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Neutrino Factory/Muon Collider Document 30-v1

Modeling of Multiple Scattering Effects in the Presence of a Strong Magnetic Field

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MuCool Note
Submitted by:
John Urish
Updated by:
John Urish
Document Created:
21 Jun 1999, 12:00
Contents Revised:
21 Jun 1999, 12:00
Metadata Revised:
21 Jun 1999, 12:00
Actually Revised:
14 Sep 2006, 13:35
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The effect of mutiple scattering in the presence of a strong focusing magnetic
field on the first and second order moment $<r>$, $<\delta r^2>$, $<\theta>$,
$<\delta \theta^2>$ and $ < r \, \theta>$ are studied using numerical
simulation. It is found that the Moliere distribution can not always be used
in a straightforward manner, because (i) uncertainties in the atomic models
(ii) for very thin absorbers and (iii) significant deviation from the linear
trajectory occurs in a very short step due to the magnetic field: the
statistical treatement used in the Moliere theory becomes invalid. Conversely,
if, in a given step, the critical scattering angle is of the same order of the
deflection angle due to the focusing field, the displacement of the particle
over such a step will be a non-trivial function of the field and the scattering
process. This in turns affects the moments of the beam
distributions. This effect is studied for a liquid hydrogen absorber (LH2) in
a multi-Tesla field longitudinal field.

Revision 2 : (i) Corrected notation about sigma versus r.m.s (ii) added
new tests on signle track (iii) corrected mean free path calculation
(iv) minor typos in emittance formulas.

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This is revision # 1
Posted by Lebrun

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Notes and Changes:
Paul Lebrun
Publication Information:
Mucool notes, draft.
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