MeV electron acceleration at 1 kHz with \textless 10 mJ laser pulses

We demonstrate laser driven acceleration of electrons to MeV-scale energies at 1kHz repetition rate using \textless 10mJ pulses focused on near-critical density He and H$_{\mathrm{2}}$ gas jets. Using the H$_{\mathrm{2}}$ gas jet, electron acceleration to \textasciitilde 0.5MeV in \textasciitilde 10fC bunches was observed with laser pulse energy as low as 1.3mJ. Increasing the pulse energy to 10mJ, we measure \textasciitilde 1pC charge bunches with \textgreater 1MeV energy for both He and H$_{\mathrm{2\thinspace }}$gas jets. Such a high repetition rate, high flux ultrafast source has immediate application to time resolved probing of matter for scientific, medical, or security applications, either using the electrons directly or using a high-Z foil converter to generate ultrafast .$\gamma $-rays.