The effect of mutiple scattering in the presence of a strong focusing magnetic
field on the first and second order moment $$, $<\delta r^2>$, $<\theta>$,
$<\delta \theta^2>$ 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.
Posted muc0030.ps to WWW
URL http://www-mucool.fnal.gov/mcnotes/muc0030.ps
This is revision # 1
Posted by Lebrun