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

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... nvergence of the laser pulse by final focusing optics. Experiments were conducted at vacuum focused laser intensities between 3.3 and 4.4×10 18 W cm −2 at peak plasma densities between 23 and 75n c , where n c is the critical density of the plasma. We introduced a scenario: the laser beam diameter at n c /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.