Track length measurement of $^{19}$F$^+$ ions with the MIMAC Dark Matter directional detector prototype

Weakly Interacting Massive Particles (WIMPs) are one of the most preferred candidate for Dark Matter. WIMPs should interact with the nuclei of detectors. If a robust signal is eventually observed in direct detection experiments, the best signature to confirm its Galactic origin would be the nuclear recoil track direction. The MIMAC collaboration has developed a low pressure gas detector providing both the kinetic energy and three-dimensional track reconstruction of nuclear recoils. In this paper we report the first ever observations of $^{19}$F nuclei tracks in a $5$ cm drift prototype MIMAC detector, in the low kinetic energy range ($6$-$26$ keV), using specially developed ion beam facilities. We have measured the recoil track lengths and found significant differences between our measurements and standard simulations. In order to understand these differences, we have performed a series of complementary experiments and simulations to study the impact of the diffusion and eventual systematics. We show an unexpected dependence of the number of read-out corresponding to the track on the electric field applied to the $512 mathrm{mu m}$ gap of the Micromegas detector. We have introduced, based on the flash-ADC observable, corrections in order to reconstruct the physical 3D track length of the primary electron clouds proposing the physics behind these corrections. We show that diffusion and space charge effects need to be taken into account to explain the differences between measurements and standard simulations. These measurements and simulations may shed a new light on the high-gain TPC ionization signals in general and particularly at low energy.