Protection of storage rings and ion-beam devices from melting

At normal incidence high-power beams can produce vapour and plasma at the surface immediately. However, the material of walls, septa, cups and other beam diagnostic devices can be protected by making use of heat conduction into cold regions. To achieve this, the material surface is tilted against the beam axis. The limiting tilt angle is evaluated from a solution of the equation of heat dissipation, as a function of beam power density and irradiation time. Of all practical materials, copper presents the largest tilt angle, for instance 1.2 mrad for a beam power density of 1.5 GW/cm2 lost over 4 μs. Since the stopping range does not appear in the formula but only in a condition of validity, the result is of interest as well for high-power proton accelerators as for heavy-ion machines in the plasma-generating regime.