Matching of a beam line and a spectrometer New beam line project at RCNP

__ *.__ B

a

Nuclear

Instruments

and Methods

in Physics Research

B 126

( 1997)

274-278

Beam Interactions with Materials & Atoms

ELSEMER

Matching of a beam line and a spectrometer New beam line project at RCNP Y. Fujita a,*, K. Hatanaka b, G.P.A. BergC, K. Hosono b, N. Matsuoka b, S. Morinobu d, T. Noro b, M. Sato b, K. Tamura b, H. Ueno a a Dept. Phy.. Osaka Univ.. Toym~ka, Osa!w 560. Japan h Research Center for Nucl. Php., Osaka Univ.. Iharaki, Osaka 567, Japan ’ Indiana Univ Cyclotron Facility Bloomington, IN 47408. USA ’ Dept. Phy., Kyushrc Univ.. Fukuokn 812, Jopan

Abstract A magnetic spectrometer combined with an accelerator is a powerful tool for the precise measurements of nuclear-reaction spectra. By applying matching techniques to the beam line connecting an accelerator and the spectrometer, it is possible to compensate the spectrum-line broadening effects caused by the beam momentum spread and reaction kinematics, and thus full capability of high resolving power of a magnetic spectrometer can be extracted. In addition to the usual matching methods, like lateral dispersion matching and focus matching, the importance of angular dispersion matching is discussed for a reaction with finite kinematic factor (K f O), which is important if the resolution of the scattering angle is needed. Based on the discussed principles, a new beam line called “WS course” is designed in order to realize the beam matching between a cyclotron and a spectrometer with a large dispersion at RCNP, Osaka. PACS: 29.2l.Eg; 29.3O.Aj Kqwvord,s: High resolution;

Dispersion

matching;

Angular

dispersion

matching

1. Introduction High-resolution nuclear-reaction experiments offer new information on nuclear structure as well as on nuclearreaction mechanisms through the study of individual excited states. A high-resolution magnetic spectrometer is an effective tool in these studies. The complete ion-optical system including spectrometer, beam line and even the accelerator should be designed so as to minimize the line width of a nuclear state in the focal plane of the spectrometer. The importance of matching between beam line and the spectrometer under varying kinematic conditions was pointed out already 35 years ago [ 1,2], and detailed matching conditions and experimental procedures have been suggested in several papers [3-S]. The first-order formalism discussed in them give conditions for kinematic correction (or kinematic displacement), lateral dispersion matching (or dispersion matching), focus matching (or kinematic defocusing) and additionally angular dispersion matching. The first three conditions are connected directly with the achievement of higher resolution and thus they have been discussed ex-

*Corresponding

author;

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6

850

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Science

B.V.

E-mail:

fujita@

rcnpax.rcnp.osaka-u.ac.jp

0168-583X/97/$17.00

PIISOl68-583X(96)01008-7

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1997 Elsevier

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tensively for cases without and with kinematic broadening effect (kinematic factor K = 0 and K # 0, respectively). Recent experiments in the sub-GeV/nucleon region have started at RCNP in order to observe new nuclear excitations, i.e., spin and isospin excitations. The high-resolution spectrometer “Grand Raiden” [6] was constructed for highresolution studies of nuclear and atomic physics in combination with a separated-sector cyclotron (ring cyclotron) with K = 400 (corresponding to a maximum proton beam energy of 400 MeV) [ 71. As the beam momentum (energy) of an accelerator increases, the momentum (energy) spread of the beam usually increases, too. The present beam-transport line connecting the ring cyclotron and the spectrometer was designed to realize the dispersion matching in order to obtain a spectrum with a momentum resolution better than the spread of the beam momentum. This technique as an example was applied for (‘He,t) reaction studies at 0”. For an incident ‘He beam energy of 450 MeV and a beam energy spread of about 300 keV (FWHM) , a total energy resolution of less than 150 keV in the spectra has been achieved. This is one of the best resolutions presently possible in (p,n)-type reactions in the intermediate energy region. The energy resolution made it possible to reveal the fine structure of the Gamow-Teller

I!

resonance

Fujira

rt

(GTR)

and then the “isospin

Raiden”

is designed

ul./Nucl.

Instr.

and

structure”

Mrth.

rn Phu.

