 °. For (A) and (C) the spectrograph frequency was set at 24.7660 MHz while for (B) and (D) the frequency was 21.1913 MHz. Charges collected for the 4 runs were (A) 400 btC, (B) 500 ~C, (C) 2000 /zC and (D) 2000 ~C.

spot position of --+0.025 cm would produce a variation of about ± 10% in the counting rate in a region where the solid angle e n h a n c e m e n t ratio is about 6. For this reason final quad tests were done with the reaction 176yb(d, p)lVvYb which had been previously studied [6]. This reaction has a slowly varying cross section around a laboratory angle of 60 ° and a b o m b a r d i n g energy of 14 MeV. It also involves a heavy target so that kinematic b r o a d e n i n g is not important. Fig. 3 shows typical spectra for quads off and quads on for the same trim pot settings but two different spectrograph fields. The two large groups on the left side of each spectrum are from the 160(d, P0)170 and 12C(d, P0)13 C reactions. Kinematic b r o a d e n i n g of these groups with quads on is quite evident, particularly for the upper left spectrum which corresponds to a quad setting for which a large angular range is focussed into the proportional counter. Fig. 4 shows an expanded version of a typical quads on a n d quads off run near the region of m a x i m u m e n h a n c e m e n t in solid angle. The resolution is essentially the same for quads on as it is

89

A.A. Rollefson et al. / Broad range magnetic spectrograph 1500

i

r

t

E

I

i

i

]

i

Q6=8

Q~= 1.5

1200

I

~

,o, /"TL5

14

~

I

Q6=IO

r 900

2 600 d UJ Z Z 300

i

1q

S

I L.) 0 n..- 5 5 0 U_l 0_

"Pl "" ""ff'i

I

I

12

i j

7 o

]

QUADS OFF

o3 I- 440 z

6 2

0 ('~ 3 3 0

220

Q3=1.5

14 / - ~

Q6 = 6

1012 /

Q3=O

~

S

j

IlO

I 400

i

I 420

]

I

2

~L

i 440

i

L 460

I

I I i I 40 80 120 160 200 DISTANCE ALONG FOCAL SURFACE (cm) L 480

CHANNEL NUMBER Fig. 4. Expanded spectra for a portion of the rz6yb(d, p)lTvyb d a t a . T h e g r o u p s s h o w n are t h e four in the v i c i n i t y of D = 96 cm on the focal surface. T h e top spectrum s h o w s the groups observed with quads on and the trim pots set at 8 and 1.5, w h i l e the bottom spectrum is for quads off. Charge accumulation for the top spectrum was 500 #C w h i l e for the bottom spectrum it was 2000/~C.

Fig. 5. R a t i o o f t h e s o l i d a n g l e s f o r q u a d s on to quads oft' f o r t h r e e d i f f e r e n t trim pot settings. Data points are from the w6yb(d, p)lV7yb reaction, w h i l e the solid c u r v e s are f r o m the ray tracing calculations d e s c r i b e d in the text.

20

i

i

15

for quads off. It is again pointed out that there is no change in position of the focal surface when the quads are turned on. Areas of the peaks from the ]76yb(d, p)177yb reaction were fitted with a split Gaussian group shape. From these areas the ratios of solid angles from runs with quads on and quads off were calculated and these are plotted in fig. 5 as a function of position on the focal surface. The error bars on the data points represent the uncertainties in the fitted areas. The solid curves are the result of the ray tracing calculations for each of the three trim pot settings shown. The alpha defining slits were set at the 6 ° position. The effective lengths of the 7.62 cm and 15.24 cm quadrupoles which were given by the manufacturer as approximately 25.4 cm were varied to reproduce the data. Final values used were 23.5 cms for the 7.62 cm quad and 26.3 cm for the 15.24 cm quad. The size of the horizontal beam spot

o 10

g

0

I I 0 0.10 0.20 HORIZONTAL BEAM SPOT SIZE

0.30 (cm)

Fig. 6. Dependence of solid a n g l e ratio for quads on to q u a d s o f f as a f u n c t i o n of horizontal beam spot size. T h e top curve is for a position n e a r the p e a k solid a n g l e e n h a n c e m e n t (D = 104 cm) w h i l e the lower two curves are for smaller e n h a n c e m e n t s , observed at D -- 135 cm and D = 186 cm.

90

A.A. Roller*on et a L / Broad range magnetic spectrograph

....

