High beam current storage at low energy for compact synchrotron

High beam current storage at low energy for compact synchrotron radiation
rings (invited)
H. Takada and Y. Tsutsui
Sumitomo Electric Industries, Ltd., Osaka Research Laboratories. Shimaya, Konohana. Osaka 554, Japan
T. Tomimasu and S. Sugiyama
Electrotechnical Laboratory, Umezono, Tsukuba, Ibaraki 305, Japan
(Presented on 1September 1988)
A study ofhigh beam current storage at a low energy is being conducted on the compact electron
storage ring NUl-I. In general, it is said that the stored beam lifetime is rapidly shortened as the
beam energy decreases, and the high beam current storage is difficult to obtain. However, a stored
beam current above a 350 mA was obtained at an injection energy of 100 MeV, and the lifetime of
the stored beam is considerably long. For example, e-folding lifetime is about 2 h at 100 MeV. In
this paper, we estimate the beam current decay rate due to the residual gas scattering, the ion
trapping effect, and the Touschek effect, and make clear these contributions to the beam lifetime.
It was clear that the Touschek lifetime is lengthened according to the bunch size growth, which is
roughly explaine<;l by the longitudinal coupled bunch instability.
INTRODUCTION
Low-energy injection is of great benefit to the compact SR
(synchrotron radiation) source for industrial use, because it
enables a low-cost system. However, it is not easy to store a
high beam current at low energy because of the short beam
lifetime and the beam instabilities. The compact SR ring
NIH-l was constructed by Electrotechnical Laboratory and
Sumitomo Electric Industries, Ltd. I Its main purpose is to
investigate the above-mentioned problems.
The shortening of the beam lifetime at a low energy is
mainly caused by the Touschek effect, but the ion-trapping
effect and beam instabilities may also affect the beam lifetime significantly. Actually, it is reported that the SR ring,
Aladdin, of the University of Wisconsin was not able to obtain high beam current without an ion clearing system. 2
Also, in NIH-l ion trapping has harmful influences at a high
beam current, and the ion clearing is necessary in order to get
the beam current above 200 mAo
The observed decay of the stored beam current is considerably affected by the beam size change. This means that
the Touschek effect has significant influence on the beam
lifetime. The Touschek effect, first observed on the small
storage ring AdA, 3 has been mainly theoretically studied4 - 9
and several experimental interpretations were also tried. 3 ,8,9
But experimental studies for a low-energy and high-current
beams have been lacking.
We have been quantitatively investigating the Touschek
effect and other mechanisms which have great influences on
the beam lifetime at a low energy.
In Sec. I, the effects of the gas pressure and the ion trapping are evaluated. And the Touschek lifetime is discussed in
connection with the bunch size growth at a low energy in
Sees. II and III.
Figure 1 is a photograph of the NUI-l and the main
parameters are tabulated in Table I. The first beam storage
was obtained in February 1986 and after several improve1630
Rev. ScLlnstrum. 60 (7), July 1989
ments stored beam currents ofabove 400 mA at a beam energy of 150 MeV and of above 350 mA at 100 MeV were
achieved.
I. DECAY OF STORED BEAM CURRENT
If the rf accelerating voltage is enough, the following
mechanisms are considered to be the causes of the decay of
the stored beam current, (A) the Tousch~k effect, (B) the
residual gas scattering, and (C) the ion trapping effect. It is
necessary to evaluate these effects quantitatively in order to
store high beam current at low energy.
A. Touschek effect
Electrons in the same bunch scatter each other elastically due to their betatron oscillation. If the change of longitudinal momentum after collision exceeds rf acceptance, these
"
FIG.
I. Photograph ofNIJI-1.
0034-6748/89/071630-06$01.30
© 1989 American Institute of Physjcs
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TABLE I. Main parameters of.NIJI-1. Parentheses signify rQJltine operation." .
."
".
