plasmapy.formulary.lengths.gyroradius(B: Unit("T"), particle: ~typing.Union[str, ~numbers.Integral, ~plasmapy.particles.particle_class.Particle, ~plasmapy.particles.particle_class.CustomParticle], *, Vperp: Unit("m / s") = <Quantity nan m / s>, T: Unit("K") = None, lorentzfactor=nan, relativistic: bool = True) -> Unit("m")

Aliases: rc_, rhoc_

Parameters
Returns

r_Li – The particle gyroradius in units of meters. This Quantity will be based on either the perpendicular component of particle velocity as inputted, or the most probable speed for a particle within a Maxwellian distribution for the particle temperature. It is relativistically accurate.

Return type

Quantity

Raises
Warns

UnitsWarning – If units are not provided, SI units are assumed.

Notes

One but not both of Vperp and T must be inputted.

lorentzfactor can be inferred from Vperp or T but near the speed of light, this can lead to rounding errors.

If any of B, Vperp, or T is a number rather than a Quantity, then SI units will be assumed and a warning will be raised.

The particle gyroradius is also known as the particle Larmor radius and is given by

$r_{Li} = \frac{γ V_⟂}{ω_{ci}}$

where $$V_⟂$$ is the component of particle velocity that is perpendicular to the magnetic field, $$ω_{ci}$$ is the particle gyrofrequency, and $$γ$$ is the Lorentz factor. If a temperature is provided, then $$V_⟂$$ will be the most probable thermal velocity of a particle at that temperature. The relativistic keyword can be set to False to avoid the relativistic correction.

Examples

>>> from astropy import units as u
<Quantity 0.002120... m>
<Quantity 0.002120... m>
<Quantity 288002.38... m>
<Quantity 48.25815... m>
<Quantity 0.003130... m>