The interaction of an intense (> 1018 W/cm2) ultrashort (~ 30 femtosecond) laser pulse with matter results in the generation of MeV electron bunches, constituting relativistic currents of hundreds of mega-amperes - a few orders of magnitude larger than the Alfven limit (H. Alfven, Phys. Rev. 55, 425 (1939)), which restricts the maximum forward current in vacuum to 17 �? kilo-amperes, � and ? being the relativistic Lorentz factors. Beyond this limit, the self-generated magnetic fields produced by the relativistic electron currents bend the electron trajectories backwards, thereby preventing the electron bunch from propagating in the forward direction. In a hot dense laser-generated plasma, however, the background plasma generates cold electron �return� currents, in a �shielding effect�, which maintains the resultant current below the Alfven limit while allowing the mega-ampere forward currents to penetrate deeper into the plasma. The relativistic forward currents, spatially interspersed with the cold electron return currents, however, induce filamentary instabilities, particularly the Weibel instability (E. S. Weibel, Phys. Rev. Lett. 2, 83 (1959)), which fragments the electron beam into filamentary channels over length-scales of a few tens of microns, thereby severely restraining collimated relativistic electron beam transport. This is of particular significance for the success of the fast ignition scheme of inertial confinement fusion (M. Tabak et al., Phys. Plasmas 1, 1626 (1994)), which crucially hinges on the efficient transport of relativistic �fast� electrons over distances several times the typical filamentation length-scales up to the overdense core of the fuel pellet to initiate nuclear fusion.
The transport of relativistic electron currents in intense laser-matter interactions has long been a subject of profound interest, with numerous experiments and numerical simulations designed to unravel the complex dynamics of the transport process. An indispensable diagnostic that mirrors the fast electron transport is the self-generated magnetic field, which may reach magnitudes of several hundreds of megagauss or even gigagauss, typically over picosecond-to-nanosecond durations, depending on laser parameters and experimental conditions.
Our earliest results (A. S. Sandhu et al., Phys. Rev. Lett. 89, 225002 (2002)) were the first measurements providing the temporal evolution of the self-generated megagauss magnetic fields in the overdense plasma with unprecedented sub-picosecond resolution. Magnetic pulses, about 6 picoseconds in duration, and reaching peak values of 27 mega-gauss (MG), were generated at moderately high intensities of ~1016 W/cm2, using Cotton-Mouton polarimetry, a magneto-optic effect which enables the mapping of the critical surface and the overdense plasma, where the largest magnetic fields are predicted by numerical simulations. Phenomenological modeling and particle-in-cell simulations were consistent with the experimental results, which provided the first direct observation of the anomalous damping of the shielding return currents produced in response to the fast electron currents penetrating deep into the bulk plasma, previously observed only in numerical simulations.
Figure - Temporal profile of the magnetic field for s- and p-polarized interaction pump laser pulse at an intensity of 1016 W/cm2. The inset shows the reflectivity and the induced ellipticity of the probe as a function of the time delay between the interaction pump pulse and the probe pulse. For further details, see A. S. Sandhu et al., Phys. Rev. Lett. 89, 225002 (2002).
Our recent experiments (S. Mondal et al., Proc. Natl. Acad. Sci. USA 109, 8011 (2012)) present direct evidence of turbulence in the self-generated megagauss magnetic fields at relativistic intensities of ~1018 W/cm2, the signature of which was observed in the magneto-optic polarigrams exhibiting a power spectrum scaling, characteristic of turbulence. In light of the ubiquity of the very nature of turbulence, ranging from astrophysical scenarios � in stars, accretion disks and interstellar media � to the well-documented macroscopic terrestrial fluid motion, our results seem even more fascinating as they portray dynamic turbulent mechanisms in highly non-equilibrium regimes.
Figure - Power spectrum of the spatial profile of the magnetic field measured at different temporal delays between the interaction pump pulse and the probe pulse, exhibiting a distinct power law scaling. The inset shows the power spectra derived from two-dimensional particle-in-cell simulations. For further details, see S. Mondal et al., Proc. Natl. Acad. Sci. USA 109, 8011 (2012).
In another recent experiment (G. Chatterjee et al., Phys. Rev. Lett. 108, 235005 (2012)), we have demonstrated how aligned carbon nanotubes serve as efficient transporters of mega-ampere relativistic fast electron currents over length-scales as large as a millimeter, nearly hundred times typical filamentation lengths of a few tens of microns. The collimation of the magnetic field structure at the rearside of the carbon nanotubes, reaching peak values as large as 120 MG with local fluctuations up to 370 MG, is well-corroborated by particle-in-cell simulations, which show a �push-pull� effect generated by the surface electric and magnetic fields, pinching the hot electron currents and confining them to the carbon nanotube walls, thereby facilitating an unhindered collimated transport over macroscopic distances hitherto unheard of.