Their invention lead to the genesis of the engineering branch of electronics.
Their applications include RADAR and defense in general, communications, plasma research and industrial heating.
"Vacuum electron devices (VEDs) are the most powerful and efficient sources of coherent radiation throughout the microwave and millimeter wave bands."
Indicative classification based on https://apps.dtic.mil/dtic/tr/fulltext/u2/a109386.pdf
1. Crossed field tubes
a. Magnetron: "Magnetrons are crossed field devices, with E l B, where E is the electric field and B the magnetic field. Electrons are emitted from the cathode and in-travelling to the anode excite the resonant cavities and give up energy to the RF field.
2. Linear field tubes
"Linear beam cubes have E || B, and consist of an electron gun, an interaction region where the electron beam is confined magnetically and interacts with a slow wave structure, and a collector."
a. Reflex Klystrons: "In this tube, the electron beam passes once through the resonant cavity and is then reflected back through the interaction gap before being
collected on the finely machined RF structure.
b. Travelling Wave Tubes (TWTs)
3. Fast Wave Tubes
a. Gyrotron: "The gyrotron is based upon the electron cyclotron effect, where an electron in a DC magretic field performs orbits with an angular frequency ω=eB/nγm where e/m is the electron charge/mass, γ the relativistic mass factor, B is the axial magnetic flux density and n is the harmonic number. In the beam, most of the electron energy is required to be transverse to the tube axis, and it is this energy which is converted with high efficiency into radiation. In the gyrotron, angular bunching of the electron beam occurs because of the relativistic mass effect and when correctly tuned, the electrons give up their transverse energy to the TE01 RF field (n=1).
A major field of application for gyrotrons has been for electron cyclotron resonance heating of plasmas in fusion research machines."
"Those microwaves that heat the food in your microwave oven come from a magnetron, the vacuum tube that made radar possible in the first half of the 20th century. Traveling wave tubes (TWTs), not solid-state amplifiers, generate the strong electromagnetic signals in communication satellites because of their exceptional on-orbit reliability and high power efficiency. And it’s the unique ability of vacuum tube electronic devices to generate high-frequency signals at chip-melting operating powers that makes possible modern aviation radar systems for navigation and collision avoidance. What’s more, there are more than 200,000 vacuum electronic devices (VEDs) now in service in the Department of Defense, powering critical communications and radar systems that cover the land, sea, air, and space.
With its new Innovative Vacuum Electronic Science and Technology (INVEST) program, DARPA aims to develop the science and technology base for new generations of more capable VEDs."
From DARPA*: “While most VEDs in common use today (traveling wave tubes (TWTs), klystrons, crossed-field amplifiers, magnetrons, gyrotrons and others) were invented in the first half of the 20th century, ongoing, intense development efforts have produced dramatic advances in their performance and reliability. Space-qualified TWTs are used for nearly all satellite communications (...)"
A Traveling Wave Tube (TWT) "is a specialized vacuum tube that is used in electronics to amplify radio frequency (RF) signals in the microwave range." "The radio wave is amplified by absorbing power from a beam of electrons as it passes down the tube." https://en.wikipedia.org/wiki/Traveling-wave_tube
The RF signal is applied on a helix copper wire inside the tube. A cathode emits electrons and these are focused on a narrow beam at the center of the tube. Due to the structural features of the helix wire, the electric field will not move with the speed of light but with a slower velocity. This electric field will interact with the beam. The positive half cycle will push electrodes forward and therefore accelerate them, while the negative half will push electrodes backward and thereby decelerate them. This will result in accelerated electrons in one segment catching up wih decelerated electrons in the adjoining segment. Due to this, there will be regions of high and low electron concentration or, in other words, electrons will tend to aggregate or bunch, and will travel in bunches. This is termed "bunching" and constitutes the result of velocity modulation linked to current density modulation. The electron beam is structured spatially by the RF input. The resulting pattern of electron density in the beam is an analog of the original RF signal. The continuous beam will be transformed in a beam with bunches which could correspond to a pulsed beam (cf LINACs Fig.32 https://cds.cern.ch/record/1982425/files/295-329%20Vretenar.pdf).
The electron bunches give their energy to the helix wire as they repel its the electrons and therefore increase the amplitude of the wave on the helix. The slightly amplified wave causes a denser electron bunch which then amplifies the signal further. The amplification is continuous as the RF wave and the electron beam travel down the length of the tube.
Relevant video: https://vimeo.com/311752241
Transcript from video at link https://youtu.be/VkpEQZEGSkE?t=336 slightly modified - added notes.
Consider a magnetron oscillator composed of a continuous cathode and an anode of three segments. The first and the third segment are connected to the positive (+) pole of an inductor and the second segment is connected to the negative (-) pole of an inductor. We consider that we have a capacitor-inductor setting (LC circuit).
Between the cathode and the anode there will exist a steady DC electric field. Also there will exist an RF field of the LC circuit. Consider an instant when the alternate anode segments have positive and negative values and the field of the RC setting (cf. circuit) is the one shown in Figure 1.
Τhe resultant of the combined fields will have different directions in region one and two, as shown in Figure 2.
"Since electrons tend to move in cycloids of right angles to the direction of the electric field, an electron leaving the cathode in region one would move" as shown in Figure 3. "It would strike an RF electric field in its proper phase relationship and give off energy to the RF field. However, an electron leaving the cathode and entering region two will not be in the proper phase relationships to give up energy to the RF field and will quickly be returned to the cathode. The net result is that more energy is given to the RF field by the electron in region 1 than is taken away from the field by the electron in region 2. In this way two blockers are overcome and oscillation can be maintained."
