Effect of strong uniform axial magnetic field on the TE and TM modes fields and injected electron dynamic in the plasma waveguide with Piet Hein cross section

Document Type : Original Article

Authors

1 Department of Laser and Photonics, Faculty of Physics, University of Kashan, Kashan, Islamic Republic of Iran.

2 Department of Laser and Photonics, Faculty of Physics,University of Kashan,Kashan, Islamic Republic of Iran

Abstract

In this paper,considering the effect of a strong uniformly axial magnetic field on the plasma dielectric tensor, electromagnetic fields and other results in a waveguide with a metal wall with a cross-section in the shape of a Piet Hein curve containing cold and strongly magnetized plasma is investigated using an appropriate approximation. First, by introducing the Pitt Hein waveguide, the electromagnetic wave equation in this type of waveguide is presented , using a suitable approximation and by separating the variables, as two separate differential equations. The electric and magnetic fields as well as the dispersion relations for the TM and TE modes are then calculated in a Piet Hein waveguide with a metal wall containing strongly magnetized cold plasma, and the dispersion relations and resulting fields are plotted., Next, the motion of an injected electron into this waveguide and the effect of a strong uniformly axial magnetic field on the electron energy is investigated. The electron motion and energy equations are written in the Pitt Hein plasma waveguide in the presence of a strong uniform axial magnetic field and are solved using fourth-order Runge Kutta method for TM and TE modes. The motion path and kinetic energy of the electrons injected into the waveguide have been graphically investigated for both modes.

