# Magnetic Bottle and the Kinetic Energy of a Charged Particle

• I

## Summary:

KE conservation in magnetic mirror

## Main Question or Discussion Point

Hello,

When a charged particle is inside a magnetic bottle at the right speed, the particle bounces back and forth and is confined inside the magnetic field.
The magnetic force does not work on the particle hence the particle's kinetic energy remains constant.

That means that the particle may change direction at the end of the bottles but will never stop (zero KE), correct? What happens is that the longitudinal speed goes to zero but not the transverse speed keeping KE constant. Essentially, the particle does not stop but simply turns out without stopping...

Is that correct?

Thanks!

## Answers and Replies

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kuruman
Homework Helper
Gold Member
That is correct.

berkeman
Mentor
Does it not lose some energy because the charged particle's acceleration generates some EM radiation?

kuruman
Homework Helper
Gold Member
Does it not lose some energy because the charged particle's acceleration generates some EM radiation?
Sure, northern lights but on a much smaller scale.

That is correct.
Thank you. I have read some author mention that the charged particle STOPs (zero KE) before changing direction...I guess that is an incorrect oversimplification. Also, my question implies that only the magnetic force $F_B$ is present (NO electric field $E$). However, there is a nonzero longitudinal magnetic field gradient in the magnetic bottle due to the nonuniform $B$ field.
• The force acting on the particles seems to be $F = B \times \nabla B$ instead of simply $F = qv \times B$
• From the charged particle perspective (frame of reference), the B field is changing in time, which causes an electric field, in virtue of Maxwell's equation. The generated $E$ field produces an electric force on the particle that slows it down...

berkeman
Mentor
I have read some author mention that the charged particle STOPs (zero KE) before changing direction...I guess that is an incorrect oversimplification
You know the rules...

jasonRF
Gold Member
Sure, northern lights but on a much smaller scale.
Actually, the optical emission we see as the northern lights is not due to radiation from accelerating charged particles. Instead, what is happening is that the precipitating particles collide with neutral atoms and molecules (mostly atomic oxygen and molecular nitrogen). Those collisions either bump those neutrals into higher energy states or ionize them. When the oxygen and nitrogen go back down to lower energy states they emit the light that we see as the aurora.

jason

kuruman
Homework Helper
Gold Member
Actually, the optical emission we see as the northern lights is not due to radiation from accelerating charged particles. Instead, what is happening is that the precipitating particles collide with neutral atoms and molecules (mostly atomic oxygen and molecular nitrogen). Those collisions either bump those neutrals into higher energy states or ionize them. When the oxygen and nitrogen go back down to lower energy states they emit the light that we see as the aurora.

jason
I stand corrected.

You know the rules...