  In the ionization region above circular planar magnetrons well defined
regions of high emissivity are observed, when the discharge is driven in the
HiPIMS regime. Once their mode is stabilized, these structures rotate in the E
x B direction with a constant rotation frequency in the hundreds of kHz range.
A phenomenological model of the phenomenon is developed, in the form of a
system of nonlinear coupled partial differential equations. The system is
solved analytically in a frame co-moving with the structure, and its solution
gives the neutral density and the plasma density once the electron density
shape is imposed. From the balance of the mechanisms of ionization, electron
loss and constant neutral refilling, a steady state configuration in the
rotating frame is achieved for the electron and neutral densities. Therefore,
the spoke experimentally observed can be sustained simply by the combination of
this highly reduced number of phenomena. Finally, a study of the sensitivity of
neutral and plasma densities to the physical parameters is also given.
