The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

OBSERVATION OF QUADRUPOLE MODE FREQUENCY
AND ITS CONNECTION WITH BEAM LOSSTomonori UESUGI, Shinji MACHIDA, Yoshiharu MORI, Masanori IKEGAMI*, Koji NODA **, Shiro NINOMIYA ***,Akira MOCHIHASHI***, Toshiyuki OKI***, Dai ARAKAWA****, and Takeshi TOYAMA****High Energy Accelerator Research Organization (KEK) Tanashi branch
3-2-1, Midori-cho, Tanashi-shi, Tokyo 188-8501, Japan*Japan Atomic Energy Research Institute (JAERI)
2-4, Shirane, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan**National Institute of Radiological Science (NIRS)
4-9-1, Anagawa, Inage-ku, Chiba 263-8555, Japan***Research Center for Nuclear Physics (RCNP)
10-1, Mihogaoka, Ibaraki-shi, Osaka 567-0047, Japan****High Energy Accelerator Research Org~ization (KEK)
1-1, Oho, Tsukuba-shi, Ibaraki 305-0801, Japan
Abstra~t

Recent Simulation results imply that the number ofparticles in a high intensity synchrotron is limited by theresonance crossing of coherent mode oscillations, not bythe incoherent one. In order to verify it, we are doing theexperiments to measure tune shift of quadrupole oscillation and beam losses in several conditions in HIMAC
synchrotron at NIRS. In this paper, we discuss the beamloss in dynamic resonance crossing, where the operating
point is moving to cross the half integer resonance.
1 Introduction

It is believed that space charge effects limit the number of particles in a high intensity synchrotron. However,the detailed mechanism of beam loss is not clear. One
model tells that the incoherent tune of an individual
partcle is reduced by tl)e space charge field to a major
resonance line, and resonate with lattice field errors. Another model, proposed by Sacherer in 1960's[l], is thatthe coherent mode oscillations of a beam resonate withlattice field errors. The incoherent model is not selfconsistent because it neglects the time evolution of distribution due to the space charge force.
Recent simulation results seem to support the lattermodel[2]. In order to verify this, we planned to measure the tune shifts of coherent mode oscillations andtheir connection with beam loss. We present our observation of the resonant behavior with approaching operating point to resonant condition.

ing account of the observation of Voy = 3.5 resonance.
Around there, the bare tunes as the functions of defocusing field strength are well known experimentally, with6voy = 0.01 accuracy. They are
Vox

v0y=
=

3.651- 0.007588(/qd- 84.48)
3.280 + 0.05948(/qd- 81.80),(1)(2)

where Iqd is the current of defocusing quadrupole in theunit of A.
The stopband width of v = 3.5 line can be controlled
by a pair of quadrupole magnets (QDS) at the opposite
sides of synchrotron, excited in counterphase. The B' L
product of a QDS is expected 0.0156T at lA of QDS
current, which is calculated from the measurement forthe same device with higher turn number of excitationcoil. The maximum QDS current is ±lOA, /3y is 3.22m
there, and thus they expand the stopband width of(3)up to ±0.11.
Table 1HIMAC BEAM AND LATTICE PARAMETERS·particle
6MeVfu He2+maximum peak current ""2x1011 ppp(264,10)rrmm-mrad
100% emittance
momentum spread
0.1%
130m
circumference

2 Experim~nts

2.2 Observation of Beam Loss in Resonance Crossing
2.1 Accelerator and Its Equipments

All of our experiments. are performed at Heavy Ion
Medical Accelerator in Chiba (HIMAC) in National Institute for Radiological Science (NIRS), using 6MeV
He2+ beam. We took the flatbase operation without
RF. Beam and lattice parameters are listed in Tablel.
Laslett tune shift is -0.0446/10 11 ppp, and that of coherent breathing mode oscillation is the 5/8 times of it.
We chose the operating point of around (3,61,3.58), tak-We observed beam loss process with DC current
transformer (DCCT), bringing the operating point gradually to a half integer resonance Vy = 3.5 and over, along
the line described in eq.2. Four types of resonance crossing schemes, in Table.2, are attempted in several QDS
strengths. In the table, time t is measured after mastertrigger, where beam is injected at t=40msec.
The DCCT waveform is in Figure 1. In the casethat resonance is crossed downward (condition (a)(c)),
the timing of resonant beam loss is not clear, while it-429-The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

occur instantaneously in upward case ( condition (b)).
For (a) and (b), we defined the "critical tune" by theposition of the largest derivative of beam current, whichis converted to the vertical bare tune by formula 2. Incase (c), having no sudden drop of beam current, we defined it by the 60% loss of injected current. In condition(d), the injected beam current were too small to define
the resonant time of about t "'1sec. It may be becauseof the other resonance, Vx + Vy = 7, which is closer tothe start point of (d) than that of (b).
Table 2RESONANCE CROSSING SCHEMESID voy at t=O(a) 3.564-0.05948(1/sec)(b) 3.417+0.05948(1/sec)(c) 3.573-0.05948(1/sec)(d) 3.406+0.05948(1/sec)

The distance between critical tune and 3.5 means
the uncorrectable stopband width, together with somespace charge effect. What we are interested in is thatwhich tune, coherent quadrupole mode or some kind ofincoherent one, is responsible for half integer resonance.
However, our experiment does not have enough accuracy
to distinguish them, at the moment. The most serious
problem here is the ambiguity to define "critical tune".

