  We report the experimental results of simultaneous measurements on the
electron and X-ray spectra from near-critical-density (NCD) double-layer
targets irradiated by relativistic femtosecond pulses at the intensity of 5E19
W/cm^2. The dependence of the electron and X-ray spectra on the density and
thickness of the NCD layer was studied. For the optimal targets, electrons with
temperature of 5.5 MeV and X-rays with critical energy of 5 keV were obtained.
2D particle-in-cell simulations based on the experimental parameters confirm
the electrons are accelerated in the plasma channel through direct laser
acceleration, resulting in temperature significantly higher than the
pondermotive temperature. Bright X-rays are generated from betatron emission
and Thomson backscattering before the electrons leave the double-layer targets.
