Temperature vs. beam study with SVD 1.4 beampipe, May 2001 (ss)
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According to IHI stress analysis for SVD 1.4 beampipe, maximal allowed
temperature difference between centre of He cooled Be part and water
cooled Al part is 5K. 

To predict if heating of the IR beampipe presents a limitation in
terms of maximal allowed current for the KEK-B operation, a study was
made using high current operating conditions from 16-May-2001:

I_LER=850mA
I_HER=750mA
n_bunch=1150 for both beams
(see figure beam_phy.eps)

We monitored the temperatures of the water cooled Al part closest to
Berillium section and centre of the Be section, and we corrected the
measured temperatures with the known offset values obtained during the
winter shutdown in January 2001 (see figure cal-1.eps)

The main source of IR heating is expected to be HOM, where the heating
power is related to the current (of a single beam) as

P =  k_l * ( i_b * n_b )**2 / (f_0 * n_b) = k_l * I**2 / (f_0 * n_b)
  = const. * I**2

i_b=bunch current
n_b=number of bunches (1150 in present KEKB operation, constant)
f_0=revolution frequency (100kHz, constant)
k_l=longitudinal loss factor (property of the cavity, constant)
I=total beam current

and thus under above conditions P = const. * I**2

In case of two beams (with approx. the same bunch current in each beam
i.e. approx. same beam current), one can thus also expect some
quadratic dependence of temperature vs. the sum of both currents.

Measured temperature difference Be-Al fits perfectly with a quadratic
curve for the current range 1100mA<I_LER+I_HER<1600mA plus the 'no
current' point in present conditions with cooling systems switched
on. The temp. difference at I=0 point is itself about 1.5K due to
convective heating of the Be part of the beampipe.  Quadratic fit
predicts the safety limit (i.e. 5K temperature difference) will be
reached at I_LER+I_HER>2.7A.

fitted function: T = P1 + P2*I + P3*I**2

		P1	P2	    P3		 chi**2/ndf	ndf
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Be-Al (backwd)	1.42157 9.69353E-05 4.74503E-07  0.3742E-01	41
Be-Al (forwd)	1.55216 4.55104E-05 3.59329E-07  0.2633E-01	41

To get more data points in the fit at lower currents, we took not only
average over a few nice runs with high beam currents, but the entire
run period 21-31 May 2001.  Fitted quadratic curve is in this case
almost the same as in the case of high current data only (see figures
beam516_0.eps, beam521-532_0.eps).

We could conclude that present (1.4) beampipe shuld be able to
withstand operation of the KEK-B with both beams exceeding 1A, which
is probably sufficient until the next upgrade in 2002. More data at
high currents is needed, which will surely soon be provided by
excellent KEK-B operation.