D.G. Kovtun - Ph. D. (Phys.-Math.), Associate Professor, Department «Physics», Volgograd State Technical University E-mail: kdmob74@gmail.com S.A. Alikov - Post-graduate Student, Department «Physics», Volgograd State Technical University E-mail: sputnik_as@mail.ru A.G. Shein - Dr. Sc. (Phys.-Math.), Professor, Department «Physics», Volgograd State Technical University E-mail: professor39@mail.ru D.L. Yeskin - Ph. D. (Phys.-Math.), Associate Professor, Volgograd Academy of Internal Affairs Ministry of RF E-mail: yd38@bk.ru

The interaction of a relativistic electron beam with a high-frequency comb-type slow-wave structure field in the approximation of con-stant amplitude is studied. Earlier the interaction with non-relativistic beam was analyzed in different papers. In this case, it can be investigated without taking into account the magnetic component. The aim of this study is to find out how the magnetic component of the comb-type slow-wave structure field influence on the electron beam. The investigation was made with numerical simulation by large particle method. Large particles were groups of electrons. Number electrons in every large particle were determined by the electron beam density and number of large particles entering the interaction space. Equations of the motion were solved for every large particle by Runge-Cutta method and one modification on the second de-rivative of Euler method. At the simulation, the delay effect was taken into account using Lienard-Wiechert potentials and their con-sequences. For propagation of the beam it was used constant crossed fields. So M type devices were discussed at the paper. In addition, synchronism condition imposed to the problem consists in the coincidence of the initial flow velocity, the E-cross-B velocity and the phase velocity of the slow wave. The results of the numerical simulation were data with information about the motion of every large particle in the interaction space. These data were analyzed and used for further calculations. Beam forms, current depending on the coordinate along the direction of the beam propagation, Lorentz force acting on a particle at the beam axis and the average velocity were compared at different amplitude of the structure wave. The numerical experiments show that magnetic component plays an important role in the interaction of the relativistic electron beam with the slow-wave structure field. It is needed to take into account it at numerical simulations and theoretical calculations. The flow can be transported over distances greater than predicted by theory in which the magnetic component is neglected. The action of the magnetic component causes deterioration of the particle grouping and decreases the amplitude of the amperage through the cross section. The numerical simulation results allow making a conclusion that these effects are related to the magnitude of the Lorentz force acting on a particle in the flow. The magnetic component causes the reduction of the Lorentz force module that reduces the range of the average velocity of particles and increases time of the grouping. In conclusion it is made a suggestion that the discussed effects lead to deterioration of the relativistic devices characteristics which can be compensated by the increase of the interaction space.

 

1. Pchelnikov Y., Yelizarov A.A. Optimization of a sheet electron beam interaction with a slow wave // IEEE Transactions on Electron Devices. 2014. V. 61. № 6. P. 1661−1665.
2. Othman M., Tamma V.A., Capolino F. Theory and new amplification regime in periodic multi modal slow wave structures with degeneracy interacting with an electron beam // IEEE Transactions on Plasma Science. 2016. V. 44. № 4. P. 594−611.
3. Eskin D.L., Kovtun D.G. SHein A.G. Generacija kombinacionnykh chastot pri usilenii signala slozhnogo spektralnogo sostava v LBV M‑tipa // Nelinejjnyjj mir. 2013. T. 11. № 3. S. 158−163.
4. Bulancev S.S., ZHoga V.V., SHein A.G. Usilenie signalov v LBVM pri nalichii periodicheskojj neodnorodnosti ehlektrostaticheskogo polja // EHlektromagnitnye volny i ehlektronnye sistemy. 2012. T. 17. № 10. S. 39−42.
5. SHein A.G., Bulancev S.S. Vlijanie periodicheski neodnorodnogo ehlektrostaticheskogo polja na gruppirovku ehlektronnogo potoka v skreshhennykh poljakh // Izvestija VolgGTU. 2011. T. 5. № 6. S. 26−30.
6. Kovtun D.G., Kravchenja P.D., SHein A.G. Vlijanie metallicheskikh stenok prostranstva vzaimodejjstvija na formu reljativistskikh ehlektronnykh potokov, dvizhushhikhsja v skreshhennykh poljakh // Izvestija VolgGTU. 2011. T. 5. № 6. S. 30−36.
7. Hong-Quan X., Pu-Kun L. Theoretical analysis of a relativistic travelling wave tube filled with plasma // Chinese Physics. 2007. V. 16. № 3. P. 766−771.
8. Rozhnev A.G., Ryskin N.M., Karetnikova T.A., Torgashev G.V., Sinitsyn N.I., Shalayev P.D., Burtsev A.A. Studying charcteristics of the slow-wave system of the travelling-wave tube with a sheet electron beam // Radiophysics and Quantum Electronics. 2013. V. 56. № 8. P. 542−553.
9. Fedorchenko A.M. Teoreticheskaja fizika. Klassicheskaja ehlektrodinamika: Ucheb. posobie. Kiev: Vishha shkola. 1988. 280 s.
10. Taranenko Z.I., Trokhimenko JA.K. Zamedljajushhie sistemy. Kiev: Tekhnika. 1965. 306 s.
11. Demidovich B.P., Maron I.A, SHuvalova EH.Z. CHislennye metody analiza: priblizhenie funkcijj, differencialnye i integralnye uravnenija. M.: Nauka. 1967. 224 s.
12. Shein A.G., Bakulin V.M., Mutovkin A.N. Computing the Space-Charge Fields of M‑Type Tubes // Journal of Communications Technology and Electronics. October 2000. V. 45. № 10. P. 1146−1149.