The gyrotron startup scenario in the single mode time dependent approach
Abstract
The paper explains how to solve the Gyrotron equation system in the Single Mode Time Dependent Approach. In particular, we point out problems encountered when solving these well-known equations. The starting current estimation approach a using time model is suggested. The solution has been implemented in the Matlab code, which is attached to the article.
Keyword : time dependent approach, gyrotron, differential equation, Matlab code
How to Cite
Nowak, K., Plinski, E. F., Wieckowski, T., & Dumbrajs, O. (2019). The gyrotron startup scenario in the single mode time dependent approach. Mathematical Modelling and Analysis, 24(4), 494-506. https://doi.org/10.3846/mma.2019.030
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Oct 25, 2019
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References
M.I. Airila, O. Dumbrajs, A. Reinfelds and U. Strautin¸ˇs. Nonstationary oscillations in gyrotrons. Physics of Plasmas, 8(10):4608–4612, 2001. https://doi.org/10.1063/1.1402173
J. Cepitis, O. Dumbrajs, H. Kalis, A. Reinfelds and U. Strautins. Analysis of equations arising in gyrotron theory. Nonlinear Analysis: Modeling and Control, 17(2):139–152, 2012.
A.J. Cerfon, E. Choi and C.D. Marchewka et al. Observation and study of low-frequency oscillations in a 1.5-MW 110-GHz gyrotron. IEEE Transactions on Plasma Science, 37(7):1219–1224, 2009. https://doi.org/10.1109/TPS.2009.2020903
O. Dumbrajs, T. Idehara, T. Saito and Y. Tatematsu. Calculations of starting currents and frequencies in frequency-tunable gyrotrons. Japanese Journal of Applied Physics, 51:126601, 2012. https://doi.org/10.1143/JJAP.51.126601
O. Dumbrajs and G.S. Nusinovich. Cold-cavity and self-consistent approaches in the theory of mode competition in gyrotrons. IEEE Transactions on Plasma Science, 20(3):133–138, 1992. https://doi.org/10.1109/27.142812
N.S. Ginzburg, G.S. Nusinovich and N.A. Zavolsky. Theory of non-stationary processes in gyrotrons with low Q resonators. International Journal of Electronics, 61(6):881–894, 1986. https://doi.org/10.1080/00207218608920927
N.S. Ginzburg, N.A. Zavolskii, G.S. Nusinovich and A.S. Sergeev. Onset of selfoscillations in electronic microwave oscillators with diffraction radiation output. Radiofizika, 29:106–114, 1986.
S. Hamdi, W.E. Schiesser and G.W. Griffiths. Method of lines. Scholarpedia, 2(7):2859, 2007. https://doi.org/10.4249/scholarpedia.2859
T. Idehara, J.C. Mudiganti and L. Agusu et al. Development of a compact sub-THz gyrotron FU CW CI for application to high power THz technologies. Journal of Infrared, Millimeter, and Terahertz Waves, 33(7):724–744, 2012. https://doi.org/10.1007/s10762-012-9911-0
H. Khatun, R.R. Rao, A.K. Sinha and S.N. Joshi. Accurate estimation of start oscillation current for maximum output power in 42 GHz, 200 kW gyrotron. Indian J. Pure Ap. Phy., 49:776–781, 2011.
T. Numakura, T. Imai, T. Kariya and et al. Code development for the calculations of time-dependent multimode oscillations in the cavity of the future high-power gyrotrons. In AIP Conference Proceedings, 030023, 2016. https://doi.org/10.1063/1.4964179
G.S. Nusinowich. Introduction to the Physics of Gyrotrons. JHU Press, 2004.
A. Reinfelds, O. Dumbrajs, H. Kalis, J. Cepitis and D. Constantinescu. Numerical experiments with single mode gyrotron equations. Mathematical Modelling and Analysis, 17(2):251–270, 2012. https://doi.org/10.3846/13926292.2012.662659
Inc. The MathWorks. Matlab manual. Online, 2006. Available from Internet: https://www.mathworks.com/help/matlab/ref/pdepe.html
A.Q. Zhao, B.S. Yu and C.T. Zhang. Startup and mode competition in a 420 GHz gyrotron. Physics of Plasmas, 24(9):093102, 2017. https://doi.org/10.1063/1.4997910
J. Cepitis, O. Dumbrajs, H. Kalis, A. Reinfelds and U. Strautins. Analysis of equations arising in gyrotron theory. Nonlinear Analysis: Modeling and Control, 17(2):139–152, 2012.
A.J. Cerfon, E. Choi and C.D. Marchewka et al. Observation and study of low-frequency oscillations in a 1.5-MW 110-GHz gyrotron. IEEE Transactions on Plasma Science, 37(7):1219–1224, 2009. https://doi.org/10.1109/TPS.2009.2020903
O. Dumbrajs, T. Idehara, T. Saito and Y. Tatematsu. Calculations of starting currents and frequencies in frequency-tunable gyrotrons. Japanese Journal of Applied Physics, 51:126601, 2012. https://doi.org/10.1143/JJAP.51.126601
O. Dumbrajs and G.S. Nusinovich. Cold-cavity and self-consistent approaches in the theory of mode competition in gyrotrons. IEEE Transactions on Plasma Science, 20(3):133–138, 1992. https://doi.org/10.1109/27.142812
N.S. Ginzburg, G.S. Nusinovich and N.A. Zavolsky. Theory of non-stationary processes in gyrotrons with low Q resonators. International Journal of Electronics, 61(6):881–894, 1986. https://doi.org/10.1080/00207218608920927
N.S. Ginzburg, N.A. Zavolskii, G.S. Nusinovich and A.S. Sergeev. Onset of selfoscillations in electronic microwave oscillators with diffraction radiation output. Radiofizika, 29:106–114, 1986.
S. Hamdi, W.E. Schiesser and G.W. Griffiths. Method of lines. Scholarpedia, 2(7):2859, 2007. https://doi.org/10.4249/scholarpedia.2859
T. Idehara, J.C. Mudiganti and L. Agusu et al. Development of a compact sub-THz gyrotron FU CW CI for application to high power THz technologies. Journal of Infrared, Millimeter, and Terahertz Waves, 33(7):724–744, 2012. https://doi.org/10.1007/s10762-012-9911-0
H. Khatun, R.R. Rao, A.K. Sinha and S.N. Joshi. Accurate estimation of start oscillation current for maximum output power in 42 GHz, 200 kW gyrotron. Indian J. Pure Ap. Phy., 49:776–781, 2011.
T. Numakura, T. Imai, T. Kariya and et al. Code development for the calculations of time-dependent multimode oscillations in the cavity of the future high-power gyrotrons. In AIP Conference Proceedings, 030023, 2016. https://doi.org/10.1063/1.4964179
G.S. Nusinowich. Introduction to the Physics of Gyrotrons. JHU Press, 2004.
A. Reinfelds, O. Dumbrajs, H. Kalis, J. Cepitis and D. Constantinescu. Numerical experiments with single mode gyrotron equations. Mathematical Modelling and Analysis, 17(2):251–270, 2012. https://doi.org/10.3846/13926292.2012.662659
Inc. The MathWorks. Matlab manual. Online, 2006. Available from Internet: https://www.mathworks.com/help/matlab/ref/pdepe.html
A.Q. Zhao, B.S. Yu and C.T. Zhang. Startup and mode competition in a 420 GHz gyrotron. Physics of Plasmas, 24(9):093102, 2017. https://doi.org/10.1063/1.4997910