As with all velocity-modulated tubes, the generation of microwave frequencies at a magnetron can be subdivided into four phases:

1. Phase: Generation and acceleration of an electron beam in a DC field
2. Phase: Velocity-modulation of the electron beam in an AC field
3. Phase: Formation of electron bunches by velocity modulation (here in form of a “space-charge wheel”)
4. Phase: Dispensing of energy to the AC field

12.2.1. Phase 1 – Generation and Acceleration of Electron Beam in DC Field

Trajectory of an electron under the influence of the electrostatic 

and the magnetic field for different magnetic flux densities.

Since the cathode is kept at a negative voltage, the static electric field is in a radial direction from (grounded) anode block to the cathode. When no magnetic field exists, heating the cathode results in a uniform and direct movement of the electron from the cathode to the anode block (the blue path in figure 5). A weak permanent magnetic field B perpendicular to the electric field bends the electron path as shown with the green path in figure 5. If the electron flow reaches the anode, so a large amount of plate current is flowing. If the strength of the magnetic field is increased, the path of the electron will have a sharper bend. Likewise, if the velocity of the electron increases, the field around it increases and the path will bend more sharply. However, when the critical field value is reached, as shown in figure 5 as a red path, the electrons are deflected away from the plate and the plate current then drops quickly to a very small value. When the field strength is made still greater, the plate current drops to zero.

These values of the anode voltage and magnetic field strength that prevent an anode current are called Hull cut-off magnetic field and cut-off voltage. When the magnetron is adjusted to the cut-off or critical value of the plate current and the electrons just fail to reach the plate in their circular motion, it can produce oscillations at microwave frequencies.

12.2.2. Phase 2 – Velocity-Modulation of Electron Beam

The influence of the high-frequency electrical field on the trajectory of an electron

The electric field in the magnetron oscillator is a summary of AC and DC fields. The DC field extends radially from adjacent anode segments to the cathode. The AC fields, extending between adjacent segments, are shown at an instant of the maximum magnitude of one alternation of the RF oscillations occurring in the cavities.

In figure 6 is shown only the assumed high-frequency electrical AC field. This AC field works in addition to the permanently available DC field. The AC field of each individual cavity increases or decreases the DC field like shown in figure 6.

Well, the electrons that fly toward the anode segments loaded at the moment more positively are accelerated in addition. These get a higher tangential speed. On the other hand, the electrons which fly toward the segments loaded at the moment more negatively are slowed down. These consequently reach a lower tangential speed.

12.2.3. Phase 3 – Forming a Space-Charge Wheel

Rotating space-charge wheel in a twelve-cavity magnetron

Due to the different speeds of the electron groups, velocity modulation leads to density modulation.

The cumulative action of many electrons returning to the cathode while others are moving toward the anode forms a pattern resembling the moving spokes of a wheel known as a “space-charge wheel,” as indicated in figure 7. The space-charge wheel rotates about the cathode at an angular velocity of 2 poles (anode segments) per cycle of the AC field. This phase relationship enables the concentration of electrons to continuously deliver energy to sustain the RF oscillations.

One of the spokes is near an anode segment which is loaded a little more negatively. The electrons are slowed down and pass their energy on to the AC field. This state isn’t static, because both the AC field and the wire wheel permanently circulate. The tangential speed of the electron spokes and the cycle speed of the wave must be brought in agreement.

12.2.4. Phase 4 – Dispensing of Energy to the AC Field

Recall that an electron moving in an E field is accelerated by the field and takes energy from the field. Also, an electron dispenses energy to a field and slows down if it is moving in the same direction as the field (positive to negative). The electron passes energy to each cavity as it passes and eventually reaches the anode when its energy is expended. Thus, the electron has helped sustain oscillations because it has taken energy from the DC field and given it to the AC field. This electron describes the path shown in figure 5 over a longer time period. Due to the multiple decelerations of the electron, its energy is optimally utilized and efficiencies of up to 80 percent are achieved.

12.2.4.1. Transient oscillation

After switching the anode voltage, there is still no RF field. The single electron moves under the influence of the static electric field of the anode voltage and the effect of the magnetic field as shown in figure 5 by the red electron path. Electrons are charge carriers: During the flyby at a gap, they give off a small part of the energy to the cavities. (Similar to a flute: A flute produces sound when a stream of air flows past an edge of a hole.) The cavity resonator begins to oscillate at its natural resonant frequency. Immediately begins the interaction between this RF field (with an initial low power) and the electron beam. The electrons are additionally influenced by the alternating field. It begins the process described in the sequence of phase 1 to 4 of the interaction between the RF field and the now velocity-modulated electrons.

