Relativistic self-focusing of TW laser pulses in high density gas jet targets
The propagation of ultrashort high intensity laser pulses in underdense
plasma is of interest for the understanding of laser interaction processes
in a new relativistically driven plasma regime. Numerous applications are
envisaged, such as laser wakefield accelerators, x-ray lasers and the fast
ignitor concept for inertial confinement fusion energy. At intensities
>1015 W/cm2 gases undergo rapid ionization right
at the leading edge of the pulse so that the subsequent interaction is
that of an intense pulse with an under-dense plasma. The propagation of
such pulses through long-scale length underdense plasmas involves a competition
between three processes: diffraction, relativistic self-focusing and ionization
induced refraction.
The
number of electrons that are produced via ionization at a particular point
of the beam path strongly depends on the prevailing local intensity. As
a consequence, any intensity variation across the beam profile would give
rise to a spatially varying index of refraction with an excess of electrons
around the beam axis, which would lead to defocusing because of the lensing
effect associated with it. In addition the diffraction of the beam leads
to a defocusing effect independent of density. A counteracting process
is the relativistically induced self-focusing due to the electron mass
increase in high intensity regions and the expulsion of electrons from
these regions by the ponderomotive force. These factors lead to a positive
focusing effect which becomes stronger as the laser beam decreases in diameter
and becomes more intense. The above schematic shows how an intense laser
beam can self-focused due to relativistic mass increase. The threshold
power for relativistic self-focusing in a uniform plasma given by the critical
power of Pc = 16.2 nc / ne
[GW], can be
reduced using higher electron densities, but at the same time the accompanying
refractive defocusing is increased.
In experiments performed with the ATLAS Ti:sapphire laser facility this competition associated with the propagation of intense laser pulses in gases at relatively high densities has been investigated by a series of measurements. As is shown in the perspective view of the gas jet target and interaction region geometry in the second figure, a 0.5 mm diameter nozzle was used to generate a pulsed gas jet in synchronization with the arrival of the interaction laser pulse. At the prevailing laser intensities, the neutral gas is quickly ionized by the leading edge of the incident pulse, which then propagates in a partially ionized plasma. The image of the transmitted pulse after the interaction is recorded by a CCD camera located along the propagation axis of the laser. A weaker but synchronized probe pulse at the second harmonic of the main pulse is used to make time resolved shadowgrams of the interaction region.
I The strikingly different behavior of the interaction for nitrogen and hydrogen is depicted in the experimental records in the figure above. For nitrogen, the time-resolved shadowgrams show an orderly progression of refraction with the beam smoothly spreading out as it propagates forward. However, for hydrogen a significantly different pattern is observed. After arriving at the vacuum focus position two prongs of light jut forward and the lateral spreading of the radiation appears constrained indicating the onset of self-focusing. Similarly, the transmitted images exhibit very different behavior. For nitrogen, the diameter increases as the transmitted spot is more and more refracted. In addition, the overall distribution of the transmitted light becomes quite smooth with a filamentary substructure similar to the filamentary appearance seen in the shadowgrams. For hydrogen on the other hand, several hot spots are observed in the transmitted radiation. This structure is indicative of large scale channeling of parts of the laser beam. The observed structures are similar from shot to shot indicating that the channeling is seeded by modulation in the laser beam profile itself. While for nitrogen refraction is the dominant process characterizing the propagation of the pulse, in the case of hydrogen gas refraction has a lesser effect due to low ionization threshold and single ionization stage. Therefore, self-focusing would dominate if the laser power is higher than the critical power Pc. Clear evidence of the onset of self-focusing was observed at electron densities of ne~1020cm-3.
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