Re: simple magnets question

[brian whatcott <inet@INTELLISYS.NET>]

At 07:50 6/26/99 -0400, John Denker wrote:
> ...
> Suppose Joe is in the lab frame.  He sets up an electromagnet consisting of
> a wire with current flowing in it.  According to Joe, at some typical point:
> * The wire has stationary positive metal ions with a density rho_p = rho_0.
> * The wire contains electrons moving with rapidity u.
> * The wire is macroscopically electrically neutral.
>   Therefore the electron density rho_e must be equal to rho_0
>   (ignoring terms of order u**2).
>
> Now suppose a test charge whizzes by at a rapidity v.  Joe sees the test
> charge deflected by the magnetic field of his magnet, and not by any
> electric field.  (Remember, Joe has no electric field.)

This setup reminds me of an amusing circumstance associated with the
 Betatron built by Kerst sixty years ago. This device had a toroidal
vacuum chamber surrounding the opposing poles of an electromagnet.
 The electromagnet featured laminated windings to use an alternating
current.
 The objective was to accelerate electrons emitted from a hot filament
into a circular orbit at a high fraction of c and via a capacitor
discharge in a steering coil, to deflect them to a target where hard
X-rays were produced.

Now it turns out that the highest electron acceleration occured near
the point in the cycle where the flux was minimal, because the device
used the transformer principle where the electromagnet
provided the primary coil, and the toroid was the one turn secondary.

After this long preamble I can now proceed to the punch line:
to explain the Betatron's operation one says,

Consider electrons emitted by the filament with velocity zero at the
 moment when the flux from the electromagnet is also zero.
 Here the delta flux per delta t is maximal and so the induced EMF
is also greatest (The flux in question is that through the whole
diameter of the toroid.)

   This EMF exerts a tangential force on the electrons which as they
approach the outer edge of the toroid find an increasing flux
(as the AC cycle proceeds) which handily turns them onto a circular
orbit where  the centripetal force balances the force arising from
 the magnetic induction i.e  m.v squared/r = e.v.B   at least in the
pre relativistic speed range.

Paraphrasing this mechanism, one can say that one obtains maximal
electron energy in the electron pulse by providing them at zero
velocity, and providing them an environment of zero magnetic flux.


brian whatcott <inet@intellisys.net>
Altus OK