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

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

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.

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 1500 - 2048 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

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

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

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

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

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

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

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