Analytical method of determining the electromagnetic field of standard current pulses flowing near to a conductive object

2019;
: pp. 49-56
Authors:
1
Institute of Electrodynamics of the National Academy of Science of Ukraine

The mathematical model based on the developed theory of the analytical solving the quasi-stationary tasks of pulse current flowing near to a conductive object with flat surface is introduced. The applied mathematical model includes an approximate solution with the use of asymptotic expansion for computing the intensity of a magnetic and electrical field in the case of transient electro-magnetic processes. It is noted that the calculations by an approximation method are limited to a certain time period from the beginning of a pulse, but, as usual, just within this time period the field changes most rapidly and accesses maximum values. The electrical field is considered at the presence of the standard current pulses such as exponentially decaying pulse, pulse represented by the difference between two decaying exponents, exponentially decaying oscillating pulse. For them the main peculiarities of applying the approximate analytical method of field calculations have been analyzed. Integral indicators for taking into account limitations by frequency and time, depending on the pulse parameters, have been found. Time dependencies have been obtained with the use of special functions and their representation as series.

  1. B. Larionov, F. Spevakova, A. Stolov, and E. Azizov, Problems of accumulation and conversion of electromagnetic energy in pulsed power systems with inductive drives. Physics and technology of powerful impulse systems. Moscow, USSR: Energoatomizdat, 1987. (Russian)
  2. V. Brzhezytskyi., I. Isakov, and V. Rudakov, High voltage engineering and electrophysics. Kharkiv, Ukraine: National Technical University “Kharkiv Polytechnic Iistitute” Tornado, 2005. (Ukrainian)
  3. E. Velihov, Physics and technology of powerful impulse systems. Moscow, USSR: Energoatomizdat, 1987. (Russian)
  4. Yu. Batygin, N. Lavinskyi, and L. Khimenko, Pulsed magnetic fields for progressive technologies. Kharkiv, Ukraine: MOST-Tornado, 2003. (Russian)
  5. Yu. Vasetskiy, D. Vlasov, O. Konovalov, and V. Mikhailov, “Some solutions to the problem of continuation of a plane field in elementary functions”, in Proc. International Conference “Simulation-2012”, pp. 232–236, Pukhov Institute for Modelling in Energy Engineering of National Academy of Sciences of Ukraine, 2012. (Russian)
  6. V. Mikhailov and N. Petrenko, “Approximation of Exact Massive Solenoid Profile for Generating Pulsed Magnetic Field”, Technical Elektrodynamics, no. 1, pp. 13-16, 2018. (Russian)  https://doi.org/10.15407/techned2018.01.013
  7. G. Stepanov and A. Babutskiy, The effect of high-density pulsed electric current on the strength of metallic materials and the stress-strain state of structural elements. Kyiv, Ukraine: Naukova dumka, 2014. (Russian)
  8. Yu. Vasetskyi, I. Kondratenko, O. Pashchyn, and K. Dziuba, “Machining welded joints with a pulsed electromagnetic field with a strong skin effect”, Works of the Institute of Electrodynamics of the National Academy of Sciences of Ukraine, no. 49, pp. 68-76, Kyiv, Ukraine: Institute of Electrodynamics of the National Academy of Sciences of Ukraine, 2018. (Ukrainian) https://doi.org/10.15407/publishing2018.49.068
  9. Yu. Vasetskiy and I. Mazurenko. “The geometric parameters of electromagnetic systems for high-frequency induction heating of metal tapes”, Technical Eletrodynamics, no. 5, pp. 9-15, 2009. (Russian)
  10. Yu. Vasetskyi and I. Mazurenko , “Approximation mathematical models of electromagnetic and thermal processes at induction heating of metal strips”, Computational Problems of Electrical Engineering, no 1, pp. 45-50, 2011.
  11. Yu. Vasetskiy, I. Kondratenko, A. Rashchepkin, and I. Mazurenko, Electromagnetic interactions between current contours and conductive medium. Kyiv, Ukraine: Pro Format, 2019. (Russian)
  12. Yu. Vasetskyi and K. Dziuba, “An analytical calculation method of quasi-stationary three-dimensional electromagnetic field created by an arbitrary current loop located near a conducting body”, Technical Electrodynamics, no. 5, pp. 7-17, 2017. (Russian)
  13. Yu. Vasetskyi and K. Dziuba, “Three-Dimensional Quasi-Stationary Electromagnetic Field Generated by Arbitrary Current Contour Near Conducting Body”, Technical Electrodynamics, no 1, pp. 3-12, 2018. https://doi.org/10.15407/techned2018.01.003
  14. A. Nayfeh, An Introduction to Perturbation Techniques. New York, USA: A Willey-Interscience Publication, 1981.
  15. V. Smirnov, Higher Mathematics, vol. 3, part 2. Moscow, USSR: Nauka, 1974. (Russian)
  16. K. Dziuba, I. Mazurenko, and Yu. Vasetskyi, “An Assessment of Accuracy of Approximate Mathematical Model of Pulse Electromagnetic Field of Current Flowing near Conductive Body”, in Proc. 16th Intern. Conference on Computational Problems of Electrical Engineering (CPEE-2015), pp. 36-38, Lviv, Ukraine: Lviv Polytechnic National University, 2015. https://doi.org/10.1109/CPEE.2015.7333331
  17. Yu. Vasetskyi, Three-dimensional quasi-stationary electromagnetic field of a current located near a conducting body. Kyiv, Ukraine: Pro Format, 2019. (Russian)  https://doi.org/10.15407/techned2018.01.003
  18. K. Polivanov, Theoretical bases of electrical engineering, vol. 3, The theory of electromagnetic field. Moscow, USSR: Energiya, 1969. (Russian)