05-19-2010
----------


Diancheng and myself were in the PVDIS meeting today. Diancheng was trying to 
independently do the current-scan analysis for determining deadtime (i.e., 
using a R/I vs I plot, where R is rate and I is beam current). He has uploaded 
his plots for discussion on his JLab webpage 
(www.jlab.org/~dwang/meeting/051910/). 
The basic idea that Diancheng was explaining was that we were supposed to see 
a slope-less line out of the  

R/I vs I 

plot if we assume R is proportional to I. We observed it having a negative 
slope instead. This could be an indication of a presence of a 2nd order 
effect. Following a suggestion from Xiaochao that observing such negative 
slope could be due to a boiling effect in deuterium target, Diancheng tried 
two things: 

(1) used lumi data to evaluate 2nd order effect, and 
(2) used aluminum data to investigate that if he could find a slope-less 
    line for the R/I vs I plot. 

Using aluminum data was very challenging, since we did not have any runs 
having various amounts of beam current. He tried to utilize the portion of 
beam ramping-up amounts of data after a beam trip so as to see a different 
rate for different current. This, ofcourse, would not have a statistical 
strength. In this try, he, kind of, sees a slope-less line for the
 
R/I vs I 

plot (see his aluminum directory on the above link). From the lumi data also, 
he observed 2nd order effect and tried to find the b-value using lumi data 
using this relation: 

r = aI - bI^2, where r is some dummy variable to represent a rate. 

Now he uses this b-value in the relation for 

r = aI -bI^2 

for deuterium runs and gets deadtime as 

(p1 -b)/(p0)^2,    [deadtime with 2nd order effect],

where p0 and p1 are some fit parameters to be explained below.

When ignoring 2nd order effect, the deadtime would simply be

p1/(p0)^2.

Here the terms p1 and p0 come from this relations (no 2nd order effect):

R = r(1 -Dr) = aI (1 - DaI) = aI - a^2DI^2, where D is deadtime,

i. e., [R/I] = a -a^2DI ----------(1)

i. e., [R/I] = p0 -p1I -----------(2).

Thus, comparing (1) and (2), we get expression for deadtime as:

D = p1/(p0)^2,     [deadtime without 2nd order effect],

where p0 and p1 are the fit parameters.

Getting b from lumi data and using it for finding deadtime for deuterium runs also
did not give expected deadtime, it still turned out to be about a micro second long.
That means we are still lacking something to calculate deadtime using the rate-scan
method. We are open for more suggestions.


I was proposing that Diancheng, Xiaoyan and myself will have to circulate our talks
for MENU2010 conference sometimes next week for comments. Our talk date is June 2 
at the College of William and Mary.