Comment on the principle of operation of the gyrotron using the formula .

For gyro devices we will use the following formula:

If the natural frequency of the resonator is close to the frequency of the rotational motion of electrons, then conditions are created for such interaction of the flow and the field, at which the generation of electromagnetic waves occurs and maintained. The electron stream that has passed through the resonator and transferred part of the kinetic energy associated with rotational motion to the resonator field falls on the walls of the waveguide collector of electrons. The energy of the electromagnetic field is transmitted through the output window to an external waveguide connecting the device to the load. Let us now consider in more detail the processes of the formation of the electron flow and its interaction with the resonator field.

Formation of the electronic flow:

In gyrotron-type devices, the electron-optical system must not only form an electron flow of a certain configuration, but also ensure the rotational movement of electrons. Moreover, the energy of rotational motion should significantly exceed the kinetic energy of translational motion.

2. Given:

Accelerating beam voltage: Ua=57 kV

Frequency: f=54 GHz

Ratio of the longitudinal and transverse electron velocity:

Solution:

1. Calculation of the magnetic field induction value:

2. The value of the total electron velocity and its longitudinal and transverse components:

So:

2. The radius of the spiral trajectory of the electron:

2. Cyclotron period is calculated by the following formula:

2. Cyclotron wavelength is determined by the formula:

Answers:

2.1

2.2

2.3

2.4

2.5

Sources: Lecture 9

Материалы к 9 Гироприборы.docx (yandex.ru)

Microwave electronics pdf.pdf