Magnetic field-generating apparatus for an installation for accelerating electrically charged particles, the particle track of which comprises curved and straight sections, contains main magnetic field generating windings and at least one supplemental winding which is provided for focusing the particles on the particle track. It should be possible to accelerate relatively large particle streams to relatively high energy levels without the need for separate preaccelerators. In the region of at least one of the curved sections of the particle track the supplemental winding is designed as a conductor arrangement forming a quadrupole triplet for focusing the particles during their acceleration phase, the turns of the supplemental winding being arranged on both sides of the plane in which the particle track lies. In particular, a conductor arrangement forming a quadrupole triplet can be provided in both regions of the curved sections of the particle track wherein these conductor arrangements together form a double-telescope system for focusing the particles.