Wave propagating inside moving charged particles

[coquelicot]

Hello. Sorry if my question sounds somewhat weird (I'm a mathematician, not a physicist). I am trying to understand something for my work. I would like to know what is your opinion about it.
Assume that there are two electrodes inside a vacuum tube, with a difference of potential between them, and that a flux of charged particles (to make thing simple at first, say electrons) is moving from one electrode to the other. Assume furthermore that a monochromatic microwave (say) is emitted continuously from one electrode, and propagates through the tube in the longitudinal direction to the other electrode. Intuitively, the wave communicates some vibration to the particles, so, when the wave reaches the extremity of the tube and exits the tube, its shape is probably different from the original one.
1) to what domain of physics does this question belong ?
2) what is qualitatively the shape of the wave after it has left the tube ?
3) how does the charge and the direction of the movement of the particles affect the wave ?
thx.

 

[ZapperZ]

Hello. Sorry if my question sounds somewhat weird (I'm a mathematician, not a physicist). I am trying to understand something for my work. I would like to know what is your opinion about it.
Assume that there are two electrodes inside a vacuum tube, with a difference of potential between them, and that a flux of charged particles (to make thing simple at first, say electrons) is moving from one electrode to the other. Assume furthermore that a monochromatic microwave (say) is emitted continuously from one electrode, and propagates through the tube in the longitudinal direction to the other electrode. Intuitively, the wave communicates some vibration to the particles, so, when the wave reaches the extremity of the tube and exits the tube, its shape is probably different from the original one.
1) to what domain of physics does this question belong ?

Classical E&M, or more precisely, the discipline that deals with particle dynamics such as this is accelerator physics. Beam physics is a major part of this field of study.

2) what is qualitatively the shape of the wave after it has left the tube ?

It depends on the charge, the field strength, and field geometry. It appears here that you have a traveling wave co-moving with the electrons. The dynamics may not be as easy. There is such a thing as "beam loading", in which the field inside a cavity is modified by the presence of the electrons. So the EM field profile can be modified by the presence of the charge particles. By how much, and to what extent, will require a more detailed description of the whole thing.

3) how does the charge and the direction of the movement of the particles affect the wave ?
thx.

See #2. Getting the full picture of this is not easy, since often, it requires computer simulations.

Zz.

 

[coquelicot]

thank you Zz. But I think what I said sufficiently described the problem : a rectilinear cylindrical tube, a "constant" difference of potential between electrodes etc. What can I specify else ? must I say : a tube of length 1m, 10 cm diameter, a wave of frequency 10GH, a difference of potential of 500V etc. etc. What does it matter ? isn't physics written in symbols ? If something needs further specifications, I agree in advance with any additional assumption.

 

[ZapperZ]

thank you Zz. But I think what I said sufficiently described the problem : a rectilinear cylindrical tube, a "constant" difference of potential between electrodes etc. What can I specify else ? must I say : a tube of length 1m, 10 cm diameter, a wave of frequency 10GH, a difference of potential of 500V etc. etc. What does it matter ? isn't physics written in symbols ? If something needs further specifications, I agree in advance with any additional assumption.

The part that I don't quite understand is that you have what appeared to be a waveguide. If this is the case, then you simply can't "propagate" any kind of EM fields, because the boundary conditions will dictate the modes that can be sustained in the waveguide. And the way you described it, the only EM fields that can exist is a standing wave, not a traveling wave, so your description is contradictory to what can physically happen. Unless you are describing a pulse of EM field (which then will cause a harmonic of frequencies to exist in that pulse), then you first need to reconcile this discrepancy.

Once you do that, then you should tell me the EM field mode and the geometry. This will then tell me how the E and B fields look like in this cavity.

Still, based on your original question, I don't know what else you are asking for. I already stated that there is some degree of beam loading involved. Are you looking for quantitative values here, because that is what I meant by needing more detailed description, and also the fact that this isn't really that easy (I can't run such simulation here at home, nor do I want to spend time setting it up). I think you already have a qualitative answer to your questions.

Zz.

 

[coquelicot]

The part that I don't quite understand is that you have what appeared to be a waveguide. If this is the case, then you simply can't "propagate" any kind of EM fields, because the boundary conditions will dictate the modes that can be sustained in the waveguide. And the way you described it, the only EM fields that can exist is a standing wave, not a traveling wave, so your description is contradictory to what can physically happen. Unless you are describing a pulse of EM field (which then will cause a harmonic of frequencies to exist in that pulse), then you first need to reconcile this discrepancy.

Once you do that, then you should tell me the EM field mode and the geometry. This will then tell me how the E and B fields look like in this cavity.

Still, based on your original question, I don't know what else you are asking for. I already stated that there is some degree of beam loading involved. Are you looking for quantitative values here, because that is what I meant by needing more detailed description, and also the fact that this isn't really that easy (I can't run such simulation here at home, nor do I want to spend time setting it up). I think you already have a qualitative answer to your questions.

Zz.

Well, I'm not sure I understand the significance of EM field mode and geometry. I will try to describe as precisely as possible the experience : Let us assume that we have a crook tube, I mean a cylindrical glass vacuum tube of, say 1m of length, and 20cm of radius. At both extremities of the tube are two plates of metal, which can be heated by a filament. The two plates are heated and a difference of potential of 1000V is applied between them. So, up to now, an approximately uniform electric field holds between the plates, and there is an electron beam. Now, at one extremity of the tube, a monochromatic sinusoidal EM wave of frequency 10GH is emitted continuously in such a way it propagates (hopefully) in the longitudinal direction of the tube (I mean, if it was empty space, it would propagate in this way, but I don't know if it can propagate inside the tube with these conditions). Notice that I do not assume the wave is guided in the tube, but only that the part of the wave inside the tube is (allegedly) propagating in the longitudinal direction. This wave is generated from a magnetron providing 40 kW peak. The question is: what is the shape of the wave outside the tube, but very near the extremity of the tube where the wave is exiting, say in the continuation of the axis of the tube.

 

[tech99]

Hello. Sorry if my question sounds somewhat weird (I'm a mathematician, not a physicist). I am trying to understand something for my work. I would like to know what is your opinion about it.
Assume that there are two electrodes inside a vacuum tube, with a difference of potential between them, and that a flux of charged particles (to make thing simple at first, say electrons) is moving from one electrode to the other. Assume furthermore that a monochromatic microwave (say) is emitted continuously from one electrode, and propagates through the tube in the longitudinal direction to the other electrode. Intuitively, the wave communicates some vibration to the particles, so, when the wave reaches the extremity of the tube and exits the tube, its shape is probably different from the original one.
1) to what domain of physics does this question belong ?
2) what is qualitatively the shape of the wave after it has left the tube ?
3) how does the charge and the direction of the movement of the particles affect the wave ?
thx.

The concept looks similar to a traveling wave tube, where an electron beam interacts with a slow EM wave. The EM wave is slowed down by a guiding structure, such as a helix, so that its speed is similar to the electrons.This produces electron bunching and produces amplification. I am unsure of the exact type of EM wave you have in mind, whether a guided wave or a freely propagating one.