Review of Gravity Probe B


3
Essentials of the GP-B Experiment


As described above, the geodetic and frame-dragging effects of relativistic gravity should cause the spin axis of a gyroscope in Earth orbit to precess. In a polar orbit the geodetic term is orthogonal to the frame-dragging term, and about 160 times larger. General relativity predicts the precession due to frame dragging to be about 42 milliarc sec/yr, or 1.2 x 10-5 deg/yr. The measured precession is expected to be 30 to 40 milliarc sec/yr, depending on the orbital altitude and the celestial declination of the chosen reference star. In order to be sensitive to such a tiny effect, the experimental strategy of GP-B is to use a drag-free satellite to minimize extraneous forces as much as possible, and to make the gyros and sensors superconducting for low noise. For redundancy four gyros are planned (two pairs made of different materials and spinning in opposite directions), with their axes pointing to the reference star. The aberration angle of the reference star varies throughout the orbit and the year, providing precise calibrations of convenient magnitude.



Figure 1. Gravity Probe B involves a precision gyroscope in low orbit and a small telescope locked onto a distant guide star. The geodetic and frame-dragging effects of relativistic gravity are expected to cause the gyro's spin axis to precess as shown throughout a yearlong experiment.


CRYOGENIC INSTRUMENTATION

The GP-B gyroscope rely on a number of unique phenomena found in superconductors. These include the generation of a magnetic field when a superconductor rotates (the London moment), and the exclusion of magnetic flux changes from the interior of cylinders and rings of superconductors (the Meissner effect).


London Moment

In the 1950s Fritz London produced a remarkable body of work on superfluids and superconductors. In his classic analysis of the symmetries related to superfluid phenomena, he discussed the quantization of circulation of flow and the related quantization of magnetic flux contained within superconducting cylinders, in integral multiples of the flux quantum 0 = hc/2e2 x 10-7 gauss cm2. (Here h is Planck's constant, c the speed of light, and e the charge of the electron.) In addition, he predicted the generation of a magnetic moment by a rotating superconductor.

London showed that electromagnetic coupling between the positive ions in a lattice and the superconducting electrons would produce a magnetic field in the interior of a spinning superconductor. The magnetic moment of a rotating sphere has a number of ideal properties for indicating the motion of a gyroscope. The field is directed along the spin axis and is independent of the specific material properties of the superconductor. Unfortunately, the London moment is numerically small, providing a field of only B 10-5 (in units of gauss), where is the spin frequency. Accurate tracking of the spin axis of a gyroscope using the London moment requires unusually sensitive measurements of changes in magnetic flux, together with a related set of designs and procedures to safeguard against spurious magnetic signals.


Spin Readout

Changes in orientation of the spin axes of GP-B's science gyroscopes are detected with a superconducting quantum interference device, or SQUID. The heart of a SQUID is a superconducting ring containing two Josephson tunnel junctions. When the magnetic flux through the ring changes, a current flows in the metal. The current flow produces a DC voltage across the pair of tunnel junctions. By using transformer coupling to the SQUID, magnetic flux signals from any number of sources can be imposed through the superconducting ring. Modern SQUIDs can detect modulated flux changes small than 10-60 in 1 sec. The SQUIDS developed for GP-B are state-of-the-art devices designed to yield optimal signals, and they have very weak magnetic coupling to the motion of the gyroscope itself. A great deal of thoughtful and creative effort has gone into the design of the electrical coupling to the SQUIDs and their shielding from environmental influences.

In the configuration used in GP-B, the SQUIDs are used as null detectors. A change in orientation of a gyroscope's London moment produces a current in a superconducting loop surrounding the sphere. That current is coupled to the SQUID by a transformer that induces a secondary current in the ring. This current produces a voltage that can be measured by external electronics. The null operation is achieved by feeding a small current back to another transformer circuit that couples the magnetic field into the SQUID ring. The sense and magnitude of the feedback current are arranged to cancel the voltage drop across the Josephson junction. A SQUID configured with such a servo-controlled current is said to be "flux-locked," since the scheme keeps the magnetic flux through the SQUID constant. The null detection method is very important to the gyroscope readout of GP-B, because it is intrinsically linear.

Operation of the SQUIDs and of their associated electronics has been thoroughly tested in conditions similar to those of the space mission. The sensitivity and long-term stability of the devices appear to be more than adequate for making the desired measurements of gyroscope precession. There is, moreover, an important redundancy in the design. Eight separate SQUID detectors are provided for the four gyroscopes. Despite the apparent complexity of the technique, it seems quite unlikely that a failure in the SQUID circuits will jeopardize the experiment.


Stray Magnetic Fields and Trapped Flux

The elegant principle involved in measuring the orientation of the London moment has one major difficulty: the moment itself is very small. In order for the desired signal to dominate, other sources of magnetic fields must be removed to an extraordinary degree. Superconductors trap the ambient field when cooled through the normal-to-superconducting phase transition. If the superconducting gyroscope surfaces trap even very small amounts of magnetic flux, thereby producing signals much larger than those related to the London moment, the experiment could be doomed. Although the effects of small remnant trapped fields may be effectively removed during later data analysis, signals from large quantities of trapped flux would dominate the SQUID readouts and render the desired data interpretation impossible.

