plasmapy.formulary.parameters.gyroradius(B: Unit("T"), particle='e-', *, Vperp: Unit("m / s") = <Quantity nan m / s>, T_i: Unit("K") = <Quantity nan K>) -> Unit("m")

Return the particle gyroradius.

Aliases: rc_, rhoc_

  • B (Quantity) – The magnetic field magnitude in units convertible to tesla.
  • particle (str, optional) – Representation of the particle species (e.g., 'p' for protons, 'D+' for deuterium, or 'He-4 +1' for singly ionized helium-4), which defaults to electrons. If no charge state information is provided, then the particles are assumed to be singly charged.
  • Vperp (Quantity, optional) – The component of particle velocity that is perpendicular to the magnetic field in units convertible to meters per second. Must be input as a keyword argument.
  • T_i (Quantity, optional) – The particle temperature in units convertible to kelvin. Must be input as a keyword argument.

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

Return type:



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


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

If any of B, Vperp, or T_i 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

\[r_{Li} = \frac{V_{\perp}}{omega_{ci}}\]

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


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