  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.