,.
where Z is the atomic number of the gas. And tJc is given by
. tJ =
80-160 MeV
230 Mev
13.256m
0.7m
( 1.37)
( 1.57)
(0.46)
7
158.4 MHz
2kW
Injection energy
Maximum energy
Circumference '
Bending radius
Horizontal betatron tune
Vertical betatron tune
Momentum compaction factor
Harmonic number
Radio frequency
Maximum rf power
A ( 7 )
..J(pz)Pz.
c
where A is the vertical half aperture of the vacuum chamber
at the bending section, (P z) is the average vertical betafunction, and Pz is the maximum vertical beta-function at
the bending secti~J.' . ..
.. .
.
The decay rate due to this process is given by
1
dII· = (0'1+ 0'2 + O'3)dmcI
dt v '
= 3.217X 1022 (0'1 + 0'2 + O'3)cPI,
electrons are lost. This process is referred to as the Touschek
effect.
'.' .
'
..
The decay rate ofthe stored beam current due to ~his
effect is expressed b y '
. .
.
dII = aI 2,
.. (1)
dt T
1
where I is the stored beam current.
Assuming that the vertical component of the transverse
mo~entum is much less ,than the horizontal componentand
transverse momentum is nonrelativistic, a is given by ,the
.
following formula4 : .
_
a=
C(E)
r
!ii~c,C(€)
.
".
O'~ (AE / E) ~ax Velr r
~ e- E +'.!-. f.oo
= -
2
.
+
2
E
(3€-€ln€+2)
2
= -ln€-2.077
(2)
In u e- "du
U
f.oo -e-"- d u
E
for
(3)
U
€~I,
where 70 is classical electron radius, c is the velocity oflight,
r is Lorentz factor, O'~ is the horizontal beam divergence,
(AE / E) max is the maximum relative energy deviation accepted by the rf system, Vis the bunch volume, e is the electron charge, Irr is the rf frequency, and € is defined by
[(AE /E)max/( rO'~) ] 2.
B. Residual gas scattering
The total cross section which causes beam loss is composed of the Rutherford scattering due to nuclei, the bremsstrahlung due to nuclei, and the Moller scattering due to
atomic electrons, these cross sections are given by
41Tdz 2
0'1=
2tJ2'
r
0'
4
2
=--7
2
137
(4)
c
0
Z Z
(
(4-In
I - -65)In-183
3
(AE/E)ma;
Z1/3'
+ I)
(5)
21T~Z
1
0'3 = - - - x - - - - r
(AE/E)max
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Rev. Sci. Instrum., Vol. 60, No.7, July 1989
(6)
(8)
where d m is the density ofgas molecules, and P (Torr) is the
pressure of the gas.
In NUI-l the components of gas molecules are mainly
CO·and H 2 and the ratio of their partial pressure is almost
1: 1 by measuring mass spectrum. The partial pressures of
CO and H 2 are estimated with a monitored pressure, taking
into account this ratio and the difference of gauge sensitivity
for each kind of gas. The decay rate due to the residual gas
scattering is calculated from these partial pressures.. Although the cross section increases as the beam energy de~
creases, SR induced gas desorption'is reduced at low" energy;
Therefore, I- dI / dt Iv is not a: maii!. cause of lim~ting beam
lifetime at low energy when the vacuum condition is good.
At present, total pressure is almost 1 n Totr at a beam energy
of 150 MeV and a beam current of 100 mA, and in this condi7
tion the contribution of I- dI/dt Iv to the. tota,l measured
decat ratel:'- dI/dt 1m is estimated to be about 20%.
c. Ion trapping effect
In NIH-1 vertical beam widening and betatron tune
shift and spread are observed as the stored beam current
increases. These phenomena are caused by ion trapping...
