Email from Jim:

Date: Mon, 27 Sep 2004 17:04:31 -0500
From: Jim Birchall 
To: Juliette Mammei , Roger Carlini ,
     Klaus Grimm , Mark Pitt ,
     Neven Simicevic , Greg Smith ,
     Allena Opper , Tony Forest ,
     Norman Morgan , Mike Finn ,
     David Armstrong , Yongguang Liang ,
     Shelley Page , Dave Mack ,
     Richard Jones 
Subject: Stepped Boston collimator

The following results use Richard's updated gukine.F - internal 
Bremsstrahlung and energy loss upstream of the vertex.

I've taken a look at a stepped version of the 10-8-22 Boston 
collimator. That is, it's blocked at the upper corners at large theta 
and large and small phi. The stepping narrows the collimator at large 
theta by using a segment of a cone (CONS shape in GEANT) so that the 
metal spokes separating the air gaps are extended at large theta by a 
few degrees. The inner edge of this cone segment has the same shape as 
the outer surface of the 8-8-22 collimator. In other words, the stepped 
collimator is the 10-8-22 at the centre and is narrowed down to the 
8-8-22 collimator at large and small phi.

The first plot shows the distribution of inelastics on a bar (302 < x < 
318 cm, -105 < y < 105 cm) for the 10-8-22 collimator (theta vertical, 
phi horizontal). Rates on the scale at the side are in MHz. The 8-8-22 
collimator cuts large angles at about 10 degrees at half max, which is 
roughly what is needed to cut out inelastics on the bar, as the first 
plot shows. I've varied the azimuthal extent of the stepping and looked 
at inelastic rate and figure of merit. From the plot, the stepping 
should start cutting at a phi of about 8 degrees from the centre of the 
collimator.

The second plot shows the percent of inelastics hitting the bar as a 
function of the stepping angle, which is the angle that the stepping 
juts into the air gap, counting both large and small phi angle sides of 
the collimator. Zero degrees corresponds to the original 10-8-22 
collimator. The fit is exponential in angle. To get to 0.02% inelastic, 
the stepping angle should be at least 7.2 degrees. The air gap in the 
10-8-22 collimator is 22 degrees wide, so it would be 22 - 7.2 = 14.8 
degrees wide in the region beyond theta of about 10 degrees.

The third plot is the figure of merit vs stepping angle. For 7.2 
degrees stepping angle, FOM = 0.48. The fourth plot shows the elastic 
rate versus stepping angle. The rate is about 570 MHz at 7.2 degrees 
stepping angle.

This is probably close to the best we can do with the Boston-type 
collimator. It doesn't help to open up at large theta in the centre 
region of the collimator, as those events do not reach the bar. We 
might be able to extend the phi angle of the collimator a little. Rate 
and FOM should go as phi.

Jim


Jim's attachments:


inelastics_on_bar.pdf

stepping.pdf

fom.pdf

elastic.pdf