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LIGO MIT NewsToo Much
ThinkingWorrying Can Get You In Trouble!
During the course of the LIGO Beam Tube installation, in fact rather late in the process, I woke up once in the middle of the night wondering why we had all been so stupid. None of us had ever thought simply to look down the Beam Tube directly and determine in the crudest possible way--with our eyes!--whether or not the tube was at least grossly aligned, and whether the baffles really worked to eliminate the reflection rings.
At the time we were doing all sorts of elegant and fancy stuff to determine the alignment to fractions of a centimeter over several kilometers with the Global Positioning System (GPS). All manner of gadgets were employed to aid in this alignment. In particular, Chicago Bridge & Iron (CB&I) had designed a precision GPS antenna translator, much like the table on a milling machine, intended to help in carrying out systematic error tests. Meanwhile we LIGOnians had contributed techniques to reduce the sensitivity to antenna back lobes as well as algorithms and techniques to improve the confidence of the alignment. With all this effort and depth of understanding in this high class technology, it should have been evident that things were in good hands. But when I awoke that night at 4am, there was a stark clarity in the anxiety that we could be pulling a blunder similar to the mensuration of the Hubble Space Telescope mirror, and that an overall baby-simple check would clearly be a good thing to do.
I called Larry Jones as soon as he got in (which was usually around 7am Pacific, after a pedal to the metal drive across the mountains from the desert). We decided that at worst it would be a small increment in the contract with CB&I to ask them to hold the equivalent of an automobile head lamp at the center of one end of a 2km module, while Larry and I looked down the tube from the other end. By the middle of that California morning it had been established that CB&I was willing to carry out the test free of charge and it was all arranged for the June 1998 CB&I/LIGO monthly meeting at Livingston.
So shortly before 8am, just before the monthly meeting, Larry and I, dressed in the protective "bunny suits," gazed intently into the blackness of the Beam Tube for Dennis Dickenson and Steve Hand of CB&I to turn on the light. We both saw it at once. The light was centered horizontally but was about a foot low in the vertical direction in the tube. The thought that the Beam Tube could have been this much out of alignment was clearly unacceptable, but then this kind of "discovery" was the basis for performing the test in the first place.
When an issue really matters, one's mind can shift into high gear real fast, even without the fuel of coffee. One immediately begins to sift through the various phenomena that one should have thought of but had neglected, or forgotten about. In less than a minute, we decided it was a pretty good bet that what we were experiencing was either vertical thermal gradients (meaning that hot air rises and is thinner), or the nonuniform atmosphere, which cause a change in pressure with height.
It turns out that it was both effects which had been at work, and had the thermal gradients been even larger, we would not have been able to see the light at all. Instead of exiting the tube a foot low after 2km, it could have been a bigger effect and the light beam would never have been seen at the exit! I don't really want to contemplate the drama of that eventuality, but our first thought would probably have been that CB&I had left a purge dam in the finished Beam Tube. And in our high state of dismay, we might have acted on that premise. The night time worrying would then have really caused some mischief.
Just recently at the end of December, after the bakeout of the Y1 module in Hanford, Mark Lubinski, Mark Guenther, Larry Garrelts and I tried this observation all over again. This time the module was pumped out and we used some glass observation ports that had been installed at the ends of the module at Mike Zucker's instruction for the serious business of interferometer alignment. Larry held a light at one end and Mark L. and I had a look from the other end. The light was clearly centered on the tube, and better still, we saw no reflection rings or diffracted light from the source. It was just as we would have predicted in the absence of air, and obviously most satisfying.
The physics of what had happened in Livingston that morning is really quite straightforward. The difference in pressure at the top of the tube from the bottom is due to the weight of the air in the tube, the pressure being slightly higher at the bottom. The density of the air varies smoothly from the top of the tube to the bottom, and causes the index of refraction of the air to be slightly smaller at the top of the tube than at the bottom. Light travels more quickly at the top of the tube than at the bottom and the normal to the planes of constant phase, the light propagation direction, gets bent downward. The atmosphere obeys a pressure dependence that is exponential with altitude. The scale height, h0 , is about 8km. Similarly, if there is a vertical temperature gradient with the tube being hotter at the top than at the bottom, one gets a downward bending as well. The vertical light deflection after a distance L is given by
where T0 is room temperature, nominally 300K, and (n-1)0 = 3 x 10-4 is the part of the index of refraction due to the gas at room temperature and standard pressure of 760 torr. In a distance L = 2km = 2 x 105 cm, the deflection downward is about 7.5 cm from the standard atmosphere and an additional 20 cm for a vertical thermal gradient of 10-3 K/cm = 0.1 K/m, a value we have by now observed frequently.