OBSERVATION AND ANALYSIS OF BEAM POSIDON MOVEMENTDURING THE ACCELERATION OF NTT NORMAL CONDUCTING RING
M.Nakajima, K.Nishimura, A.Shibayama
LSI Laboratories, Nippon Telegraph and Telephone Corporation
3-1 Morinosato Wakamiya, Atsugi-Shi, Kanagawa Prefecture 243-01, Japan
Abstract
RF frequency modulation is not thought necessary for an electron
synchrotron above a few MeV at which electrons attain relativistic
velocitiesl. In our ring, however, though electrons are injected at 15
MeV; a slight increase in electron velocity(Pe) has proved to cause
serious horizontal beam position movement if electrons areaccelerated in constant RF frequency.
Introduction
The NTT normal conducting ring2 is an 800 MeV storage ring
dedicated to synchrotron radiation applications, which also functions
as a booster synchrotron for NTT superconducting storage ring3. A
15 MeV injection energy is adopted in order to conduct a feasibility
study of a low energy injection scheme.

According to the beam position measurement performed with
twelve position monitors, 10 to 20 mm horizontal movements areobserved in the early stage of the acceleration. The analysis hasshown that these movements are due to the increase in Pe· To solve
this problem, the RF frequency is modulated in proportion to Pe.
which makes it possible to accelerate electrons nearly on the constantorbit.
Lattice parameters
The ring has four long straight sections and four short straightsections with eight bending magnets (Fig. I). The designed lattice ·parameters are described in Ref.2. For insertion devices in the future,a Chasman-Green type lattice is adopted to obtain low emittance andto realize achromatic condition at long straight sections.
However, we. are operating in a non-achromatic condition. The
reason for this will be described later. The lattice functions derived
from the operating conditions are shown in Fig.2. Typical lattice
parameters are listed in Table 1.
Table 1
Lattice parameters referred to in this paper
Designed

In operationvx
vy

3.25

-3.14

1.25

-1.11

Momentum comp. (a)

0.022

0.042

Operatingpoint

Dispersion
function (TJ)at QFl

O.Om

1.5 m

at QF21.8m

0.7m

RF frequency

125MHzCircumference

52.76mBeam position measurement

Fig.l Layout ofthe ringQFl QD

BQF2

B

QD QFlFig.2 Lattice functions in operation

Twelve sets of four button type electrodes are placed in the ring inorder to measure beam positions in the storage mode (Fig.l,3). The
structure and the calibration method of the monitor are referred to in
the system used in Tristan AR4,5.
To meas~ a beam position during the acceleration, a set of fourelectrodes 1s selected and the signal from each electrode is coaxswitched every 2 msec to a heterodyne detection circuit. The raw data
!1fC sto~ in a data logger and are analyzed with a personal computer
mto pos1t1on data after a cycle of the acceleration.
As a position data is reconstructed from a series offour raw data, the beam position can be measured every 8msec. Beam losses in a shorttime(within 8 msec) are sosmall that no serious measurement errors are expected. The
beam size is large (over 10mm) near injection energy
because of the long damping
time while the calibration data
are derived from a test benchsystem with an antenna which
imitates the line beam. ThisFig.3 Beam position monitor
may cause calibration errors.

-279-According to the lattice parameters in Table I, electron rest energy
mc2=0.51 (MeV), and injection energy E=l5 (MeV), fatal movement( > 40 mm at QF2 ) is expected in the achromatic(designed) condition
while the movement remains allowable ( < 20 mm at QFl ), thoughstill large, in the operation condition. This is the reason why we areoperating in the non-achromatic condition.
Fig.4(b) shows calculated movement from Eq.(8), which is ingood agreement with the experimental results (Fig.4(a)).

0Nsg---c::~"'0t:>.

§II)

lXI

0.04./'./.12/.

t (sec)(b),..,//

Frequency modulation.16(a)//

llnjection~ ~-'~------------------------------------_J
Fig.4 Beam position movement(a) measured

From Eq.(3), I - ~e is only 5.4 x 10·4 at 15 MeV injection energy,
which quickly disappears in proportion to 1/(E+mc2)2. The RF
signal frequency from the synthesizer can easily be modulated inproportion to ~e (from 124.93 MHz to 125.00 MHz) in providing a
modulation pattern to the synthesizer from an arbitrary functiongenerator (Fig.5). No resonance frequency control of RF cavity itself
is required because of the low RF voltage at injection energy.
As a result of this frequency modulation, electrons are accelerated
practically on the constant orbit.

(b) calculated
LinacThe simulation has estimated this kind of errors to be less than a few
millimeters on the assumption that the horizontal beam size (<rx) is
about 10mm.
The beam position vs. time measured at one of the focusing
quadrupoles (QF1) is shown in Fig.4(a). The ramping rate is 150
MeVIsec. The beam position moves outwards in a horizontal plane
about 20 mm in 200 msec just after the injection.

\Analysis
Electrons above a few MeV can be accelerated with constant RF
frequency in the first electron synchrotrons which are small andcircular shape. Normalized electron velocity is expressed as~e = ( 1 - m2c4 I V{2 ) 1{2(1)Fig.5 Block diagram of RF frequency modulation system= ( I - m2c4 1 (E + mc2)2) 112(2)

where W is total energy and E is kinetic energy of an electron while
mc2 is electron rest energy. AtE = 2 (MeV), ~e is about 0.98 andorbit radius (R) is 2 % smaller than the final radius (Ro) after theacceleration. If Ro is 50 em, R increases only 10 mm during theacceleration.
On the contrary, this is not the case for the latest electron
synchrotrons, which are larger and have straight sections. In general,the beam position movement is calculated as a function of electronenergy as shown in below.
When E is sufficiently larger than mc2, Eq.(2) is approximated to(3)Conclusion
Beam positions were measured during the acceleration. Horizontal
movement due to the increase in ~e is observed. This problem caneasily be solved in modulating the frequency of the RF signal
generated from the synthesizer.
Acknowledgements
We would like to express our appreciation to all the members of
the synchrotron radiation facility at NTT for their kind advice andsuggestions.

If accelerated in constant RF frequency, the closed orbit displaces sothat orbit length(L) is proportionate to ~e· SoL changes as

MJL = - m2c4 I 2 (E + mc2) 2(4)which corresponds to momentum errordplp = 1la ' dL/L
= - m2c4 I 2a (E + mc2) 2(5)(6)

where a is the momentum compaction factor. As a result, horizontal
displacement is derived from dispersion function Tl
dX =Tj !}pip= - TJ m2c4 I 2a (E + mc2) 2(7)

(8)

-280-

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