The II th Symposium on Accelerator Science and Technology, Harima Science Garden City1 I997

DESIGN OF SLOW EXTRACTION SYSTEM AT BOOSTERSYNCHROTRON FOR MUSES
T.Ohkawa, RII<EN, Wako, Saitarna 351-01, Japan
T.Katayama, Center for Nuclear Study, Graduate School of Science, University of Tokyo
Tanashi, Tokyo 188, Japan
Abstractstraight section A

The Booster Synchrotron Ring (BSR) is a part of MultiUSe Experimental Storage rings (MUSES). BSR
functions exclusively for the acceleration of ion andelectron beams. The maximum accelerating energy is, forexample, to be 3 GeV for proton; 1.45 GeV /nucleon forlight ions of q/A=l/2; 800 MeV/nucleon for heavy ionsof q/A=l/3. Electron beam is accelerated to2.5 GeV fromthe injection energy 300 MeV. The acceleratedion andelectron beams will be fast extracted and injected into theDouble Storage Rings (DSR) by one turn injection. As
another operation mode, ion beams will be slowly
extracted for the experiments. In this paper, injection andextraction procedures of the BSR, especially slow
extraction, are presented.

Length61. 7m

QD4
QF4QD1lon injection
electron extraction
straight section B1 BSR LATTICE DESCRIPTION

Fig.l A Layout of BSR

As shown in Fig.l, the BSR consists of two arc
sections and two long straight sections. Each arc section
is mirror symmetrical system, and there are two bending
cells. The dispersion in the straight sections outside thearc section is zero. The lattice is specified for eightfamilies of quadrupoles; QFl and QDl, QF4 and QD4 in
the arcs, QF2 and QD2, QF3 and QD3 in the longstraight sections.

2 INJECTION AND EXTRACTION
An arrangements of the injection and extraction
magnets are shown in Figs 2 and 3. The BSR lattice isdesigned to be able to operate with two different extraction
mode for ion beams; fast extraction and slow extraction.
As seen in Fig.2, an electrostatic septum(ES), four
septum magnets(SMl, SM2, SM3, SM4) and three bumpmagnets(BMl) are used for the electron beam multi-tum
injection. These magnets except bump magnets, are used

- - - l o n beamelectron beam

ion slow extraction

ESQFI

i ~eleotro"

SMISM2l"je<tloo

QFIo,J,!~-----1 ---------j!JJ o •~ll'---r--,.0 -~..-.n'--r--T0--!~ 0 iiilf---+-'-,tp~-QD2 QF2QD3 QF3 QD3QF2Fig. 2 An arrangement of straight section A-285-QD2

The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

- - - lon. beamelectron beam
QFl

QFl

QF2 SM2QD3 QF3 QD3 SM2

Fig. 3 An arrangement of straight section B
for ion beam slow extraction which is carried out by
using third order resonance (Vres=20/3).
As seen in Fig.3, three septum magnets(SM2,SM3, SMS), four bump magnets(BM2) and ten kicker
magnets(Kl) are used for the ion beam one turn injection.
These magnets are also used for electron beam fast
extraction. The ion beam from the ACR is injected into
the septum magnet SMS at an angle of with respect tothe straight section of the BSR. The ion beam is finallykicked and placed in the reference orbit by the kicker
magnets. This kicker magnets are used for ion beam fast
extraction. So, kicker magnets must be risen and fallen
less than 50 ns.
3 SLOW EXTRACTION

On· slow extraction process, at the first, sextupolemagnets as a resonance exciter are excited. Secondly
horizontal tune is moved from the operating value 6.691
to a value near the third order resonance(20/3) by changing
excitation currents of the quadrupole magnets. Beams
which have deviated to the distance more than 25 mm
inside from the central orbit at the entrance of the ES are
deflectedinward as large as 3 mrad by the static highvoltage of the ES.
The betatron oscillation can be expressed by thefollowing relation

1

X=-1 [Y1+a 2 +a]2(x-y)

fi1

Y=-1 [Y1+a2-a]2(x+y)

fiy=-~-x'
Y1+a2

Let 'l'i be the deflection due to the i-th sextupole magnet
SEi2B·"'Pj=gixi ,gi-2~p'where xi is the displacement of the orbit from theequilibrium orbit at SEi and gi is the strength of the Sei.
Here we assume that ·the transfer matrix ri from electric
septum to sextupole magnet is

In the third resonance, particles pass each sextupole

magnets three times a period. Therefore, taking
summations of contributions from each magnet over one
period, we have
H= _£.(x2+y2)~ l:g:xf'JV 1+a2 I I2=-£.{x2+y2)+~ :E{(x3-3xy2)~Ai+(Y3-3yx2)g~sJ2
3V 1+a2.
whereg:1

here we put~iI~-J1+af Y1+a2g·1'

Ai =-3-{y l+a2 -arl"{(acbi)3-3(V l+a2 +af(ai+bi)2(~-bi)}sfi

3-{ Vl+a 2 +a~{(ai+bif-3( Vl+a 2 -a)2(a.-bi \2(a-+bi)}
Bi =gfiI} . I-286-The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

I: means the summation over one revolution. Putting theangle of rotation of the coordinates as '¥, given by
tan3'¥=- B/A,the coordinates are transformed assin'¥ )( x)cos'¥ y .

dp/p: 0.1% to that with dp/p=- -0.1% by turns. When abeam with dp/p=O has horizontal tune value Q0 , a beamwith dp/p=0.1% has Q0+~Qodp/p. If £ is same value, theextracted direction of the beam is same~ Result of thesimulation is shown in Fig.4. As shown in Fig.4, at theentrance of ES the outgoing trajectories is overlapped eachother.

PHASE SPACEThen, we cail rewrite the Hamiltonian as.,.,20.

,....10~from which we can obtain following three unstable fixed
points:

A:(X't.Y't)=( f1±Ci!

.

~gY A2+B 2fi 0x=·-5.0mm
px = 0.0 mrad ·'R.1o

SEl: k2 = 20.2 m-3
SE2: k2 = 2.0 m-3,o)~-200 20 40

X[mm]
B: (X'2.Y'2)=(; X't. -1!-X't)
Fig.4 The separatrices and outgoing trajectories of beams
with dp/p=-0.1 %, 0%, 0.1 %, respectively, at ES

C: (X'3,Y'3) =( ; X't.Yf-X't)

Transforming back to the (x,x') plane, we obtain thefollowing unstable fixed point:

4SUMMARY
We have found that ion beam slow extraction iscarried out by using third order resonance (Vres=20/3).
This procedure is required to be further investigated indetail for the installation of all the necessary hardwares.
Optimization of the lattice of the BSR is under progress.

B:(x2,x'2 ) ={Gcos ('II-X+}1t).- ~Gcos {'lf+X+}1t))

REFERENCES

C: (x3,x'3 ) =(Gcos ('II-X i1t),-Yif"Gcos {'1/+X i1t))[1] Y.Kobayashi, "Theory of the resonant beam ejectionfrom synchrotrons", p.77-87, 1970.
[2] T. Ohkawa et al., Proc. 1997 Particle Accelerator
Conf., Vancouver, to be published.

wheretanx= V1+a2 +<xand3Ge(l+a2)4~gVA2+s2.
The area of the triangular separatrix in the (x,x') plane isgiven by

S is assumed to be 1On mm.mrad. The momentum spread
is dp/p=±O.l %. So a beam is extracted from that with-287-