E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

DYNAMIC APERTURE OF THE STRONG RFDYNAMIC APERTURE OF THE STRONG RFFOCUSING STORAGE RINGFOCUSING STORAGE RING

E.LevichevE.Levichev, P.Piminov, P.Piminov

(Budker Institute of Nuclear Physics, Novosibirsk)(Budker Institute of Nuclear Physics, Novosibirsk)

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Main goal

Simulation of the dynamic aperture and non-linear effects in the SRFF regime for the DAFNE storage ring with strong coupling of the transverse and longitudinal particle motion.

It was expected that powerful synchro-betatron resonances can reduce the area of the beam stable area.

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Tool

6D tracking code Acceleraticum which used G.Ripken (DESY) formalism with realistic path elongation in magnetic elements.

Canonical variables are:

Transformation of the longitudinal coordinate

0

0),()(,,,,E

EEstcsspzpx zx

2/1222)(11/ yxxshdsd

was solved explicitly for various magnetic elements.

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Model

DAFNE “structure A” (C.Biscari) with high compaction factor and high synchrotron tune. Main parameters:

Qx/Qz 4.824/5.212

Qs at URF = 5 MV 0.2406

at IP 0.0727

x0/z0 –6.27/–13.53

x/z sext OFF 3.58/–17.43

x/z sext ON 0.36/–10.79

x 6.37×10-7 m-rad

E/E 3.82×10-4

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Bunch length modulation

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

On-energy dynamic aperture

► Wigglers only.

► Wigglers+sexts

6.10 x

27.00 z

mm

mm

40 x

5.110 z

m

m

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Main transverse resonances

Maximum DA (mm) as a function of the tune point.

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Main resonance harmonics

Cos Sin Cnm

Horizontal harmonics

A15 (m-1/2) –0.08 –0.17 –1.11

A314 (m-1/2) 0.28 –0.15 0.68

Coupled harmonics

B15 (m-1/2) 0.27 –0.37 –2.60

B+15 (m-1/2) 0.72 0.20 3.01

B- -6 (m-1/2) 0.65 –0.23 1.72

176.05 xQ

473.0143 xQ

176.05 xQ

248.0152 zx QQ

401.062 zx QQ

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Transverse space trajectories

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Off-energy dynamic aperture

Sigma_E = 0.04%

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Transverse DA vs. synchrotron tune

25.0sQ 25.0sQ

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Energy dynamic aperture

max0/ pp

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Longitudinal phase space

0 MV 1 MV

5 MV 10 MV

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Off-energy tune scan - 1

Initial amplitude of energy oscillation = 0

Black – betatron resonancesRed – satellites

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Off-energy tune scan - 2

Initial amplitude of energy oscillation = 0.25 %

Black – betatron resonancesRed – satellites

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Off-energy tune scan - 3

Initial amplitude of energy oscillation = 0.5 %

Black – betatron resonancesRed – satellites

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Synchrobetatron resonances

(a) Resonances excited by the dispersion in the chromatic sextupoles

nQQ sx 2 k

ki

xxxxeDmlQ 2)(ˆ

nQQ sz 2 k

ki

zxzzeDmlQ 2)(ˆ

nQQ sx 2 k

k

ixx

x

xxeDmlQ

22

)(2

ˆ

Resonance Width

(b) Resonances excited by momentum oscillation + chromaticity (vert.!)

Satellite strength

s

zzm QmJ

s

ˆ nQmQmQm sszzxx

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Alternative tune point

Old tunes: (4.825, 5.212)

New tunes: (4.939, 5.212)

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Example of the SBR study at VEPP-4M (single beam)

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Example of the SBR study at VEPP-4M (colliding beams)

E Levichev -- Dynamic Aperture of the SRFF Storage Ring

Frontiers of Short Bunches in Storage RingsINFN-LNF, Frascati, 7-8 Nov 2005

Conclusions

(1) Due to the strong coupling, synchrobetatron resonances decrease the dynamic aperture in the chosen tune point.

(2) It is possible to find alternative working point by fine tune adjustment to obtain the dynamic aperture which seems large enough.

(3) Improvement in the vertical chromaticity compensation seems reasonable to reduce strength of the modulation synchrobetatron resonances.

(4) New sextupole arrangement may provide both chromaticity correction and reduction of the synchrobetatron lattice factors.