Pitch angle (particle motion)

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The pitch angle of a

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 mirror and continue to be trapped.

${\displaystyle {\begin{aligned}\sin ^{2}\left(\alpha _{0}\right)={\frac {B_{0}}{B_{m}}}\end{aligned}}}$

Where ${\displaystyle \alpha _{0}}$ is the equatorial pitch angle of the particle, ${\displaystyle B_{0}}$ is the equatorial magnetic field strength at the surface of the earth, and ${\displaystyle B_{m}}$ is the field strength at the mirror point. Notice that this is independent of charge, mass, or kinetic energy.

This is due to the invariance of the magnetic moment ${\displaystyle \mu }$. At the point of reflection, the particle has zero parallel velocity or a pitch angle of 90 degrees. As a result,

${\displaystyle \mu ={\frac {1}{2}}{\frac {mv_{\perp 0}^{2}}{B_{0}}}={\frac {1}{2}}{\frac {mv^{2}\sin ^{2}\left(\alpha _{0}\right)}{B_{0}}}={\frac {1}{2}}{\frac {mv^{2}}{B_{m}}}}$

See also

• Adiabatic invariant
• Magnetic mirror

External links

• Oulu Space Physics Textbook
• IMAGE mission glossary