Nanowire charging in collisionless plasma

We calculate the collision cross section of a charged finite cylinder (nanowire) with a beam of ions and electrons in collisionless plasma. We find that, while the shape and area of the cross section has complex dependence on the charge and orientation of the nanowire relative to the charged beam, its orientational average has a remarkably simple form: for attractive interactions, it is a linear function of the electrostatic ratio q_j q_p e₂ /4π₀ L₀ kT, where q_j e is the charge of the ions/electrons, q_p e is the charge on the cylinder, L₀ is the half-length of the nanowire, T is the temperature of the charged species, and₀ is the permittivity of free space. This linearity persists into the repulsive regime up until the cross sectional area is reduced to about 5% of its value for neutral collisions. We calculate the corresponding charging currents and show that the charging behavior of the nanowire in Maxwellian plasma is described by an equivalent sphere whose radius depends only on the aspect ratio of the nanowire. For small aspect ratios, the equivalent sphere has the same surface area as the nanowire.