COMPUTER PROGRAMS USING ZONAL HARMONICS FOR MAGNETIC PROPERTIES OF CURRENT SYSTEMS WITH SPECIAL REFERENCE TO THE IBM 7090

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The magnetic vector and scalar potentials, magnetic field components and their derivatives, and flux linkage for single current systems, and the mutual inductance, forces and torques between two such systems, whose axes are coplanar but not necessarily coincident are discussed. Each system may include a combination of coaxial loops, cylindrical or plane annular current sheets, and cylindrical coils of rectagular section. Working equations are listed, following an outline of theory. A discussion of errors and of means for reducing them leads to specific suggestions ior use of the method with any programmed computer. An existing comprehensive program for the IBM ... continued below

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Pages: 46

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Garrett, M.W. December 1, 1962.

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Description

The magnetic vector and scalar potentials, magnetic field components and their derivatives, and flux linkage for single current systems, and the mutual inductance, forces and torques between two such systems, whose axes are coplanar but not necessarily coincident are discussed. Each system may include a combination of coaxial loops, cylindrical or plane annular current sheets, and cylindrical coils of rectagular section. Working equations are listed, following an outline of theory. A discussion of errors and of means for reducing them leads to specific suggestions ior use of the method with any programmed computer. An existing comprehensive program for the IBM 7090 is described in detail. The rate of convergence of the harmonic series depends on the ratio R of the polar radius of the field point to that of the current discontinuity nearest the origin. In some cases the precision reaches 1000 parts per million even at R = 0.95, improving to 1 or 2 parts at R = 0.80. Since the origin is arbitrary, the practical range of the method often includes the whole space that is accessible to experiment. For very close approach to the windings one must resort to elliptic integrai methods or their equivalent. Alternative programs that were previously used are compared with the method of zonal harmonics, but they are slower by more than a factor of 10 when large numbers of field calculations must be made on a complex curCent system. One example is the problem of following individual ions through paths in the order of 100 turns in a field that is generated by 20 coaxial thick coils; available competing methods would have required too much computer time. The zonal harmonlc method also has superior flexibility in attacking a wide range of problems. This is especially true for the calculation of rates of change, with respect to coordinates of the field or of the generating system, and for problems in which some property of a system must be not only calculated, but also adjusted to meet a specification. (auth)

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Pages: 46

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  • Other Information: Orig. Receipt Date: 31-DEC-63

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  • Report No.: ORNL-3318
  • Grant Number: W-7405-ENG-26
  • DOI: 10.2172/4764485 | External Link
  • Office of Scientific & Technical Information Report Number: 4764485
  • Archival Resource Key: ark:/67531/metadc1028643

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Creation Date

  • December 1, 1962

Added to The UNT Digital Library

  • Oct. 18, 2017, 7:39 a.m.

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  • Oct. 23, 2017, 12:24 p.m.

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Garrett, M.W. COMPUTER PROGRAMS USING ZONAL HARMONICS FOR MAGNETIC PROPERTIES OF CURRENT SYSTEMS WITH SPECIAL REFERENCE TO THE IBM 7090, report, December 1, 1962; Oak Ridge, Tennessee. (digital.library.unt.edu/ark:/67531/metadc1028643/: accessed October 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.