Rex

El /XI

(19V7l

274-278

175

of the

*

GTR 181. “Grand

D = 15.45 m and a small magnification

dispersion -0.417

to have a large momentum

in order to realize to D/M.

is proportional therefore.

a high resolving

For lateral dispersiotl

a very large beam momentum

M =

power

which

matching.

dispersion

of about

D = 37 m is required at the target location of the spectrometer Due IO this large required

dispersion,

momentum

(FWHM ) has a total width

spread of 3 x 1O-J

the beam with a

of more than 20 mm. Such a large horizontal size causes the scattering 20-30

angle to be uncertain

mr, due to different

locations

of the nuclear

scattering

reaction

beam spot within

about

angles for different

in the target. The present

beam line. however. does not consider the angular dispersion matching,

which

is not acceptable

for many experiments

L

target

in

view of the large angle uncertainty. In this report. we consider the angular dispersion matching for cases with K # 0 as well as K = 0 in addition to the usual heam matching siderations

are incorporated

and analysis

i +T / \

methods. The results of these conin the design of a new transport

Fig. and

system for the beam.

I. The

relationship

n scattered

incident

parttcle

particle

2. Matching

between beam line and spectrometer

scattering

Using TRANSPORT per by Martin the entrance

sition

[ 91 and following

xu =

matrix

the pa-

[ 41, we assume that a particle leaves

et al.

point of the beam-line

with the coordinates the transfer

notations

system (source

( .cc~. &I,&).

point)

It is transformed

by

B down the beam line to the target po-

in the scattering

chamber,

natcs are given by XI =

where the particle

coordi-

(xl, 8,,81). The momenta 81 and

& are identical.

because the energy has not been changed.

The coordinates

are transformed

xl

=

by the target matrix

in gwen

Here. &r

ray.

to the beam angle

the “effective”

the position< the

and

by 0 = O2 -

It rhould

particle

angle

angle

be noted

IS given

by the spectrometer

Let us consider target position

angle

relative

from

rhc “absolute”

by p = n + Hz -

Ht. ‘Then

to the central

ray

H,.

in the dis-

angle, because it has the meaning

scattering angle of an arbitrary

we choose 0 as a free parameter

assumption

ray. In the fo-

against the usual

of using 02 1451. The relationship

between 6~

and 81 (= 81) is then given hy

T to

matrix

the transformation

xr t

= KO i- Cc?,.

S. of coordinates

x2. If the reaction angle in the labora-

where K is the “kinematic

factor (of tirst order)” defined ( 1/pciui)( +J~,,,,/~(Y)and is 0 at 0”. C is the “dispersion

tory frame is cy and the target angle from the normal direction of beam incidence

matching

is &,

(4)

at the by

as shown in Fig. 1, we get

factor”

defined by C = (pi”/‘p,,,,r) ( ~pp,,,/8pln) and

is C = 1 for elastic scattering. By combining

T=cos(n

- q!q)/COS(q+r).

T is called

(1)

the target function

[3-51.

If a particle

with an incident

angle 81 is scattered by the target with an

angle 82 relative

to the scattering

“absolute”

Details on these functions

scattering

angle cy (see Fig.

I ), the

angle /? is given by

p=cu+@!-01,

B. T and S. the transformations

exit of the spectrometer

x=xo(stib117-+

are given by

wbx)

SBo(sIIbl~Tfsl2bzz) (2)

scattering

in the

bending plane from the source point of the beam line to the

+&(n1b16T

+ snbx, + s,oC)

+O(s~z + SINK). and thus the relative

(5)

angle 0 from the scattering Similarly

angle (Y is expressed as -81.

are

found in Refs. [3.5].

_Y,= Tr , .

B=&

that

_I,

of nn

of the t‘xget

It should be noted that this value 0 is significant

lowing.

angle

Hz and the scattering

63 of the particle

cussion on the scattering of “effective”

partwlc

the

( _Q,Oz,& ) at the target location and further to x =

(x, 0.6)

where

particle

an Incident among

is the in~hnatton

direction.

0 of a specific scattering

of

relationship

81. that of a scattered

n for the reference the normal

between x2,

(3) IX. ION OPTICS/MASS

SPECI-ROMETRY

+@(I(

.~21 h12’r

+

s22b

beam line project

3. New “WS”

)

f-8( ST2-t S2h K)

16) Based on the considerations

1. 2 and 6 of the matrix

Here. sufiices

.x. H and 8. respectively.

The minimum

thus the best resolution the coefficients

that the coefficient

of the scattering of 60 in Eq. (6)

of herd

the condition

represent

size of image x and

is achieved with the conditions

of 80, St, and 0 in Eq. (5)

for a good definition

that

arc zero. Also

angle 8. we request

should be zero. Under

dispersior~ matching between the

beam line and the spectrometer, ambiguity

elements

in the determination

beam from the RCNP cyclotron Raiden” “matched

(i) Achieving

the procedure

given in Refs.

for a system

[ 4.5 1, the coeffi-

ing the horizontal

quadrupole

moment of the spectrometer.

dition

of .SI? = -sleK,

of Eqs. (5) ditions

and (6).

the coefficients

depend on K explicitly.

