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

A Beam Simulation of the Proton Storage Ring for the Neutron Science Project
Fumiaki NODA*, Michikazu KINSHO, Joichi KUSANO and Motoharu MIZUMOTO
Japan Atomic Energy Research InstituteTokai-mura, Naka-gun, Ibaraki-ken, 319-11, Japan* Hitachi, Ltd.
2-1, Omika-cyo, 7-chome, Hitachi-shi, Ibaraki-ken, 319-12, Japan
Abstract
We have started the design study of a 1.5GeV proton
storage ring for the Neutron Science Project at JAERI[1l. Thisring stores the 1.5GeV proton beam up to 2.5MW with charge
exchange injection. It is important for us to control a beamloss in the ring to meet the requirement for hands on
maintenance. For this reason, we have developed thesimulation cores for estimation of injection and storage
process. We have evaluated these processes using these newcodes. In this paper, some preliminary simulations oftransverse and longitudinal beam tracking for controlling thebeam loss are reported.
1. Introduction
Many technical problems in injection and storage
process have to be solved because storage beam power is very
high up to 2.5MW in our ring. Table 1 and Table 2 show theparameters of injection beam and preliminary ring,respectively. The peak current of injection beam(R) is 30mA,
and pulse length is 670nsec (filling factor is 60% ). At first, thenumber of turns in the ring is nearly 2780 which corresponds
to about 1.86msec in time. Injection turn number is very large,
so it is very important to reduce a foil hitting probability ofcirculating beam(H+). Secondly, the number of circulating
particles is 2.08 x 1014 at the end of injection, so we have toprepare a large ring acceptance. In the present estimation,transverse emittance is about 200n-mm-mrad for reducing thefoil hitting probability. On the other hand, the emittance ofinjection beam is very small (2:n:-mm-mrad, 100%-unnormalized). We have to expand the emittance of injection
beam up to 200:n:-mm-mrad using thepainting method Thirdly, we have to keep the bunchedstructure of stored beam in the ring during injection andstorage process, because we must use the fast (single tum)extraction method for the experiments of neutron science. If
we cannot keep the bunched structure, the beam loss at
extraction process increases. Finally, the circulating beam
current is very large. It is up to 50A at the end of injection. We
have to make the bunching factor sufficiently large for
reducing the effect of beam loading in the rf cavity which isused to keep the bunch structure.
For these reasons mentioned above, we have developed
two simulation cores (transverse and longitudinal) for
estimation of injection and storage process. In the following,
we report the brief explanations of these codes and somepreliminary simulation results.

2. Beam simulation
A. Transverse

The transverse simulation code is a multi particle
tracking com using transfer matrix method Basic input
parameters of this com are the calculated results of the MAD
which was developed at CERN, Bump orbits are produced by
one set of bump magnets for each direction x, y. We set thephase advance between bump magnets to be :n:. In thispreliminary simulation, we neglected the effect of spacecharge and momentum spread.
We have simulated some injection processes using thiscode. The magnet lattice is temporarily selected to be normal
12 cell FBDO lattice[2l. FBDO lattice is chosen forits smooth
betatron function around the ring. We assumed that

Table 2 Parameters of preliminary ring

Table 1 Parameters of injection beam
Energy{3yPulse structurex(100%,urmonnalized)

2.0 n:mm·m~ad£ y(100%,umonnalized)

2.0 n:mm·m~ad

momentum spread

±0.2%

E

TypeSuper periodicity
Orannstance

1.5 GeV
0.923
2.599
On: 400nsec
Off: 270nsec-350-12rell FBDO
12185 ill
2.599
1.49MHz'fiansition yciJculating frequency
Ring acceptance
OpeJating tune(nx,ny)

200 rcmm · mrad
(3 85,3 75)

