4. Calculation of the time of one electron revolution (cyclotron period)

Cyclotron period formula [38]:

T_c = (68)

Using the formula (68), the cyclotron period is equal to:

T_c = = = 2,18 10^-11 s

5. Calculation of the step of the spiral trajectory (cyclotron wavelength)

Cyclotron wavelength formula [38]:

= T_c (69)

Using the formula (69), we calculate the cyclotron wavelength:

= T_c = 2,18 10^-11 4,82 10⁷ = 1,05 10^-3 m = 1,05 mm

Answer:

1. Magnetic field induction:

B = 1,64 T

2. Total electron velocity and its longitudinal and transverse components:

v = 1,08 10⁸ m/s – full electron velocity

= 4,82 10⁷ m/s – longitudinal component

= 9,64 10⁷ m/s – transverse component

3. Radius of the spiral trajectory of the electron, the value of the radius of the resonator:

= 334,3 m – radius of the spiral trajectory

= 3,98 mm – resonator radius

4. Time of one electron revolution (cyclotron period):

T_c = 2,18 10^-11 s

5. Step of the spiral trajectory (cyclotron wavelength):

= 1,05 mm

2 балл

LIST OF USED LITERATURE

1. Traveling and reverse wave tubes [Electronic resource]: URL//: http://tubeamplifier.narod.ru/mess066.htm

2. Grigoriev A.D., Ivanov V. A., Molokovsky S. I. G 83 Microwave electronics: Textbook / Edited by A. D. Grigoriev., St. Petersburg: Lan Publishing House, 2016. p. 269.

3. Traveling-Wave Tube (TWT) [Electronic resource]: URL//: http://bourabai.ru/physics/1913.html

4. The motion of electrons in crossed homogeneous electric and magnetic fields [Electronic resource]: URL//: http://rateli.ru/books/item/f00/s00/z0000001/st005.shtml

5. Ivanov V. A. lecture materials 8 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%208ой%20%20лекции%20Приборы%20%20М-типа. p. 4.

6. Ivanov V. A. lecture materials 7 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%207ой%20лекции%20Приборы%20%20с%20динам%20упр%20ЛБВ%20ЛОВ. p. 4.

7. Ivanov V. A. lecture materials 2 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%202ой%20лекции%20Уравнения. p. 10.

8. Cyclotron frequency [Electronic resource]: // URL: https://www.booksite.ru/fulltext/1/001/008/120/966.htm

9. Static characteristics of the triode [Electronic resource]: // URL: https://www.elel.ru/triod2.html

10. Ivanov V. A. lecture materials 5 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%205ой%20лекции%20Вакуумные%20квазистатика. p. 15.

11. Ivanov V. A. lecture materials 3 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%203ей%20лекции%20Законы%20сохранения. p. 19.

12. Ivanov V. A. lecture materials 3 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%203ей%20лекции%20Законы%20сохранения. p. 23.

13. Fedorov N. D. Microwave electronic devices and quantum devices [Electronic resource]: // URL: http://svch.sfu-kras.ru/files/fedorov_n.d._elektronnye_pribory_svch_i_kvantovye_pribory.pdf.

14. Application of microwave radiation [Electronic resource]: // URL: http://rnbo.khb.ru/files/cor/13069.htm

15. Ivanov V. A. lecture materials 6 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%203ей%20лекции%20Законы%20сохранения. p. 10.

16. Ivanov V. A. lecture materials 6 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%203ей%20лекции%20Законы%20сохранения. p. 10.

17. Electric current density: what is it, formula, unit of measurement [Electronic resource]: // URL: https://www.asutpp.ru/plotnost-toka.html

18. Ivanov V. A. lecture materials 6 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%203ей%20лекции%20Законы%20сохранения. p. 9.s

19. Ivanov V. A. lecture materials 3 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%203ей%20лекции%20Законы%20сохранения. p. 23.

20. Ivanov V. A. lecture materials 5 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%203ей%20лекции%20Законы%20сохранения. p. 13.

21. Ivanov V. A. lecture materials 7 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%207ой%20лекции%20Приборы%20%20с%20динам%20упр%20ЛБВ%20ЛОВ. p. 6.

22. Ivanov V. A. lecture materials 7 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%207ой%20лекции%20Приборы%20%20с%20динам%20упр%20ЛБВ%20ЛОВ. p. 11.

23. Ivanov V. A. lecture materials 7 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%207ой%20лекции%20Приборы%20%20с%20динам%20упр%20ЛБВ%20ЛОВ. p. 15.

24. Amplifier on a traveling-wave tube (TWT). Device and principle of operation [Electronic resource]: // URL: http://rateli.ru/books/item/f00/s00/z0000001/st004.shtml

25. Traveling-wave tubes of type O (TWTO) [Electronic resource]: // URL: https://siblec.ru/radiotekhnika-i-elektronika/pribory-svch-i-opticheskogo-diapazona/4-lampy-begushchej-volny-tipa-o-lbvo

26. Grigoriev A.D., Ivanov V. A., Molokovsky S. I. G 83 Microwave electronics: Textbook / Edited by A. D. Grigoriev., St. Petersburg: Lan Publishing House, 2016. p. 216.

27. Grigoriev A.D., Ivanov V. A., Molokovsky S. I. G 83 Microwave electronics: Textbook / Edited by A. D. Grigoriev., St. Petersburg: Lan Publishing House, 2016. p. 316.

28. Motion of charged particles in electromagnetic fields [Electronic resource]: // URL: http://medphysics-irk.ru/teaching/shendrik/pdf/pres.pdf

29. The potential difference of the electrostatic field. Voltage. The relationship between the voltage and the intensity of a homogeneous electrostatic field [Electronic resource]: // URL: http://profil.adu.by/mod/book/view.php?id=3212&chapterid=9307

30. Motion of charged particles in electromagnetic fields [Electronic resource]: // URL: http://medphysics-irk.ru/teaching/shendrik/pdf/pres.pdf

31. Microwave appliances and devices. Methodological guidelines for laboratory work / Comp.: A.D. Grigoriev, V. A. Ivanov, A. A. Kolomiytsev, S. I. Molokovsky, V. B. Yankevich. St. Petersburg: Publishing House of SPbGETU "LETI", 2006. p.

32. J. M. Luginsland and G. A. Westenskow, "Gyrotron Theory," in Gyrotrons: High Power Microwave and Millimeter Wave Technology, ed. by G. G. Denisov and S. V. Mishakin (Springer-Verlag, Berlin, 2014).

33. V. L. Granatstein and C. D. Striffler, "Gyrotron Devices and Amplifiers," in Handbook of Microwave Technology, ed. by M. S. Shur and A. K. Hoorfar (Academic Press, 1995).

34. Microwave appliances and devices. Methodological guidelines for laboratory work / Comp.: A.D. Grigoriev, V. A. Ivanov, A. A. Kolomiytsev, S. I. Molokovsky, V. B. Yankevich. St. Petersburg: Publishing House of SPbGETU "LETI", 2006. p. 326.

35. Ivanov V. A. lecture materials 9 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%209ой%20лекции%20Гиро-приборы%20Релятивистские. p. 9.

36. Ivanov V. A. lecture materials 9 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%209ой%20лекции%20Гиро-приборы%20Релятивистские. p. 15.

37. Ivanov V. A. lecture materials 9 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%209ой%20лекции%20Гиро-приборы%20Релятивистские. p. 16.

38. Ivanov V. A. lecture materials 9 [Electronic resource]: // URL: https://disk.yandex.ru/d/LfNrHSyYQsjzxg/материалы%209ой%20лекции%20Гиро-приборы%20Релятивистские. p. 8.