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Hrachya, it is good to hear from you again. Find my responses below.<br>
-Richard J.<br>
<br>
Hrachya.Hakobyan wrote:
<blockquote type="cite" cite="mid:Pine.LNX.4.64.0909171949180.26135@mail.yerphi.am">
<pre wrap="">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. </pre>
</blockquote>
Eventually it does saturate. The particular choice we have made for
Hall D is not in the saturated region because we want to maintain a
high tagging efficiency. But if we were willing to go to low tagging
efficiency (level of 10%) then the polarization would saturate at the
value given by the pure coherent component.<br>
<br>
<blockquote type="cite" cite="mid:Pine.LNX.4.64.0909171949180.26135@mail.yerphi.am">
<pre wrap="">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?
</pre>
</blockquote>
More multiple scattering does mean we must open up the collimator for
the sake of tagging efficiency, yes, but that does not increase the
figure of merit. More multiple scattering decreases the figure of
merit. In the analytical calculation, the multiple scattering in the
target is treated continuously (i.e. with N layers of 20/N microns
thickness, where N->infinity). This analytical model is what we are
using to compute the performance parameters of the source (e.g.
polarization, beam rates, beam profile, tagging efficiency, etc.) The
simulation uses the analytical model to generate the bremsstrahlung
events inside the target. All of this is to say that the
many-thin-layer approach to simulating coherent bremsstrahlung is what
we are already doing.<br>
<br>
<br>
<br>
<br>
<blockquote type="cite" cite="mid:Pine.LNX.4.64.0909171949180.26135@mail.yerphi.am">
<pre wrap="">On Wed, 16 Sep 2009, Richard Jones wrote:
</pre>
<blockquote type="cite">
<pre wrap="">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
</pre>
</blockquote>
<pre wrap="">k
</pre>
</blockquote>
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