Pitch angle

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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.

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[edit] 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 field. 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).

[edit] 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:

\begin{align} P &= \frac{\Omega}{2\pi} = \int_{0}^{\alpha_{0}} \sin\alpha d\alpha = 1-\cos\alpha_{0} \\ &= 1-\sqrt{1-\sin^{2}\alpha_{0}} \\ &= 1-\sqrt{1-\frac{B_{0}}{B_{m}}} \end{align}

Where Ω is the solid angle we are concerned with, α0 is the equatorial pitch angle of the particle, B0 is the equatorial magnetic field strength, and Bm is the maximum field strength. Notice that this is independent of charge, mass, or kinetic energy.

[edit] Engineering

Angle Relationships, ANSI/AGMA 1012-G05
Angle Relationships, ANSI/AGMA 1012-G05
Angles, ANSI/AGMA 1012-G05
Angles, ANSI/AGMA 1012-G05

Pitch angle in bevel gears, is the angle between an element of a pitch cone and its axis. In external and internal bevel gears, the pitch angles are respectively less than and greater than 90 degrees.

Face (tip) angle in a bevel or hypoid gear, is the angle between an element of the face cone and its axis.

Root angle in a bevel or hypoid gear, is the angle between an element of the root cone and its axis.

Addendum angle in a bevel gear, is the angle between elements of the face cone and pitch cone.

Dedendum angle in a bevel gear, is the angle between elements of the root cone and pitch cone.1










[edit] See also

Adiabatic invariant

[edit] External links

[edit] Notes

1. ANSI/AGMA 1012-G05, "Gear Nomenclature, Definition of Terms with Symbols".

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