A pump device for pumping an amplifying laser medium (1), having a radiation source (13) with a plurality of laser diodes (15, 16) that emit laser beams (17) which have parallel beam axes (a) extending in the direction of a z axis and which diverge at least twice as much in the direction of an x axis perpendicular to the z axis as in the direction of a y axis perpendicular to the z axis and to the x axis. The pump device also has at least one optical component (22, 22′, 22″) with at least one cylinder surface (23), with which at least some of the laser beams (17) emitted by the laser diodes (15, 16) interact. The cylinder surface (23) lies parallel to the x axis and is curved on a plane perpendicular to the x axis.