Unfortunately, the transient oscillation doesn’t begin with a predictable phase. Each transient oscillation occurs with a random phase. The transmitting pulses that are generated by a magnetron are therefore not coherent.

However, it is possible to get phase coherence, if the magnetron is fed with a continuous priming signal from a coherent oscillator.[2]

Modes of Oscillation

Modes of the magnetron

(Anode segments are represented “unwound”)

Cutaway view of a magnetron (vane-type) showing the strapping rings and the slots.

The operation frequency depends on the sizes of the cavities and the interaction space between anode and cathode. But the single cavities are coupled over the interaction space with each other. Therefore several resonant frequencies exist for the complete system. Two of the four possible waveforms of a magnetron with 12 cavities are in figure 9 represented. Several other modes of oscillation are possible (¾π mode, ½π mode, ¼π mode) but a magnetron operating in the π mode has a higher output power and is most commonly used.

Figure 8 shows three of the four possible oscillation modes of a 12-resonator magnetron. When operating the magnetron in one of the other modes (¾π, ½π, ¼π) the power or the efficiency and the oscillation frequency decrease.

To ensure that a stable operational condition can be set in the optimal π mode, two constructive measures are possible:

12.2.4.2. Strapping Rings

The frequency of the π mode is separated from the frequency of the other modes by strapping to ensure that the alternate segments have identical polarities. For the π mode, all parts of each strapping ring are at the same potential, but the two rings have alternately opposing potentials. For other modes, however, a phase difference exists between the successive segments connected to a given strapping ring which causes current to flow in the straps.

• Use of cavities with different resonance frequencies, e.g., such a variant is the anode form “rising sun.”

12.2.4.3. Magnetron coupling methods

Energy (rf) can be removed from a magnetron by means of a coupling loop as shown in figure 9 into the bottom one resonator. At frequencies lower than 10,000 megahertz, the coupling loop is made by bending the inner conductor of a coaxial line into a loop. The loop is then soldered to the end of the outer conductor so that it projects into the cavity, as shown in figure 10 also. Locating the loop at the end of the cavity, as shown in figure 11, causes the magnetron to obtain sufficient pickup at higher frequencies.

The segment-fed loop method is shown in figure 12. The loop intercepts the magnetic lines passing between cavities. The strap-fed loop method figure 13, intercepts the energy between the strap and the segment. On the output side, the coaxial line feeds another coaxial line directly or feeds a waveguide through a choke joint. The vacuum seal at the inner conductor helps to support the line. Aperture or slot coupling is illustrated in figure 14. Energy is coupled directly to a waveguide through an iris (made from either glass or ceramic).

Magnetron Tuning

Inductive magnetron tuning

An example of a tunable magnetron is the M5114B used by the ATC Radar ASR-910. To reduce mutual interferences, the ASR-910 can work on different assigned frequencies. The frequency of the transmitter must be tunable, therefore. This magnetron is provided with a mechanism to adjust the Tx frequency of the ASR-910 exactly.

The image below 16 shows the inductive tuning elements of the TH3123 magnetron used in ATC radar Thomson ER713S. Note that the adjacent filament supply lines resonant cavity and the coupling loop cavity are not tunable!

Resonant cavities of a hole-and-slot-type magnetron with inductive tuning elements

Magnetron M5114B of the ATC radar ASR-910

Magnetron VMX1090 of the ATC radar PAR-80 This magnetron is even equipped

with the permanent magnets necessary for the work.

12.2.4.4. Upper-Frequency Limit

Documented sources state that the upper-frequency limit for the use of magnetrons to generate power is about 95 GHz. There are some other indicators throughout the industry of higher frequencies but with little supporting documentation. 

A cavity resonator in a magnetron should have the dimensions of about half the wavelength of the oscillation to be generated. At 96 GHz, the wavelength is in the range of 3.125 mm. The hole should, therefore, have a diameter of about 1.5 mm. However, the accuracy should be far below 5 percent because all cavity resonators should have the same resonant frequency so that oscillation is amplified. So we already have a required mechanical accuracy of a few hundredths of a millimeter. Perhaps feasible so far.

But if a resonant frequency of 300 or even 400 GHz is claimed, then the required dimensions of the cavity resonators are in the range of tenths of a millimeter for a resonance. The required accuracy would then have to be in the range of a few thousandths of a millimeter. Even if one could imagine these mechanical challenges for a laboratory instrument, it fails because these small distances of tenths of a millimeter no longer permit a high anode voltage. Instead of a high-frequency oscillation, there is then a spark gap like with a spark plug. These considerations make such data rather unlikely for such high frequencies.

