Modification of the loss cone for energetic particles

The optimal pitch angle which maximizes the penetration distance, along the magnetic field, of relativistic charged particles injected from the midplane of an axisymmetric field is investigated analytically and numerically. Higher‐order terms of the magnetic moment invariant are necessary to correct...

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Bibliographic Details
Published in:Geophysical research letters 2014-11, Vol.41 (22), p.8107-8113
Main Authors: Porazik, Peter, Johnson, Jay R., Kaganovich, Igor, Sanchez, Ennio
Format: Article
Language:English
Subjects:
Atmosphere
Atoms & subatomic particles
beam injection from space
Charged particles
Distance
energetic particle precipitation
Energetic particles
Exact solutions
Flux
Injection
Integration
Invariants
loss cone
Magnetic field
Magnetic fields
magnetic mirror
Magnetic moment
magnetic moment invariant
Magnetic moments
Magnetosphere
Magnetospheres
Mathematical analysis
Mirror point
Numerical integration
Optimization
Orbits
Orientation
Particle physics
Penetration
Pitch (inclination)
Pitch angle
Relativism
Spacecraft
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Summary:The optimal pitch angle which maximizes the penetration distance, along the magnetic field, of relativistic charged particles injected from the midplane of an axisymmetric field is investigated analytically and numerically. Higher‐order terms of the magnetic moment invariant are necessary to correctly determine the mirror point of trapped energetic particles, and therefore the loss cone. The modified loss cone resulting from the inclusion of higher‐order terms is no longer entirely defined by the pitch angle but also by the phase angle of the particle at the point of injection. The optimal orientation of the injection has a nonzero component perpendicular to the magnetic field line, and is in the plane tangential to the flux surface. Numerical integration of particle orbits were carried out for a relativistic electron in a dipole field, showing agreement with analytic expressions. The results are relevant to experiments, which are concerned with injection of relativistic beams into the atmosphere from aboard a spacecraft in the magnetosphere. Key PointsLoss cones of energetic and low‐energy particles may be significantly differentThe difference results from next order terms of the magnetic momentThe qualitative and quantitative changes affect energetic particle precipitation
ISSN:0094-8276
1944-8007
DOI:10.1002/2014GL061869