[en] Methods of adiabatic demagnetization were limited until very recently to one-shot operations or to power levels below 1 mW. This paper describes the results of a reciprocating magnetic refrigerator operating between 1.8 K and 4.2 K, with a useful power greater than 1 watt. In this type of machine there are various problems associated with heat transfer between magnetic substance and heat sources and inside the substance itself. The refrigerator described here overcomes some of these problems and achieves good efficiency