From https://en.wikipedia.org/wiki/Cyclotron

$\gamma = \frac{1}{\sqrt{1 - \beta^2}} =$ Lorentz gamma = 4-velocity time component.
$\beta = \frac{v}{c} =$ Lorentz beta
$m_0 =$ particle rest-mass, in $kg$.
$m = \gamma m_0 =$ particle relativistic mass, in $kg$.

relativistic cyclotron frequency:
$f_0 = \frac{q B}{2 \pi m_0} =$ non-relativistic cyclotron frequency, in $[\frac{1}{s}]$.
$\omega_0 = 2 \pi f_0 = \frac{q B}{m_0} =$ non-relativistic cyclotron angular momentum, in $[\frac{1}{s}]$.
$f = \frac{q B}{2 \pi m} = \frac{q B}{2 \pi \gamma m_0} = \frac{f_0}{\gamma} =$ relativistic cyclotron frequency, in $[\frac{1}{s}]$.
$\omega = 2 \pi f = \frac{q B}{m} = \frac{\omega_0}{\gamma} =$ relativistic cyclotron angular momentum, in $[\frac{1}{s}]$.
$r = \frac{v_\perp}{\omega} = \frac{v_\perp m}{q B} =$ relativistic gyroradius, in $[m]$.
2003 Loverich uses $v_{th,ion}$ for $v_\perp$.
2003 Loverich and 2014 Abgrall, Kumar both use $B_0$ (their reference magnetic field) for $B$.