We report on a detailed study of the focusing properties of inhomogeneous m
agnetic fields. The experiment is performed using cold cesium atom clouds r
eleased from a magneto-optical trap. The sample longitudinal distributions
are being compressed under the influence of a pulsed parabolic magnetic pot
ential. Achromatic imaging potentialities are demonstrated. Analogies with
usual optics are pointed out. A velocity compression is obtained, leading t
o a cloud longitudinal effective temperature down to 220 nK For a proper ch
oice of the experimental parameters. The observation of strong compressions
is corroborated by numerical simulations in excellent agreement with the e
xperimental data. The principle of the method is presented in view of an el
ementary one-dimensional model and its limits an discussed. [S1050-2947(99)
05206-3].