Several measures have been taken in the design of GP-B to remove unwanted magnetic fields. The first relies on another property of superconductors. The amount of flux trapped within a superconductor is quantized in integral multiples of 0. The relevant procedure, devised through careful experiments by the GP-B group over the past 30 years, involves the exclusion of magnetic flux from the interior of a superconducting cylinder by sequential expansion of superconducting lead shields. After many repetitions, such a process could lead to a region with no magnetic field. The enclosure within the Dewar housing the GP-B gyroscopes has the final lead shield following multiple applications of the lead-bag expansion technique. Each step of shielding excludes flux by the ratio of the initial to final area of the expandable bag. In principle, even the last quantum of flux can be removed. The method has been developed by the GP-B group to a point where it is quite reliable. The initial magnetic field for the apparatus can be quite small indeed. The only problems related to trapped ambient flux are likely to come from magnetic fields associated with the support apparatus for gyroscope, or those that arise when the spheres are cooled.

Another important problem related to residual magnetic flux is that associated with the gyroscope sphere itself. Even in conditions of zero external magnetic field, superconducting bodies frequently produce significant trapped fields as they are cooled through the superconducting transition. Small thermal gradients in the metal at the time of the phase transition produce thermoelectric currents in the metal. Magnetic fields from such currents become trapped in the final superconducting state. In order to avoid such effects, great care must be taken in "annealing" the metal into its final state. Thermal gradients in the sphere at the transition temperature must be very small. Thermally induced magnetic flux in the superconducting spheres of GP-B has been measured and satisfactorily removed through sequences of repeated slow cooling through the superconducting transition. Relevant tests on the final apparatus can be conducted on the gyroscope spheres after they have been cooled to low temperatures, prior to launch of the satellite. The GP-B team has made careful studies of these phenomena, and it seems likely that trapped flux can be eliminated from the apparatus used in the experiment.

With regard to materials used in the apparatus, extensive tests and measurements have been made of all components located inside the lead shield. Some materials have been rejected becuase of their residually small (but still undesirable) magnetic properties. Only those components with innocuous magnetic properties have been retained in the final design.


Reliability

The low-temperature portion of the apparatus for GP-B is exceptionally complex. Many interrelated systems must work without recourse to room temperature recycling for repairs. Although the task group has found no obvious flaws in the concept, design, or ground tests of the apparatus, it notes that success of the GP-B experiment requires a sizable number of separate state-of-the-art devices to work correctly and simultaneously.

The gyroscopes are sensitive to torques thousands of times smaller than any that have been previously measured. This, the most critical aspect of the experiment, cannot be tested in normal gravity at the Earth's surface. Full sensitivity can be obtained only in conditions of near-zero effective gravity. As with any instrumentation attempting such a large jump in sensitivity, unanticipated problems or even new physical phenomena could interfere with the desired measurement of torques on the gyroscopes.


THE GENERATED SIGNAL

The London moment of each spinning gyro in GP-B is sensed by a pickup loop in a plane containing the star-tracking telescope axis. Along with the rest of the satellite, the loop rolls about that axis at a low (0.004-Hz) frequency. Any misalignment between the gyro and telescope axes is kept small, 100 arc sec. Since the gyro axis and the normal to the loop are nearly perpendicular, the London flux through the pickup is proportional to the small misalignment angle, corresponding to a magnetic field of the order 10-13 gauss. This flux is modulated at the roll frequency. The pickup loop is part of the superconducting primary circuit of the transformer in a DC SQUID magnetometer, the remainder consisting of the SQUID input coil. Conservation of magnetic flux through the primary circuit is maintained by a current in the transformer's secondary circuit. The resulting output signal is a voltage proportional to that of the secondary current. With two pickups on each of four gyros, eight such voltages are digitized and recorded with 16-bit precision.

Magnetometer signals appear also at other frequencies. Flux quanta trapped in the superconducting gyro rotors produce signals modulated at the spin frequency, around 125 Hz. The motion of the rotor's spin direction in its own body frame, called "polhoding," produces flux variations at the spin frequency, multiplied by a tiny factor arising from the 10-ppm fractional difference in the gyro's principal moments of inertia. Aberration of light from the reference star occurs both at the satellite's Earth orbital frequency and at the annual frequency of motion around the Sun. These aberrations are manifested as apparent precessions of the gyro axes at those frequencies. Also modulated at the satellite's Earth-orbital frequency and its harmonics are other effects, including periodic occultation of the reference star by the Earth.

The effects of relativistic gravity to be measured in the GP-B experiment include the 6600 milliarc sec/yr geodetic precession of the gyro axis in the satellite's polar orbital plane, and the frame-dragging precession, amounting to 42 milliarc sec/yr normal to that plane. Additional effects include a 7 milliarc sec/yr correction arising from the orbital eccentricity about the oblate Earth and a 19 milliarc sec/yr geodetic precession caused by the Earth's orbit around the Sun. Absolute calibration of the magnitude of the gyroscope precession signal will be achieved by comparing it to the signals caused by aberrations of the reference star.

Because the spacecraft rolls about the reference-star axis, separation of the frame-dragging and geodetic effects requires absolute determination of the roll phase. The goal of a 0.1 milliarc sec/yr contribution from this source to errors in the frame-dragging measurement requires determining the roll phase to 3 arc sec. Although it is monitored by an auxiliary "star blipper" telescope, the roll phase will be determined primarily by analysis of the reference-star aberrations mentioned above. the important role of annual aberration in this analysis severely bounds the time interval over which data must be acquired. For example, the GP-B experiment can be as much as five times more precise after 1 year of data collection than after 6 months.

During the extended data acquisition period of GP-B it will be desirable to update the analysis frequently. For this purpose an intermediate set of variables has been defined, in terms of which the analysis is linear. This makes possible the optimal use of a recursive Kalman filter for updating the experiment's status. Obtaining the quantities of ultimate interest requires a subsequent nonlinear analysis that can be done periodically. The performance of the relevant software, and of a significant portion of the GP-B hardware and data acquisition system, has already been tested by simulating the expected input signals to the SQUID and exercising the readout and analysis sequence.




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