Abstract
In particle accelerators the process of beam absorption is vital. At CERN particle beams are accelerated at energies of the order of TeV. In the event of a system failure or following collisions, the beam needs to be safely absorbed by dedicated protecting blocks. The thermal shock caused by the rapid energy deposition within the absorbing block causes thermal stresses that may rise above critical levels. The present paper provides a convenient expression of such stresses under hypotheses described hereafter. The temperature field caused by the beam energy deposition is assumed to be Gaussian. Such a field models a non-diffusive heat deposition. These effects are described as thermoelastic as long as the stresses remain below the proportional limit and can be analytically modeled by the coupled equations of thermoelasticity. The analytical solution to the uncoupled thermoelastic problem in an infinite domain is presented herein and matched with a finite unit radius sphere. The assumption of zero diffusion as well as the validity of the match with a finite geometry is quantified such that the obtained solutions can be rigorously applied to real problems. Furthermore, truncated series solutions, which are not novel, are used for comparison purposes. All quantities are nondimensional and the problem reduces to a dependence of five dimensionless parameters. The equations of elasticity are presented in the potential formulation where the shear potential is assumed to be nil due to the source being a gradient and the absence of boundaries. Nevertheless equivalent three-dimensional stresses are computed using the compressive potential and optimized using standard analytical optimization methods. An alternative algorithm for finding the critical points of the three-dimensional stress function is presented. Finally, a case study concerning the proton synchrotron booster dump is presented where the aforementioned analytical solutions are used and the preceding assumptions verified.
Highlights
Beam dumps and beam stoppers are blocks of material dedicated to absorbing charged particles and removing them from circulating beams
The thermal shock caused by the rapid energy deposition within the absorbing block causes thermal stresses that may rise above critical levels
For beam energies in GeV or TeV range as in the proton synchrotron booster (PSB) and LHC respectively, the physics involved in the energy deposited is governed by the electromagnetic shower development initiated by nuclear reactions of beam particles impacting the material lattice [1]
Summary
Beam dumps and beam stoppers are blocks of material dedicated to absorbing charged particles and removing them from circulating beams. At CERN, energies of the accelerated particle beams range from a few KeV to 7 TeV and within time intervals ranging from ns to ms resulting in high temperature gradients which in turn give rise to severe quasistatic or dynamic stresses [6,7,8]. Analytical solutions of the nondimensionalized problem in infinite space are very useful for the initial stages of the design of a BID. The expressions developed can be used to compare the dynamic effects versus the quasistatic approximation and allow us to decide whether a dynamic computation is necessary This analysis is applicable for the design of BID’s and for proton beam cancer therapy [18,19,20]. A peak of power density function tp pulselength σ standard deviation of Gaussian power density
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