Mathematical expressions for the analytical duty cycle associated with different overtones in overtone mobility spectrometry are derived Indinavir sulfate from the widths of the transmitted packets of ions under different instrumental operating conditions. 8 While traditional IMS has enjoyed a resurgence in popularity limitations in achieving very high resolving capabilities spawned the development of a range of related techniques such as traveling wave ion mobility spectrometry (TWIMS) [9-12] differential mobility analysis (DMA) [13-15] field asymmetric waveform ion mobility spectrometry (FAIMS) [16-19] and overtone mobility spectrometry (OMS) [20-24]. The latter three methods act as selective filters for desired ions and are capable of very high resolving capabilities [19 22 while the former is more analogous to standard IMS in that ions are temporally dispersed. OMS shows limited similarity to TWIMS with both using a pulsed sequence of applied potentials each of which repeats in space along the length of the drift tube. As opposed to TWIMS in OMS certain ions are eliminated instead of separated by the wave leading to a change in the overall mechanism of separation reflected in the resolving power equation. Effectively this process reduces the ability of ions that have either diffused away or are mobility mismatched to diffuse back towards the center of a mobilitymatched ion swarm [20 21 The preferential removal of ions whose mobility does not match the field application frequency results in a very different technique with an increased potential for garnering high resolving power as compared to traditional IMS [20 21 and TWIMS. As related to TWIMS in the use of alternating fields OMS may also provide a greater understanding of the former technique. For example an increased understanding of mobility matching requirements may aid TWIMS experimental design particularly for the separation of high mobility species as often such ions are observed to travel at the wave velocity. Finally it is noted that OMS is usually distinguished from TWIMS in that a true collision cross section can be decided from OMS measurements whereas the TWIMS approach requires a calibration method. One interesting aspect of OMS is that the technique can be used to transmit ions having specific mobilities (and these mobilities Col4a2 can be compared directly to theory as a means of determining structure as in traditional IMS). The use of an entrance and exit gate in IMS in a scanning mode yields the limiting case of OMS-one segment-and the use of Indinavir sulfate multiple segments to improve resolving power scaling has been discussed previously [20 21 The observation that ions can be transmitted at multiples of the fundamental frequency (i.e. Indinavir sulfate in overtone regions of the spectrum) presents opportunities to explore transitions between structures in a new way . Experimentally it is observed that beyond a certain overtone no additional ions are transmitted [20-24]. It is of interest to Indinavir sulfate understand the origin of this limit. In this paper we present mathematical expressions for the analytical duty cycle associated with different overtones for a range of possible experimental conditions. This theoretical treatment is usually supported by detailed ion trajectory simulations. The outcome is an understanding of the maximum overtone that can still transmit ions for a given experiment. In the treatment offered below we presume an OMS configuration based on a series of Tyndall gates  although this is not required. A standard spacing between gates along with a standard electric field yields a direct correspondence between the mobility of the selected ions and the drift field application frequency which is the frequency of application of a defined quantity of different fields ? [20 21 Overtones appear where ions traverse a single segment in the same time but at a field application frequency that is some multiple of the fundamental frequency in each dimensions where is the Diffusion coefficient and is the time step as explained by Mason and McDaniel . The locations of grids where ions could potentially be eliminated were go through into the program independently. As fields alternated the possibility of a grid acting to neutralize ions as an removal region was determined by whether each grid contained a local potential minimum. A detector was placed at the end of the drift tube and any ion that joined the detector was neutralized and added to the count of signal. A separate simulation was run for each field application time the time for which a field was applied before transitioning to the next applied.