"The energy given up by the electrons to the RF field will change the polarity of those fields so that at the end of one half cycle the RF field will be reversed. Thus the electron which has completed one half cycle in region one will now strike region two in the proper phase relationship to give energy to that RF field (Figure 4).
This process will continue until the electron eventually reaches the anode. All electrons which move from the cathode to the anode will follow this course" (Figure 5).
"Now let's look at a typical magnetron (Figure 6). Imagine the six anode segments of the plane magnetron arranged in a circle around the cathode. The distributed inductance and the inter electrode capacitance form the necessary tank circuit for oscillation in the microwave region.
With a magnetron oscillating at this frequency, electrons leaving the cathode are governed by the same forces as those in the plane magnetron. The electrons leaving the cathode will move in the usual cycloid, passing two segments per cycle of the oscillator, until they finally reach the anode. By using a segmented anode the electrons are made to work against an alternating electric field crosswise to the steady field. In this mode, the RF field gives the electron a finite transit time which is two anode segments per cycle."
"In actual practice, large numbers of electrons will leave the cathode at the same instant. Those entering the RF field out of phase of course will be returned immediately to the cathode. But those entering in phase will follow the usual orbit until they strike the anode. Thus, there will be bunches or clouds of electrons in the phase region and very few in the outer phase regions (Figure 7). And the cloud will revolve in the same direction as the individual electrons always approaching a RF negative segment of the anode. In this way, the kinetic energy which the electrons obtain from the DC potential is given up to the RF field and oscillations are sustained."
Please refer to section starting at https://youtu.be/VkpEQZEGSkE?t=240 for introductory knowledge or background.
(Note: Klystron https://youtu.be/VkpEQZEGSkE?t=754)
https://youtu.be/kp33ZprO0Ck?t=213 "The real engineering in the microwave oven lies in creating the magnetron that generates high-powered radio waves. It's truly an amazing and revolutionary device. The vacuum tube is inside here. These are cooling fins, thin pieces of metal that dissipate the heat as the magnetron operates. The key parts are these two magnets and the vacuum tube."
https://youtu.be/kp33ZprO0Ck?t=244 "You apply a large voltage across both the inner filament and the circular copper outside. This voltage boils electrons off the center filament and they fly toward the circular copper section. (...) The magnets bend these electrons so that they swing back towards the center filament. We adjust the magnetic strength so that the now orbiting electrons just brush past the opening of these cavities, like blowing over a half-filled pop bottle to make it whistle. This creates an oscillating wave, the microwave radiation that heats food."
A capacitor with circular plates at AC voltage of high frequency develops a changing magnetic field with a strength that is dependent on the radius from the center axis. This magnetic field creates a changing electric field. These dependencies necessitate a series of corrections for the magnetic and electric field which result in a solution which includes an infinite series and a function known as the Bessel function.
Based on these calculations for a capacitor with circular plates we can calculate the electric and magnetic field inside a closed can which can be considered to constitute a resonant cavity.
As expected there is a dependence of the electric and magnetic fields on the radius from the center.
Figure 8: Use of a wavelength that can fit inside the microwave oven. Consumer ovens usually use a frequency of 2.45 gigahertz (GHz) corresponding to a wavelength of 12.2 centimetres (4.80 inches).
Cavity Resonators - The Magnetron and the Klystron
The Klystron https://en.wikipedia.org/wiki/Klystron#Two-cavity_klystron: An electron "beam first passes through the "buncher" cavity resonator, through grids attached to each side. The buncher grids have an oscillating AC potential across them, produced by standing wave oscillations within the cavity, excited by the input signal at the cavity's resonant frequency applied by a coaxial cable or waveguide. The direction of the field between the grids changes twice per cycle of the input signal. Electrons entering when the entrance grid is negative and the exit grid is positive encounter an electric field in the same direction as their motion, and are accelerated by the field. Electrons entering a half-cycle later, when the polarity is opposite, encounter an electric field which opposes their motion, and are decelerated.
Beyond the buncher grids is a space called the drift space. This space is long enough so that the accelerated electrons catch up with electrons that were accelerated at an earlier time, forming "bunches" longitudinally along the beam axis. Its length is chosen to allow maximum bunching at the resonant frequency, and may be several feet long.
The electrons then pass through a second cavity, called the "catcher", through a similar pair of grids on each side of the cavity. The function of the catcher grids is to absorb energy from the electron beam. The bunches of electrons passing through excite standing waves in the cavity, which has the same resonant frequency as the buncher cavity. Each bunch of electrons passes between the grids at a point in the cycle when the exit grid is negative with respect to the entrance grid, so the electric field in the cavity between the grids opposes the electrons motion. The electrons thus do work on the electric field, and are decelerated, their kinetic energy is converted to electric potential energy, increasing the amplitude of the oscillating electric field in the cavity. Thus the oscillating field in the catcher cavity is an amplified copy of the signal applied to the buncher cavity. The amplified signal is extracted from the catcher cavity through a coaxial cable or waveguide."
Video | Magnetron and Klystron https://youtu.be/VkpEQZEGSkE?t=746
Figure: The Klystron - By Charly Whisky