Ope~ating cycle

50Hz00The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

the operatingtune(vx,vy) is (3.85,3.75). In the following, wereport two typical cases of painting process. The number ofmacroparticles of injection is 20 at a time and this beam isstored for 10 tums. For this reason, we cannot estimate theexact foil hitting probability due to the limited number ofsimulated particle, but we can compare the differences of theresults among various painting patterns. Figure 1 andFigure2 show the beam distributions at the end of the injection in thephase space and the x-y space respectively. In the figures, thesolid curves show the density distribution of the beam. Thebump orbits for x and y directions change as the following
function respectively.
easel:

B. Longitudinal· We have to extract the stored beam with fast extraction
method for the neutron scattering experiment. Kicker magnets
require about 150nsec for the field rise time, so we have to
make a non beam area wider than about l:SOnsec. Injected pul~ebeams have a 400nsec-on and 270nsec-off structure. We haveto maintain the bunch length growth with less than 120nsec.
To estimate this effect, we dweloped the additional
longitudinal simulation code. This simulation code is also amulti particle tracking code using the following difference
equations in longitudinal phase space.

!ill;,.= 11E; 11 _ 1 + qek,V.n(sin <!>in - U;,. / V..J

X=X0 +~(~f, Y=Y 0 +11y.Jl-f/',rh.

Case2:

X=Xo+ ~v=/',rh'fi,n1-f. Y=Yo+ t,y.J 1-f

Here x0(y0) is the offset, 11x(/1y) is the maximum distance ofbump orbit, tis the time and Tis the injection period. In easel,the shape of distribution in the x-y space is circle, and thedensity distribution for each direction is nearly Gaussian. Incase2, the shape of distribution in the x-y space is square. In
general, the circular beam is better than the square beam fromthe point of the view of stability. However, the foil hitting
probability is low and the ring aperture is small in case2,
because bump orbit can be reduced with painting process forboth x andy direction. These effects are important to design
our ring. From only these estimations, we cannot draw
conclusions which is better, easel or case2.
For the further calculation as the next step, we wiii
have to consider the effect of space charge force and estimate
the sensitivity of beam behavior for various lattice structures,for instance FBDO, triplet and so on.

'1\n-1+ 2n; ( hrJ~n /',E. )
n.

~~sp~
sp,'"

-in

Here E is the energy of beam, q is the charge state, e is 1, V isthe radio frequency(rt) voltage, U is the space-charge voltage
induced on the beam, cj> is the phase for rf voltage, Q is theangular frequency, P is the momentum of beam, R is theaverage radius of ring and 11 is the slippage factor, respectively.
The subscripts i and n are particle number and tum number,respectively. The subscript s stands for the parameter ofsynchronous particle. The phase of synchronous particle is 0,
because the beam is not accelerated in our ring. In this code,particle position is calculated each tum. The number ofmacroparticles is about 250 at a time and is stored In theabove equations, V consists of the space charge voltage U andthe additional capture voltage vcap which corresponds to thevoltage due to the momentum spread Firstly, we calculated
the capture voltage using the following equation.

- Kjf71P~n:3B2(/',p)2

eV~-Bep

Here K is the dilution factor, 11 is the slippage factor, ~ is therelativistic velocity, E is the energy of beam, B is thecorrection factor for bunched beam and £ is the charge to massratio.

0,015

0,01

0.01

0.005

0.006
0.004

'il~ 0.005!o;..

0·0.005.(),004

·0,01

·0.02

00.02

0.04

0.06

x[m]

·0.04

·0.02

00.02

0.04

·0.04 ·0.02

y[m]

0.04

0.04

0.02

0.02

~000.02

0.04

x[m]

·0.04

.().02

0

0.02

y[m]

~0·0.02-0.02·0.04 L....,.-~-~~-~·0.02
00.02 0.04 0.06
x[m]-0.04 L....,.-~-~--......-0.04 -0.02
00.02 0.04
x[m]Fig.l Beam distribution in phase and real space

Fig.2 Beam distribution in phase and real space-351-0.04

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

In the present simulation, we took k=2, 11=0.068 and B=0.6.
We assumed that 6. p/p was ± 0.49% to avoid the longitudinalbeam instability, but we did not include longitudinal painting.
Then Vcap becomes about 13.5kV. Secondly, we calculated thespace-charge force using the following equation.

