Reduction of Beam Emittance of Pep-X Using Quadruple Bend Achromat Cell Page: 2 of 4
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REDUCTION OF BEAM EMITTANCE OF PEP-X USING QUADRUPLE
BEND ACHROMAT CELL*
Min-Huey Wangt, Y. Cai, R. Hettel, Y. Nosochkov, SLAC, Menlo Park, USAAbstract
SLAC National Accelerator Laboratory is studying an
option of building a high brightness synchrotron light
source machine, PEP-X, in the existing PEP-II tunnel [1,
2]. By replacing 6 arcs of FODO cells of PEPII High
Energy Ring (HER) with two arcs of DBA and four arcs
of TME and installation of 89.3 m long damping wiggler
an ultra low beam emittance of 0.14 nm-rad (including
intra-beam scattering) at 4.5 GeV is achieved. In this
paper we study the possibility to further reduce the beam
emittance by releasing the constraint of the dispersion
free in the DBA straight. The QBA (Quadruple Bend
Achromat) cell is used to replace the DBA. The ratio of
outer and inner bending angle is optimized. The
dispersion function in the non-dispersion straight is
controlled to compromise with lower emittance and beam
size at the dispersion straight. An undulator of period
length 23 mm, maximum magnetic field of 1.053 T, and
total periods of 150 is used to put in the 30 straights to
simulate the effects of these IDs on the beam emittance
and energy spread. The brightness including all the ID
effects is calculated and compared to the original PEP-X
design.
INTRODUCTION
The horizontal (natural) emittance of an electron beam
in an electron storage ring is determined by the
equilibrium between quantum fluctuations and radiation
damping. The resulting emittance of electron beams isI -I4
(1)
where y is the relativistic energy factor. The radiation
integrals are I,= f/p2ds, I4= JDx /p(1lp2 +2K)ds and I,=
JH l I p i ds, where s is the length coordinate along the
accelerator, p is the bending radius of dipoles, Dx is the
dispersion function, K is the focusing function, and the H-
function is
Here, D'x is the derivative of the dispersion function with
respect to s, fx is the betatron amplitude function, and
ax= 1 (d3 / ds). The minimization of beam emittance
requires minimizing the average H-function through the
dipoles. Using a small angle approximation, the minimum
emittance for the DBA and the TME lattices are
*Work supported by the U.S. Department of Energy under Contract
number DE-AC02 76SF00515.
timhwang@slac.stanford.edu8MEDBA =3
1 C)"2 3
Te =-3MEDBA 3
8TM 12457 J(3)
(4)where cq = 55h/(32J3mc) = 3.83x10-13m, Jx~1 is the
horizontal damping partition number, and 0 is the
bending angle of dipoles in one bending section. Relaxing
the achromatic condition, the emittance can generally be
reduced by a factor of 3.
This article studies the option of the quadruple-bend
achromat (QBA) lattice, which is defined as a super cell
composed of two TME and two DBA dipoles with
unequal bending strengths for the outer and inner dipoles.
QBA CELL
The modified lattice is based on the PEP-X baseline
design [2]. Two DBA cells are replaced by one QBA cell.
In order to match the H function between dispersion
matching dipole (outer dipole) and non dispersion
matching dipole (inner dipole) the bending angle of inner
dipole should be 313 larger than the outer dipole. This can
be achieved by lengthening the inner dipole (same p as
outer dipole) or increasing the dipole strength of the inner
dipole (different p from outer dipole). To save the space
of the QBA cell the latter is used in the design. The dipole
length is 1 m. The bending angle of inner dipole is 2.25
and outer is 1.5g. The allowed dispersion function in the
middle straight section is controlled to compromise with
lower emittance and beam size at the dispersion straight.
In this case the emittance is not optimized instead the
brightness is tried to. The dispersion at middle straight is
constrained to less or equal to 0.03 m to control the beam
size increase due to the dispersion to less than one sigma
beam size without dispersion. Figure 1 shows one of the
QBA cells.-..:1 1 [.r
PEP Ill.g umar clt.~7IrJvI
4~ 16.
0.0 -
00 5 10- 15 '0 15 30)II]
-~J1 VG/8 14.'5.4/ 02
-all
- 0
0.10
607
S0.03
*002
*0-01
n0
35-* 40Figure 1: Optic function of QBA cell. The dispersion is
0.02 m at the middle straight.
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Wang, Min-Huey; Cai, Yunhai; Hettel, Robert & Nosochkov, Yuri. Reduction of Beam Emittance of Pep-X Using Quadruple Bend Achromat Cell, article, May 26, 2009; United States. (https://digital.library.unt.edu/ark:/67531/metadc927389/m1/2/: accessed April 20, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.