,?'

!

(a)

ii

~ 3.54

t•

.

3.52

•

.. .

3.5

(b)

-,.

3.48

c:a.

(o)

a.

::0~

.

c
$.5

~

!'--ro~laos

Fig. 2 Critical value of bare tune to half integer resonance (a)(b). For (b), it is approximately-0.0015lqds + 3.476 in the region -5 < lqds·

0·0.5

(b)

0.

f~

3.46

0.5

c:a.
::0~

0.5

ci

0·0.5

c:a.

(c)

a.

::0~.
i.5;~

0.5

3.54 1-!·(·:.c....:l...............

0·0.5,............................. .Li ................

... ~·~"" 3.52~~

c:a.
a.

::0~

0.5

3.5 1-···l···········•···············'·························•·························•································l·····'

11$.5

0-o.5

0.5

1.52

3.48 !-·+··························+·······················+·······················+time( soc)

Fig. 1 The beam loss waveform when the vertical tunecrosses 3.5 resonance line. Those about several
stopband widths are superimposed. The symbol (a),...,(d) correspond to those in Table 2.
Figure 2 and 3 show the critical tune as the function of QDS current. Linear dependence are seen inseries (b) and (c). Its coefficients are -0.00153/A and+0.00166/ A, while the half of stopband width expectedfrom QDS field strength is 0.011/ A. The reason of thisdisagreement is not clear. We plan to calibrate the field
gradient of QDS.
Since there is no relation between QDS current andcritical tune in (a), the sudden drop of current in (a)may be independent of half integer resonance.

........................, ..

3.46 1-·!···························!························+························+····························+·······10·510IQDSFig. 3 Critical value of bare tune to half integer resonance (c). It is approximately -0.00165Iqds +3.532 in the region -3 < lqds·

3 Multi-Particle Simulation
In order to understand the behavior of emittanceblow up and beam loss in dynamic resonance crossing,
upward and downward, we employed a multi-particle
simulation. We discuss our simulation method and thefirst results here.

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The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

3.1 Simulation Method
Our simulation tracks the transverse motions ofmacroparticles. Axisymmetric focusing force are appliedinstead of alternating gradient focusing. Space charge
field is also calculated on the assumption of axisymmetric charge distribution. Generalized perveance is determined by that of KV beam with the same rms beam
sizes having 0.04 tune shift. Simulation parameters arein Table 3. Neither dispersion nor chromaticity is taken
into account.
Focusing force is variable linearly, in order to approach the operating point to resonance line.
Table 3SIMULATION PARAMETERSlattice
12 FO cell/revolutionstructure of a cell(length) F(0.1)+0(0.9)
no. of multiparticle
10000
particle distribution
waterbagno. of integration steps
100/cellno. of radial grid points
100/10rrms
aparture limitr < 6x(initial Trms)

~ 6~

><

3.5

(a)

3.51
revolution.e o.8~54
32
1
0 3.49(b)

3.5
revolution

:e 11

II

I! 0.8!o.&
10.4!o.&10.4.. '\.49

..

~ 0.2

~ 0.2

3.5

3.51
revolution

03.49

3.5
revolution

Fig. 4 Beam blow up and beam loss in dynamic resonance crossing. Hatched area shows the stopband.
[1] F.J.Sacherer, Ph.D.Thesis(1968).
[2] S.Machida, Proceeding of EPAC'98(1998).
[3] F.J.Sacherer, IEEE Trans.Nucl.Sci, 18(3)(1971).

3.2 Simulation Results
We simulated the dynamic resonance crossing. The
operating points started at (a)3.491 and (b)3.508,
and approached to 3.500 resonance with a speed of0. 7742 f 106 revolution, which is over 1000 times larger
than our experiment. Lattice error fields are applied in
2 of 12 focusing section, as ±1% error of field strengths.
After crossing v = 3.5 line, almost all particles arelossed. Fig.4 shows the blow up of rms beam sizes andbeam loss versus bare tune.
Unlike the results of our experiment (Fig.1), the behavior of beam loss does not differ between upward crossing case and downward one. In addition, the timing of
beam loss seems to be se~sitive to the aparture limit.
Simulation with realistic speed to approach is in process.

4 SUMMARY
We observed the beam loss, approaching the operating point to half integer resonance, in HIMAC synchrotron. The beam loss beh~vior was quite different between the resonance crossing direction. The tune where
the beam loss occur seemed to have linear dependence
on stopband width. We are performing a multi-particle
simulation in order to understand the beam loss behavior.

5 ACKNOWLEDGEMENT,We would like to thank the staff of Accelerator Engineering Company for the help of our experiment inHIMAC.
References-431-