When the current and current density of electrons accelerated in the anode‐cathode gap of a field emission tube reach sufficiently high values, the induced self‐magnetic field begins to dominate the electron trajectories. As a result, the spatial distribution of electrons arriving at the anode becomes strongly peaked in the center of the anode. It has been found possible to prevent such beam collapse with relatively modest external magnetic fields. The field is applied parallel to the electron flow (perpendicular to the anode plane). A scaling law which determines the necessary field strength based on a simple orbit model is found to agree with experimental results over a wide range of electron‐beam parameters.