Assuming that the charge of ion is + 1, that transverse
distribution of ions is a gaussian distribution which is a duplicate of that of the electron beam and that an 'electric field
produced by ions is linear, the betatron tune shift Avx,z is
given by
J
O'z,x d ; Px,zds,
(9)
O'x + O'z
where d; is the density of the trapped ions, O'x,z is the transverse beam size, PX,z is beta-function, sis longitudinal length,
and x and z means horizontal and vertical directions. Accordingly, d; can be estimated by measuring Avx,z and O'x,z'
The betatron tune is measured by the rf-knockout method
and the transverse beam size is measured by using the arrayed photodiodes.
In calculating, we use the average beam size which is
estimated according to the following relations:
Avx,z
= -70
r
(O'x,z)
=
LL O'x,z (s)ds/L,
O'x (s) =..J €xePx (s)
Industrial application
+ rp<s)(~E /E)2,
( 10)
(11)
1631
(12)
Uz(s) =..jEz f3z(S) ,
8E)2
(Ii
E
z
=
U
1
2·
= [U xO (so) - Exo f3x (SO)] r/(SO) ,
~, (so)
f3z (so)
,
(13 )
(14)
where L is the circumference of the ring, Exo is the natural
horizontal emittance, and U x 0 and U z 0 are the observed horizontal and vertical beam size, respectively, at the longitudinal position s = So in the ring.
In order to suppress the ion-trapping dc ion-clearing
field is applied to button electrodes which are the same ones
used for the beam position monitor installed at three points
in the ring. Figure 2 shows the clearing voltage dependence
of the ion density di estimated by using Eq. (9). The ion
density rapidly decreases and is almost saturated as the
clearing voltage increases, and this saturating voltage is reduced as the beam energy decreases as shown in Fig. 2. This
tendency can be interpreted with bunch size growth by decreasing energy which results in the reduction of beam potential. Bunch size change is described in detail in the following section.
The influences on beam lifetime due to ion trapping are
thought to be from the trapped ion scattering and the change
ofTouschek effect due to the beam size change, as long as the
operating point is not shifted to the dangerous resonance
line. In order to understand them quantitatively the decay
rate due to the trapped ion scattering I - dI / dt I; is calculated by use ofestimated d;. Figure 3 is an example of the decay
rate plot. As shown in Fig. 3, the measured decay rate
I - dI/dt Im without ion clearing is less than that with ion
clearing in the beam current range 20-150 mAo This can be
explained by the decrease ofTouschek effect due to the vertical beam size growth. Therefore in this region ofstored beam
current, the Touschek effect has a much greater effect than
that of trapped ion scattering. This agrees with the evaluated
value of! - dI/dt I;.
Above 150 mA, the measured decay rate without ion
clearing considerably increases as the stored beam current
increases. But an ion clearing suppresses the fast decay in
high beam current and allows us to obtain more current. The
5r------~-----__._____,
.aOMeV
o
150MeV
""
I
FIG. 3. Decay rate of the stored beam current as a function of the stored
beam current with clearing dc voltage of 0, - 0.2, and - 0.4 kV. Solid lines
indicate measured decay rate and broken lines show estimated decay rate
due to the trapped ion scattering.
evaluated I - dI/dt I; considerably decreases as clearing
voltage increases, and the ratio of I - dI / dt VI - dI/dt 1m
can be reduced to about 10%.
As a result, the ion trapping effect may limit stored
beam current and shorten lifetime at high beam current
without ion clearing, but an adequate ion clearing system
can supress this.
II. BUNCH SIZE
A. Bunch size growth
Since the Touschek lifetime depends on the bunch volume as in Eq. (2), it is important to know the bunch size.
The horizontal, vertical beam size U x ' U z and the bunch
length u/ is given by
Ux =..jEx f3x
+ rlc uE/E) 2 ,
(15)
Uz = ..jKEx f3z,
(16)
u/ = (cap/OJ s )/(uE/E),
(17)
E
'0
FIG. 2. Trapped ion densities vs ion clearing dc voltage. Ion densities with
100 rnA at 80 MeV and 150 MeV are indicated by closed circles and open
circles, respectively.
where K is the coupling constant of betatron oscillation, Ex is
the horizontal emittance, 1] is the dispersion function,·
(uE/E) is the energy spread, a p is the momentum compaction factor, and OJ s /21T is the synchrotron frequency.
