boiling

Boiling corrections 04/11/06

This is something that Jason has looked at in great detail.
http://www.jlab.org/~cseely/xem/lumi/boilcor.html
http://www.jlab.org/~cseely/xem/lumiold/boilcor.html
http://www.jlab.org/~cseely/xem/lumiold/lumiplots2.html
http://www.jlab.org/~cseely/xem/lumiold/lumiplots.html

Lumi runs that have LH2 and/or LD2
49506-49518    (June)
51439-51470    (XEM)

Jason saw in his analysis that Carbon appears to boil !! It is not clear what is the reason for this, but it appears that BCM2 has an offset. An offset when integrated over a run, produces a non-zero charge that becomes more significant at lower beam currents.
Carbon plot (scaled to give a normalized yield of 1 at infinite beam current)

It was assumed that the Carbon normalized yield was independent of the real beam current, and a BCM2 offset (dI) was adjusted to make this so.

The real beam current was given by
I₀ =I_rmeas / (1 + dI/I_rmeas)    =>   I₀ / I_rmeas = 1/ (1 + dI/I_rmeas)

                                             => Y_rmeas(I) = Y₀I₀ / I_rmeas= Y₀/ (1 + dI/I_rmeas)

So, the carbon charge normalized yield was fit with the parameterization
Y_rmeas(I) = Y₀ / (1 + dI/I_rmeas)

The corrected yields will then be given by
Y_corrected(I) = Y_meas (1+dI/I_rmeas)

Note that the yields are not corrected in this way for production data, because there is no guarantee that dI will be the same. Only the yields in the lumi scan are corrected using dI.

Jason's results when using the corrected yields (NB 1,2,etc are different lumi scans):
C_1
C_2
C_3
C_4
LH2
LD2_1
LD2_2

The final results for LH2 and LD2 is that no boiling was seen. The boiling correction will be 1.0.

For LH2, the fitted slope was 2.1 +- 5.4 e-5 %/uC, so the error in the boiling correction will be about 7.5e-5 %/uC. This corresponds to about 0.5%relative error in the normalized yield at 65 uC.

For LD2, the error in the boiling correction is about 9e-5 %/uC, which corresponds to about 0.6 % relative error in the normalized yield.