to be discussed,

K dependence

should note here that implicit troduced

in matrix

the quadrupole neous equations Eqs. (5)

b,h=--0

elements

moment

(iii

we

,r,j due to the adjustment

(iii)

of

‘The simulta-

which make the coefficients

of 80 terms in

is also beneficial

Placing

the ion-optical

Such

background

;III

IL-

of‘ beanr

for the reduction

by piacIng

points.

elements as symmetrically

so that the adjustment

Establishing

locations

beam

polariz,ation.

beam

polarization

‘1s

of the hcam lilne pa-

Symmetrical

for accurate

Especially in

points

producing

arranpemL‘nt

measureincn:

for

dcterminin;;

the horizontal

before

should

plant.

ol the

.1 y:!il

be placed

and after

spin rotation

for a polarized

:II

a bending

rix

section

angle of around 90” or 77!1-

(mainly

proton)

beam.

(7)

T

Sl 1

rangcment

focusing

c +sIlS2hK-S2lSlf,K)-,

so that phase \p;~‘c’

of the beam become simpler.

of beam fine polarimeters

and (6) to be zero is solved as Slh

focus in the beam transport

is ::ssociated with the benefit of smaller aberr,jtionr.

has been in-

of the spectrometer.

point-to-point

rameters becomes simpler.

con-

Also

were considcr[:tt

properties

possible,

of the other terms

the other matching

idea of providing

baffle slits at the focusing

correction. Under the con-

and therefore

to the principal

halo and thus the experimental

cient of the 0 term in Eq. (5) can be made zero by adjustThe process is called kinematic

‘GI
Hall IhrGuph it:.:

several basic principles

from one section to the following,

with large dispersion. Following

beam”,

, ,ty

in the design of the beam line.

this term brings the largest of 6, especially

to the specir’onlcter

located in the West Experimental

south inlet port. In addition

Y

for the beam tnat&ir:g.

designed a new beam line called “WS course” providin;:

and

bJ,i = (S?ISI~ - .~lI.s2h)c.

(8)

~22- SI? S:I = I is used to

Here, the relationship

s11

make the expression

simpler.

They show that the parame-

ters of the beam line 616 (lateral gular dispersion)

should be adjusted

with the changes in parameters realization

of kinematic

in accordance

dispersion)

with

and b?h (an-

solely

in accordance

of the spectrometer

correction and of the reaction, i.e.,

the requirements

inherent

tion of interest at the target. The matching and (8)

and angular

dispersion

matching,

conditions

respectively.

the focusing

R =

of the xo term of Eq. magnification.

conditions

of overall

satisfied,

With

(5) and matching

dent of operating

SlhbllK).

(10)

conditions

realistic properties

dc-

on the Sl?

calculations

beam showed that

and simultaneous

reduction

ot

dispersion

of the cyclotron

to LJ = 0.1 m could be achieved. The

results were well

small beam size

Pre-ana/vzer.

clotron

from

accclerassuming

the momentum calculated (ii)

in the preceding

for the extracted

spatial double-focusing

through

Mw = (SII~IT-

to the point

in Fig. 2 is used to

beam achromatically

[ 71. Ion-optical

ator complex

ing magnet

it is given, as in Ref. 141,

(SPj”

so that the subsequent beam optics becomes indepcn-

(9)

where M,,, is the coefficient

Point

focus the extracted

power of the matched system is given by

has the meaning

functions.

point of the ring cyclotron

noted by “Source

at the target (Jo-

( I/~.uI) ( s~/Mo, ),

(iv ) quadrupole magnet for the (u( v) two triplet-quadrupoles.

rlisprrsior~ rtttt~chiag and

traction

).

The resolving

sections.

prc-analyzer.

(i) AchrornclticSoc.using scctiotl. The section from the cx-

It is known

[4,.5] by adjusting

focusing section, (ii)

These sections have the following

given

of 00 term in Eq. (5) can be made zero condition

(iii ) grand-analyzer. gubr

matching

that the coefficient cus mntchirtg

They are; (i) achromatic

to the reac-

are called larernl dispersion

by Eqs. (7)

for the

The schematic layout of the proposed beam line is shown in Fig. 2. The beam line consists of five functional

proved

by the observed

(< I mm) at SP.

This section consisting and quadrupole

the existing

shield-wall

of D = 4.3 m.

of a 40”

lenses guides

vault and the experimental

dispersion

D = 2 m at the exit

separating

bcnd-

the beam the cy-

hall. It has a small

Y: Fujito

et al./NwA.

In.s~r. and Meth.

in Ply.

