Polar molecules, in strong-field seeking states, can be transported and focused by an alternating sequence of electric field gradients that focus in one transverse direction while defocusing in the other. We show, by calculation and numerical simulation, how one may greatly improve the alternating gradient transport and focusing of molecules. We use a new optimized multipole lens design, a FODO-lattice beam transport line, and lenses to match the beam transport line to the beam source and to the final focus. We derive analytic expressions for the potentials, fields, and gradients that may be used to design these lenses. We describe a simple lens optimization procedure and derive the equations of motion for tracking molecules through a beam transport line. As an example, we model a straight beamline that transports a 560 m/s jet-source beam of methyl fluoride15 m from its source and focuses it to 2 mm diameter. We calculate the beam transport line acceptance and beam survival, for a beam with a velocity spread, and estimate the transmitted intensity for specified source conditions. Possible applications are discussed.
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