This question is doomed to remain hypothetical, since there seems
to exist no set up allowing to focus two separate parallel electron
beams withing the same guiding E and B fields.
If you calibrate your fields to have an electron stream to be
focussed, then you can have only one beam in the fields.
Ref: "Principles of Charged Particle Acceleration", Wiley & Sons,
by S. Humphries.
Um. Yes! I had forgotten about Z-pinch in plasmas. Obviously there is
something going on here that needs some thought. The current in a
plasma actually DOES produce a self-focusing effect! Of course it's
not particularly stable much to the dismay of the early fusion people,
but that is of no consequence to the discussion here.
So what we observe so far seems to be:
1. electrons in a beam do NOT self-focus. This implies that the
magnetic field is moving with the electrons so that a reference frame
attached to the electrons won't see any anomalous magnetic fields
arising from electrons that appear to be at rest.
2. A MIXTURE of positive (ions) and negative (electrons) in a plasma
DO self-focus. This somehow implies that the magnetic field generated
by current through the plasma is able to act back upon that plasma to
3. A MIXTURE of positive (protons) and negative (electrons) charges in
a WIRE also are able to create a magnetic field which apparently is
not moving at the velocity of the basic charged particles. If wires
were like hollow tubes which electrons fired down then wires carrying
current would NOT attract! As it is, we know that electrons in metals
are bouncing around in there like mad and only move forward with a
drift velocity. Somehow this fact allows magnetic motional forces to
exist between the wires. And indeed I believe that there are observed
"self-focusing" effects of a sort which is the current distributions
found in heavy current DC bus bars due to the internal magnetic
Therefore it seems to me that there are two situations here. One is
the pure case of electron beams and the other are the cases of charged
particles bouncing around in a mix in plasmas and inside wires.
Methinks there could be some fundamental physics here!
Good point, Szczepan!
It seems that electrons in a beam behave according to the current density.
See the pages 18 and 19 (Alfven current) of::
It should be also density dependent.
".. heavy current DC" = The current density which give a noticeable effect.
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