  Nonlinear axisymmetric cylindrical plasma oscillations in magnetized
collisionless plasmas are a model for the electron fluid collapse on the axis
behind an ultrashort relativisically intense laser pulse exciting a plasma wake
wave. We present an analytical description of the strongly nonlinear
oscillations showing that the magnetic field prevents closing of the cavity
formed behind the laser pulse. This effect is demonstrated with 3D PIC
simulations of the laser-plasma interaction. An analysis of the betatron
oscillations of fast electrons in the presence of the magnetic field reveals a
characteristic "Four-Ray Star" pattern which has been observed in the image of
the electron bunch in experiments [T. Hosokai, et al., Phys. Rev. Lett. 97,
075004 (2006)].