In NUl-I, the observed bunch size is much larger than
the natural bunch size. At first, it was thought to be caused
by both the longitudinal coupled bunch instability and the
multiple intrabeam scattering in a bunch. 10
The frequency spectrum of the beam signal shows several side bands separated by the synchrotron frequency around
the harmonics of the revolution frequency, and these side
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x
o
------0
c
o
-0-
o
0.5
Vdc (kV)
Rev. Sci.lnstrum., Vol. 60, No.7, July 1989
1632
bands do not disappear even if a beam current decreases to
0.1 mAo Therefore, the growth of the longitudinal coupled
bunch instability is significant in NIH-I.
The bunch size, due to the longitudinal coupled bunch
instability, is determined by the balance ofthe growth and
the damping rate of the instability. The bunch length and the
horizontal beam size due to this effect is given byll
O'JO'/O = (lIIth
O'x = ~Exf3x
(18)
)0.2,
+ rl(O'EIE)2(lIIth )0.4
for I>Ith , (19)
where I th is threshold current and 0'/0 and (O'EIE)o are the
natural bunch length and energy spread, respectively.
The bunch size growth due to the multiple intrabeam
scattering is expected to be not significant above 200 MeV.
Therefore, we investigated at a beam energy of21O MeV and
at lower energies in order to distinguish this effect.
B. Stored beam current dependence
The observed horizontal beam size O'x and the bunch
length 0'/ depend on the stored beam current as shown in Fig.
4(a) and (b). They are almost proportional to 1°·2 at both
energies of 80 and 210 MeV. This dependence agrees with
the theory of the longitudinal coupled bunch instability,
even though multiple intrabeam scattering is expected to be
dominant at a beam energy of 80 MeV.
The beam current dependence of the vertical beam size
O'z is larger than that of O'x, however, it cannot be fully explained yet.
As a result, the bunch volume V = (41T) 3/2 0'xO'zO'/ increases almost linearly as the beam current increases, and
the Touschek lifetime is almost constant against the beam
current.
(a)
.80MeV
o 210MeV
200
E~
.;; 100
..§.
C. Beam energy dependence
The beam energy dependence ofthe observed bunch size
is shown in Fig. 5. It is noteworthy that the bunch length
increases just a little as the beam energy decreases. According to the theory of longitudinal coupled bunch instability,
the bunch length is independent of the beam energy because
the energy dependence of I?i,2 and 0'/0 are compensated in
Eq. (18). If the multiple intrabeam scattering was dominant, the bunch length could be expected to considerably
increase as the beam energy decreases from 210 MeV. Consequently, the bunch size growth due to the multiple intrabeam scattering is much less than that due to the longitudinal coupled bunch instability.
The energy dependence of the horizontal beam size O'x
also mostly agrees with the theory of the longitudinal coupled bunch instability. In addition, the vertical beam size O'z
increases rapidly as the energy decreases below 150 MeV as
shown in Fig. 5. Consequently, the bunch volume enlargement against the beam energy is considerable.
D. rf accelerating voltage dependence
In routine operation in NUl-I, the rf accelerating voltage Vrf is empirically chosen to be about 24 kV to obtain
high injection efficiency and long lifetime, then the overvoltage factor is very large. Accordingly, the synchrotron
frequency OJ s 121T is almost proportional to V~(2, and
0'I ex V rf- 0.2 and 0'x ex VOr f·3 are expected by the theory of the
longitudinal coupled bunch instability. These dependencies
almost agree with the observed data as shown in Fig. 6. The
vertical beam size does not change much and is almost constant against the rfvoltage. As a result the bunch volume is
nearly constant against the rf voltage. because the dependence of the O'x and the 0'/ almost compensate.
