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In several high-energy physics experiments the possibility of using the so-called pebble-bed targets is being considered. They consist of a large number of small spheres, in which a proton beam deposits heat energy with exceptionally high density. The article discusses thermal shock in a sphere, caused by a rapid temperature rise by a beam pulse of finite length, under the conditions of uniform heat energy deposition within the volume of the sphere. The character of the response depends on the duration of the pulse length relative to the time it takes for the stress wave to travel the distance of the sphere radius. For short pulses a stress-focusing effect takes place near the sphere core. The convergence of the series that defines the stress components is discussed using an analytical test. The influence of damping on the stress level has been considered, by introducing a flexible model of damping. It is shown that for very short pulses damping plays an important role in the determination of the magnitude of the stress spikes near the sphere core. The solution approach renders itself much better to convergence studies and is computationally more efficient than the available finite element codes, such as LS-Dyna.

Thermal shock in a sphere due to a proton beam pulse