On the interpretation of particle tagging data

We develop a formalism for the interpretation of optical tagging data obtained from laser-induced fluorescence (LIF) experiments. There are three basic components to the calculation. The first is the modification, due to optical pumping, of the state-density velocity distribution function. The central part is the calculation of the two-point conditional probability function for ion orbits in the (phase-space) vicinity of a central guide orbit that contributes to the signal. The final part is the calculation of the modified LIF signal of the search laser due to the test-particle distribution function. As a special case we consider the model of a steady, uniform plasma in a straight magnetic field under the assumption of a constant (Lenard-Bernstein) velocity-space diffusion coefficient. In this case there is no need of the guide-orbit expansion in order to evaluate 12 of the thirteen integrals involved analytically. These twelve integrals cover the instrumental selection of initial and final phase-space coordinates of the test-particles. The remaining integral over time must be performed numerically and can be used to evaluate the test-particle transfer function in either the time or frequency domains (the latter being appropriate for experiments involving ``chopped'' lasers). The effect of finite quantum state lifetime (due, for example, to collisional quenching in the case of metastable states) is included.