Revista 27 - 3

Published

2007-09-01

A review of magnetic insulation

Una revisión del fenómeno de aislamiento magnético

DOI:

https://doi.org/10.15446/ing.investig.v27n3.14857

Keywords:

magnetic insulation, power flow, stationary flow, Child-Langmuir condition, plane vacuum diode, Vlasov-Maxwell solutions, upper and lower solutions (en)
aislamiento magnético, flujo de potencia, flujo estacionario, condición de Child-Langmuir, diodo plano al vacío, sistema Vlasov-Maxwell, soluciones superiores e inferiores (es)

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Authors

  • Zósimo Arévalo Velosa Universidad de lbagué
  • Alexander V. Sinitsyn Universidad de Ibagué
  • Octavio Alejandro Castañeda U. Universidad de Ibagué
  • Miguel Hernando Camelo B. Universidad de Ibagué

High energy devices are designed to work with extremely high electric and magnetic fields. As a consequence, these devices show non-linear phenomena and behavior, such as magnetic insulation which alters electron trajectory. A mathematical analysis and review of magnetic insulation were carried out as a consequence of nonlinearity to find frontier conditions and solutions to the problem. This paper was aimed at presenting the topic in a way which is easier for that part of the academic community which is unfamiliar with it to understand it. The paper gives a description of the phenomena developed by high electric and magnetic fields in a vacuum plane diode, some equations modelling the phenomenon, proves its existence and finds positive solutions based on upper and lower solutions for boundary limit problems and gives some practical applications.

Los dispositivos de alta energía son diseñados para que funcionen con campos eléctricos y magnéticos extremadamente altos. Debido a esto, dichos dispositivos presentan fenómenos y comportamientos no lineales, como el aislamiento magnético que altera el transporte de los electrones. La no linealidad ha obligado a analizar y revisar desde el punto de vista matemático las condiciones de frontera y las soluciones del problema. El objetivo de este trabajo es exponer el tema a un nivel que facilite su difusión entre la comunidad académica no familiarizada con el mismo. Para ello, el trabajo presenta una descripción de los fenómenos que se generan cuando hay campos eléctricos y magnéticos muy altos, tomando el caso de un diodo plano al vacío, así como las ecuaciones que modelan el fenómeno de aislamiento magnético; también demuestra la existencia de las soluciones y encuentra las positivas en base a los métodos de solución superior e inferior para problemas de valor de frontera, y proporciona algunos ejemplos de aplicación del fenómeno de aislamiento magnético.

References

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Creedon, J. M., “Magnetic cutoff in high-current diodes”, en J. Appl. Phys., Vol. 48, No. 3, 1977, pp. 1070-1077. DOI: https://doi.org/10.1063/1.323782

Degond, P.; Raviart, P. A., “An asymptotic analysis for the one-dimensional Vlasov-Poisson system”, en Asymptotic Anal. 4, 1991, pp.187-214. DOI: https://doi.org/10.3233/ASY-1991-4301

“On a penalization of the Child-Langmuir emission condition for the one dimensional Vlasov-Poisson equation”, en Asymptotic Anal. 6, 1992, pp. 1-27. DOI: https://doi.org/10.3233/ASY-1992-6101

Dulov, E. V.; Sinitsyn, A. V., “A numerical modeling of the limit problem for the magnetically noninsulated diode”, en Appl. Mathematics and Computation, Vol. 162, 2005, pp. 115-154. DOI: https://doi.org/10.1016/j.amc.2003.12.082

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Enciclopedia Wikipedia., disponible en: http://en.wikipedia.org/wiki/Vacuum_diode#History Of Development, consultado en Nov. de 2007.

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Langmuir, I.; Compton, K. T., “Electrical discharges in Gases: Part II., Fundamental Phenomena in Electrical Discharges”, en Rev. Mod. Phys., 3, 1931, pp. 191-257. DOI: https://doi.org/10.1103/RevModPhys.3.191

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Sinitsyn, A. V., “Positive solutions of nonlinear singular boundary-value problem of magnetic insulation”, Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Matemáticas, Reportes Internos, No. 84, 2002.

