Magnetization directions and geometries of helical microswimmers for linear velocity-frequency response

Recently, there has been much progress in creating microswimmers or microrobots capable of controlled propulsion in fluidic environments. These microswimmers have numerous possible applications in biomedicine, microfabrication, and sensing. One type of effective microrobot consists of rigid magnetic helical microswimmers that are propelled when rotated at a range of frequencies by an external rotating magnetic field. Here we focus on investigating which magnetic dipoles and helical geometries optimally lead to linear velocity-frequency response, which may be desirable for the precise control and positioning of microswimmers. We identify a class of optimal magnetic field moments. We connect our results to the wobbling behavior previously observed and studied in helical microswimmers. In contrast to previous studies, we find that when the full helical geometry is taken into account, wobble-free motion is not possible for magnetic fields rotating in a plane. Our results compare well quantitatively to previously reported experiments, validating the theoretical analysis method. Finally, in the context of our optimal moments, we identify helical geometries for minimization of wobbling and maximization of swimming velocities.