Intra-beam Scattering Study for Low Emittance of BAPS

S.K.Tian(IHEP)

Outline

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