U =- egaR dA.
2EoYz· ds
Here g0 is the geometrical factor, E 0 is the penneability of freespace, y is the relativistic energy and dA/ ds is the longitudinal
gradient of electric charge in the beam. Here we neglected theeffects of inductive wall current in beam duct. We assumed thatthe ratio of beam radius and beam duct radius was 1.5 and g0
was 1.81, respectively. If the beam distribution has aparabolic distribution, the space-charge voltage induced on thebeam is about 7.5kV. Total rf voltage becomes 21kV.
We simulated the storage process using this code. We
assumed that the distribution of injection beam is uniform andthis beam is stored for 100 turns. We calculated the stored
beam distribution each turn. The rf voltage at start is 13.5kVand increases to 21kV during the injection. At first, wesimulated the longitudinal motion with only first hannonic rf
bucket (easel). Figure 3 shows the beam distribution at theend of injection in a longitudinal phase space. The horizontal
axis shows phase for radio frequency. In this figure, the solid
curve shows separatrix for the first harmonic rf voltage. The
bunch length in time increased from 400nsec to 425nsec. But
it was well contained within 120nsec. The bunching factor
is to be about 0.33. We analitically estimated that bunching
factor was 0.4 from filling factor and parabolic distribution,
but result of simulation showed that bunching factor issmaller than the estimated value. Secondly, we simulated thelongitudinal motion with the first and second hannonic rf
buckets for reducing the space-charge force at the beam centerand increasing the bunching factor (case2). We took the rf
voltage of second hannonic to be 10.5kV which is half of thefirst harmonic voltage. Figure 4 shows the beam distribution
at the end of injection in a longitudinal phase space. In thisfigure, the solid curve shows the separatrix for the sum of thefirst and second harmonic rf voltages. This result shows thatthe density distribution is close to uniform shape, andbunching factor is bigger than case 1. In this simulation, thebunching factor is about 0.45. The maximum momentum
spread is smaller, and the beam size becomes smaller comparedto the result of case 1.
As the next step, we will estimate the effect of beamloading, the effect of the barrier bucket and necessity of
longitudinal painting.

3. Summary
We started the study of the 1.5GeV Proton Storage
Ring for Neutron Science Project at JAERI. We havedeveloped the beam tracking cores for transverse andlongitudinal orbit. We estimated the effects for the beam
injection and the storage process in our ring which has 12cell
FBDO lattice. We can summarize these results of theestimations as follows: First, the foil hitting probability
becomes small using painting method Secondly, thebunching factor becomes big and momentum spread becomes
small using the second harmonic bucket. Finally, the bunch
structure of the stored beam is well kept. We will have toestimate a detailed study of injection and storage process toobtain more precise results. For instance, we have to consider
the effects of space charge and the effect of momentum spreadfor transverse tracking code, and the effects of the beam loading
for longitudinal tracking code. In the future, we will couple thetransverse tracking with longitudinal one in order to study
these effects in detail.

4. References[1] M.Mizumoto et al, A High Intensity Proton Linac
Development for Neutron Science Research Program XVIII
Intemational Linac Conference, LINAC96, Geneva,
Switzerland 26-30 August 1996, p662-664[2]M. Kinsho et al, : A Preliminary Study of the Proton
Storage Ring for the Neutron Science Project at JAERI, inthese proceeding

0.5

'if.

.:::-0B -0.5
-1-1.5-4-3-2-1

0

2

3

4

ifJ[rad]ifl[rad]Fig.3 Longitudinal phase space distribution

Fig.4 Longitudinal phase space distribution-352-