## Moment Theory of Ion Motion in Traps and Similar Devices. III Two-Temperature Treatment of Quadrupole Ion Traps.

The two-temperature moment theory of ion motion in devices where the external fields vary with position and time is applied to ideal quadrupole ion traps. In first approximation, the theory gives differential equations with collision frequencies that vary with the effective temperature characterizing the relative kinetic energy of the ion-neutral collisions. Solutions of the set of coupled differential equations provide the ion number density, average velocities, average energy and average temperature as functions of time and of position in the apparatus. That information also enables the effective temperature for the ion ensemble and the position-dependent energy density to be determinedmore »