1. LNF site 1.2 Km LER lattice: preliminary dynamic acceptance studies
M. Biagini, LNF-INFN
on behalf of
M. H. Donald, Y. Nosochov, J. Yocky
IX SuperB Meeting, Perugia 16-19/6/2009

2. Dynamic aperture
Dynamic aperture has been checked with tracking with MAD, Merlin, LEGO
MAD and Lego trajectories agree
Merlin and MAD/LEGO do not agree: in Merlin the kinematic term in the IP doublets is missing, so the Hamiltonian is truncated to 3° order. An octupole could be added to take care of this effect, or a 4° order term should be added to the Hamiltonian, as it was done in LEGO for the CDR lattice
For the moment we are using MAD tracking, Lie4 option
Need to compare results and optimize DA with Acceleraticum code (BINP) too

3. Example from the CDR (Y. Cai)
The paraxial approximation:
is not accurate enough for the quadrupole magnets in the FF. A better approximation includes the fourth-order momentum terms in the Hamiltonian.
The dynamic aperture obtained using the paraxial approximation (left) is artificially small compared to that obtained with the exact Hamiltonian (right). Note different scales (x twice, y 3 times larger).
The reduction in dynamic aperture could be mostly restored by adding the fourth-order term (px2+py2)2=[8(1+d)] into the paraxial approximation.

4. LER (4.18 GeV) tracking with MAD
Turn-by-Turn tracking in MAD:
5 starting amplitudes tracked at 3 sigma spacing (3, 6, 9, 12, 15), x and y plane separate
turns
ex=1.6E-09
ey= ex/2 (full coupling)
Included FF
No crab sextupoles
RF ON and OFF
Nominal tunes: frac(nx) = 0.575, frac (ny) = 0.595
For Y-plane also tune vs amplitude computed

5. x,x’ plane, ex=1.6E-09, ey= ex/2 (full coupling)
d = +0.25%, RF ON
d = +0.5%, RF ON
d = 0, RF ON
d = -0.25%, RF ON
d = -0. 5%, RF ON

6. y/y’ plane, ex=1.6E-09, ey= ex/2 (full coupling)
d = 0, RF ON
d = +5x10-3, RF ON
d = 0, RF OFF
d = +5x10-3, RF OFF

7. y/y’ plane, ex=2.8E-09,ey= ex/2 (full coupling)
d = 0, RF ON
d = +2.5x10-3, RF OFF

8. x,y trajectories, 10 sigmas each
50 sx
20 sx
x, d = 0, RF OFF
x, d = 1%, RF OFF
x, d = -1%, RF OFF
20 sy
40 sy
y, d = 0, RF OFF
y, d = 1%, RF OFF
y, d = -1%, RF OFF

9. LER bandwidth vs d -2%<d<2% vs d -1%<d<1% vs d

10. LER tracking with LEGO
LEGO tracking agrees better with MAD result than with Merlin.
The effect of quadrupole non-linear fringe field does not make difference to aperture.
The suspected difference with Merlin is in the approximation of Hamiltonian.
MAD and LEGO expand it for better accuracy, while Merlin may be using only the leading term. This makes difference in lattices with very strong final focus systems.
blue: d = 0
red: d = 0.54%
black: 10s beam

11. Summary
Dynamic aperture studies for the new 1.2 Km LNF lattice just started
LER and HER have same betatron functions in the arcs and the IR
Tracking with MAD (Lie4 option) agrees with LEGO, while Merlin has a paraxial approximation too sharp for the strong FF doublets
First results, without crab sextupoles, are encouraging
Study of different working points is needed
Optimization of sextupoles and insertion of crab sextupoles in progress
Need comparison with Acceleraticum code too