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VOLUME 22, NUMBER 15 PHYSICAL REVIEW LETTERS 14APRIL1969 and the linearized Boltzmann equation solved for the perturbed velocity distribution. The current density can then be calculated and related back to the electric field by means of Maxwell's equations so determining the coefficients a n . For a) «w. and a Maxwellian velocity distribution in the unperturbed state,where B(a) is the amplitude of the magnetic field at x = ±a, c 0 is the most probable speed of electrons, Z(|) is the plasma dispersion function, 7 and £ zz 2av(i-(x)/v)('nc ( fi)~1. The electromagnetic field and the current distributions are then determined, leading to a value for R. In making these calculations we put i>= ^en + ^ei> where the electron-ion collision frequency u e i was obtained from an expression for the resistivity of a fully ionized plasma given by Spitzer. 8 The theory confirms the presence of a critical frequency and density for which R is much greater than predicted by cold plasma theory. Theoretical values of R are shown in Fig. 1 for a frequency near the critical value. Despite the plane geometry used in the theoretical treatment, the theory gives a good description of the observed field penetration. On the other hand, the coldplasma theory in plane geometry giveswhich is plotted in Fig. 1 for the same value of

The presence of superconducting surfaces in the vicinity of current sources may be interpreted in terms of image theory. This concept has both experimental and theoretical practicality. Experimentally, sensing coils for magnetic detection, when placed near such surfaces, perform in a gradiometric fashion. In order to explain this effect explicitly, a theoretical treatment of the magnetic fields in the presence of superconducting surfaces and coils is presented. Expressions are derived for planar and spherical geometries that approximate practical experimental situations. These expressions may be used to predict the expected gradiometric response of a coil as a function of the positions of the source and coil relative to the surface.

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RECEIVEDAbstract-A superconducting imaging-surface system was constructed using 12 coplanar thin-am SQUID magnetometers located parallel to and spaced 2 cm from a 25 cm diameter l a d imaging-plane. Some measurements included two additional sensors on the "back" side of the superconducting imaging-plane to study the field symmetry for our system. Performance was measured in a shielded can and in the open laboratory environment. Data from this system has been used to: (a) A phantom source field was measured at the sensors as a function of phantom distance from the sensor array to verify the imaging theory. Both the shape and absolute values of the measured and predicted curves agree very well indicating the system is behaving as a gradiometer in accordance with theory. The output from SQUIDS located behind the imaging surface that sense background fields can be used for software or analog background cancellation. Fields arising from sources close to the imaging plane were shielded form the background sensors by more than a factor of 1000. Measurement of the symmetry of sensor sensitivity to uniform fields exactry followed theoreticaI predictions.