Directional Dark Matter Detection (DDMD) can open a new signature for Weakly Massive Interacting Particles (WIMPs) Dark Matter. The directional signature provides in addition, an unique way to overcome the neutron and neutrino backgrounds. In order to get the directional signature, the DDM detectors should be sensitive to low nuclear energy recoils in the keV range and have an angular resolution better than $20^{circ}$. We have performed experiments with low energy ($<30,mathrm{keV}$) ion beam facilities to measure the angular distribution of nuclear recoil tracks in a MIMAC detector prototype. In this paper, we study angular spreads with respect to the electron drift direction ($0^{circ}$ incident angle) of Fluorine nuclear tracks in this low energy range, and show nuclear recoil angle reconstruction produced by a monoenergetic neutron field experiment. We find that a high-gain systematic effect leads to a high angular resolution along the electron drift direction. The measured angular distribution is impacted by diffusion, and space charge or ion feedback effects, which can be corrected for by an asymmetry factor observed in the flash-ADC profile. The estimated angular resolution of the $0^{circ}$ incident ion is better than $15^{circ}$ at $10$ keV kinetic energy and agrees with the simulations within $20$%. The distributions from the nuclear recoils have been compared with simulated results based on a modified Garfield++ code. Our study shows that protons would be a more adapted target than heavier nuclei for DDMD of light WIMPs. We demonstrate that directional signature from the Galactic halo origin of a Dark Matter WIMP signal is experimentally achievable, with a deep understanding of the operating conditions of a low pressure detector with its diffusion mechanism.
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