  Relativistic transparency enables volumetric laser interaction with overdense
plasmas and direct laser acceleration of electrons to relativistic velocities.
The dense electron current generates a magnetic filament with field strength of
the order of the laser amplitude ($>$10$^5$ T). The magnetic filament traps the
electrons radially, enabling efficient acceleration and conversion of laser
energy into MeV photons by electron oscillations in the filament. The use of
microstructured targets stabilizes the hosing instabilities associated with
relativistically transparent interactions, resulting in robust and repeatable
production of this phenomenon. Analytical scaling laws are derived to describe
the radiated photon spectrum and energy from the magnetic filament phenomenon
in terms of the laser intensity, focal radius, pulse duration, and the plasma
density. These scaling laws are compared to 3-D particle-in-cell (PIC)
simulations, demonstrating agreement over two regimes of focal radius.
Preliminary experiments to study this phenomenon at moderate intensity ($a_0
\sim 30$) were performed on the Texas Petawatt Laser. Experimental signatures
of the magnetic filament phenomenon are observed in the electron and photon
spectra recorded in a subset of these experiments that is consistent with the
experimental design, analytical scaling and 3-D PIC simulations. Implications
for future experimental campaigns are discussed.
