An x-ray source generated by an electron beam produced using a Self-Modulated Laser Wakefield Accelerator (SM-LWFA) is explored for use in high energy density science facilities. By colliding the electron beam, with a maximum energy of 380 MeV, total charge of >10 nC and a divergence of 64 × 100 mrad, from a SM-LWFA driven by a 1 ps 120 J laser, into a high-Z foil, an x/gamma-ray source was generated. A broadband bremsstrahlung energy spectrum with temperatures ranging from 0.8 to 2 MeV was measured with an almost 2 orders of magnitude flux increase when compared with other schemes using LWFA. GEANT4 simulations were done to calculate the source size and divergence.