Mathematical analysis of ion motion in a gas subjected to an alternating-sign periodic asymmetric-waveform electric field

The motion of ions in a gas subjected to an alternating-sign periodic asymmetric-waveform electric field is mathematically analyzed based on solving the continuity equation. Solutions to the transfer equation are found that describe the ion distribution in the gas in planar and cylindrical cavities. The effect of ion focusing arising in the spatially nonuniform field is evaluated. The analytical results may be helpful in designing ion mobility increment spectrometers—instruments that detect microadditives of explosives, drugs, and other hazardous materials.