A transverse Zeeman slower composed of an array of compact discrete neodymium magnets is considered. A simple and precise model of such a slower based on magnetic dipoles is developed. The theory of a general Zeeman slower is modified to include spatial nonuniformity of the slowing laser beam intensity due to its convergence and absorption by slowed atoms. The slower needs no high currents or water cooling and the spatial distribution of its magnetic field can be adjusted. In addition the slower provides a possibility to cool the slowed atoms transversally along the whole length of the slower. Such a slower would be ideal for transportable optical atomic clocks and their future applications in space physics.

17 pages, 9 figures