Keywords


[1]    E.Snitzer “Cylindrical Dielectric Waveguide Modes,” Journal of the Optical Society of America, vol. 51, pp. 491-498, 1961
[2]    A. Kumar, Thyagaranjan V, Ghatak AK: “Analysis of Rectangular Core Dielectric Waveguides: An Accurate Perturbation Approach,” Optics Letters, vol. 8,  pp. 63-65, 1983.
[3]    C. Yeh,.“Elliptical Dielectric Waveguide,” Journal of Applied Physics, Vol. 33, pp. 3235-3242, 1962.
[4]    C. Yeh, “Modes in Weakly Guiding Elliptical Optical Fibers,” Optical and Quantum Electronics, vol. 8, pp.43-47, 1976.
[5]    R. B. Dyott, “Glass-fiber Waveguide with Triangular Core,”Electronics Letters, vol. 9, pp. 288-290, 1973.
[6]    J. R. James and I. N. L. Gallett, “Modal Analysis of Triangular Cored Fiber Waveguide,” Proceedings of the Institution of Electrical Engineers, vol. 120, pp. 1362-1370, 1973.
[7]    M. P. S. Rao, B. Prasad, P. Khastgir, and S. P. Ojha, “Modal Cutoff Conditions for an Optical Waveguide with a Hypocycloidal Cross Section,” Microwave and Optical Technology Letters, vol. 14, pp. 177-180, 1997.
[8]    M. P. S. Rao, V. Singh, B. Prasad, P. Khastgir, and S. P. Ojha, “An Analytical Study of the Dispersion Curves of an Annular Waveguide Made of Liquid Crystal,” Photonics Optoelectron, vol.  5, pp. 73-78, 1998.
[9]    V. N. Mishra, V. Singh, B. Prasad, and S.P. Ojha, “An Analytical Investigation of the Dispersion Characteristic of a Lightguide with an Annular Core Cross-Section Bounded by Two Cardiods,” Microwave and Optical Technology Letters, vol. 23, pp. 221-224, 1999. 
[10]  V. Mishra, “A Study on Piet Hein and Other Unconventional Geometry in Optical Waveguides,” PhD. Thesis, Deptartment of Applied Physics, I. T. B. H. U. Varanasi, India 1997. 
[11]  V. Singh, B. Prasad, and S. P. Ojha, “Effect of Axial Sinusoidal Size Variation on the Modal Characteristics of an Annular Optical Fiber,” Microwave and Optical Technology Letters, vol. 31, pp. 211-214, 2001. 
[12]  V. Singh, B. Prasad, and S. P. Ojha, “Weak Guidance Modal Analysis and Dispersion Curves of an Infrared-Lightguide Having a Core Cross-Section with a New Type of Asymmetric Loop Boundary,” Optical Fiber Technology, vol. 6, pp. 290-298, 2000.
[13]  V. Singh, M. Joshi, B. Prasad, and S. P. Ojha, “Modal Dispersion Characteristics and Waveguide Dispersion of an Optical Waveguide Having a New Unconventional Core Cross-Section,” Journal of Electromagnetic Waves and Applications, vol. 18, pp. 455-468, 2004.
[14]  V. Singh, B. Prasad, and S. P. Ojha: “Theoretical Analysis and Dispersion Curves of an Annular Lightguide with a Cross-Section Bounded by Two Piet-Hein Curves,” Journal of Electromagnetic Waves and Applications,  vol. 17 pp. 1025-1036, 2003.
[15]  V. Singh, S. N. Maurya, B. Prasad, and S. P. Ojha, “Conducting Sheath Helical Winding on the Core-Cladding Interface of a Lightguide Having a Piet Hein Super Elliptical Core Cross-Section and a Standard Optical Fiber of Circular Cross-Section - A Comparative Modal Analysis,” Progress in Electromagnetics Research, PIER, vol. 59, pp. 231-249, 2006.
[16]  F. Nazari, H. Aliakbarian, and S. Radiom, “Design and Fabrication of Dielectric Constant Measurement Setup without Sample Holder in C band Motor, Scientific,” Journal of Applied Electromagnetics, vol. 4, pp. 1-10, 2016 (In Persian).
[17]  S. Jalil Seyedhoseini, R. A. Sadeghzadeh, and H. Aliakbarian, “An Improved TEM-TE11 Mode-Treansducing Sectoral Antenna Using Dual Dielectric Window, Scientific,” Journal of Applied Electromagnetics, vol. 4, pp. 21-16, 2016 (In Persian).
[18]  B. F. Mohamed  and A. M. Gouda, “Electron Acceleration by Microwave Radiation Inside a Rectangular Waveguide,” Plasma Science and Technology vol. 13,  pp. 357-361, 2011.
[19]  B. F. Mohamed, A. M. Gouda, and L. Z. Ismail, “Electron Dynamics in Presence of Static Helical Magnet Inside Circular Waveguide,” IEEE Transactions on Plasma Science, vol. 39, pp. 842-846, 2011.
[20]  S. Kumar and M. Yoon, “Electron Dynamics and Acceleration Study in a Magnetized Plasma-Filled Cylindrical Waveguide,” Journal of Applied Physics, vol. 103, pp. 023302, 2008.
[21]  S. Kumar and M. Yoon, “Electron Acceleration in a Warm Magnetized Plasma-Filled Cylindrical Waveguide,” Journal of Applied Physics, vol. 104, pp. 073303, 2008.
[22]  H. K. Malik,  S. Kumar, and K. P. Singh, “Electron Acceleration in a Rectangular Waveguide Filled with Unmagnetized Inhomogeneous Cold Plasma,” Laser and Particle Beams, vol. 26, pp. 197-205, 2008.
[23]  S. K. Jawla,  S. Kumar, and H. K. Malik, “Evaluation of Mode Fields in a Magnetized Plasma Waveguide and Electron Acceleration,” Optics communications, vol. 251, pp. 346-360, 2005.
[24]  D. N.  Gupta N. Kant,D.E .Kim and H. Suk,     “Electron Acceleration to GeV Energy by a Radially Polarized Laser,” Physics Letters A, vol. 368, pp. 402-407, 2007.
[25]  M. Litos,  et al. “High-Efficiency Acceleration of an Electron Beam in a Plasma Wakefield Accelerator,” Nature, vol. 515, pp. 92-95, 2014.
[26]  X., Liling, W. Gai, and X. Sun, “Field Analysis of a Dielectric-Loaded Rectangular Waveguide Accelerating Structure,” Physical Review E, vol. 65, pp. 016505, 2001.
[27]  A. Abdoli-Arani  and M. J. Basiry, “Influence of Electron–Ion Collisions in Plasma on the Electron Energy Gain Using the TE11 Mode Inside an Elliptical Waveguide,” Physica Scripta, vol. 91, pp. 095602, 2016.
[28]  A. Abdoli-Arani  and M. Moghaddasi, “Study of Electron Acceleration through the Mode in a Collisional Plasma-Filled Cylindrical Waveguide,” Waves in Random and Complex Media, vol. 26, pp. 339-347, 2016.
[29]  A. Abdoli-Arani, “Electron Acceleration Considering Pondermotive Force Effect in a Plasma-Filled Rectangular Waveguide by Microwave Radiation,” Waves in Random and Complex Media, vol. 26, pp. 407-416, 2016.
[30]  A. Abdoli-Arani  and N. Ghanbari, “Nonlinear Effect of Microwave Longitudinal Ponderomotive Force on the Dynamics and Energy of an Externally Injected Electron in an Inhomogeneous Plasma-Filled Circular and Elliptical Cylinder Waveguides,” Waves in Random and Complex Media, vol. 31, pp. 165-181, 2021.
[31]  A. Abdoli-Arani, “Electron Energy Gain in the Transverse Electric Mode of a Coaxial Waveguide Filled with Plasma by Microwave Radiation,” Waves in Random and Complex Media, vol. 25,  pp. 350-360, 2015.
[32]  A. Abdoli-Arani, “Electron Energy Gain in the Fundamental Mode of an Elliptical Waveguide in the Presence of Static Helical Magnet by Microwave Radiation,” Waves in Random and Complex Media, vol. 25, pp. 243-258, 2015.
[33]  A. Abdoli-Arani,  M. Kadkhodaei, and Z. Rahmani Nooshabadi, “Single Electron Acceleration in an Isosceles Right Triangular Waveguide,” Indian Journal of Physics, vol. 94, 1279-1292, 2020.