280 research outputs found
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
Enhanced Optical Cooling of Ion Beams for LHC
The possibility of the enhanced optical cooling (EOC) of Lead ions in LHC is
investigated. Non-exponential feature of cooling and requirements to the ring
lattice, optical and laser systems are discussed. Comparison with optical
stochastic cooling (OSC) is represented.Comment: 4 page
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
Computing the critical points of the distance function between two Keplerian orbits via rigorous global optimization
Propagation of large uncertainty sets in orbital dynamics by automatic domain splitting
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
A Comparison of Polarization Observables in Electron Scattering from the Proton and Deuteron
Recoil proton polarization observables were measured for both the p(,e) and d(,en reactions at two values of Q using a newly commissioned proton
Focal Plane Polarimeter at the M.I.T.-Bates Linear Accelerator Center. The
hydrogen and deuterium spin-dependent observables and
, the induced polarization and the form factor ratio
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
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