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.
An electrostatic lens with three focusing elements in an alternating-gradient configuration is used to focus a fountain of cesium atoms in their ground (strong-field-seeking) state. The lens electrodes are shaped to produce only sextupole plus dipole equipotentials which avoids adding the unnecessary nonlinear forces present in cylindrical lenses. Defocusing between lenses is greatly reduced by having all of the main electric fields point in the same direction and be of nearly equal magnitude. The addition of the third lens gave us better control of the focusing strength in the two transverse planes and allowed focusing of the beam to half the image size in both planes. The beam envelope was calculated for lens voltages selected to produced specific focusing properties. The calculations, starting from first principles, were compared with measured beam sizes and found to be in good agreement. Application to fountain experiments, atomic clocks, and focusing polar molecules in strong-field-seeking states is discussed.
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