Investigation of Microwave Instability on Electron Storage Ring TLS Page: 3 of 3
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1.
41,
1A
V_
A
N
V0 10 20 30 40 50
Beam current (mA=2.5e9 e-)
Figure 5: Tracking results of microwave beam instability
of pipe radius approximately equal the bunch length (case
II). The labels and units are same as in Figure 4.
DISCUSSION
Results from particle tracking and from Oide's code
agree well in both cases I and II. In case I the bunch
length is less than b, the impedance can be capacitive to
the bunch, therefore the bunch sometimes shows
shortening in the potential well distortion region as seen
in the upper plot of figure 4. In the potential well
distortion region the energy spread does not change. The
threshold current of the microwave instability is about
130 mA. This value is larger than that derived from the
Boussard criterion of Eq.(1) which gives 32 mA. The shift
of bunch center toward positive z direction as bunch
current increases is the energy compensation of the bunch
for the energy loss due to the resistive part of the
impedance as shown in lower plot of figure 4. In the
microwave instability region the bunch not only shows
the bunch length and energy spread turbulence, presented
by the large standard deviation, but also executes rigid
dipole motion. The oscillation amplitude of the
synchrotron motion is vI times the standard deviation
shown in the lower part of figure 4. The oscillation
amplitude is about 4 a7 and 3.675 a>0 for (z, e).
In case II the bunch length is slightly longer than the
beam pipe radius, the impedance is inductive to the bunch;
therefore the bunch is lengthened in the potential well
distortion region as shown in the upper plot of figure 5.
There are two beam instability regions in this case. The
instability first onsets at beam current about 20 mA where
the bunch length is equal to the pipe radius like in case I
and companies rigid dipole oscillation. Beyond 40 mA,
the dipole oscillation disappears and the slope of the
bunch lengthening versus beam current is different. The
threshold current derived from Boussard criterion is about
6.7 mA in case II. The discrepancy between simulation
and Boussard criterion had been explained by Oide
[Ref.2]. The potential well distortion plays a role to
prevent the instability in the simulation. We count on the
simulation more than on the Boussard criterion since the
simulation reflects more reality of beam behaviour.6 37ooe/ /,
2
4 -
2
2 c
- <Zz4
The bunch length measurement shown in figure 1 can
be fitted by two resonator impedance models as shown in
figure 6. The resonance frequency is wY = c /0.005 with
Q = 0.51, Z/n = 2 Q and Q = 1, Z/n = 1.5 Q. Due to
a wide range of uncertainty in the broad band impedance
based on model dependent measurements, however, we
have used in our simulations the model with Q = 1, Z In
= 1 Q. Scaling to other values of Z In can be obtained
by simple scaling of the beam current.
Concluding from the above, the new measurement of
effective broad band impedance is higher than the old
measurement. However the determination of the broad
band impedance from the bunch length measurement is
sensitive to the choice of the beam pipe b. It is somewhat
ambiguous to use single b value in the calculation. In a
continuation of this work, we plan to include two broad
band resonators to model the storage ring impedance
more realistically. We also plan to explicitly include the
effect of a Landau cavity.
.14
measured data
13 = c/U.005, 0=0.51, vn=2
1.5 r= 01O 005, 0=1, N~n=1 5
1.3
1.25
r
S12
0
c 1.15
*1.1
1.05
10 2 4 6 8 10 12 14
Beam current (mA)
Figure 6: The bunch length measurement data compare
with two impedance with the same a, = c /0.005 and
Q=0.51, Z/n =2 Q or Q=1, Zin = 1.5 Q.
AKNOWLEDGEMENT
The authors would like to thank Dr. K. Oide of KEK
for kindly allowing us to use his code. We also like to
thank Dr. K. L. Bane of SLAC for providing us his input
example of the code and patient discussions.
REFERENCES
[1] M.H. Wang, et al.,"Longitudinal Beam Instability
Observation with streak Camera at SRRC", EPAC'96,
p. 1120. K.T. Hsu, et al., "Damping Rates of the SRRC
Storage Ring", PAC'95, p. 579.
[2] K. Oide, "Longitudinal Single-Bunch Instability in
Electron Storage Rings", KEK Preprint 90-10.
[3] D. Boussard, CERN Lab II/RF/Int 75-2 (1975).
[4] Alex Chao, "Physics of Collective Beam Instabilities
in High Energy Accelerator", Wiley 1993.
[5] K.L.F. Bane, K. Oide, "Simulations of the
Longitudinal Instability in the Damping Ring", PAC'93, p.
3339.
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Wang, M.-H. & Chao, A. Investigation of Microwave Instability on Electron Storage Ring TLS, article, May 17, 2005; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc884286/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.