Analysis of Ion Motion and Diffusion Confinement in Inverted Drift Tubes and Trapped Ion Mobility Spectrometry Devices

Ion motion in trapped ion mobility spectrometers (TIMS) and inverted drift tubes (IDT) has been investigated. The two-dimensional (2D) axisymmetric analytical solution to the Nernst-Planck equation for constant gas flows and opposed linearly increasing fields is presented for the first time and is used to study the dynamics of ion distributions in the ramp region. It is shown that axial diffusion confinement is possible and that broad packets of ions injected initially into the system can be contracted. This comes at the expense of the generation of a residual radial field that pushes the ions outward. This residual electric field is of significant importance as it hampers sensitivity and resolution when parabolic velocity profiles form. When radio frequency (RF) is employed at low pressures, this radial field affects the stability of ions inside the mobility cell. Trajectories and frequencies for stable motion are determined through the study of Mathieu's equation. Finally, effective resolutions for the ramp and plateau regions of the TIMS instrument are provided. While resolution depends on the inverse of the square root of mobility, when proper parameters are used, resolutions in the thousands can be achieved theoretically for modest distances and large mobilities.