Linear Accelerator

[jsmith613]

Homework Statement

Could someone please fill in the gaps in my knowledge about Linear Accelerators.

The drift tubes are spaced equally apart. BUT the electrons speed up in between the tubes so surely the distance between the tubes should increase as does the length of the drift tubes

What ensures no force is felt inside the tubes? and what causes the force on the electrons between the tubes?

If I get this I will hoepfully understand Linac's but may come across a few more questions later.

Thanks for any help

Homework Equations

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The Attempt at a Solution

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[grzz]

There is no electric field E in the hollow of the tubes but there is an electric field E between the tubes.
Remember that electric force = Eq

 

[jsmith613]

would it not be better so put it like this (I've been doing a lot of reading about).

no force acts inside the tube as the electrodes are equally attracting in all directions so the electrons continue moving in their initial directions.

Half way through the tube the AC voltage on the drift tube changes and the electron is repelled from the tube it is in and towards the next tube.

Only when it is outside the drift tubes does the electron experience an electric field that causes it to accelerate?

is that a better way to think of it?

 

[cmb]

The drift tubes are spaced equally apart. BUT the electrons speed up in between the tubes so surely the distance between the tubes should increase as does the length of the drift tubes

I guess you are talking about a multi MeV electron accelerator.

You should note that accelerators consist of an initial stage (or series of) in which there may be stages where the drift tubes are of different lengths. However, at some large fraction of c, it is no longer true that the electrons will speed up (or at least, to a degree that causes them to desynchronise with the fields). In other words, at high relativistic energies, they begin to gain mass instead of 'laboratory-speed' as they accelerate through the fields, thus the drift tubes of the final stages of an accelerator can be of similar length.

This is as far as I understand it, and that I presume this is on the point you are raising.

 

[jsmith613]

If we assume non-relativistic speeds are my points above correct?

 

[cmb]

Like grz said, there is no e-field in the tubes. At the fringes of the tube, then you get a field. By adjusting the geometry, you can also achieve axial focussing. (This is independent of whether the accelerated particles are relativistic.)

 

[jsmith613]

just to check why do you get a field at the fringes?

 

[cmb]

The ends of the tubes are a discontinuity. So the e-fields between the tubes will take on convex forms. They can be further shaped so that any particle riding through will (integration wise) have more work done on it by e-fields inwards than outwards, thus focussing it.