Sinitsyn, A.V.; Dulov, E. V., “Trabajos propuestos para el I semestre de 2005., Maestría en Matemática Aplicada”, Universidad Nacional, Bogotá, www.unal.edu.co, consultada en febrero de 2007.

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How to Cite

APA

Arévalo Velosa, Z., V. Sinitsyn, A., Castañeda U., O. A. & Camelo B., M. H. (2007). A review of magnetic insulation. Ingeniería e Investigación, 27(3), 159–171. https://doi.org/10.15446/ing.investig.v27n3.14857

ACM

[1]
Arévalo Velosa, Z., V. Sinitsyn, A., Castañeda U., O.A. and Camelo B., M.H. 2007. A review of magnetic insulation. Ingeniería e Investigación. 27, 3 (Sep. 2007), 159–171. DOI:https://doi.org/10.15446/ing.investig.v27n3.14857.

ACS

(1)
Arévalo Velosa, Z.; V. Sinitsyn, A.; Castañeda U., O. A.; Camelo B., M. H. A review of magnetic insulation. Ing. Inv. 2007, 27, 159-171.

ABNT

ARÉVALO VELOSA, Z.; V. SINITSYN, A.; CASTAÑEDA U., O. A.; CAMELO B., M. H. A review of magnetic insulation. Ingeniería e Investigación, [S. l.], v. 27, n. 3, p. 159–171, 2007. DOI: 10.15446/ing.investig.v27n3.14857. Disponível em: https://revistas.unal.edu.co/index.php/ingeinv/article/view/14857. Acesso em: 27 dec. 2025.

Chicago

Arévalo Velosa, Zósimo, Alexander V. Sinitsyn, Octavio Alejandro Castañeda U., and Miguel Hernando Camelo B. 2007. “A review of magnetic insulation”. Ingeniería E Investigación 27 (3):159-71. https://doi.org/10.15446/ing.investig.v27n3.14857.

Harvard

Arévalo Velosa, Z., V. Sinitsyn, A., Castañeda U., O. A. and Camelo B., M. H. (2007) “A review of magnetic insulation”, Ingeniería e Investigación, 27(3), pp. 159–171. doi: 10.15446/ing.investig.v27n3.14857.

IEEE

[1]
Z. Arévalo Velosa, A. V. Sinitsyn, O. A. Castañeda U., and M. H. Camelo B., “A review of magnetic insulation”, Ing. Inv., vol. 27, no. 3, pp. 159–171, Sep. 2007.

MLA

Arévalo Velosa, Z., A. V. Sinitsyn, O. A. Castañeda U., and M. H. Camelo B. “A review of magnetic insulation”. Ingeniería e Investigación, vol. 27, no. 3, Sept. 2007, pp. 159-71, doi:10.15446/ing.investig.v27n3.14857.

Turabian

Arévalo Velosa, Zósimo, Alexander V. Sinitsyn, Octavio Alejandro Castañeda U., and Miguel Hernando Camelo B. “A review of magnetic insulation”. Ingeniería e Investigación 27, no. 3 (September 1, 2007): 159–171. Accessed December 27, 2025. https://revistas.unal.edu.co/index.php/ingeinv/article/view/14857.

Vancouver

1.
Arévalo Velosa Z, V. Sinitsyn A, Castañeda U. OA, Camelo B. MH. A review of magnetic insulation. Ing. Inv. [Internet]. 2007 Sep. 1 [cited 2025 Dec. 27];27(3):159-71. Available from: https://revistas.unal.edu.co/index.php/ingeinv/article/view/14857

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Copyright (c) 2007 Zósimo Arévalo Velosa, Alexander V. Sinitsyn, Octavio Alejandro Castañeda U., Miguel Hernando Camelo B.

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