Normally raising the rf voltage is not very effective in
extending the Touschek lifetime, because the bunch volume
is reduced with the rf voltage. But when the longitudinal
coupled bunch instability occurs, the bunch volume is not
reduced and it helps the Touschek lifetime to extend as the rf
voltage increases.
50
10
20
50
100
200300
Vrf=24kV
I=100mA
I (mA)
2.0
(b)
•
(Jx
.... (Jz
1 80M V
r
e
o
(Jx
"(Jz
_
r 21 OMeV
1.0
.s
10
'C:
..§.
0
05
~
0.5
~
100
0
E
E
'oS
c O'.e
I
20
200
E
O'x
0
E'O.5
0
o
.s
~
00
O'z
0.2
02
0.1 l.--=':5o:-------:-10~0:----:2:-:070 -:::3700;;---- 10
0.1 5
10
20
50
100
200 300
E (MeV)
I (mA)
FIG. 4. (a) Horizontal, vertical beam size (ITx,ITz ) and (b) bunch length
(IT,) measured at 80 and 210 MeV as a function of the stored beam current.
FIG. 5. Horizontal, vertical beam size (ITx,ITz ) and bunch length (IT,) vs
electron energy E. Solid lines indicate the dependencies of E - 0.5 for ITx and
constant against E for IT/.
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Industrial application
Rev. ScLlnstrum., Vol. 60, No.7, July 1989
1633
10' ...---,--....,..--,---.
E=110MeV
I=100mA
(JQ.
2
E
E
'0 1.0
~
V~
o
Vrf=24kV
200
O•2
E
~03
100
E
~
~
~
50
0.5
10
20 30
Vrf (kV)
FIG. 6. Horizontal, vertical beam size (O'x,uz) and bunch length (0',) vs rf
accelerating voltage Vn" Solid lines indicate the dependencies of V~i' for O'x
and V,r 0.2 for 0'" and the broken line indicate constant against Vn"
1 o35':;o:----:1-=o";:"o--1:;-;5~0:---::2:':OO::---:2:-!50
E (MeV)
FIG. 8. Energy dependence of the Touschek lifetime with V,r = 24 kY. The
error bar shows the variation of I - dI I dt 1/ taken at stored beam currents.
Solid line indicates the calculated value by Eqs. (I )-( 3) substituting observed bunch volume.
III. EVALUATION OF THE TOUSCHEK LIFETIME
As described in Sec. I, the decay rate due to the Touschek effect is estimated by
1- I = I- I -I - I-I - I'
df
dt
df
dt
T
df
dt
m
df
dt
i
(20)
v
where I - df I dt Ii is sufficiently reduced by ion clearing. An
example of this separation is shown in Fig. 7. It is verified
that the beam lifetime is mostly determined by the Touschek
effect and the Touschek lifetime f 11- df Idt IT is almost
constant against the beam current because I- df I dt IT is
almost proportional to 1.
The beam energy dependence ofthe Touschek lifetime is
shown in Fig. 8. And the solid line indicates the calculated
value by use of Eqs. (1)-(3) substituting the observed
bunch volume. Both f II - df Idt IT' by the use ofEq. (20)
and the solid line have a minimum of around 150-180 MeV,
and these tendencies are caused by the remarkable growth of
the bunch volume as the beam energy decreases.
Although Eqs. ( 1)-( 3) have some assumptions and approximations, the Touschek lifetime calculated by use of
Eqs. (1 )-(3) roughly agrees with the value estimated from
the measured decay rate as shown in Fig. 8. As a result, it was
found that the Touschek lifetime can be evaluated by use of
Eqs. (1)-(3), even if the stored beam size is considerably
enlarged by the longitudinal coupled bunch instability at low
energy.
