Frequency and diffusion maps for the SNS ring

Abstract

Using a single particle dynamics approach, the major magnetic non-linearities of the SNS accumulator ring are studied. Frequency maps are employed in order to display the global dynamics of the beam, for several working points. By means of diffusion maps the major resonances are explored and their bandwidth is estimated. The global tune diffusion coefficient is finally used to compare and choose the best working point. THE SNS ACCUMULATOR RINGThe SNS ring is designed to accumulate a high-intensity beam with a beam power of up to 2MW. The ring lattice has a 4-fold symmetry and consists of FODO arcs and quadrupole doublet straight sections [1]. The beam dynamics is mostly dominated by multi-particle effects such as space-charge [2] and other collective instabilities (e.g. electron-proton [3]), which are mostly intensity dependent. On the other hand, the strict fractional beam loss, dictated by the permissible radiation level for hands-on maintenance [4], imposes a very good control and correction of all non-linear effects. This includes the ones coming from magnet imperfections, the impact of which is amplified due to the large beam emittance. Indeed, in the early commissioning stages where the beam intensity will be low, the dominant effects will be of a single-particle nature. One of them is the chromaticity: in order to reduce the effect of collective instabilities the longitudinal phase space is painted to a large momentum spread of p = p= 0 :7%, with the bucket size set at p = p= 1 % and the momentum aperture at p = p = 2%. Taken the bucket size as the reference, the chromatic tune-shift is around 0.08, which is close to the space charge tune-shift of 0:15 ; 0:20. Another key issue for the performance of the SNS ring is the proper working point (w.p.) choice. After an extensive tuning campaign [5], we have concentrated on 4 potential w.p. candidates, due to optical matching and aperture considerations. Two of them have a tune-split of more than half a unit, in order to avoid strong coupling from spacecharge and/or magnet errors: (Q x Q y ) = (6:3 5:8), the old "nominal" w.p. for which most of the past studies have order resonances and (Q x Q y ) = (6:4 6:3). In order to choose the best w.p., with respect to the non-linear particle Work performed under the auspices of the US Department of Energy y papap@bnl.gov behavior, we use Laskar's frequency map analysis [6]. In brief, the frequency map is a detailed tune footprint. Due to the very high precision of the tune determination through a refined Fourier analysis using the NAFF algorithm, all the excited resonances appear as line distortions of the footprint. The tune variation along the particle trajectory can give a good estimation of the diffusion rate, which can then be mapped to the real space, for each particle initial condition. Finally, the average tune diffusion coefficient can be used as a global quality factor for comparison between the dynamics of the different designs. WORKING POINT COMPARISONWe choose a standard SNS ring lattice matched for...

Numerical analysis techniques for non-linear dynamics

“…It has been introduced by Laskar in astronomy [42][43][44][45][46] and subsequently used in several physics applications ranging from atomic physics [47] to Hamiltonian toy models [48][49][50]. During the last two decades, it became a standard tool of beam dynamics analysis for a variety of accelerators, such as hadron colliders [51][52][53][54][55], synchrotron light sources [56][57][58][59][60], high-intensity rings [61,62], B-factories [63] and linear collider damping rings [64]. The method relies on the high precision estimation [65] of the associated frequencies of motion (or "tunes" in the accelerator jargon), which are supposed to be invariant (i.e.…”

“…An example is given in Fig. 21, where the value of the tune diffusion coefficient is plotted versus the momentum deviation δp/p, for all working points of the Spallation Neutron Source accumulator ring [61], currently in operation in Oak-Ridge National Laboratory and holding the beam power world record. The single-particle dynamics of this ring is dominated by edge effects in the magnets, and especially the quadrupole fringe fields, which are octupole-like [11,73,74], at leading order, and given by the hard-edge Hamiltonian for a quadrupole with strength Q :…”

Detecting chaos in particle accelerators through the frequency map analysis method

“…4, where the value of the tune diffusion It is clear that (6.23,6.20) is the best choice, followed by (6.4,6.3). Their performance can be further improved by using the available multi-pole correctors 57 , for correcting the normal and skew 3rd order resonances, in the case of (6.4,6.…”

“…4. Tune diffusion coefficients for four SNS working points versus the different momentumdeviations 57. the current CERN Proton Synchrotron.…”

Small-emittance and low-beta lattice designs and optimizations

“…The total diffusion rate is then given by the summation of all the particle diffusion rates. The idea of using total diffusion rate as an objective to optimize dynamic aperture of a lattice is not new [6,[24][25][26]. However, we successfully implemented it in the genetic optimization.…”