Details of the electron cloud in a magnetron: density and size?

[cmb]

In a standard kitchen-microwave magnetron, like all magnetrons, a cloud of electrons forms which whizzes around and generates GHz electric currents in an outer ring electrode.

For such a standard kitchen appliance, 800W made with ferrite magnets, what is the typical volume and density of the electron 'charge wheel' that spins around?

 

[Baluncore]

There is a picture at the top of this page; https://en.wikipedia.org/wiki/Cavity_magnetron
The size of the resonant cavities in a magnetron is a function of wavelength. For a 10 cavity magnetron producing 2.45 GHz the outside diameter is about 40 mm. The open central cavity surrounding the heated cathode is about 10 mm diameter. The axial length of the cavities is about 15 mm. The two rings are the “Pi strapping” that lock the phase of the cavities and increase efficiency.
Knowing the voltage is about 3 kV and the power 800 watt, the current is about 250 mA.

 

[cmb]

I think the problem here is that "250mA" would not be related to the number of electrons, which have to circulate around the cathode X(?) times to generate that microwave current.

250mA may represent 250mC of electrons entering the working space per second, thus in equilibrium the same number leaving (i.e. a current), but how long do they last in there? If they last for one second then yes there would be 250mC of electrons in the working space. If they last a millisecond then there would be 0.25mC instead.

Is that right? And if so, then how to calculate, and/or measure, that?

 

[tech99]

I think the problem here is that "250mA" would not be related to the number of electrons, which have to circulate around the cathode X(?) times to generate that microwave current.

250mA may represent 250mC of electrons entering the working space per second, thus in equilibrium the same number leaving (i.e. a current), but how long do they last in there? If they last for one second then yes there would be 250mC of electrons in the working space. If they last a millisecond then there would be 0.25mC instead.

Is that right? And if so, then how to calculate, and/or measure, that?

The cavity has a very high Q of several thousand, but it is shunted by the load, which brings the loaded Q down to a low value such as 10. The cavity then stores a lot of energy, such that the energy it loses per cycle is less than the energy stored. Q = 2 pi energy stored/energy lost per cycle. The circulating electrons seem to be equivalent to the circulating current in the cavity and the electrons leaving the system seem equivalent to the load current. So I imagine that the ratio of these two is equal to sqrt Q.

 

[Baluncore]

When it is difficult to measure or calculate a parameter we should ask, “why do we need to know the value?”. Once that question is answered we will know how to estimate the parameter.

 

[cmb]

The cavity has a very high Q of several thousand, but it is shunted by the load, which brings the loaded Q down to a low value such as 10. The cavity then stores a lot of energy, such that the energy it loses per cycle is less than the energy stored. Q = 2 pi energy stored/energy lost per cycle. The circulating electrons seem to be equivalent to the circulating current in the cavity and the electrons leaving the system seem equivalent to the load current. So I imagine that the ratio of these two is equal to sqrt Q.

Very useful, it has prompted me to find some relevant and useful further links.

I had not thought about the magnetron as a device for which the 'Q' is the number of merit, but that has opened that up for me. If you have any further links or direct information on calculating magnetron Q values (if you could PM me and pdfs and such) that'd be really really super helpful.