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An electron irradiated by a linearly polarized relativistic intensity laserpulse in a cylindrical plasma channel can gain significant energy from thepulse. The laser electric and magnetic fields drive electron oscillations in aplane making it natural to expect the electron trajectory to be flat. We showthat strong modulations of the relativistic $\gamma$-factor associated with theenergy enhancement cause the free oscillations perpendicular to the plane ofthe driven motion to become unstable. As a consequence, out of planedisplacements grow to become comparable to the amplitude of the drivenoscillations and the electron trajectory becomes essentially three-dimensional,even if at an early stage of the acceleration it was flat. The development ofthe instability profoundly affects the x-ray emission, causing considerabledivergence of the radiation perpendicular to the plane of the drivenoscillations, while also reducing the overall emitted energy.

Spontaneous emergence of non-planar electron orbits during direct laser acceleration by a linearly polarized laser pulse