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Neutrino Factory/Muon Collider Document 114-v1

Non-distorting phase rotation

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MuCool Note
Submitted by:
John Urish
Updated by:
John Urish
Document Created:
13 Apr 2000, 12:00
Contents Revised:
13 Apr 2000, 12:00
Metadata Revised:
13 Apr 2000, 12:00
Actually Revised:
14 Sep 2006, 13:35
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Non-distorting phase rotation

R.B. Palmer

A distribution of particles, large in energy and small in time, can be "phase rotated" to reduce its energy spread. A simple way of doing this is to allow the particles to drift (the low energy particles fall back with respect to the high energy ones), and follow this by a time dependent acceleration (e.g. induction acceleration) to level out the energies. But with this simple method, relativistic effects cause the resulting final energy spread to be far larger for the early part of the bunch, and far less for the latter: the bunch is distorted. In this note we show that with two drifts and two different accelerations, this distortion can be removed. The final rms energy spread is then less than half of its distorted value.

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