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Trapped Radiation and the South Atlantic Anomaly

Trapped Radiation

Due to the combined effects of the magnetosphere and atmospheric effects, charged particles are trapped around the Earth in the form of radiation belts. The exact reasons for the formation of stable particle populations in these radiation belts are complex, but are partly explained by the helical motion of charge particles along the magnetic field lines between the Earth's poles.

Charged particles tend to travel in a spiral path along magnetic field lines due to the Lorentz force:

where B is the magnetic field strength, q is the particle charge, and v is the particle velocity. The force acts in a direction at right angles to both the magnetic field and the particle velocity.

In vector notation, with more conventional units,

where Z is the atomic number of the particle. This causes the particle to move in a spiral motion along the magnetic field line, since the particle velocity will have components both parallel and perpendicular to B. The gyroradius of the particle's rotation is given by

where:

= the velocity component perpendicular to the field;
m = the particle's relativistic mass .
For example, the gyroradius for a 1 MeV electron near the equator at 500 km altitude is approximately 1 km. The gyroradius for a 1 MeV proton in the same region would be approximately 10 km.

The other important quantity that defines the motion of the particle along the magnetic field line is the pitch angle . The pitch angle describes the angle of the helical motion around the field line, and depends on both the particle's velocity component parallel to the field, and the frequency of rotation of the particle around the field line (the gyrofrequency). It is found that the pitch angle at the magnetic equator, , is a minimum ( <) or a maximum ( >), and increases (or decreases) to a value of at some magnetic latitude, .

When the pitch angle is (the mirror point) the motion of the particle is instantaneously circular, and so stops moving towards the magnetic pole. Consequently the mirror point represents the point on the particle's trajectory where the motion reverses, and the particle 'bounces' back towards the magnetic equator.

Therefore the particle spirals back to the magnetic equator, passing through and continuing until it arrives at the conjugate mirror point in the opposite hemisphere, where its pitch angle is again . Once here, it "bounces" back, oscillating between the two mirror points at frequencies of the order of a few hertz. In this way, radiation is trapped in belts that follow the magnetic field lines between the magnetic poles. If the mirror point is at low altitude (less than 100km), the particle is likely to be absorbed into the atmosphere, and will therefore be lost from the trapped population.

For low altitude spacecraft (e.g. less than 1,000 km altitude), there is one region where the a significant population of trapped protons is encountered - known as the South Atlantic Anomaly (SAA).

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