Spinning of spherical grains in dusty plasmas

It is shown that the angular momentum transfer to spherical dust grain from ion flux in the process of grain charging is not zero if the ion attachment coefficient at the grain surface is inhomogeneous. An exact analytical solution is found for a spherical grain having the ion attachment coefficient in one hemisphere κ₊ different from that in the other hemisphere κ_$and for the charge being uniformly distributed on the grain sphere. The transfer of the angular momentum occurs in presence of the ion flow determined by the ion drift velocity u. The direction of the angular momentum and the direction of the grain rotation axis is determined by the vector product [u × n], where n is a unit vector directed from one hemisphere with κ₊ to another hemisphere with κ_-. The angle θ between n and u determines the range of impact parameters and the range of impact angles of ions which reaches either one or the other grain hemisphere. This gives an analytical algebraic equation for the range of angles of the impact parameters of ions in the plane perpendicular to the flow which determines the transfer of the angular momentum. The solution of this equation and integration with respect to the impact parameters is obtained numerically. The angular momentum transfer is proportional to (κ₊-κ_-)2u²a²m_isin(θ)F(θ,z), where z=2Z_de²/am_iu² is the dust dimensionless charge, a is the dust radius, and m_i the ion mass. The function F(θ,z) is found numerically and for z=2 is approximately equal to F=1+0.24sin⁸(θ). With the decrease of z, the absolute value of F (reached at sin(θ)=1) gradually decreases and for z=0.1 it is equal to 0.001. The terms with larger power of sin²(θ) are prevailing at smaller values of the dust charges. The solution of the equation for the dust rotation was found by taking into account the angular momentum transfer in charging, the friction in neutral gas, and the dust angular momentum inertia. It is shown that in general, after switching on the ion flow, the dust rotates several times until it is aligned to the ion flow (vectors n a- nd u being antiparallel). The number of rotations depends on the the ratio of the friction force to the angular momentum inertia force. The effect of the grain alignment to the ion flow can be used both for the nonmagnetic and ferromagnetic dust grains. The ferromagnetic dust grains can be used to create magnetic fields by dust in absence of external magnetic fields. Continuous dust rotation can be excited by a modulated ion flow.