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The Magnetic Bottle

How does a magnetic mirror reflect charged particles?

    When a charged particle travels through a magnetic field, its motion is governed by the magnetic force given by:

The force on a charged particle in a magnetic field

The Lorentz equation

The force is always perpendicular to the velocity and the magnetic field

    And its direction can be found using Fleming's Left Hand Grip:

     The diagram below shows a model of a magnetic bottle :

The magnetic bottle

IMAGE - The magnetic bottle, similar to the Earth's magnetic field

     where the magnetic field is represented by the blue lines and the path of a charged particle is the helical red path.

The magnetic bottle's magnetic field The path taken by a positive charge in the magnetic bottle

IMAGE - The magnetic field and the magnetic bottle

The magnetic field makes a charged particle of a certain velocity follow the red helical path

     Particles near either end of the bottle experience a magnetic force back towards the centre. This can be seen clearly below:

The magnetic bottle

IMAGE - the magnetic bottle explained

When a charged particle is in the middle of the bottle, by applying the Lorentz equation, it can be shown that there is a force towards the centre of the bottle. Similarly, when the charged particle is at either end it can be shown the force is still pointing towards the centre of the bottle. It is this force which confines a charged particle to a magnetic bottle. In much the same way, the Earth's magnetic field produces a force which confines charged particles which gives rise to the Auroras Borealis

     If a particle is initially very energetic, the magnetic bottle will not be able to confine the particle and it will escape. In exactly the same way, the aurora borealis and the aurora australis (Northern and Southern Lights) occurs when charged particles escape from the Van Allen radiation belt. These interact with the atmosphere through optical excitations of the gaseous atoms.

The Northern Lights - Auroras Borealis

IMAGE - The Auroras Borealis

The University of Birmingham 

Physics and Astronomy Department, The University of Birmingham