Trying to understand the oscillation of electrons in the magnetic fiel

[hb1547]

Working on understanding the physics of how an electron oscillates along the Earth's magnetic field. I understand that an electron will spiral around the magnetic field line, that's easy to tell from the Lorentz force. What I don't understand is what causes the oscillation.

My best guess is that, as the magnetic field lines come close together as they come close to the Earth, this simulates a changing magnetic field from the electron's view, and induces an electric field in the direction that would dampen the electron's motion and reverse it. What's giving me a hard time is understanding specifically how an electric field is created in that direction.

Any insight or tips?

 

[mfb]

Electromagnetic fields depend on your reference frame.

In the frame of earth, we have a magnetic field, and an electron with a component perpendicular to that field -> Lorentz force. No electric fields are involved.
If you transform this field into the frame of the electron, the field gets an electric component, leading to the same force.

 

[hb1547]

Electromagnetic fields depend on your reference frame.

In the frame of earth, we have a magnetic field, and an electron with a component perpendicular to that field -> Lorentz force. No electric fields are involved.
If you transform this field into the frame of the electron, the field gets an electric component, leading to the same force.

Yes, this makes sense, and I know I can think of it either as purely magnetic (Earth's frame) or as an electric field (electron's frame). I thought the electron's frame would be easier but it hasn't been.

Then to me it seems that perhaps the converging of the magnetic field lines might help to explain why the parallel component of the velocity is lost, but I'm still having trouble.

 

[mfb]

The parallel component is not lost, but it can get reduced if the field strength increases, or the particle collides with other particles.

 

[hb1547]

The parallel component is not lost, but it can get reduced if the field strength increases, or the particle collides with other particles.

Yes, but what is the physics behind the reduction in the parallel component? Why does it reduce?

I found http://faculty.uml.edu/cbaird/95.657%282012%29/Ionosphere.pdf, which explains it well in terms of a dipole, but perhaps there's an explanation in terms of just the particle?

 

[mfb]

Yes, but what is the physics behind the reduction in the parallel component? Why does it reduce?

Increasing field strength correspond to an "inwards" component of the magnetic field (into the spiral). The velocity component orthogonal to this component gives a net force backwards, if I rotated those coordinates correctly.