We demonstrate laser-plasma acceleration of high charge electron beams to the ~10 MeV scale using ultrashort laser pulses with as little energy as 10 mJ. This result is made possible by an extremely dense and thin hydrogen gas jet. Total charge up to ~0.5 nC is measured for energies >1 MeV. Acceleration is correlated to the presence of a relativistically self-focused laser filament accompanied by an intense coherent broadband light flash, associated with wavebreaking, which can radiate more than ~3% of the laser energy in a sub-femtosecond bandwidth consistent with half-cycle optical emission. Our results enable truly portable applications of laser-driven acceleration, such as low dose radiography, ultrafast probing of matter, and isotope production.Laser-driven electron acceleration in plasmas has achieved many successes in recent years, including record acceleration up to 4 GeV in a low emittance quasi-monoenergetic bunch [1] and generation of high energy photons [2][3][4][5]. In these experiments, the driver laser pulse typically propagates in the 'bubble' or 'blow-out' regime [6,7] for a normalized peak vector potential 2 0 0 / 1 a eA mc = > > . Plasma densities are deliberately kept low for resonant laser excitation and to avoid dephasing [7]. Essentially all of these experiments use 10 TW −1 PW laser drivers, with repetition rates ranging from 10 Hz to an hour between shots [8].For many modest lab scale and portable applications, however, a compact, relatively inexpensive, high average current source of laser-accelerated relativistic electrons is sufficient and desirable. In this paper we describe experiments using a very dense, thin hydrogen gas jet, where the relativistic self-focusing threshold is exceeded even with ~10 mJ laser pulses and MeV-scale energy electron bunches are generated. This enables applications, such as ultrafast low dose medical radiography, which would benefit from a truly portable source of relativistic particle beams. We note that prior work has shown electron bunch generation of modest charge and acceleration (~10 fC/pulse, <150 keV) from a 1 kHz, ~10 mJ laser driving a thin (~100 μm), low density continuous flow argon or helium jet [9].Central to our experiment is a thin, high density pulsed hydrogen sonic gas jet, which reaches a maximum peak molecular density of 9×10 at our laser wavelength of λ 0 =800nm. The density profile is near-Gaussian, with a full width at half maximum (FWHM) in the range 150-250 μm, depending on the height of the optical axis above the jet orifice. Earlier versions of this jet were run in both pulsed [10] and continuous flow [11] for nitrogen and argon. High densities are achieved using a combination of high valve backing pressure and cryogenic cooling of the valve feed gas, which is forced through a 100μm diameter needle orifice. Cooling to −160C enables a significant density increase for a given valve backing pressure. Figure 1 shows the experimental