Re: FUN: high-speed electrostatic air-threads

[Leigh Palmer <palmer@sfu.ca>]

> Take an electron
> beam in a vacuum for example.  You're essentially saying that there is
> some value of current which, if exceeded, leads the electrons to ATTRACT?

No. Electrons in a cathode ray beam will always diverge. One can see
that by considering them in their rest frame. If the beam has a small
current, however, this divergence will be negligible for spot size
considerations.

> I don't understand how this could occur.  I don't see how a magnetic field
> could ever cause contraction of a moving volume of *net* charge, since
> "current" in this situation is observer dependant.  Isn't the b-field
> simply the same as e-field under special relativity?  If my ion stream is
> moving at 5kph and I should run alongside it, I will see zero current.  My
> uniform motion has eliminated the pinch force, but my motion does not
> cause the ion stream to suddenly expand.  Only if the moving charges
> exceeded c would they be time reversed and might contract.  :)

If you run alongside a current carrier which is neutral at rest you
will observe a net charge which will just balance the remaining pinch
effect force. This is a computable consequence using only the Lorentz
contraction formula.

> My mental model tells me that pinch effect cannot collapse an electron
> beam or an ion cloud.  It can "weaken" the electrostatic repulsion, but
> can never cause a net radial attraction.  However, it can collapse an
> electric current composed of relative motion between equal population of +
> and - charges, such as current in a metal conductor or a current in a
> plasma.  If these ion-streams contained equal and opposite flows of
> oppositely charged ions, then I would suspect Pinch Effect.  But if
> negative air is leaving a negative needle, where is the opposite flow of
> positive air?

It is flowing toward the needle. What's wrong with that?

Leigh