COHERENT SYNCHROTRON RADIATION ANALYSIS FOR THE PHOTOINJECTED ENERGY RECOVERY LINAC AND UVFEL PROJECTS AT THE NSLS. Page: 4 of 5
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bunch is being compressed, the head particles have higher
energy, the energy spread keeps growing due to the CSR
vertical stretching, and reaches the peak value at the middle
straight section. Then during the decompression, the head
particles now have lower energy, the energy spread is ef-
fectively reduced due to the CSR effect. In our PERL case,
when the bunch entered the compression part of the arc,
the local energy spread was 4.66 x 10-4. When it comes to
the middle straight section, the local energy spread grows
to be 5.32 x 10-4. After the decompression, the local en-
ergy spread reduces to be 4.76 x 10-4. This CSR induced
energy spread cancellation mechanism ensures the energy
- -. -.'
(' nil prti wr t
Figure 1: Longitudinal emittance cancell
and the CSR induced energy spread. The full emittance
dilution for the coherent process could be written as 
c2 ,l.z E2 [(Ax2) + (a (Ax21 + (Ax121)2
(x2) = (JRib (s) d ds )
(Ax'2) = (1R26 (s) dds .
a is the relative energy spread, Eo is the initial emittance,
a and # are the Twiss parameters at the end of the beam
line. If the bunch length is constant, then the CSR induced
d is constant. Hence d could be factored out from the
integration. Therefore, if the lattice is designed such that
f Ri(s)ds = 0 and f R26(s)ds = 0, then no net emit-
tance growth is expected, even though it may oscillate.
In a bunch compressor, either an Arc or a Chicane, the
.r. bunch length is no longer a constant, hence, d is no
Ik-oriuni prc.r longer a constant. So, along the beam line, the CSR kicks
will have different strength. The CSR kick originated at
nation mechanism. location x will cause the electron to follow a betatron os-
cillation in the downstream beam line. Hence, the trans-
verse emittance is modified. In periodic structure, we then
could adjust the lattice design such that there will be a half-
0% integer phase advance[E7 between two identical cells, there-
fore, two CSR kicks will be 180 out of phase, and this
leads to the cancellation.
In Fig. 3, we demonstrate an ideal case. The particle
was initially following the solid line, due to the CSR, it
is kicked to the dashed line. After it traverses a cell, it
meets a second kick with the same strength. If these two
kicks are (2n+1)7r in betatron phase away from each other.
The second kick will bring the particle from the dashed line
back to the solid line. So, the CSR induced kicks cancel
0 500 with each other pair-wise. In the real case, the two kicks do
not have the same strength, but as long as there is a half-
or 1 OMnusl integer phase advance between them, they are 180w out of
phase, hence they cancel partially.
Figure 2: The variation of the bunch length and the energy
The R56 in a chicane compressor, has an opposite sign
to that in the arc compressor. During the compression, we
need to chirp the bunch so that the head particles have lower
energy, and the tail particles have higher energy. Due to
the CSR effect, the head particles will gain energy, hence
the bunch gets compressed also in the vertical direction,
therefore, a smaller energy spread.
2.2 Transverse Emittance
In the dispersion region, the chromatic transfer function
introduces correlations between the transverse phase space
3 PERL ARC COMPRESSOR
In the PERL project, we use two arcs as bunch
compressors. In our design, the beam initial parameters
are: Ut = 3 ps, En = 0.5 7r mm - mrad, z ~ 9.3 x 10-4
at E = 25 MeV, and Qo = 0.15 nC. The bunch is chirped
during the acceleration to 300 MeV, then it enters the
small arc, where the bunch is compressed to Ut = 0.4ps.
Since the bunch is relatively long in this compressor, the
CSR effect is not significant. The transverse emittance
grows 7%, and ' grows 3%. The beam is further accel-
erated to 3 GeV, and then enters the big arc. For the first
90 degree, the net R56 = 0, hence, there is no compres-
sion. In the remaining 90 degree, the bunch is compressed
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WU, J.H.; MURPHY, J.B.; YAKIMENKO, V.; BEN-ZVI, I.; GRAVES, W.; JOHNSON, E. et al. COHERENT SYNCHROTRON RADIATION ANALYSIS FOR THE PHOTOINJECTED ENERGY RECOVERY LINAC AND UVFEL PROJECTS AT THE NSLS., article, August 16, 2001; Upton, New York. (digital.library.unt.edu/ark:/67531/metadc722411/m1/4/: accessed December 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.