  In this work, the rotating spoke mode in the radio frequency (RF) magnetron
discharge, which features the potential hump and the RF-modulated ionization,
is observed and analyzed by means of the two dimensional axial-azimuthal (z-y)
particle-in-cell/Monte Carlo collision method. The kinetic model combined with
the linear analysis of the perturbation reveals that the cathode sheath (axial)
electric field $E_z$ triggers the gradient drift instability (GDI), deforming
the local potential until the instability condition is not fulfilled and the
fluctuation growth stops in which moment the instability becomes saturated. The
potential deformation consequently leads to the formation of the potential
hump, surrounding which the azimuthal electric field $E_y$ is present. The
saturation level of $E_y$ is found to be synchronized with and proportional to
the time-changing voltage applied at the cathode, resulting in the
RF-modulation of the electron heating in the $E_y$ due to $\nabla B$ drift. In
the instability saturated stage, it is shown that the rotation velocity and
direction of the spoke present in the simulations agree well with the
experimental observation. In the instability linear stage, the instability mode
wavelength and the growth rate are also found to be in good agreement with the
prediction of the GDI linear fluid theory.