Res. B 126 (1997)

274-278

277

For polarization measurements of the vertically polarized beam, the entrance of the grand-analyzer is the best location for a beam-line polarimeter. For the horizontally polarized beam, a pair of beam-line polarimeters can be placed at the entrance and at the intermediate focusing point after the bending angle of 110’. The accompanying spin-rotation angle between these

positions is calculated to be 270’ for a horizontally polarized proton beam of 350 MeV. Reasonable spinrotation angles are expected for proton beams in the energy range from 200 to 400 MeV.

(iv) Quadrupole magnetfor the angular dispersion matching. A quadrupole magnet will be plac& at the final

Source Point (SP) Fig. 2. Schematic

layout

persion marching,

angulardispersion

sating the kinematic calculation. porwtion

of the proposed beam line capable

effect

realizing

the lateml

by exciting

of the grand analyzer.

andfocus

at the target position,

The result of calculation

sion matching

matching

of lnteral

and a result of ion-optical

is shown for a dispersive

dispersion

marching

the qundrupole-lens

For the ion-optical

dis-

matching compen-

matching.

beam trans-

and the ongulor

disper-

placed at the focusing

calculations.

focusing point of the grand-analyzer. In a thin-lens approximation, a quadrupole magnet bends the beam direction in proportion to the distance from the center. Since the quadtupole magnet is placed at the spatial focusing point and the beam spread is caused by the dispersion of the beam line, it can adjust the angular dispersion on target without affecting the focus on target significantly. (VI TWOtriplet-quudrupoles. Two quadtupole triplets are necessary in the straight section between the exit of the analyzer and the target for tuning purposes and for the realization of the correct sign of the dispersion on target. These quadtupoles should have wide openings in order to guide the beam with large dispersion without creating any background. This is especially important in smal-angle measurement including 0” transmission modes. The two quadtupole triplets allow adjustments of following beam matching conditions. (a) Tuning of the beam-line magnification to achieve lateral dispersion matching for varying kinematic conditions. (b) Adjustment of the focusing position to achieve focus

programs

point

TRAM-

PORT

and GIOS

(iii)

The grand-analyzer consists of four 55” bending dipole magnets with bending radii of 3 m and quadrupole lenses. The system is designed to make a total dispersion of about 55 m at the focus of the grand analyzer in the dispersive mode. This is sufficient to achieve lateral dispersionmatching for various reaction conditions at the target. T.vo identical analyzers are combined to form an anti-mirror symmetric system. There is an intermediate dispersive focusing point in the middle. The point can be used to eliminate undesired beam halos by setting cleaning slits. The system can also be operated& achromatic mode allowing maximum beam transmission with small target spot size in cases where a moderate resolution is sufficient. In both modes, horizontal and vertical magnifications are almost unity at the exit of this section.

4. Discussion and summary

were used.

Grand-analyzer.

.

The matching conditions between a spectrometer and a beam line were studied ion-optically for the case K + 0. By taking into account the correlation between 81 and 82 through 8 defined by 8 = 01 - $2, the conditions for latera1 dispersion matching and angular dispersion matching were explicitly expressed by using ion-optical parameters of the spectrometer and those inherent to a reaction. Based on considerations for the matching conditions, a new beam line transporting “matched beams” from RCNP ring cyclotron to spectrometer “Grand Raiden” is proposed. For the measurement of high-resolution spectra using a spectrometer with typically large dispersion, it is very important to establish angular dispersion matching for the precise measurement of reaction scattering angle under the condition of lateral dispersion matching, where large horizontal beam spot sizes are expected. By performing “perfect” beam matching, a momentum resolving power of R = 4 x I O4 and

IX. ION OPTICS/MASS SPECTROMETRY

278

1: FI
a scattering

angle detinition

of better than 5 mrad can be

achieved.

References

1I 1 B.L. Cohen. Rev. / ‘21 B. SjGgren. Nucl. 1i 1 D.L. Hcndrie. in:

Sci. Ittstr. 30 ( 1959) 4 15. Instr. and M& 7 ( 1960) 76. Nuclear Spectroscopy and Reactions part A, ed. J. Cemy (Academic Press. New York. 1974) p. 365.

I-4) S.A. Matm et xl.. Nucl. Instr. and Meth. 214 t 1983) 281. I5! AhI. vilu den Bq. KVI report KVI-1651 (1991 1 / 61 hf. k,JlWi? et ill.. KCNP Annual Report 1989, p, 201. [ 1 I I. M~uraet al.. KCNP Annual Report 1989. p. 175; Proc. lnt. Conf 01, Cyclotrons and their Applications, Vancouver. Canada. I992 ( World Scientific, Smgapore, 1992) p. 3. 18 1 Y. Fujita et al.. Phys. Lett. B 365 ( 1996) 29. (9 1 K.L. Brcwn et ttl.. tt computer program for designtng charged particle beam transport system. CERN-80-04 (Geneva 1980)