SLOK BEAl'l E'>cl'RACTION FRO£'! TARN II

A. Noda, N. Yoshizawa, K. Chida, F. Saga and A. Nizobuchi
Institute for Nuclear Stud;v, University of Tokyo
Hidori-cho 3-2-1, Tanashi-city, Tokyo 188, Japan
Abstract

BEM·I BEHA\Il0UR [~.J TRANS\IERSE PHfSE SP.A.CE

A slow beam extraction system for TARN II isunder construction to provide heavy-ion beams (p,a ~Ne) at intermediate energy ( 150~ 350 HeV /u) . The thirdorder resonance extraction with tuning of lattice quadrupole magnets is to be used. The emittance of the extracted beam and the extraction efficiency are estimated to be 5~r mm · mrad and more than 89%, respectively.

-%E = 0"'~0.00

0·0.02Introduction
At Institute for Nuclear Study, University ofTokyo, a synchrotron/cooler ring, TAR~ II, has been under construction since 1984. TARN II aims at
acceleration of heavy ions up to Ne into the intermediate energy region (150~ 350 HeV/u) and capability
to reduce the emittance and momentum spread of the ion
beam with an electron beam cooling. 1 In order torespond to the demands for hea>~ ions with intermediate
energy to utilize for fundamental research of biomedical irradiation, a slow beam extraction system has been
designed and its hardware equipments have been alreadyunder construction.'•J
In the present paper, the scheme of the slow beam
extraction adopted at TARN II is described at first.
Then the results of beam tracking simulation based on
this system are presented. Finally, the expected
quality of the extracted beam is given.
Slow Beam Extraction System
The layout of the sloH beam extraction system isshown in Fig. 1 together with the arrangement of themain magnets of TARN II. The essential parameters of
this extraction system are listed up in Table· 1.
The operating point of TARN II at the injection
stage is chosen to be around (1.75, 1.80). If the halfinteger resonance ( v u=3/2) is to be used, it needs
crossing of the third order resonance (V n=5/3), which
requires additional care for compensating the third order stopband. Hainly from this reason, the third orderresonant beam extraction is adopted here.
The extraction process is performed in the following procedure.
a) Nearly at the end of beam acceleration stage, suchan orbit bump as makes aperture minimum at theentrance of an electrostatic septum (ES) is madeby exciting bump coils 1, 2 and 3, Hhich are woundat backlegs of main dipole magnets.

'if/e
-0.2%

·0.04
-0.!

Fig. 20.1

Behaviour of the injection beam with emmitanceof 150~r mm · mrad in transverse phase spacewith full excitation of the resonance exciter.

b) The operating point is moved from (1.75, 1.80) to(1.6667, 1.80) by changing the excitation
currents of the quadrupole magnets in the lattice
after the completion of process a). Precise tunechange is made by exciting additional coils
attached to the main quadrupole magnets after
reaching close enough to the resonance (v u=5/3).
c) Beams which have deviated to the distance morethan 75 mm outside from the central orbit at theentrance of the ES are deflected outward as large
as 5.8 mrad by the static high voltage of the ES.
d) A septum magnet (SH), Hhich is located almost one
cell downstream from the ES to accept all thedeflected beams in procedure c), gives much larger
deflection angle ( 85 mrad) to guide the beamoutside the ring.
A sextupole magnet for excitation of the thirdorder resonance, v •=5/3, is located at the positionindicated in Fig. 1. Throughout the whole process frominjection to extraction, it is energized at the level
corresponding to the extraction beam energy, The effect of existence of such a rather strong sextupole
field during injection and acceleration stage is investigated by beam tracking with a computer. Typicalresult is shown in Fig. 2. It is seen that although
the effect of nonlinear magnetic field is observed, thebeam motion is still bounded and stable acceleration
can be expected Hith existence of such a sextupole
field. In this situation, rather large chromaticities
in both horizontal and vertical directions are anticipated, however tune spread of the beam with fractional momentum spread of ± 0.2% remains well inside
the triangular region surrounded with nearby resonances
as shown in Fig. 3. So we have decided to use the sextupole magnet with DC characteristics• as a resonanceexciter.
Table 1
Parameters of SloH Extraction System of TAR~ IIIon Species
Beam Energy
Extraction Scheme
Operating PointSeptum Position
Beam EmittanceFig. 1 Layout of the Slow Extraction System of TARN II.

