MAGNETIC FIELDS

Six permanent magnets cemented to the test masses and other interferometer 
optics are used to position the optics. The pole strengths and orientations 
of the magnets are balanced to minimize the coupling of optic motion 
to time-varying ambient magnetic fields. Even so, the optics will shake if 
the pole strengths of the magnets are not identical or if different magnets 
are subject to different ambient fields. To estimate the displacement noise 
using ambient field data and to better understand this problem for current 
and future versions of LIGO, we have undertaken four projects. First, 
measurements of ambient fields inside and outside of BSC vacuum chambers. 
Second, development of a diagnostic system to shake the optics using 
externally generated magnetic fields. Third, investigation of the transfer 
function from outside to inside of the chambers. And fourth, experimental 
measurements of the gradients produced by optic support structures subjected 
to known fields. Robert Schofield presented a talk at the Stanford LSC
meeting detailing progress on these projects; progress is summarized below 
but additional details are available from the transparencies 
at http://www.ligo.caltech.edu/LIGO_web/9907lsc/9907trans.html

1) Measurements of ambient fields inside and outside of BSC chambers

We have measured ambient magnetic fields inside of two BSC chambers, BSC-8 
and BSC-7. The seismic isolation stacks and optical tables were in place but 
the optics and optic support structures were not. Measurements inside of 
BSC-8 were preliminary measurements made while Robert was helping install 
the down-tube assembly. The door was open and the Bartington MAG03 
magnetometer positioned by hand. The door was closed for measurements inside 
of BSC-7; two magnetometers were affixed one foot apart on a plunger and 
slid along inside of a 4 inch fiberglass tube connecting ports on opposite 
sides of the chamber. Field measurements were recorded for all three axes of 
each of the two magnetometers at each location. Approximate field gradients
were obtained in a second set of measurements by subtracting the magnetometer 
signals in a Stanford SR560 preamp. To check these gradient measurements, 
gradients were also calculated by subtracting 60 Hz field measurements for 
successive positions along the tube. The two sets of 60 Hz gradient values 
were in agreement. The positioning repeatability and the relative calibrations 
of the two magnetometers were determined using generated fields and were 
both 7% or less for all axes. The absolute calibration of the magnetometers 
was checked by comparing measured field values and values calculated from 
coil geometry and current.

The average and standard deviation of the 60 Hz field at seven locations 
inside of BSC-7 was 3.73 (+/-0.22) nT rms. For the three locations in BSC-8 
the average was 1.64 (+/-0.21) nT rms. The averages of the fields around 
these chambers were about 3 times higher. A more detailed table of 
measurements inside and outside of the chambers as well as a comparison 
with outside measurements by Weiss and Savage and Johnson et al. are 
available at   http://www.ligo.caltech.edu/LIGO_web/9907lsc/9907trans.html. 
Field noise inside BSC-7 averaged about 9.6 (+/- 1.4) pT/sqrt Hz rms at 50 Hz. 
Magnetic field gradients at 60 Hz were 2.3(+/- 0.92) nT/m rms and gradient 
noise at 50 Hz was greater than 7 and less than 20 pT/m sqrt Hz rms. 

A simplified model of the coupling between fields and mirror motion similar 
to one used by Dennis Coyne but including the measured variation of magnetic 
fields over the distance between magnets was used to calculate displacement 
noise from the measured fields and gradients. The displacement noise due to 
the measured gradients was estimated to be below 2 x 10e-20 m/ sqrt Hz at 
50 Hz. This is more than a factor of three below the allowable level for 
displacement noise terms in LIGO 1. The displacement noise estimated from 
measured fields (coupling through torques on the magnets and a 1mm assumed 
offset of the beam from the mirror center) was more than an order of magnitude 
below the estimated displacement noise due to measured field gradients. 
These fractions of the LIGO standard were relatively consistent over the 
5-800 Hz frequency range. 

2) Diagnostic system for magnetically shaking optics

To shake optics, we constructed two 1m diameter coils of 12 gauge varnished 
copper wire wound on plywood spools. Either 10, 30, 60 or 100 turns can be 
selected. The coils are mounted on aluminum tripods with a 5 to 8 foot 
adjustable height. Two coils were built so that the coils could be placed 
on opposite sides of the chamber in a Helmholtz-like configuration in order 
to produce either fairly uniform fields or, with the current direction in 
one coil reversed, fairly uniform field gradients in the central region of 
the vacuum chamber.

We decided to map out the field that the coils produced inside of a chamber 
for a positioning of the coils that would work for any of the variable 
BSC configurations. The field produced by the coils in the selected position 
was measured along the transept of the ambient field measurements mentioned 
above. The fiberglass tube was then repositioned between a second set of 
ports to provide an `X' shaped distribution of measurements in the plane 
containing the main laser beam and the center of the coils. To map out the 
fields for frequencies between 1 and 1000 Hz, the coils were driven in series 
by a 3Vp-p swept sinusoidal signal from the HP 35670A analyzer. The signal 
analyzer recorded the ratio of the voltage from the magnetometer inside the 
chamber to the voltage drop across a resistor in series with the generating 
coils; this ratio is proportional to the ratio of the measured internal field 
strength to the generated field strength. At 1000 Hz, the ratio of internal 
to generated field strength was about 1/20 of its value at 1 Hz because 
of attenuation due to eddy currents in the chamber walls. Field maps for 
the constant gradient coil configuration showed that the measured gradients 
were relatively constant in the central region of the chamber, as designed.

3) An approximate transfer function

The swept sine measurements mentioned above can be used to obtain an 
approximate transfer function for magnetic fields from outside of the chamber 
to inside. This transfer function is of interest because the planned position 
of magnetometers is outside of the chambers.

If the wall of the BSC is imagined to be a planar circuit in a normal 
magnetic field, we would expect the functional form of the attenuation due 
to eddy currents to be that of a single pole low-pass filter. A fit of data 
from near the central axis of the coils gave the following ratio of fields 
with and without the chamber present:

Away from the axis and above 100 Hz this fit departs increasingly from the 
data. This departure is thought to be due to the increasing importance of 
the variation from the assumed geometry for locations that were off-axis and 
for higher frequencies. We believe that more sophisticated models should 
be pursued.

Nevertheless, this transfer function, obtained from measurements of generated 
fields, works quite well for 60 Hz ambient fields. This transfer function 
predicts an attenuation factor of about 0.32 at 60 Hz. The ratio of the 
average value of 7 ambient field measurements inside of BSC-7 (mentioned above) 
to the average of 12 measurements at outside locations around the chamber 
was 0.35. This ratio for four measurements inside and 7 measurement locations 
outside of BSC-8 was 0.37

4) Experimental measurement of gradients produced by optic support structures

Magnetic field gradients produced by optic support structures may significantly 
increase the displacement noise of an optic. The support structures were not 
in place for our measurements because it would be difficult and dangerous 
to measure fields near an in-place optic. We plan to measure gradients produced 
by an isolated optic support structure. The support structure will be subjected 
to ambient fields and fields produced by our coils.

In addition to continuing with the four projects mentioned above, we plan to 
investigate sources of ambient fields. We have, for example, suggested that 
the wall mounted emergency light be moved away form BSC-8 because its 
transformer is a large source. We have also noticed that the seismic isolation 
piers are magnetized, in some cases turning a compass needle through 180 
degrees at 1m. A back of the envelope-type calculation suggests that the 
field noise produced by vibrating piers will be small compared to measured 
field noise but we would like to investigate this further. Field noise 
produced by lightning strikes may also be a useful area for us to investigate.