A magnetic field apparatus for a particle accelerator having a particle track having curved sections contains several magnetic field-generating windings, and at least one supplemental winding provided for focusing the electrically charged particles. The system does not require pre-accelerators and relatively large particle streams should be capable of being accelerated nevertheless to relatively high energy levels. In the region of at least one of the curved sections of the particle track, an azimuthal guiding field for the particles is generated by the supplemental winding during the acceleration phase. This supplemental winding is designed as an appropriately curved electric conductor arrangement which in part encloses the particle track and which is designed in the manner of a hollow channel open toward the outside. The conductor arrangement is appropriately structured for suppressing eddy currents and carries a current transversely to the particle track.