Deflections in Magnet Fringe Fields

A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of magnets whose end designs introduce no extraneous components, {\it i.e.} fields not required to be present by Maxwell's equations. Analytic evaluations of the deflections are obtained in various approximations. Mainly emphasized is a ``straight-line approximation'', in which particle orbits are treated as straight lines through the fringe field regions. This approximation leads to a readily-evaluated figure of merit, the ratio of r.m.s. end deflection to nominal body deflection, that can be used to determine whether or not a fringe field can be neglected. Deflections in ``critical'' cases (e.g. near intersection regions) are analysed in the same approximation.Comment: To be published in Physical Review

Fringe Fields and Dynamic Aperture in the FNAL Muon Storage Ring

Quadrupole fringe fields can limit the dynamic aperture of muon storage rings.Using the computer code COSY INFINITY for particle tracking and normal-form analysis, we evaluate the importance of fringe fields in the FNAL muon storage ring, and identify the regions of the machine where they are most critical. Dynamic aperture and linear tune shifts with amplitude are calculated considering an ideal machine without any errors or misalignments. We also explore the efficiency of various nonlinear correction schemes, study the momentum acceptance, and evaluate the spin decoherence over the transverse phase space

Lagrangian Reachabililty

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201

A Comparison of Polarization Observables in Electron Scattering from the Proton and Deuteron

Recoil proton polarization observables were measured for both the p($\vec {\rm e}$,e$^\prime\vec{\rm p}\,$) and d($\vec {\rm e}$,e$^\prime\vec{\rm p}\,)$n reactions at two values of Q$^2$ using a newly commissioned proton Focal Plane Polarimeter at the M.I.T.-Bates Linear Accelerator Center. The hydrogen and deuterium spin-dependent observables $D_{\ell\ell}$ and $D_{{\ell}t}$, the induced polarization $P_n$ and the form factor ratio $G^p_E/G^p_M$ were measured under identical kinematics. The deuterium and hydrogen results are in good agreement with each other and with the plane-wave impulse approximation (PWIA).Comment: 9 pages, 1 figure; accepted by Phys. Rev. Let

Measurement of E2 Transitions in the Coulomb Dissociation of 8B

In an effort to understand the implications of Coulomb dissociation experiments for the determination of the 7Be(p,gamma)8B reaction rate, longitudinal momentum distributions of 7Be fragments produced in the Coulomb dissociation of 44 and 81 MeV/nucleon 8B beams on a Pb target were measured. These distributions are characterized by asymmetries interpreted as the result of interference between E1 and E2 transition amplitudes in the Coulomb breakup. At the lower beam energy, both the asymmetries and the measured cross sections are well reproduced by perturbation theory calculations, allowing a determination of the E2 strength.Comment: 8 pages, 3 figure

Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction

We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By "sufficiently large", we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reaction-diffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method

Memory for pitch in congenital amusia: Beyond a fine-grained pitch discrimination problem

Congenital amusia is a disorder that affects the perception and production of music. While amusia has been associated with deficits in pitch discrimination, several reports suggest that memory deficits also play a role. The present study investigated short-term memory span for pitch-based and verbal information in 14 individuals with amusia and matched controls. Analogous adaptive-tracking procedures were used to generate tone and digit spans using stimuli that exceeded psychophysically measured pitch perception thresholds. Individuals with amusia had significantly smaller tone spans, whereas their digits spans were a similar size to those of controls. An automated operation span task was used to determine working memory capacity. Working memory deficits were seen in only a small subgroup of individuals with amusia. These findings support the existence of a pitch-specific component within short-term memory and suggest that congenital amusia is more than a disorder of fine-grained pitch discrimination

Measurement of the Induced Proton Polarization P_n in the 12C(e,e'\vec{p}) Reaction

The first measurements of the induced proton polarization, P_n, for the 12C (e,e'\vec{p}) reaction are reported. The experiment was performed at quasifree kinematics for energy and momentum transfer (\omega,q) \approx (294 MeV, 756 MeV/c) and sampled a recoil momentum range of 0-250 MeV/c. The induced polarization arises from final-state interactions and for these kinematics is dominated by the real part of the spin-orbit optical potential. The distorted-wave impulse approximation provides good agreement with data for the 1p_{3/2} shell. The data for the continuum suggest that both the 1s_{1/2} shell and underlying l > 1 configurations contribute.Comment: 5 pages LaTeX, 2 postscript figures, accepted by Physical Reveiw Letter