Charged particles through various B field shapes quesion

[Salvador]

Hi, first of all I wan to ask a few simple questions ,
when we move a piece of wire perpendicular to a uniform magnetic field like between the faces of two magnets facing N-S we get a current either one or the other way in the wire , yet when we would shoot an electron beam the same path as the wire was the beam would bend around to form a circle , why is that , is it simply because the electrons in a wire have a medium they can only travel along so they travel along that medium while the electron beam is in a vacuum and so the electrons are free to move wherever the field pushes them ?
Also for the very same reason how come a CRT deflection coil manages to steer the electron beam and doesn't spoil the beam and the beam doesn't get spread out due to the particles forming circular motion once they pass through a magnetic field?

the other question is ,(some aspects here are purely theoretical I'm more interested in the concept) if I have a neutral plasma and I have two cases , in case one the plasma beam passes through two magnets located on each side of the beam with their field perpendicular to the beam the particles in the beam get deflected and after the magnets they shoot in opposite directions, electrons one way and protons the other correct? (see attached picture)

now in case two i take that same beam and shoot it through a solenoid type coil , what happens now, the protons and electrons each rotate the other way but they are carried along the length of the coil due to the field at the same time?
Also I wonder , does passing plasma through such solenoid focuses the plasma into a more beam like structure or not?
If I'm correct the gyroradius of these particles traveling through such uniform magnetic field is dependent on the velocity of the particle and the magnetic field strength combined ? increasing one or both reduces the radius and leads to a more focused beam ?

also does such passing through a B field exerts a sort of backpressure or constraint on the particles and decreases their velocity much like a sliding rope being grabbed by hand and braked down ?

 

[mfb]

when we move a piece of wire perpendicular to a uniform magnetic field like between the faces of two magnets facing N-S we get a current either one or the other way in the wire , yet when we would shoot an electron beam the same path as the wire was the beam would bend around to form a circle , why is that , is it simply because the electrons in a wire have a medium they can only travel along so they travel along that medium while the electron beam is in a vacuum and so the electrons are free to move wherever the field pushes them ?

Right.

Also for the very same reason how come a CRT deflection coil manages to steer the electron beam and doesn't spoil the beam and the beam doesn't get spread out due to the particles forming circular motion once they pass through a magnetic field?

Why should the beam get spread out? All electrons are deflected in (nearly) the same way. The magnetic field is too small and too weak to lead to a full circle.

the other question is ,(some aspects here are purely theoretical I'm more interested in the concept) if I have a neutral plasma and I have two cases , in case one the plasma beam passes through two magnets located on each side of the beam with their field perpendicular to the beam the particles in the beam get deflected and after the magnets they shoot in opposite directions, electrons one way and protons the other correct? (see attached picture)

You would need a really thin plasma or really strong fields for that.

Not much would happen with the solenoid. You can stop the beam from diverging, but in general it also won't get focused.

 

[Salvador]

Well with the solenoid then , isn't the tokamak for example just a big circled solenoid to make a torus aka toroidal field for the plasma (I know there are other shaping coils too), then I wonder if the particle velocity gets high enough when the conditions approach burning plasma , I assume every particle with enough energy would then diverge while running around into such a field until it would hit the magnet or the wall between the magnet , am I right?

 

[mfb]

To first order, the particles follow a helix around the plasma lines, which are closed in a tokamak, so the particles are contained. Collisions with other particles can lead to drift and other effects.