IV. CONCLUSIONS
FIG. 7. Decay rate separation into that due to the Touschek effect, that due
to the trapped ion scattering and that due to the residual gas scattering.
Open circles represent the measured decay rate. Broken line and dashed line
show estimated decay rate components due to the residual gas scattering
and due to the trapped ion scattering. Closed circles indicate the measured
decay rate subtracted by these components.
The beam loss mechanism in low energy was investigated quantitatively in the compact SR ring NUl-I.
Although the ion trapping may harmfully affect the
stored beam, the beam decay due to this effect can be reduced by ion clearing. Consequently, the Touschek effect is
the main cause which determines the beam lifetime.
Since the Touschek effect depends on the bunch volume,
the phenomena which affect bunch size are very important.
In NUI-l the bunch size growth is remarkaple and it is
roughly interpreted with the longitudinal coupled bunch instability except for the vertical beam size. In general, the
bunch size growth at low energy is expected to be mainly
caused by multiple intrabeam scattering, but our results indicate that multiple intrabeam scattering makes a small contribution by taking into account the energy dependence of
the bunch size. The vertical beam size growth may be caused
by other instabilities or the residual ion trapping, but cannot
be fully explained now. The energy dependence of the Touschek lifetime is also affected by the rapid bunch growth as
the beam energy decreases, consequently the lifetime has a
minimum of around 150-180 MeV and becomes long at lower energy~
Since the Touschek effect is reduced by the bunch size
1634
Industrial application
E=150MeV
Vrf=24kV
Vdc=-lkV
5.0
2.0
o
c
'E
0
0
..
0
0
o •
•
0
0
"- 1.0
«
E
0
0
I
/;
II
0
~
'6 0.5
0
"......
"
I
0
0
0
I
/f
I
0.2
//1 /
0.1
1
1
1
005
1
10
20
1
I
/
/
/
50
100 200
I (rnA)
Rev. ScLlnstrum., Vol. 60, No.7, July 1989
growth due to the longitudinal coupled bunch instability or
multiple intrabeam scattering, the shortening of the beam
lifetime at a low energy is confirmed to be no longer serious.
But the other phenomena which are occasionally observed in
NUl-I, such as an abrupt beam loss and an unusual fast
decay, are apt to occur at a low energy. Further investigation
of these problems has to be continued.
Electrotechnical Laboratory, and engineers of Sumitomo
Electric Industries, Ltd. for their support.
IH. Takada, K. Furukawa, and T. Tomimasu, Opt. Eng. 27, SSO (1988).
2B. Schwarzchild, Phys. Today, March 19 (1986).
3c. Berrardini, G. F. Corazza, G. Di Giugno, G. Ghigo, J. Haissinski, P.
The authors would like to thank the staff of the High
Energy Radiation Section, Quantum Technology Division,
Marin, R. Querzoli, and B. Touschek, Phys. Rev. Lett. 10, 407 (1963).
4H. Bruck, Accelerateurs Circulaires de Particules (Presses Universitaires
de France, Paris, 1966).
sB. Gittelman and D. M. Riston, HEPL-291, Stanford University (19Q3).
6U. V6lkle, DESY 67/S (1967).
7H. Wiedemann, PEP Note-27, SLAC (1973).
8H. Bruck and J. Le Duff, in Proceedings ofthe 5th International Conference on High Energy Accelerators, Frascati, 1965, p. 282.
9y' Miyahara, Jpn. J. AppI. Phys. 24, L742 (198S).
10M. S. Zisman, Lawrence Berkeley Laboratory Report No. LBL-19l91
Preprint (198S).
liS. Asaoka, G. lsoyama, H. Mikuni, Y. Miyahara, and H. Nishimura,
NucI. lnstrum. Methods 215, 493 (1983).
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ACKNOWLEDGMENTS
Rev. Sci.lnstrum., Vol. 60, No.7, July 1989
1635