Behaviour of an accelerating beam of electron.

[Nemika]

If a beam of electrons starts to accelerate from rest due to a uniform electric field in vacuum will the electrons feel any mutual repulsion or attraction? Will the beam first expand then contract?

If yes, how does this happen? This was a question under magnetism head.

 

[BvU]

Hi,
We had a recent thread on this. There's also magnetic focusing which google
Electrons repel each other, so you have to make an effort to collimate and focus. It's a complete area of expertise in high energy physics.
[edit]@ZapperZ corrects me here (see below): it's a separate field. But physics .

 

[Nemika]

Hi,
We had a recent thread on this. There's also magnetic focusing which google
Electrons repel each other, so you have to make an effort to collimate and focus. It's a complete area of expertise in high energy physics.

Thanks for the reply.
I have studied about crt's working previously but I'm confused in this case since there wasn't any external magnetic field mentioned. How would the beam expand or contract if it's only accelerated by an electric field?

 

[Drakkith]

How would the beam expand or contract if it's only accelerated by an electric field?

I believe the beam is expanded by the electric field of the electrons themselves. In the rest frame of the electrons in the beam there are no magnetic effects (from the other electrons) so it should simply be that the beam expands unless an external field acts on them.

 

[ZapperZ]

If a beam of electrons starts to accelerate from rest due to a uniform electric field in vacuum will the electrons feel any mutual repulsion or attraction? Will the beam first expand then contract?

If yes, how does this happen? This was a question under magnetism head.

In accelerator physics, this is known as "space charge" effects. (BTW, this is often the domain of accelerator science, not HEP).

However, the severeness of this effect depends on (i) the amount of charge being emitted per unit time, (ii) the electron beam size, and (iii) the accelerating voltage. For CRT, I do not think that the effect will be that severe because of the amount of charge being emitted and how much it has been accelerated. The higher the gradient, the less the effect will be because the electrons will be spread out even more.

As for trying to get them back together, that is what the focusing magnets do. You can either use a solenoid (http://pitz.desy.de/sites/site_pitz/content/e108/e9/e1246/infoboxContent1247/PITZphysics_eng.pdf), or quadrupole magnets, etc., depending on the severity and the type of electron beam. These are common (or even necessary) components in a particle accelerator.

Zz.

 

[sophiecentaur]

Without any focussing, an electron beam will spread during and after its acceleration. There are two ways to focus a beam; you can either use a magnetic field (often a quadruple field) or pass the beam through a negatively charged tube, which will bend the conical beam back towards to a focus. But, of course, the mutual repulsion will eventually spread the beam out again. The secret is to make the focus coincide with the CRT screen and get as small a spot as possible.
In a CRT, the beam is formed in an 'electron gun' which give it the energy and the long drift space between gun and tube face allows the beam to cover a large picture area.
The CRT was a terrific invention at the time but we are largely pleased / relieved that it has been superseded by flat screen technology because it was such a knife edge situation to set up with good geometry and with colour purity and convergence.

 

[Nemika]

There are two ways to focus a beam; you can either use a magnetic field (often a quadruple field) or pass the beam through a negatively charged tube, which will bend the conical beam back towards to a focus.

The initial question was a multiple choice correct and the correct options were, that the moving electrons (in the beam)-
a) initially experience a force of mutual repulsion
b) experience a force of mutual attraction after traveling a certain distance.
How could the second option be possibly correct, if none of the two ways that you mentioned are actually present?
(And also the incorrect options were-
c) will follow parallel lines because there is no force of attraction between them.
d) will continue to diverge due to electrostatic repulsion.)

 

[BvU]

In homework fora, please state the complete problem statement.

 

[sophiecentaur]

How would the beam expand or contract if it's only accelerated by an electric field?

The answer to this is the mutual repulsion of the Electric electrons and the radial force caused by the magnetic field due to the beam current and the current that is effectively being carried by each individual moving electron. This has to be reduced by some electron optics.

The initial question was a multiple choice correct and the correct options were, that the moving electrons (in the beam)-

I was thinking about the problem from a practical standpoint. How is the beam formed in the first place? What will be accelerating it? I assume that the beam was actually fired across the gap between two infinite (?) charged plates, through a hole in the negative plate. This link deals with the way a moving beam of electrons behaves. There's a lot to read but I think the answers to the OP lie in there. As @BvU says, the problem needs to be stated in detail because the numbers count.

 

[sophiecentaur]

I believe the beam is expanded by the electric field of the electrons themselves. In the rest frame of the electrons in the beam there are no magnetic effects (from the other electrons) so it should simply be that the beam expands unless an external field acts on them.

I re-read this. Where does the Pinch Effect come in here? I was assuming it would apply to an electron beam but does it only apply to plasma beams?

 

[Drakkith]

I re-read this. Where does the Pinch Effect come in here? I was assuming it would apply to an electron beam but does it only apply to plasma beams?

That's a good question and I confess that I don't know the answer.