12.2.4.5. Crossed-Field Amplifier

Other names are sometimes used for the crossed-field amplifier in the literature:

• Platinotron
• Amplitron
• Stabilotron

The crossed-field amplifier (CFA) is a broadband microwave amplifier that can also be used as an oscillator (stabilotron). It is a so-called velocity-modulated tube. The CFA is similar in operation to the magnetron and is capable of providing relatively large amounts of power with high efficiency. In contrast to the magnetron, the CFA have an odd number of resonant cavities coupled with each other. These resonant cavities work as a slow-wave structure: An oscillating resonant cavity excites the next cavity. The actual oscillation will be led from the input waveguide to the output waveguide.

Water-cooled Crossed-Field Amplifier L–4756A in its transport case

Subset of the cycloidal electron paths into a Crossed-Field Amplifier

The electric and magnetic fields in a CFA are perpendicular to each other (“crossed fields”). Without an input signal and the influence of both the electric field (anode voltage) and the magnetic field (a strong permanent magnet) all electrons will move uniformly from the cathode to the anode on a cycloidal path as shown in figure 2. (This case should be avoided in practice, because the CFA will generate a high level of noise then.)

The input signal starts the excitation of the first resonant cavity

If the input waveguide introduces an oscillation into the first resonator (as shown in figure 3), the vanes of the resonator get a voltage difference synchronously to the oscillation. Under the influence of this additional field flying past electrons get acceleration (at the positively charged vane) or they are decelerated (at the negatively charged vane). This causes a difference in the speed of the electrons. The faster electrons catch the slower electrons and form electron bunches in the interaction space between the cathode and the anode. These bunches of electrons rotate like the “space-charge wheel” known from the magnetron operation. But they cannot rotate in full circle, the “space-charge wheel” will be interrupted because the odd number of cavities causes an opposite phase in the last odd cavity (this bottom one between the waveguides). To avoid negative feedback, this resonant cavity may include a graphite block to decouple input and output.

The oscillation is still very weak into the first cavity. But the electron bunches will hit the vanes of the following cavities and will dispense their energy synchronously to the oscillation. The alternating microwave field causes the electrons to alternately speed up and slow down near the next cavity. Simultaneously, the anode near the vanes is hit by the first electrons in the cycle of oscillation. This causes amplification: The oscillation will be stronger from cavity to cavity therefore. At the resonant cavity with the coupled output waveguide these electron bunches are solved: all but electrons hit the anode and cause the anode current.

The bandwidth of the CFA, at any given instant, is approximately plus or minus 5 percent of the rated center frequency. Any incoming signals within this bandwidth are amplified. Peak power levels of many megawatts and average power levels of tens of kilowatts average are, with efficiency ratings in excess of 70 percent, possible with crossed-field amplifiers.

To avoid ineffective modes of operation the construction of CFA contains strapping wires like those used in magnetrons. Because of the desirable characteristics of wide bandwidth, high efficiency, and the ability to handle large amounts of power, the CFA is used in many applications in microwave electronic systems. When used as the intermediate or final stage in high-power radar systems, all of the advantages of the CFA are used.

Interaction between a cavity resonator and the rotating “Space-Charge Wheel”

The interrupted “Space-Charge Wheel” into a Crossed-Field Amplifier

The amplifiers in this type of power-amplifier transmitter must be broadband microwave amplifiers that amplify the input signals without frequency distortion. Typically, the first stage and the second stage are traveling-wave tubes (TWT) and the final stage is a crossed-field amplifier. Recent technological advances in the field of solid-state microwave amplifiers have produced solid-state amplifiers with enough output power to be used as the first stage in some systems. Transmitters with more than three stages usually use crossed-field amplifiers in the third and any additional stages. Both traveling-wave tubes and crossed-field amplifiers have a very flat amplification response over a relatively wide frequency range.

Crossed-field amplifiers have another advantage when used as the final stages of a transmitter; that is, the design of the crossed-field amplifier allows RF energy to pass through the tube virtually unaffected when the tube is not pulsed. When no pulse is present, the tube acts as a section of waveguide. Therefore, if less than maximum output power is desired, the final and preceding cross-field amplifier stages can be shut off as needed. This feature also allows a transmitter to operate at reduced power, even when the final crossed-field amplifier is defective. If the anode voltage is switched on then the CFA will provide a gain of 3 to 20 dB.