'> in terms of decreasing number of antennas, a key point will be
'> calibration -- what are fast switching timescales and slew distances
'> that will be required given the lower instantaneous sensitivity?
Fast Switching was originally concieved of with the MMA, 40 8m antennas.
It basically worked. Going to 64 12m antennas actually didn't improve
fast switching's efficiency by a great deal --
consider these numbers (derived from 64 x 8m antennas):
@ 345 GHz (with appropriate conditions given dynamic scheduling
-- not the best, not the worst):
... for the "median" calibrator source, the time required to
sufficiantly detect that calibrator at 90 GHz is 0.28 s;
that calibrator is 80 mJy, and is located 1.4 deg away. The time
required to MOVE (roundtrip) is about 3 s. SO, the phase errors
we make and the efficiency that is lost due to cal time is dominated by
the MOVE time.
(If we don't calibrate at 90 GHz, but 345 GHz, a simpler observing
strategy, we need slightly more time on a more distant and somewhat
fainter calibrator: 60 mJy, 2.2 deg away, 2x slew time is 3.7 s,
and the integration time is 0.54 s -- we are still dominated by
the move time.)
My interpretation: we have a LOT OF SLACK in the system --
we can live with a) the sky not having quite as many calibrators
as the model suggests, or b) ALMA not being as sensitive as we hoped,
or even c) not having as many antennas as we wanted, and the end
result will be nearly as good as the 64x12 result. ie, I estimate
the change in overall eficiency will be less than 1% -- going
from 85% efficient, say, to 84.6% (these numbers are pure guesses).
ONLY if we are observing at 650 or 850 GHz and we are not calibrating
at 90 GHz, but at the observing frequency, does the calibrator integration
time become comparable to the slewing time to and from the calibrator.
IN THIS SITUATION, reduction in antenna number will result in a modest
increase in the integration time on the calibrator, which will be felt
modestly in the final fast switching efficiency (perhaps 1%, perhaps
more). HOWEVER, this is a really spongy mathematical system with
many degrees of freedom (OK, we'll go just a little further out to
find just a little bit brighter source and we'll integrate just a
little bit longer, and we'll trade off that slight decrease in
decorrelation efficiency by increasing the cycle time just a bit
to increase the time efficiency.... you get the picture -- there
are many dimensions to compensate when one of the assumptions
sours a bit).
When we went to 64 x 12m antennas, fast switching did not drastically
improve over 40 x 8m. Therefore, going to 50 x 12m won't drastically
decrease our phase calibration ability.
My 2 cents: these calculations WILL be performed again, sooner or later;
I actually had an error in the source counts code, which UNDERESTIMATED
the number of sources; there will be other reasons to redo the calc.
When enough reasons pile up, we'll redo the calcs using 50 x 12m
and the other "improvements in our modelling of reality". Is now that
time? I say no, what do you say?
- 21 Feb 2005