Energy conservation in a magnetron

[Carl2017]

I am trying to understand how energy is conserved in a magnetron. If the electrons are following a circular path in the magnetic field and never reach the anode will there be zero current between the anode and the cathode? If so how does the device consume power from the external circuit supplying the anode voltage? The electrons appear to be orbiting on at a constant potential in the electric field so how does the electric field impart energy to them?
I think I am missing something fundamental about how this works, can anyone help? Thanks.

 

[scottdave]

You might like this video, by Bill Hammack (the Engineerguy). http://www.engineerguy.com/elements/videos/video-microwave.htm

I have the book (but cannot locate it right now). The chapter which talks about magnetrons goes into more detail.
In short, as the electron moves past the cavity, an electric field is induced in the cavity. This changing electric field is what causes the electromagnetic wave emission. Since the EM wave leaves the magnetron, that is where the energy goes.
You also might find this helpful. http://www.phy.davidson.edu/instrumentation/Files/NEETS/Mod11 - Microwave Principles.pdf

 

[Carl2017]

Thanks for your reply. I can see where the energy emerges and where it goes, but I am still puzzled about where it comes from. I had a look at the video and at 4:21 the animation shows the electrons being bent by the magnetic field and if the magnetic field is strong enough they never reach the anode [Hull cut-off criterion]. At this point it seems to me there would be no current flowing between the cathode and the anode. If the power from the external circuit providing the anode voltage is voltage X current then it looks as if the external circuit is not supplying any power, so how does the electric field supply energy to the electrons? I will have a look at the document you sent to see if I can learn some more. Thanks very much for the information and your prompt reply.

 

[tech99]

You might like this video, by Bill Hammack (the Engineerguy). http://www.engineerguy.com/elements/videos/video-microwave.htm

I have the book (but cannot locate it right now). The chapter which talks about magnetrons goes into more detail.
In short, as the electron moves past the cavity, an electric field is induced in the cavity. This changing electric field is what causes the electromagnetic wave emission. Since the EM wave leaves the magnetron, that is where the energy goes.
You also might find this helpful. http://www.phy.davidson.edu/instrumentation/Files/NEETS/Mod11 - Microwave Principles.pdf

I don't think it is true that an EM wave leaves the magnetron, but rather, an alternating current is generated by the magnetron and is usually delivered via a coaxial probe.

 

[davenn]

I don't think it is true that an EM wave leaves the magnetron, but rather, an alternating current is generated by the magnetron and is usually delivered via a coaxial probe.

yes, RF is usually taken from one of the cavities via a probe and fed to the main waveguide that opens up into the oven cavity or WG feed to an antenna ( depending on specific use)
but it can also leave directly from one of the cavities and into the external waveguide

a couple of examples

the first 2 examples use probes
the third example has waveguide coming directly off one of the cavities

Naval Training Manual
http://www.phy.davidson.edu/instrumentation/Files/NEETS/Mod11 - Microwave Principles.pdf

this is from the above link that @scottdave suppliedthe ol' saying, " there is always more than one way to skin a cat "Dave

 

[scottdave]

Here is another site, which you may find helpful. http://www.radartutorial.eu/08.transmitters/Magnetron.en.html
This one actually does come out and state that the electrons do reach the anode (completing the "circuit"). I knew that this needs to happen, or there would be no need to keep emitting more electrons from the cathode, if they are not going anywhere.

 

[tech99]

I agree with this; I was just trying to avoid the idea that a magnetron is functionally somehow like an atom.

 

[tech99]

The magnetic field is first adjusted so the tube is cut-off, with the tube not oscillating. When oscillation occurs, electrons hit the lips of the cavity resonators and create the oscillatory current in the walls of the cavities. The electrons then flow to the + terminal of the power supply and constitute the DC anode current, and if we multiply this current by the supply voltage it gives us the DC input power. I believe about half this power is converted to RF, the rest being wasted as heat.
As a matter of interest, in 2017 do I say B-supply, HT supply or just high voltage anode supply?

 

[sophiecentaur]

The power of RF that the magnetron generates will depend on the dissipation in the load (food). Ideally, the phase of the current and voltage in the circulating electron beam will be more or less in quadrature with no load and almost in phase when there is a suitably matched load. This is the same in one way or another for any transmitting amplifier when the load is totally mismatched. I am ignoring the fact that many amplifiers can suffer from excess current or volts if the load is badly matched / removed.
There is a parallel here with the way a transformer will only take or supply power when a load is actually connected to it.

 

[Carl2017]

I had a look at the radar tutorial, thanks for the information. So in a practical magnetron the electrons do not stay in the Hull cut off condition shown in step one because they form a space charge wheel and eventually some of them reach the anode. I am still puzzled about what would happen if the electrons could be maintained in the Hull cut off condition. In theory you could have a device with just a simple cylinder as the anode with no cavities. If the magnetic and electric fields were the appropriate strengths surely the electrons would be trapped in the space between the anode and the cathode. The accumulated space charge would repel any electrons emerging from the cathode and there would be no anode current, but the accelerating electrons would radiate energy which has to come from somewhere. That can't be correct but I don't understand why. Thanks for all your help.

 

[marcusl]

The energy supplied to the electrons, which eventually is transferred to the RF output, comes from the high electric potential applied between cathode and anode.

 

[Carl2017]

Thanks for your reply. Yes, during the ordinary operation of a magnetron, but when the electrons are in the Hull cut-off condition they orbit around an equipotential and there is no anode current, so how is energy transferred in this case?

 

[marcusl]

If there's no anode current, then no RF power can be extracted at the output.

 

[Carl2017]

But if the electrons are accelerated but do not reach the anode, aren't they radiating energy? That is the part I can't understand, sorry if I am still not getting it. Thanks for your help.

 

[marcusl]

So the statement that there is "no" anode current is incorrect--it is small compared to the value when it is supplying power to the load.

EDIT: Keep in mind that radiation is small when electron speeds are well below the speed of light.

 

[Carl2017]

I am think about a device more like Hull's original magnetron from the 1920's with a simple circular anode with no cavities. I don't understand why the anode current is not zero. I thought that was the definition of the Hull cut-off condition. The radiated energy might be very small but it is not zero. Sorry, I don't understand where it comes from. Thanks for your help.

 

[marcusl]

The magnetron equations you refer to are idealizations that ignore a number of small effects such as energy loss due to radiation. There are only two energy sources in the device: the hot cathode that boils electrons off of its surface, and the electric field between it and the anode. The first is tiny, the second is dominant. You can consider any energy carried out of the device as provided by the latter. Radiated energy miniscule, so the plate current will also be minuscule--approximately zero.