[Halld-tagger] Info for the IPR 2009 review

[Hrachya.Hakobyan]

Hello Richard,

In the presence of the beam divergence and multiple coulomb scattering
the collimation dependence of polarisation seems has a saturation 
toward the collimation decrease. If so the 50 micron case probably may be 
used with a wider collimation so with gain in FOM, For the precise  study the 
Coulomb scattering probably has to be simulated by decomposing the crystal
into thin layers(5x10micron f.e.). What do you think about?

Cheers, Hrachya

On Wed, 16 Sep 2009, Richard Jones wrote:

> Eugene,
> 
> Several things change at the same time, so it takes some thought to make
> a true comparison.  Under fixed collimation conditions, the polarization
> is not very sensitive to the crystal thickness.  However, it is really
> the tagging efficiency that determines what polarization we run at, and
> the tagging efficiency is somewhat more sensitive.  If we were not
> concerned with tagging efficiency then we could narrow the collimator
> arbitrarily small and compensate with higher e-beam current, such that
> the polarization attains that of the pure coherent component.  So to make
> a fair comparison, I fix the tagging efficiency at its nominal value for
> the standard configuraration (3.4mm collimator, 20 micron diamond) and
> when I change the diamond thickness I vary the collimator diameter to
> keep the tagging efficiency the same at the coherent peak.  When I do
> that, I get the following results:
>
>     1. 20 micron diamond:
>        o  peak polarization = 41.4 %
>        o  hadronic bg rate (low-energy beam flux, arb. units) = 1.9
>
>     2. 50 micron diamond:
>        o  peak polarization = 39.4 %
>        o  hadronic bg rate (low-energy beam flux, arb. units) = 2.1
> 
> The figure-of-merit for a polarization observable is rate *
> polarization^2.  Here I am going to assume that we are bg limited (at the
> trigger level) so the hadronic bg sets the running rate.  Under these
> conditions, going from a 20 micron to 50 micron diamond costs a FOM
> factor of 20%.  If errors are purely statistical then this means 20%
> longer run time to achieve the same level of precision.  In our case,
> errors are more likely to be systematics dominated, in which case the
> higher polarization and lower bg with a 20 micron diamond will result in
> increased sensitivity to small signals.
> 
> -Richard Jones
> 
> 
k