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• The wave propagates along the azimuthal angle, across an external axial steady magnetic field, and is referred to as the azimuthal surface wave.

• Otherwise, lower-hybrid waves would have accumulated, propagating around the periodic system.

• The physical polarities of electromagnetic waves propagating in a magnetoplasma-filled cylindrical waveguide are studied by numerical calculations and simple analytical analyses.

• The images show an isotropic expanding ionization cloud, but also thin jets propagating at higher speed, produced in the laser focal spot region.

• The theory developed is based on a closed consistent description of the steady wave propagating across the magnetic field.

• In this case, a burn wave propagates into the dense core away from the incoming laser while hydrodynamics free expansion proceeds towards the beam.

• Thus, there are two independent electromagnetic beams propagating in the direction of the magnetostatic field.

• Such an oppositely propagating pair of beams may arise from a reconnection event, for example.