# Electron beam in magnetic field - increase or decrease the field?

When I fire an electron beam into homogenous magnetic field ( eg. inside Helmholtz coil ) it will bend into a circle => it will form a coil ( = current loop ) itself. The magnetic field created by this current loop have a) the same or b) the opposite orientation than the homogenous magnetic field which caused the bending?

This is probably quite simple question, which can be perhaps easily answered by Lorenz-Force and right hand rule. The problem is that I always get lost in the sign conventions.

Connected questions:

1. If the field is increased by the beam, can this method be used ( theoretically, even though it may be impractical ) to make a virtual coil. Is it used somewhere? E.g. it would be useful in places where is very high temperature and/or radiation which would damage metal or superconductor coils ( like inside thermonuclear reactor ).

2. If the field is decreased by the beam in this case, are there any other (perhaps more complex ) configurations of intertwined magnetic fields and beams of charged particle, which creates some stable structure, where magnetic field is stronger then the original magnetic field without the beams ? I have read about plasmoid which is something like that. Can be (theoretically) used something like plasmoid to create very strong magnetic field in some place using some charged particle beams?

I mean, because of the Maxwell law $\nabla \cdot \vec B = 0$ you're going to find that it increases in one place and decreases in another.
The Lorentz force is $\vec F = q ~ (\vec v \times \vec B),$ so an electron (negative $q$) travelling "forward" through an "upward" magnetic field will try to curve "left."
The resulting current loop, as you say, is a counterclockwise circle of electrons (when viewed from the top) which is a clockwise current (again, negative $q$). Then $B$ curls around this (positive) current, pointing "downward" through the loop but "upward" outside of it. So there is an effective "pocket" of lower magnetic field with a higher magnetic field outside.