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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.