If gain is:

Spiral SWS length:

Характеристики:

Picture 3– Frequency response characteristic

Picture 4 – Amplitude characteristic

The dependence shown by the solid line is a typical characteristic. Since the gain constant , as the coupling resistance decreases, the power decreases, and the dependence becomes lower on the graph (the dotted line).

Answers:

Current of electron beam:

Power of electronic beam:

Step of the spiral of the slowing system: p = 0.006699 m

Spiral SWS length:

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Task 5

1. Dynamically controlled devices. M-type devices

5.1.1. Calculate the value of the critical magnetic induction for the value of [mm] and the value of the potential Ua from problem No.4

2. Assuming , calculate the cyclotron frequency and determine the height of the near-cathode electron layer y_max.

3. Calculate the step of the electron trajectory h.

4. Assuming the potential distribution in the interelectrode gap to be linear, find the value of the maximum velocity in the electron cloud.

5. How will the generation frequency of the magnetron change if the magnetic field is increased in 6 times.

Given:

The interelectrode gap

The value of the potential

2. Solving:

The critical magnetic induction: [1]

Let's accept the field value:

Then the cyclotron frequency is: [10]

Height of the near-cathode electron layer: [1]

Step of the electronic trajectory: [1]

The maximum velocity in the electron field will be at the apex of the cycloid. The potential between the cathode and anode is distributed linearly. We find the voltage per unit length and multiply it by the height of the cycloid.

Fiel increase:

The magnetron synchronism condition under which π-oscillations occur: [10]

Then the relationship between frequency and field induction:

By increasing the field by 6 times, the generation frequency will drop by 6 times.

Answers:

Critical magnetic induction: B_crit = 0.068 T

Cyclotron frequency:

Height of the near-cathode electron layer:

Step of the electronic trajectory:

The maximum velocity:

Generation frequency change:

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Task 6

1. Dynamically controlled devices. Gyro-resonant devices. Gyrotron.

   1. Explain why gyrotrons are used primarily in the mm-wavelength range. What is mode selection, and how is it achieved? Describe how high output power is achieved in the mm-wavelength range.

   2. Comment on the operating principle of a gyrotron using the formula

6.1.3. Calculate the parameters of the spiral trajectory of a gyrotron electron beam:

• The significance of magnetic field induction B. Is it difficult to obtain such a field in practice?

• Values ​​of the total velocity of an electron and its longitudinal and transverse components.

• The radius of the electron's spiral trajectory ρ. What should the resonator radius be?

• The time it takes for an electron to complete one revolution - the cyclotron period Tc.

• The pitch of the spiral trajectory - the cyclotron wavelength λс.

Given:

Beam accelerating voltage

Fiel frequency

The ratio of the transverse and longitudinal velocities of an electron