Earth magnetic field is produced by electric currents that flows into Earth core. It is approximately a dipolar field. Its poles are inverted in respect to geographic poles, its axis is inclined 11° in respect to Earth rotation axis and the dipole center is displaced about 320 km in respect to Earth center.
Earth magnetic field is slowly changing trough years, with an observable drift of magnetic poles.
Outer regions of the magnetic field are modified by the interaction with solar magnetic field transported by solar wind. This effect becomes more important for very high orbits. A region 10 RE far (on the side of the Sun) is considered as the magnetosphere boundaries. Solar field compresses a side of the magnetosphere and spreads opposite side.
Geomagnetic field deflects charged particles and shields Earth from solar wind and cosmic rays. This comes from the interaction of a magnetic field with a moving charged particle. The magnetic field exerts on a moving charged particle a force (named Lorentz force) perpendicular to the plane formed by the velocity vector v and the magnetic field vector B deflecting the particle. If v and B are aligned the force is null. In a more formal way Lorentz force is the cross product between v and B (in this order) times the particle charge:
F = q v x B
If the magnetic field and the velocity vector are constant and perpendicular each other particle trajectory is a circumference around magnetic field vector (as in particle accelerators).
Concerning geomagnetic field the particles arriving at the equator are deflected back, while those arriving at the poles follow magnetic field lines without being deflected. As already stated, cosmic rays at the poles reach low altitudes interacting with the ionosphere (between 100 and 500 km). They collide with atoms in the atmosphere, causing the atoms to emit visible light. Such collisions are the origin of the beautiful Aurora Borealis, or Northern Lights, in the northern hemisphere and the Aurora Australis in the southern hemisphere. Auroras commonly seen are produced by electrons, while auroras produced by protons require special instruments to be seen. Auroras can be seen even from space and also on other planets.
Aurora borealis over Bear Lake in Alaska (Wikipedia)
Aurora australis seen in 2005 by NASA satellite Image (Wikipedia)
Saturn Aurora seen by Hubble Space Telescope in 2005 (NASA-JPL)
Let’s consider a charged particle moving in the atmosphere. We can backtrack its trajectory and have three possible starting points:
The particle originates on Earth ground
The particle remains indefinitely in a finite volume around Earth
The particle comes from outer space
Trajectories 1) and 2) were considered “forbidden” because they are not related to any primary cosmic ray reaching Earth from space. The third one is an “allowed” trajectory.
“Forbidden” trajectories were not considered, although mathematically known, until 1958 when Van Allen with Explorer I and II observed that particle detectors stopped to work at altitudes exceeding 2000 km. Particle detectors saturated because they could not bear the increasing flux. Van Allen had discovered two radiation belts around Earth containing trapped particles: the inner belt mainly composed by protons and the outer belt rich in electrons.
High energy cosmic rays interact with the atmosphere producing neutrons. Neutrons are not charged so they can easily penetrate Earth magnetic shield. But free neutrons are unstable and they decay into protons and electrons that are then trapped in the radiation belts. Trapped particles move following trajectories that are the combination of three periodic motions:
Circular motion around field lines
Oscillation along field lines around equatorial plane between two “mirror” points
South Atlantic Anomaly (SAA)
Since the center of the magnetic pole is displaced in respect to Earth center, there is a region at about 200-300 km far from Brazil coast where Van Allen belts reach very low altitudes. This region is known as the South Atlantic Anomaly.
keywords: cosmic radiation, cosmic rays, trajectory of particle in a magnetic field, particle motion in earth’s magnetic field