Homentum Spread-309-p, a ~ Ne
150 ~ 350 MeV/u
Third Order Resonance Extraction( 1.6667' 1.80)
75 mm outside from centeral orbit
Circulating Beam ;:l; 50~r mm · mrad
~ 5~r mm · mrad
Extracted Beam

± 0.2%

1:5"""'0~'. t,;Fig. 3..
u0.008. Finally after the tune difference comes to0.0033, the beam begins to move on the separatrix
shown in Fig. 4(c) and its amplitude blows up. For
the purpose of checking the validity of such tracking,an analytical calculation of the unstable fixed points
and the separatrix is performeds assuming the beamemittance of 50n mm • mrad and the same orbit bump as
the tracking. The solid lines in Fig. 4(c) show theones obtained by such a calculation, Hhich coincide
Hell in global feature with the tracking result.
wnen the deviation of the beam from the central
orbit at the entrance of the ES exceeds the septum
position of t,he ES(75 mm in the present case), theresults are traced back to three turns before and thebeam positions at the whole circumference in theseturns are calculated. In Fig. 5, a typical example ofsuch calculation is shown. From the figure, it isseen that the largest deviation of the beam positionat other places than the ES occurs at the position of

0 2%
=.

at injection sta!'(e with fullresonance exciter.

BEAM BEHAVI0UR IN TR,oi.NSVERSE PHJ'.SE SPACE

Hardware equipments for the extraction systemdescribed above are listed up in Table 2 with theirmain specifications.
Beam Tracking during the Rxtraction Process
At TARN II, the horizontal aperture is basicallydesigned to be ± 100 mm, but it is limited at muchsmaller value as ± 70 mm at several places where
electrostatic pick-ups are installed. It is enevitable
to investigate the beam trajectory just before extraction over the whole circumference and make it sure it
can safely circulate in the ring until it enters into
the aperture of the ES. For this purpose, beam tracking is performed. Beam motion in transverse phasespaces is traced with use of transfer-matrix formalism.
The nonlinear element is treated with thin lens approximation. The beam momentum is kept at the certain
value because during the extraction process no RF voltage is to be applied to make flat time structure of theextracted beam. The horizontal tune of the ring is
gradually shifted from 1.75 to 1.6667 by changing theexcitation levels of quadrupole magnets linearly. InFig. 4, typical example is given for such a beam withcentral momentum and emittance of 50n mm • mrad. As theresult of the procedure (a) in the previous section,
the deviation of the bump orbit from the central orbit
and its derivative at the entrance of the ES as large
as 22 mm and -5. 2 mrad are taken into account. The behaviour of the beam in the horizontal transverse phasespace at the entrance of the ES is shown in Fig. 4(a)through the whole process from just after acceleration
to the end of extraction. In order to clarify thissituation, the beam behaviour is displayed separately
aecording to the horizontal tune in Fig. 4 (b) and (c).
The beam's motion is almost not affected by the nonlinear field of the resonance exciter and the beam circulates on a ellipse as shown in Fig. 4(b) while v •remains higher than 1. 68. Then the motion begins to be
distorted and the ellipse is distorted to triangularshape little by little after the distance from theresonance in the tune.diagram approaches closer than

0.00--0.01--"'~
0(a) throughout the whole process
BEM BEHe.\1]0UR IN TRI\NS\IERSE PHI'ISE SPACE

o.oo f----0.01-I-o.~_L05,_....~-~~..,o~~~~~...,o,J_o;;:s:-'-~--~o.1
0RBIT OEVIATIIJN (M)(b) v. = 1.75 -1.68

BE.A.M BEHAVI0UR IN TRANSVERSE PHASE SP.O,CE
0.01

Table 2Hardware Equipments for Slow Beam Extraction
Se,.,:tupole Magnet
Electrostatic Septum
Septum Magnet
Bump Coil 1II2II

3B"L/Bp = 0.3015 1/m• (DC mode)
E = 70-85 kV/cm, L = 1.0 m,
Deflection Angle = 5.8 mrad,
Septum Thiclmess = 0. 15 mm
B = 5 kG, L = 1.0 m,
Deflection Angle = 85.2 mrad,
Septum Thickness = 9 mmDeflection Angle = 5. 4 mrad
11=-7 .1 mrad
11=7.1mrad=(c) v u
1.670
Fig. 4 Beam behaviour in the horizontal transverse
phase space at the entrance of the ES.

