  We study the interaction of intense ultrashort laser pulses with cryogenic He
jets using 2d/3v relativistic Particle-in-Cell simulations (XOOPIC). Of
particular interest are laser intensities $(10^{15}-10^{20})$ W/cm$^2$, pulse
lengths $\le 100$ fs, and the frequency regime $\sim 800$ nm for which the jets
are initially transparent and subsequently not homogeneously ionized. Pulses
$\ge 10^{16}$ W/cm$^2$ are found to drive ionization along the jet and outside
the laser spot, the ionization-front propagates along the jet at a fraction of
the speed of light. Within the ionized region, there is a highly transient
field, which may be interpreted as two-surface wave decay and as a result of
the charge-neutralizing disturbance at the jet-vacuum interface. The ionized
region has solid-like densities and temperatures of few to hundreds of eV,
i.e., warm and hot dense matter regimes. Such extreme conditions are relevant
for high-energy densities as found, e.g., in shock-wave experiments and
inertial confinement fusion studies. The temporal evolution of the ionization
is studied considering theoretically a pump-probe x-ray Thomson scattering
(XRTS) scheme. We observe plasmon and non-collective modes that are generated
in the jet, and their amplitude is proportional to the ionized volume. Our
theoretical findings could be tested at free-electron laser facilities such as
FLASH and the European XFEL (Hamburg) and the LCLS (Stanford).
