gyroradius

plasmapy.formulary.lengths.gyroradius(B: Unit("T"), particle: ~plasmapy.particles.particle_class.Particle, *, Vperp: Unit("m / s") = <Quantity nan m / s>, T_i: Unit("K") = None, T: Unit("K") = None) -> Unit("m")

Return the particle gyroradius.

Aliases: rc_, rhoc_

Parameters
  • B (Quantity) – The magnetic field magnitude in units convertible to tesla.

  • particle (Particle) – Representation of the particle species (e.g., 'p' for protons, 'D+' for deuterium, or 'He-4 +1' for singly ionized helium-4). If no charge state information is provided, then the particles are assumed to be singly charged.

  • Vperp (Quantity, optional, keyword-only) – The component of particle velocity that is perpendicular to the magnetic field in units convertible to meters per second.

  • T (Quantity, optional, keyword-only) – The particle temperature in units convertible to kelvin.

  • T_i (Quantity, optional, keyword-only) – The particle temperature in units convertible to kelvin. Note: Deprecated. Use T instead.

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.

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.

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

\[r_{Li} = \frac{V_{\perp}}{ω_{ci}}\]

where \(V_⟂\) is the component of particle velocity that is perpendicular to the magnetic field and \(ω_{ci}\) is the particle gyrofrequency. If a temperature is provided, then \(V_⟂\) will be the most probable thermal velocity of a particle at that temperature.

Examples

>>> from astropy import units as u
>>> gyroradius(0.2*u.T, particle='p+', T=1e5*u.K)
<Quantity 0.002120... m>
>>> gyroradius(0.2*u.T, particle='p+', T=1e5*u.K)
<Quantity 0.002120... m>
>>> gyroradius(5*u.uG, particle='alpha', T=1*u.eV)
<Quantity 288002.38... m>
>>> gyroradius(400*u.G, particle='Fe+++', Vperp=1e7*u.m/u.s)
<Quantity 48.23129... m>
>>> gyroradius(B=0.01*u.T, particle='e-', T=1e6*u.K)
<Quantity 0.003130... m>
>>> gyroradius(0.01*u.T, 'e-', Vperp=1e6*u.m/u.s)
<Quantity 0.000568... m>
>>> gyroradius(0.2*u.T, 'e-', T=1e5*u.K)
<Quantity 4.94949...e-05 m>
>>> gyroradius(5*u.uG, 'e-', T=1*u.eV)
<Quantity 6744.25... m>
>>> gyroradius(400*u.G, 'e-', Vperp=1e7*u.m/u.s)
<Quantity 0.001421... m>