Post on 31-Dec-2015
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Intra-beam scattering theory
BAPS machine parameters(a temporary design lattice )
Recent BAPS IBS calculations
Intra-Beam Scattering
Particles in a circular accelerator execute transverse betatron oscillations, the transverse velocities are statistically distributed, these particles can be scattered by collisions so transferring transverse momenta into longitudinal momenta, In general, one should distinguish between:
large-angle single scattering ---TOUSCHEK effect---Lift time multiple small-angle scattering---intra-beam scattering---Rise time
Sketch maps
1
1, , , , , ( ) ( )
2
N
k k kj
collision x xp y yp z p j jN
Conventional theory of IBSConventional IBS theory in Accelerator Physics (Bjorken-Mtingwa) derive Ti by the formula:
1/2
1/20
1 1 14 (log) ( ) 3 ( )
det( )i i
i
A d TrLTr Tr LT L I L IL I
min
max min
20
2 3
( ) ( )
4
( )
2log ln ln
64
h v s p
p h v
b
b
r cA
Coulomb logari
L L L L
h
N
t m
2( )
2
2( )
2( )
0 0 0
0 1 0
0 0 0
1 0
0
0 0 0
0 0 0
0
0 1
p
p
h
h h hh
h h
v v vv
v v
v
L
L
L
2 2, , , , , , ,
, , , , ,
1[ ( ) ] /
21
/2
h v h v h v h v h v h v h v
h v h v h v h v h v
<……> indicates that the integral is to be averaged around the accelerator lattice
1/2 1/2
1/2 1/2
1 1 1 1 1 1; ;p v h
p p v v h h
the growth times for the relative energy spread andhorizontal and
d d d
T dt T dt T dt
vertical emittances
•
•
••
•
•S6
S1
S5S4
S3
S2
1
1
1 1
1
1 1;
, 0
: ( , , , ...)
Mm m
mmi i
M
m m
S S
T C T
S C S
S S elements drift quadrupole bend magnet cell
Basic Parameters of BAPSParameter Symbol, unit Value
Beam energy E, GeV 5
Circumference C, m 1364.8
Beam current I0, mA 100
Bunch number nb 1836
Number of particles per bunch Nb 1.55109
Natural bunch length l0, mm 2.9
RF frequency frf, MHz 500
Harmonic number h 2276
Natural energy spread e0 1.5103
Momentum compaction factor p 4105
Betatron tune x/y 113.4/39.3
Synchrotron tune s 0.004
Damping time (H/V/s) x/y/z, ms 28, 43, 29
Emittance (horz./vert.) x/y, pm 10/10
Trans. beam size (horz./vert.) x/y, m 4.4/7.4
Lattice functions in the BAPS ring
Circumference: 1364.8 m, 2 superperiods, 36 supercellsWorking point: 111.39, 39.30Natural chromaticity: -184, -181Natural emittance: 51 pm.rad
Y. Jiao
Recent BAPS IBS calculationsIBS effect – Scan on Energy
Steady-state horizontal emittance VS. energy @coupling=0.01
Recent BAPS IBS calculations
IBS effect---particle numbers
Steady-state horizontal emittance VS. bunch current@coupling=0.01
20
2 3 4
1
64i h v s p
r cNA
T
Recent BAPS IBS calculations
IBS effect – Scan on coupling factor
=
1=
1+
=1+= +
y x
x nat
y nat
nat x y
Steady-state horizontal emittance VS. the coupling factor@I=100mA
For simplicity and for the purpose of IBS calculations, we assume that the vertical emittance is primarily generated by the coupling, and the effects of the vertical dispersion can be ignored.
20
2 3 4
1
64 hi v s p
r cNA
T
Recent BAPS IBS calculations
IBS effect – damping wiggler
2 30
0
41
15( )
11
2
q xw w
w x x nat w w
nat xww w
w
CN
J J
JN
the emittance reduction depends on the wiggler period length, the wiggler peak field, and the total wiggler length.
Relative emittance reduction versus wiggler lengthRelative emittance reduction versus wiggler field
Recent BAPS IBS calculations
Damping Ratio: 0.27618 elegant:ex0 (m) = 1.403855e-011 Emittance_w0: 14.09157 [pm]U0 (MeV) = 1.072198e+000 6.259949e+000
Recent BAPS IBS calculations
Steady-state horizontal emittance @different current and different emity
Recent BAPS IBS calculations
( ) ( ) ( ) 2 2, , , , , , ,
1 1[ ( ) ] /
2p h v
h v h v h v h v h v h v h vi
L L L LT
Accumulated growth rates in x VS. Hx along the ring
Conclusions
Intra-beam scattering is an effect which becomes important in future low emittance ring-base light sources and becomes a limiting factor for reaching ultimate storage ring.
To compensate the IBS emittance growth, we can use one or more strong damping wigglers in dispersion-free regions.
Changing the coupling factor can reduce the IBS effect, how to obtain k=1 in electron storage rings is an interesting topic.
Reference:• M. Borland, "elegant: A Flexible SDDS-
Compliant Code for Accelerator Simulation,“ Advanced Photon Source LS-287, September 2000.
• Karl Bane, Kirk Bertsche, Yunhai Cai , etc A Design Report of the Baseline for PEP-X: an Ultra-Low Emittance Storage Ring