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

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