Beams Document 3927-v1

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Diffusion model for the time evolution of particle loss rates in collimator scans: a method for measuring stochastic trasverse beam dynamics in circular accelerators

Document #:
Beams-doc-3927-v1
Document type:
Note
Submitted by:
Giulio Stancari
Updated by:
Giulio Stancari
Document Created:
25 Aug 2011, 00:02
Contents Revised:
25 Aug 2011, 00:02
Metadata Revised:
25 Aug 2011, 00:02
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Abstract:
A diffusion model of the time evolution of loss rates caused by a
step in collimator position is presented. It builds upon the model
of Seidel (1994) and its assumptions: (1) constant
diffusion rate within the range of the step and (2) linear halo
tails. These hypotheses allow one to obtain analytical expressions
for the solutions of the diffusion equation and for the
corresponding loss rates vs. time. The present model addresses some
of the limitiations of the previous model and expands it in the
following ways: (a) losses before, during, and after the step are
predicted; (b) different steady-state rates before and after are
explained; (c) determination of the model parameters (diffusion
coefficient, tail population, detector calibration, and background
rate) is more robust and precise. These calculations are the basis
for the measurement of transverse beam diffusion rates as a function
of particle amplitude with collimator scans. The results of these
measurements in the Tevatron will be presented in a separate report.
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