  Ultra-intense lasers that ionize and accelerate electrons in solids to near
the speed of light can lead to kinetic instabilities that alter the laser
absorption and subsequent electron transport, isochoric heating, and ion
acceleration. These instabilities can be difficult to characterize, but a novel
approach using X-ray scattering at keV energies allows for their visualization
with femtosecond temporal resolution on the few nanometer mesoscale. Our
experiments on laser-driven flat silicon membranes show the development of
structure with a dominant scale of $~60\unit{nm}$ in the plane of the laser
axis and laser polarization, and $~95\unit{nm}$ in the vertical direction with
a growth rate faster than $0.1/\mathrm{fs}$. Combining the XFEL experiments
with simulations provides a complete picture of the structural evolution of
ultra-fast laser-induced instability development, indicating the excitation of
surface plasmons and the growth of a new type of filamentation instability.
These findings provide new insight into the ultra-fast instability processes in
solids under extreme conditions at the nanometer level with important
implications for inertial confinement fusion and laboratory astrophysics.
