Challenging space missions include those at very low altitudes, where the atmosphere is source of aerodynamic drag on the spacecraft. To extend the lifetime of such missions, an efficient propulsion system is required. One solution is Atmosphere-Breathing Electric Propulsion (ABEP) that collects atmospheric particles to be used as propellant for an electric thruster. The system would minimize the requirement of limited propellant availability and can also be applied to any planetary body with atmosphere, enabling new missions at low altitude ranges for longer times. IRS is developing, within the H2020 DISCOVERER project, an intake and a thruster for an ABEP system. The article describes the design and simulation of the intake, optimized to feed the radio frequency (RF) Helicon-based plasma thruster developed at IRS. The article deals in particular with the design of intakes based on diffuse and specular reflecting materials, which are analysed by the PICLas DSMC-PIC tool. Orbital altitudes $h=150-250$ km and the respective species based on the NRLMSISE-00 model (O, $N_2$, $O_2$, He, Ar, H, N) are investigated for several concepts based on fully diffuse and specular scattering, including hybrid designs. The major focus has been on the intake efficiency defined as $eta_c=dot{N}_{out}/dot{N}_{in}$, with $dot{N}_{in}$ the incoming particle flux, and $dot{N}_{out}$ the one collected by the intake. Finally, two concepts are selected and presented providing the best expected performance for the operation with the selected thruster. The first one is based on fully diffuse accommodation yielding to $eta_c<0.46$ and the second one based un fully specular accommodation yielding to $eta_c<0.94$. Finally, also the influence of misalignment with the flow is analysed, highlighting a strong dependence of $eta_c$ in the diffuse-based intake while, ...