Pitch angle
Encyclopedia
The pitch angle of a charged particle
is the angle between the particle's velocity vector and the local magnetic field
. This is a common measurement and topic when studying the magnetosphere
. See Aurora
and Ring current
. In the Northern Hemisphere
this particle would be heading down toward the Earth (and the opposite in the Southern Hemisphere
). A pitch angle of 90 degrees is a particle that is locally mirroring (see: Magnetosphere particle motion
).
Where
is the solid angle we are concerned with, 
is the equatorial pitch angle of the particle, 
is the equatorial magnetic field strength, and 
is the maximum field strength. Notice that this is independent of charge, mass, or kinetic energy.
Charged particle
In physics, a charged particle is a particle with an electric charge. It may be either a subatomic particle or an ion. A collection of charged particles, or even a gas containing a proportion of charged particles, is called a plasma, which is called the fourth state of matter because its...
is the angle between the particle's velocity vector and the local magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
. This is a common measurement and topic when studying the magnetosphere
Magnetosphere
A magnetosphere is formed when a stream of charged particles, such as the solar wind, interacts with and is deflected by the intrinsic magnetic field of a planet or similar body. Earth is surrounded by a magnetosphere, as are the other planets with intrinsic magnetic fields: Mercury, Jupiter,...
. See Aurora
Aurora (astronomy)
An aurora is a natural light display in the sky particularly in the high latitude regions, caused by the collision of energetic charged particles with atoms in the high altitude atmosphere...
and Ring current
Ring current
A ring current is an electric current carried by charged particles trapped in a planet's magnetosphere. It is caused by the longitudinal drift of energetic particles.-Earth's ring current:...
Usage: Particle motion
It is customary to discuss the direction a particle is heading by its pitch angle. A pitch angle of 0 degrees is a particle whose parallel motion is perfectly along the local magnetic fieldMagnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
. In the Northern Hemisphere
Northern Hemisphere
The Northern Hemisphere is the half of a planet that is north of its equator—the word hemisphere literally means “half sphere”. It is also that half of the celestial sphere north of the celestial equator...
this particle would be heading down toward the Earth (and the opposite in the Southern Hemisphere
Southern Hemisphere
The Southern Hemisphere is the part of Earth that lies south of the equator. The word hemisphere literally means 'half ball' or "half sphere"...
). A pitch angle of 90 degrees is a particle that is locally mirroring (see: Magnetosphere particle motion
Magnetosphere particle motion
The ions and electrons of a plasma interacting with the Earth's magnetic field generally follow its magnetic field lines. These represent the force that a north magnetic pole would experience at any given point...
).
Special Case: Equatorial Pitch angle
The equatorial pitch angle of a particle is the pitch angle of the particle at the Earth's geomagnetic equator. This angle defines the loss cone of a particle. The loss cone is the set of angles where the particle will strike the atmosphere and no longer be trapped in the magnetosphere while particles with pitch angles outside the loss cone will continue to be trapped. The loss cone is defined as the probability of particle loss from the magnetic bottle which is:Where
is the solid angle we are concerned with, is the equatorial pitch angle of the particle, is the equatorial magnetic field strength, and is the maximum field strength. Notice that this is independent of charge, mass, or kinetic energy.