2. Solving:

   1. The mm-wavelength range using: [4], [11]

Gyrotrons are vacuum devices used to generate and amplify electromagnetic oscillations. Their operating principle is based on the interaction of an electron beam with the high-frequency fields of resonators or waveguides. Since this interaction is not related to the device's surfaces, its dimensions can be much larger than the wavelength. This eliminates the main limitation to achieving high power in O- and M-type devices: the small size of resonant and slow-wave structures. For electromagnetic wave generation to occur, the frequency of the electron rotation must be close to the resonator's natural frequency. Therefore, based on the typical dimensions of gyrotron resonators, the wavelength is in the millimeter range.

Oscillatory mode selection is the selection of a single operating mode (oscillation mode) of the resonator from a variety of possible modes to ensure stable generation and high efficiency. In gyrotrons, selection is achieved in several ways: by using an open resonator, by electron selection, and by using structural elements.

High power is achieved by using an open resonator and its sufficiently large size; use of high-current beams;

2. Explanation of the principle by formula:

In the case of a gyrotron, the power formula takes the form:

An electron in a gyrotron moves along a spiral trajectory and its velocity has an azimuthal component , caused by the azimuthal component of the field , therefore azimuthal grouping occurs.

3. Parameters of the spiral trajectory of a gyrotron electron beam

From the cyclotron resonance condition:[1]

The speed of the electron in the field will:

The velocity vector can be decomposed into the sum of the squares of the perpendicular components:

The radius of the spiral trajectory is expressed by the formula:[12]

The cyclotron period and wavelength can be found using the formulas:[12]

Answers:

Magnetic induction:

Full velocity:

Transverse component of velocity:

Longitudinal component of velocity:

Radius of the spiral trajectory:

Cyclotron period:

Cyclotron wavelength:

1.5 Балл Sources

1. Ivanov V. A. «Task No. 2 Vacuum devices» [Electronic resource]: // URL: https://disk.yandex.ru/d/FJ4Cg3U6Y5w3mA/1Самостоятельная%20работа/Задание%20№2

2. Dyatlov Yu. V., Kozlov L. N. Mitrons. M.: Sov. radio, 1967. 50 p.

3. Grigoriev A.D. (ed.) Microwave electronics. Saint Petersburg: Lan', 2015. 637 p.

4. Sushkov A. D. Vacuum electronics. Physical and technical foundations: a tutorial. — St. Petersburg; Moscow; Krasnodar: Lan, 2004. — 464 p.

5. Ivanov V. A. lecture materials 5 [Electronic resource]: // URL: https://disk.yandex.ru/d/FJ4Cg3U6Y5w3mA/материалы%205-ой%20лекции%20Вакуумные%20квазистатика p. 15

6. Ivanov V. A. lecture materials 3 «Conservation laws» [Electronic resource]: // URL: https://disk.yandex.ru/d/FJ4Cg3U6Y5w3mA/материалы%203-ей%20лекции%20Законы%20сохранения p.23

7. Ivanov V. A. lecture materials 6 [Electronic resource]: // URL: https://disk.yandex.ru/d/FJ4Cg3U6Y5w3mA/материалы%206-ой%20лекции%20Приборы%20с%20динам%20управлением%20клистрон p. 8

8. Grigoriev A.D. (ed.) Microwave electronics. Saint Petersburg: Lan', 2015. p. 142

9. Ivanov V. A. lecture materials 7 [Electronic resource]: // URL: https://disk.yandex.ru/d/FJ4Cg3U6Y5w3mA/материалы%207-ой%20лекции%20Приборы%20%20с%20динам%20упр%20ЛБВ%20ЛОВ p. 11

10. Materials about magnetron [Electronic resource]: // URL: https://disk.yandex.ru/d/FJ4Cg3U6Y5w3mA/материалы%208-ой%20%20лекции%20Приборы%20%20М-типа p. 2

11. Ivanov V. A. «Materials for 9 gyroscopic devices » [Electronic resource]: // URL: https://disk.yandex.ru/d/FJ4Cg3U6Y5w3mA/материалы%209-ой%20лекции%20Гиро-приборы%20Релятивистские

12. Ivanov V. A. lecture materials 9 «Gyro-resonance devices» [Electronic resource]: // URL: https://disk.yandex.ru/d/FJ4Cg3U6Y5w3mA/материалы%209-ой%20лекции%20Гиро-приборы%20Релятивистские p. 8