4 cm

Zone

2 cm

Zone

1.27cm

Zone

( proportional

counter)

A 6.0

E 5.0

,,, 4 . 0 .J 5.0

'~Z 2 . 0

Zd.o.. o °/°

--

~g,~,_,~_,,~ _

°"°~..,a ~'~ ~' ~ ~, ~, °'-o....

o.~

(2)

)~'°'<>°-o-o-c .o-o- o - o •o - ~ • o - o . o - o . o - o . o _ o . o _ o . o _ o . o _ o . o - o

was used. This is below the lowest curve in fig. 6 and it is seen that the solid angle is i n d e p e n d e n t of b e a m spot size under these conditions. One possible solution to the problem of sensitivity to b e a m spot size and postion is to use photographic plates. If the particle groups are focussed to a width which is less than the width of the zone-defining slits ahead of the plates, then a motion of the group on the focal surface could be observed when the plates are scanned and appropriate corrections made. Alternatively a wide (4 cm) two dimensional proportional counter could be used. Fig. 7 shows a comparison of the calculated solid angle for the 1 0 / 3 pot setting and a 0.17 cm by 0.05 cm b e a m spot for the proportional counter, a 2 c m wide zone, and a 4 c m wide zone. Variation of the solid angles as a function of distance along the focal surface is also shown for quads off for all three cases.

I i i i 40 80 120 160 200 DISTANCE ALONG FOCAL SURFACE ( c m ) 5. S u m m a f f

Fig. 7. Solid angles for 1.27 cm, 2 cm, and 4 cm zones as a function of position on the focal surface. The top three curves are for quads on with trim pot settings of 10 and 3, beam spot of 0.17 × 0.05 cm, and a divergence angle defining slit setting of 6 ° , while the lower curves are for the same three cases with quads off.

was also varied slightly to give agreement with the m a x i m u m solid angle ratio observed experimentally. This beam spot had been estimated to be 0.18 cm from the geometry of the defining slits, target angle and spectrograph angle and a final value of 0.17 cm was used for the curves shown. The sensitivity of the m a x i m u m solid angle enhancem e n t for the proportional counter for the 10/3 trim pot settings is shown as the top curve in fig. 6 as a function of horizontal b e a m spot size. As the beam spot size is decreased the solid angle ratio increases until a b e a m spot size of about 0.12 cm is reached. At this point all particles passing through the spectrograph with magnetic rigidities corresponding to the m a x i m u m enhancem e n t region are focussed into the proportional counter. Further reduction of the b e a m spot does not result in any additional increase in solid angle ratio. Sensitivity of the solid angle ratio away from the peak is m u c h less, as is shown by the lower two curves which are for the same trim pot settings but further up the focal surface at D - - 135 a n d D : 186 cm, respectively. Data which were taken at smaller e n h a n c e m e n t s of solid angle and thus less sensitivity to b e a m spot size and motion have been pusblished [7]. A n e n h a n c e m e n t ratio of a b o u t 3

The use of a magnetic quadrupole doublet ahead of the 100 cm broadrange magnetic spectrograph has been shown to greatly enhance the data-taking capability of the instrument without compromising the capabilities for absolute accuracy of energy measurements. Solid angle e n h a n c e m e n t s of over a factor of 13 have been observed experimentally. (This corresponds to a solid angle of 5.0 msr when using the proportional counter. For photographic plates where larger zone widths can be used, the corresponding solid angle is 6.8 msr.) It is anticipated that the increased solid angle capability will prove extremely valuable in measuring angular distributions for low cross section reactions and for observation of reactions induced by polarized ions where the beam intensity is low.

References

[1] J.D. Goss, A.A. Rollefson, and C.P. Browne, Nucl. Instr. and Meth. 109 (1973) 13. [2] Harold A. Enge, Rev. Sci. Instr. 29 (1958) 885. [3] J.K. Cobb and J.J. Muray, IEEE Transactions on Nuclear Science NS-12 (1965) 395. [4] R.M. Johnson, Internal Report Bev-687, Lawrence Radiation Laboratory, Berkeley, California ( 1961). [5] D.J. Craik and P.M. Griffiths, Proc. Phys. Soc. B70 (1957) 1000.

[6] R.W. Tarara and C.P. Browne, Phys. Rev. 19 (1979) 674. [7] R.W. Tarara, J.D. Zumbro, and C.P. Browne, Phys. Re','. 18 (1978) 1064.