Pulsed Magnetic Field Measurement Outside Finite Length Solenoid: Experimental Results & Mathematical Verification

Shibaji Basu, Siddhartha Shankar Pany, Partha Bannerjee, Sabyasachi Mitra

Accelerator & Pulse Power Division, Bhabha Atomic Research Centre, Mumbai, India.
Accelerator & Pulse Power Division, Bhabha Atomic Research Centre, Vishakapatnam, India.
Electronics & Instrumentation Services Division, Bhabha Atomic Research Centre, Mumbai, India.
Energetics & Electromagnetics Division, Bhabha Atomic Research Centre, Vishakapatnam, India.

DOI: 10.4236/jemaa.2013.510059                

Abstract

The paper deals with magnetic field mapping outside a finite length solenoid electromagnet, by an in-house designed and calibrated inductive pick-up or search coil. The search coil is calibrated in a unique methodology based on the azimuthal magnetic field component generated by a straight wire. This unique calibration technique helps us to avoid additional circuitry to integrate the signal obtained from search coil. The methodology proves advantageous in diffusion, implosion studies where the signal frequency changes with dimension and material of experimental job-piece (hollow metal tube). Remedial measures have been taken to avoid electrostatic capacitive pick-up (which eventually exacerbates with integration) keeping measurement simple and accurate. The experimentally measured field values have also been compared with electromagnetic field results obtained from mathematical calculations and finite element based simulations. Two different mathematical approaches have been demonstrated for field computation based on Biot-Savart Law. Both the methods have taken into account the exact geometry of the solenoid, including the inter-turn gaps. The methods use appropriate combination of closed-form mathematical expression and numerical integration techniques and are capable of determining all the vector components of magnetic field anywhere around the finite length solenoid. The mathematical computations are equally significant contributions in the paper especially because exact determination of magnetic fields outside finite length solenoids has not been discussed in sufficient specific details in already existing literature. The mathematical computations, finite element simulations and experimental verification together provide a holistic solution to magnetic field determination problems in pulse power applications that have not been discussed in available literature or books in specific details.

Keywords

Pulsed Magnetic Field; Biot-Savart Law; Search Coil

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	O. Espinosa and V. Slusarenko, “The Magnetic Field of Infinite Solenoid,” American Journal of Physics, Vol. 71, No. 9, 2003, pp. 953-954. http://dx.doi.org/10.1119/1.1571841
[2]	J. Farley and R. H. Price, “Field Just Outside a Long Solenoid,” American Journal of Physics, Vol. 69, No. 7, 2001, p. 751. http://dx.doi.org/10.1119/1.1362694
[3]	B. B. Dasgupta, “Magnetic Field Due to a Solenoid,” American Journal of Physics, Vol. 53, No. 8, 1985, pp. 782-783. http://dx.doi.org/10.1119/1.14318
[4]	H. E. Knoepfel, “Pulsed High Magnetic Fields,” North-Holland Publishing Company, Amsterdam, London.
[5]	V. Labinac, N. Erceg and D. Kotnik-Karuza, “Magnetic Field of a Cylindrical Coil,” American Journal of Physics, Vol. 74, No. 7, 2006, p. 621.
[6]	A. I. Rusinov, “High Precision Computation of Solenoid Magnetic Fields by Garrett’s Methods,” IEEE Transactions on Magnetics, Vol. 30, No. 4, 1994, pp. 2685-2688. http://dx.doi.org/10.1109/20.305833
[7]	V. I. Danilov and M. Ianovic, “Magnetic Fields of Thick Finite DC Solenoids,” Nuclear Instruments and Methods, Vol. 94, No. 3, 1971, pp. 541-550. http://dx.doi.org/10.1016/0029-554X(71)90019-X
[8]	H. E. Knoepfel, “A Comprehensive Theoretical Treatise for Practical Use,” John Wiley Sons, INC., Hoboken.
[9]	A. S. Bozek and E. J. Strait, “Manufacturing of Magnetic Probe Coils for DIII-D,” General Atomics Report GAA24492.
[10]	P. G. Mattocks, “Copper-Beryllium Search Coils and the Measurement of Small Magnetization Pulsed Magnetic Fields,” Journal of Physics E: Scientific Instruments, Vol. 12, No. 7, 1979, p. 658.
[11]	J. Novickij, R. Kacianauskas and A. Kaceniauskas, “Axial Magnetic Field Measurements of Pulsed,” Elektronika IR Elektrotechnika, 2004. Nr. 2(51).
[12]	S.E. Segre and J.E. Allen, “Magnetic Probes of High Frequency Response,” Journal of Scientific Instruments, Vol. 37, No. 10, 1960, p. 369.
[13]	S. Basu, et al., “Pulsed Magnetic Field Measurement outside Finite Long Solenoid Implementing Novel Calibration Technique,” 7th IEEE International Vacuum Electronics Conference, Bangalore, 21-24 February 2011, pp. 415-416.
[14]	MIT Lecture Notes, Chapter 9, pp. 4-6. http://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide09.pdf