The Electron Beam Ion Trap (EBIT) of the National Superconducting Cyclotron Laboratory at Michigan State University is used as a charge booster and injector for the currently commissioned rare isotope re-accelerator facility ReA. This EBIT charge breeder is equipped with a unique superconducting magnet configuration, a combination of a solenoid and a pair of Helmholtz coils, allowing for a direct observation of the ion cloud while maintaining the advantages of a long ion trapping region. The current density of its electron beam is a key factor for efficient capture and fast charge breeding of continuously injected, short-lived isotope beams. It depends on the radius of the magnetically compressed electron beam. This radius is measured by imaging the highly charged ion cloud trapped within the electron beam with a pinhole camera, which is sensitive to X-rays emitted by the ions with photon energies between 2 keV and 10 keV. The 80%-radius of a cylindrical 800 mA electron beam with an energy of 15 keV is determined to be r(80%) = (212 ± 19)μm in a 4 T magnetic field. From this, a current density of j = (454 ± 83)A/cm(2) is derived. These results are in good agreement with electron beam trajectory simulations performed with TriComp and serve as a test for future electron gun design developments.