The generation of an electron beam by a hollow cathode gun in a cusp magnetic field is discussed. Such a gun is proposed for an electron cooling device without toroids. In a section with a homogeneous magnetic field, this beam experiences a disturbance region near the axis where the electron temperature becomes higher. The main purpose of the article is to define conditions for generating the beam so as to restrict the extent of this region as much as possible. It is shown that a state with a virtual cathode in the vicinity of the zero magnetic field point is the most suitable for this aim. The experimental and essential analytical results are presented. ©1997 American Institute of Physics.