Plasma density limits for hole boring by intense laser pulses

High-power lasers in the relativistic intensity regime with multi-picosecond pulse durations are available in many laboratories around the world. Laser pulses at these intensities reach giga-bar level radiation pressures, which can push the plasma critical surface where laser light is reflected. This process is referred to as the laser hole boring (HB), which is critical for plasma heating, hence essential for laser-based applications. Here we derive the limit density for HB, which is the maximum plasma density the laser can reach, as a function of laser intensity. The time scale for when the laser pulse reaches the limit density is also derived. These theories are confirmed by a series of particle-in-cell simulations. After reaching the limit density, the plasma starts to blowout back toward the laser, and is accompanied by copious superthermal electrons; therefore, the electron energy can be determined by varying the laser pulse length.