Theory for laser heated plasma channel formation

Guiding channels are frequently used to increase the acceleration length and electron energy in laser wakefield accelerators. To obtain a parametric description for improved insight and design control, we develop a theoretical framework to describe the evolution of plasma channels heated by short-pulse lasers at intensities of 10¹⁵ - 10¹⁷ W/cm². In this range, heating occurs through Above Threshold Ionization and Inverse Bremsstrahhlung Absorption, allowing tunable energy deposition and resulting in improved control over the channel properties. We describe the initial plasma column formation by a reduced 1D cylindrical model which, by incorporating self-consistent ionization and energy deposition by the heating laser pulse, shows excellent agreement with PIC simulations. The subsequent hydrodynamic expansion and shock formation are driven by radial heat conduction, for which new self-similar solutions are derived. These provide analytic relations for the evolution of the channel radius and density profile that are tested against hydrodynamic simulations. We improve upon existing relations obtained from blast-wave models, which do not exhibit the evolution of the shock structure and the post shock profiles. Our model and solutions offer enhanced insight for engineering high intensity laser pulse guiding.