Distortion of a Magnetic Field by the Motion of a Cylindrical Conductor


Book Description

Motion of a conductor relative to a magnetic field distorts the field. This paper considers a cylindrical slug moving in a two-dimensional magnetic field, represented by the vector potential A sub 0 theta, where the partial derivative of A sub 0 with respect to theta = 0. Maxwell's equations are solved for the distorted potential A theta in the form of a rapidly converging series A = & A sub n. The A sub n's are given in a form suitable for evaluation by a digital computer. The nonequivalence of the apparently analogous problem of a stationary slug in a time-varying field is noted and discussed. (Author).




On the Theory of Boolean Formulas


Book Description

The theory of substitutions for Boolean formulas developed in a previous report is applied here to the determination of those s-tuples of formulas that may be allowable replacements for s -tuples of sub-formulas of given Boolean formulas. The criteria of allowability are very general and flexible, yet may be expressed with great precision and ease. The results formalize and extend various known isolated instances. They may be used for the study of a large number of problems in the theory and application of Boolean formulas and functions.










Asymptotic Solutions of Dipoles in a Semi-infinite Medium


Book Description

A theoretical analysis is made of the electromagnetic fields in two homogeneous media separated by a plane interface with a point source located in the denser medium. The solution is expressed in the form of integrals which cannot be evaluated explicitly. Asymptotic evaluations of the integrals have been made by many investigators using the saddlepoint technique. In the present work, all known asymptotic results are presented in one comprehensive form, using a modification of the method suggested by Lighthill for the asymptotic evaluation of the Fourier integrals. The regions of validity of the solutions are indicated wherever possible. The advantage of this method over others is its ease and simplicity. The present results agree term by term with the earlier ones of Banos and Wesley (1953-1954), and Paul (1959), who investigated the case of a source and receiver close to the interface, and an arbitrary location of source and receiver, respectively. The results obtained in the report are also compared with those of Stein (1955). (Author).







Production of H− (1s2) by Hydrogen Atom Collisions


Book Description

The prior and post Born matrix elements are used to calculate the cross sections for H( - )(1s2) production in hydrogen atom collisions. In contrast to the original version of this work done by Mapleton in 1960, the plane wave approximation to the Coulomb function is partially corrected. The same H( - ) wave functions are used, and the post cross sections are substantially unaltered. Cross sections calculated with the improved H( - ) wave function as compared with the other H( - ) wave functions are from twenty to thirty-five per cent larger for the prior case and twenty to thirty per cent larger for the post case. The post-prior discrepancy, expressed as a ratio, varies between 0.001 and 0.33. (Author).







Directivity and Beamwidth Approximations for Large Scanning Dolph-Chebyshev Arrays


Book Description

Directivity and beamwidth for radiation patterns corresponding to the optimum Dolph-Chebyshev design have heretofore been determined by means of formulas that, although exact, are intractable to computation and not particularly open to physical interpretation. Approximate but accurate formulas are presented here in closed form, for the purpose of easy examination and computation of directivity and beamwidth for large scannable Dolph-Chebyshev arrays. Array length, number of array elements, the spacing of these elements, and the sidelobe level desired are parameters in this study. The maximum achievable directivity for Chebyshev arrays is in principle limited, regardless of how large the array becomes. Data is given to establish the array length required to obtain a value of directivity at some prescribed level below the maximum value. Comparisons between exact and approximate theory are presented in graphical form in such a way as to illustrate the lower limits of array size for which the approximations are valid. Element spacings less than a half-wavelength are included in this study. (Author).




Ferrous Ammonium Sulfate - Cupric Chloride Solutions for Dosimetry of a Kilocurie Cobalt-60 Source


Book Description

Aqueous solutions of ferrous ammonium sulfate with cupric chloride were studied as a means for determining the uniformity of the dose rate around a multikilocurie cylindrical array of cobalt-60. Ferric ion was measured spectrophotometrically at 305 millimicrons. The solution selected to satisfy the requirements for dosimetry contained 0.0005 M ferrous ammonium sulfate and 0.005 M cupric chloride in 0.001 N sulfuric acid. Spectrophotometric measurements of ferric ion were made in solutions brought to 0.15 N acid concentration, instead of the conventional 0.8 N, in order to minimize spurious oxidation. The molar extinction coefficient at this normality proved to be the same as that in 0.8 N solutions. The G value, as compared to the standard ferrous-ferric dosimeter, was 0.65. Using these solutions, no detectable variation in dose rate was found at symmetrically equivalent positions at the center of the cobalt-60 source. The average dose rate at each end of the cylindrical array proved to be 12 percent lower than that at the center. The dose rate was also less uniform at the ends, varying by = 4 percent from point-to-point. At a distance of fifteen inches from the center of the source array, the dose rate decreased as the square of the distance. (Author).