*

We present the results of experiments performed on the Texas Petawatt Laser, in which a high-intensity (>10²¹ W/cm²) laser pulse interacts with a relativistically transparent plasma (n_c < n_e < n_ca₀, for critical density n_c, electron density n_e, and normalized laser amplitude a₀). The intense laser pulse drives an axial electron current and generates a magnetic filament with field strength of the order of the laser amplitude (>10⁵ T). When the electron density is greater than 0.01×n_ca₀, this magnetic filament traps electrons, enabling direct laser acceleration of the electrons and efficient conversion of laser energy into MeV photons by synchrotron-like radiation. Analytical scaling laws predict that the radiated gamma-ray energy and efficiency both scale inversely with density. We present the results of experiments using a₀ ∼ 30 and varying the electron density by an order of magnitude. Experimental signatures of magnetic filament radiation were recorded in the electron and photon spectra. The results are compared with predictions from scaling laws and 3-D particle-in-cell simulations to assess the dependence of electron acceleration on plasma density. We discuss the prospects for scaling this phenomenon to higher intensities: above 6×10²¹ W/cm², laser conversion efficiency into MeV photons is predicted to exceed 10%.