  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.
