Computation of two-dimensional electric field from the ion laser induced fluorescence measurements

This paper presents a method of computing two-dimensional electric field from ion laser induced fluorescence (LIF) measurements in a plasma flow. The expression for the field is derived by taking velocity moments of the Boltzmann equation for ions. It was found that the pressure tensor, related to the width of the ion velocity distribution, plays a critical role in the computation of the electric field. Even with the assumption of cold ion flow, the pressure tensor contribution may be significant when velocity spread is caused by other forces. Such a situation occurs in the flow of a Hall thruster, where velocity spread is caused by the ions born at different potentials. LIF measurements of the cylindrical hall thruster plume were used to demonstrate practical application of the derived method. Whenever the pressure tensor components are small as compared to the mean ion drift velocity, the electric field calculations reduce to a simple expression given in terms of mean ion drift velocity and its divergence.