Focus optimization of relativistic self-focusing for anomalous laser penetration into overdense plasmas (super-penetration)

Relativistic electron motion in a plasma due to an intense laser pulse modifies the refractive index and leads to two effects: relativistic induced transparency and relativistic self-focusing. A combination of the above two effects enables transmission of laser energy deep into plasmas which is useful for fast ignition of inertial fusion. This so-called super-penetration sensitively depends on the focal position of the laser intensity due to the inhomogeneous density profile of the plasma and convergence of the laser pulse by final focusing optics. Experiments were conducted at vacuum focused laser intensities between 3.3 and 4. 4 × 1018 W cm−2 at peak plasma densities between 23 and 75nc, where nc is the critical density of the plasma. We introduced a scenario: the laser beam diameter at nc/4 density must be smaller than the plasma wavelength to achieve whole beam self-focusing. An optimum focus was found experimentally by measuring the plasma channel, laser transmittance and electron spectra. All three data are consistent with one another and numerical calculations based on a paraxial approximation model suggest that this optimum focus corresponds to the scenario described above.