Some comments on the variation of rms width versus angle, measured by Peter.

Peter has plotted the ratio of signal width to pedestal width as a function of angle.   In the absence of discharges, the pedestal width should reflect the non-VPT electronic noise of the system.  Since we are interested in the behaviour of the VPTs, it is more interesting to consider the (quadratic) difference of the signal and pedestal widths, rather than their ratio.

In the attached Note I show that the signal width is expected to vary with angle in the field according to the expression:

s_S / S = Ö(F N) / N = Ö(F / N)

(I hope that you have 'Rich Text' enabled!)

Where F is the excess noise factor given by:
                                                F(q) = [1 + 1/g(q)] / T_pe(q)

(see the note for the definitions).

Substituting g(0) = 7, g(15) = 10, T_pe(0) = 0.5, T_pe(15) = 0.45, we find:

                                                F(0) =  2.29  and F(15) = 2.44.

Thus although F increases with angle in this angular range (the decrease in grid transparency winning out over the increase in gain), the change is small.  Thus the signal width should just increase in proportion to the increase in gain.  (At q = 30, the increase in F will be more significant.)

Bob.

PS, I have also attached the contents of this mail as a WORD file, for the benefit of those of you who do not use Outlook....

<<Excess Noise factor.doc>> <<Some comments on the variation of rms width versus angle.doc>>

-----Original Message-----
From: Peter Hobson [mailto:Peter.Hobson@brunel.ac.uk]
Sent: 02 July 2008 08:44
To: Brad Cox; Brown, RM (Bob) - PPD
Cc: Bob Hirosky; Adolf Bornheim; Mike Arenton; Dave Cockerill; Alexander Ledovskoy; Michael Arenton; Dawn Leslie; Bell, Ken; Bruce.Kennedy@rl.ac.uk

Subject: VPT angle scan Brunel (H:\CMS\VPTx\Response vs angle\June 2008 Angle Test Summary.doc)

Finally, some data for you all to think about. You will note that we have some interesting differences between the two tubes, particularly in the relative pulsed LED response vs. angle (figure 4) and that in 1133 we see a systematic increase in the signal rms with angle to 4T field (see figure 7); no obvious spiky noise seen however.

I'm sure you will have lots of questions; please could DaveC add this to his splendid web page too. Peter
 
Professor Peter R Hobson
School of Engineering and Design, Brunel University, Uxbridge UB8 3PH
+44(0)1895 266799
http://people.brunel.ac.uk/~eestprh