-310-Table 3LAST THREE TURNS PLUS EXTRACTED BEAN

Turn Separation and Extraction Efficiency
0.1Condition ofCirculating Beam/'; p/pEmittance(%)
lmm· mrad)
0.25n~I..

o.oo.o5n5n50n50n50n"'"'

·0.1

-0.2
0.2
0.0
-0.2

TurnSeparation(mm)Extraction
Efficiency(%)

2.5
4.0
6.3
1.4
2.6
4.2

94
96
98
89
94
96

eooo
40
20
OISTA.NCE Al0NG THE BEA.Ii 0RBIT IHJ

Fig. 5 Beam positions in the horizontal direction
during last three turns just before extraction
and after deflection by extraction septums.
just before the ES and its size is assured toremain inside of the vacuum chamber in the Qr magnet
I± 95 mm). The beam positions in such three turns arestudied for all the beams with fractional momentum
spread of ± 0.2% and emittance from 5n (simulates beamwith very small amplitude) to 50n mm · mrad and arechecked to be well inside of the aperture of thevarious equipments distributed around the ring including the electrostatic pick-ups with the minimum aperture.
Qr magnet

Characteristics of the Extracted Beam
The turn separation (the amplitude growth of beamin three turns) just before entering into the apertureof the ES can be studied at the same time <-~ith the beam
Thetracki~~ described in the previous section.
results are surrunarized in Table 3 for various beam conditions. The turn separation of the beam is calculated
anal>~ically <-~ith the treatment given by D. A.
Edwards•. The calculated result for the beam withemittance of 50n mm• mrad and central momentum is 3 mm,<-~hich seems to be in good agreement with the above
result. The septum wire of the ES is 0.09 mm indiameter, hoHever its effective thickness is estimatedto be 0.15 mm considering the deformation and misalignment of the <-~ire. The extraction efficiency given inTable 3 is calculated assuming this value.
In order to estimate the emittance of the extracted beam, beam location in the horizontaltransverse phase space at the exit of the SM is calculated as shown in Fig. 6. In the calculation, the apx'(rddl

plied electric field on the ES is changed from 85 kV/cm
to 70 kV/cm from the beginning to the end of the extraction process to compensate the angle difference ofthe extracted beam at the entrance of ES depending on
the oscillation amplitude of the beam before extraction. During the slow extraction, the beam with thelargest emittance of 50n mm · mrad begins to be extracted at first and then gradually beams of the smaller eminttance are extracted according to the approachof the horizontal tune to the resonance and finallyvery small emittance (here we use 5n mm · mrad insteadof 0 from computational reason) beam near the equilibrium orbit is extracted. The instantaneous beamemittance is estimated ~ 2n mm · mrad. However, itvaries depending on time. Time integrated emittance ofthe extracted beam is estimated ~ 5n mm · mrad. In Fig.
7, the beam trajectory of the extracted beam is shownfor the straight section where the SM is located. It
is seen that all the beams deflected by the ES locatedupstream are guided into the aperture of the SM clearing its septum thickness of 9 mm.

.....
5Q",+a.2X",+O.Z~~ .6~~~:.-o.24

0.30

o.zo

0.100..

0~1Im)

Fig. 7 Orbits of the extracted beam at the straightsection where the SM is located.

o.oas

Acknowledgements~~~:!=SOn-,The authors would like to present their sincere
thanks to Prof. T. Nakamura at Cyclotron Radioisotope
Center, Tohoku Univers~ty for his continuous encouragement throughout the work. This work was supported bythe Grant in Aid for Special Research of Cancer of theMinistry of Education, Science and Culture. The computer calculations were performed with FACOM M780-10S
at the Computer Center of Institute for Nuclear Study.

,f••0.2Y.
0.080
SOn:,-0.27.
5n:,-Q.27.

References
0.075

0.10

0.11

0.12

0.13x(m)Fig. 6 The shape of the extracted beam in the horizontal phase space at the exit of the SH. Valuesof n e and /'; p/p in the figure represent ones
while circulating in the ring.

1) T. Katayama et al. , Contribution to this Symposium.
2) M. Yoshizawa et al., Proc. of the th Symp. on Accelerator Science and Technology, 1987, pp 175-177.
3) A. Noda et al., Contribution Paper to the 1989 Particle Accelerator Conference, Chicago, 1989, to bepublished.
~) A. Noda et al., INS Preprint, INS-NUMA-50, 1983.
5) E. J. N. Wilson, CERN 77-13, 1977, pp 111-138.
6) D. A. Edwards, Fermilab Preprint TH-842, 1978.

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