Abstract
This article investigates the acceleration of an injected electron inside a waveguide with a Piet-Hein cross section and a perfect electric conductor wall containing cold non-magnetized plasma. At first, by applying the boundary conditions, the electromagnetic field components are calculated numerically for TE modes. Then the dispersion curves will be drawn, and the cutoff frequency of different modes will be analyzed. In the following, by injecting an electron into the waveguide and considering its interaction with the electromagnetic field, the relativistic equations of energy and momentum will be solved, and the acceleration of the electron will be calculated. Acceleration gradient, deflection angle, and electron trajectory will be discussed. Also, the effect of plasma density on particle acceleration is investigated and compared.
Similar content being viewed by others
Data Availability Statement
No data associated in the manuscript.
References
D.A. Pinnow, T.C. Rich, F.W. Ostermayer Jr., M. DiDomenico Jr., Fundamental optical attenuation limits in the liquid and glassy state with application to fiber optical waveguide materials. Appl. Phys. Lett. 22(10), 527–529 (1973)
R.A. Nadkarni, Applications of microwave oven sample dissolution in analysis. Anal. Chem. 56(12), 2233–2237 (1984)
M.S. Pinho, M.L. Gregori, R.C.R. Nunes, B.G. Soares, Performance of radar absorbing materials by waveguide measurements for X- and Ku-band frequencies. Eur. Polymer J. 38(11), 2321–2327 (2002)
L.J. Wong, A. Fallahi, F.X. Kärtner, Compact electron acceleration and bunch compression in THz waveguides. Opt. Express 21(8), 9792–9806 (2013)
E. Snitzer, Cylindrical dielectric waveguide modes. JOSA 51(5), 491–498 (1961)
A. Kumar, K. Thyagarajan, A.K. Ghatak, Analysis of rectangular-core dielectric waveguides: an accurate perturbation approach. Opt. Lett. 8(1), 63–65 (1983)
C. Yeh, Elliptical dielectric waveguides. J. Appl. Phys. 33(11), 3235–3243 (1962)
C. Yeh, Modes in weakly guiding elliptical optical fibres. Opt. Quantum Electron. 8, 43–47 (1976)
R.B. Dyott, C.R. Day, M.C. Brain, Glass-fibre waveguide with a triangular core. Electron. Lett. 13(9), 288–290 (1973)
V. Misra, P.K. Choudhury, P. Khastgir, S.P. Ojha, Electromagnetic wave propagation through a dielectric guide having Piet Hein cross-sectional geometry. Microw. Opt. Technol. Lett. 12(5), 250–254 (1996)
P.K. Choudhury, Power characteristics of dielectric optical Piet Hein waveguides. Microw. Opt. Technol. Lett. 35(3), 236–240 (2002)
V. Singh, B. Prasad, S.P. Ojha, Theoretical analysis and dispersion curves of an annular light guide with a cross-section bounded by two Piet-Hein curves. J. Electromagn. Waves Appl. 17(7), 1025–1036 (2003)
V. Singh, B. Prasad, S.P. Ojha, A comparative study of the modal characteristics and waveguide dispersion of optical waveguides with three different closed loop cross-sectional boundaries. Optik 115(6), 281–288 (2004)
Y. Prajapati, V. Singh, J.P. Saini, Modal analysis of a super-elliptical Bragg waveguide with a small number of periodic cladding layers based on a very simple analytical technology. Optik 120(1), 14–19 (2009)
S.K. Jawla, S. Kumar, H.K. Malik, Evaluation of mode fields in a magnetized plasma waveguide and electron acceleration. Opt. Commun. 251(4–6), 346–360 (2005)
H.K. Malik, S. Kumar, K.P. Singh, Electron acceleration in a rectangular waveguide filled with unmagnetized inhomogeneous cold plasma. Laser Part. Beams 26(2), 197–205 (2008)
A.G. York, H.M. Milchberg, J.P. Palastro, T.M. Antonsen, Direct acceleration of electrons in a corrugated plasma waveguide. Phys. Rev. Lett. 100(19), 195001 (2008)
C. Nantista, S. Tantawi, V. Dolgashev, Low-field accelerator structure couplers and design techniques. Phys. Rev. Spec. Top. Accel. Beams 7(7), 072001 (2004)
A.K. Aria, H.K. Malik, Numerical studies on wakefield excited by Gaussian-like microwave pulse in a plasma filled waveguide. Opt. Commun. 282(3), 423–426 (2009)
H.K. Malik, Analytical calculations of wake field generated by microwave pulses in a plasma filled waveguide for electron acceleration. J. Appl. Phys. 104(5), 053308 (2008)
H.K. Malik, S. Kumar, Y. Nishida, Electron acceleration by laser produced wake field: pulse shape effect. Opt. Commun. 280(2), 417–423 (2007)
H.K. Malik, A.K. Aria, Microwave and plasma interaction in a rectangular waveguide: effect of ponderomotive force. J. Appl. Phys. 108(1), 013109 (2010)
H.K. Malik, Density bunch formation by microwave in a plasma-filled cylindrical waveguide. Europhys. Lett. 106(5), 55002 (2014)
M.B. Abrahimi, A. Abdoli-Arani, Investigation of TE and TM modes fields and injected electron dynamic in the plasma waveguide with Piet Hein cross section. Phys. Scr. 97(3), 035505 (2022)
M.B. Abrahimi, A. Abdoli-Arani, Fields and injected electron dynamic in the coaxial waveguide with Piet Hein cross section filled plasma considering TE and TM modes. Eur. Phys. J. Plus 137(1), 167 (2022)
L. Malik, In-flight plume control and thrust tuning in magnetic nozzle using tapered-coils system under the effect of density gradient. IEEE Trans. Plasma Sci. 51, 1325 (2023)
L. Malik, Tapered coils system for space propulsion with enhanced thrust: a concept of plasma detachment. Propuls. Power Res. 11(2), 171–180 (2022)
L. Malik, Novel concept of tailorable magnetic field and electron pressure distribution in a magnetic nozzle for effective space propulsion. Propuls. Power Res. 12(1), 59–68 (2023)
L. Malik, A. Escarguel, M. Kumar, A. Tevatia, R.S. Sirohi, Uncovering the remarkable contribution of lasers peak intensity region in holography. Laser Phys. Lett. 18(8), 086003 (2021)
R.B. Lehoucq, D.C. Sorensen, C. Yang, ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (Society for Industrial and Applied Mathematics, Philadelphia, 1998)
H.K. Malik, Energy gain by an electron in the fundamental mode of a rectangular waveguide by microwave radiation. J. Plasma Phys. 69(1), 59–67 (2003)
H.K. Malik, Effect of plasma density on proton acceleration in a rectangular waveguide. Plasma Sci. Technol. 6(5), 2456 (2004)
H.K. Malik, Application of obliquely interfering TE10 modes for electron energy gain. Opt. Commun. 278(2), 387–394 (2007)
S. Kumar, H.K. Malik, Electron acceleration in a plasma filled rectangular waveguide under obliquely applied magnetic field. J. Plasma Phys. 72(6), 983–987 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Abrahimi, M.B., Abdoli Arani, A. Simulation of the electron acceleration in the waveguide with Piet-Hein cross section. Eur. Phys. J. Plus 139, 164 (2024). https://doi.org/10.1140/epjp/s13360-024-04957-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-024-04957-y