This paper presents a scheme for strong self-focusing of a laser beam interacting with a cone-guided fast-ignition inertial confinement fusion target using cone pre-plasma filling as an optical medium for reducing the laser beam waist. The objective is to reduce the focal spot size at the interior of the tip of the re-entrant cone to that required for efficient coupling to the dense imploded fuel core. This is challenging to achieve in a large laser system using the standard optical components of a chirped-pulse-amplified (CPA) laser-beam chain where the spot sizes produced are often significantly larger than would be desirable for fast ignition. The approach described also makes use of the presence of pre-plasma in the cone. Such pre-plasma filling is difficult to avoid entirely when illuminating a cone with a high-energy CPA laser system due to the challenges of reducing laser pre-pulse to below the threshold for plasma production. For deriving the differential equation which governs the progress of the laser beam-width with propagation distance, paraxial theory in a WKB approximation has been used. A simulation is performed assuming strong self-focusing in accordance with the laser parameters and plasma density profile chosen.

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The recent studies proved that stimulated backward Raman scattering of a laser is affected significantly by the existence of magnetic field and density rippled plasma. At lower hybrid frequencies, the localized radial and azimuthal modes can be supported by the magnetized plasma. The density ripple interacts with the Raman process’s main Langmuir wave, producing in a secondary Langmuir wave with a higher wave number that is highly Landau damped on the electrons. Numerically, the influence of various modes on the growth rate revealed that the ripple and local effects greatly decrease the growth rate of stimulated Raman backscattering. As a result, the Raman process is controlled by the magnetized density rippled plasma and the growth rate is reduced significantly.

Stimulated Raman scattering (SRS) is one of the mechanisms limiting power scaling
in inertial confinement fusion (ICF). In this work, we demonstrate the effective
suppression of SRS by the combined effects of static density fluctuations and an
azimuthal magnetic field with a propagating chirped laser pulse. In the presence of
an azimuthal magnetic field, chirped laser pulse propagates through a density-rippled
plasma and undergoes stimulated-forward Raman scattering (SFRS), resulting in
two radially localized electromagnetic sidebands waves and a lower-hybrid wave.
Absolute and growing modes saturate due to ion density fluctuations, which then
suppress instability growth through mode coupling. The modes modified by the
combined effect of chirp and azimuthal magnetic field are effectively damped after
saturation. As a result, the overall growth rate of the instability reduces. The
comparison of positive and negative chirp demonstrated that when a positive chirp is
being used, instability is more effectively suppressed. Based on non-local theory, we
have analyzed the growth of the SFRS for positive and negative chirp and estimated
it for ICF-relevant parameters and observed the effect of the growth rate.