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An analytical model for hole boring proton acceleration by a circularly-polarized CO2 laser pulse in a gas jet is developed. The plasma density profile near the density peak is taken to be rectangular, with inner region thickness l around a laser wavelength and density 10% above the critical, while the outside density is 10% below the critical. On the rear side, plasma density falls off rapidly to a small value. The laser suffers strong reflection from the central region and, at normalized amplitude a0≥1, creates a double layer. The space charge field of the double layer, moving with velocity vfzˆ, reflects up-stream protons to 2vf velocity, incurring momentum loss at a rate comparable to radiation pressure. Reflection occurs for vf≤ωpzflm/mp, where m and mp are the electron and proton masses, zf is the distance traveled by the compressed electron layer and ωp is the plasma frequency. For Gaussian temporal profile of the laser and parabolic density profile of the upstream plasma, the proton energy distribution is narrowly peaked

Laser radiation pressure proton acceleration in gaseous target