Theoretical Modeling for the Thermal Stability of Solid Targets in a Positron-Driven Muon Collider

A future multi-TeV muon collider requires new ideas to tackle the problems of muon production, accumulation and acceleration. In the Low EMittance Muon Accelerator concept a 45 GeV positron beam, stored in an accumulation ring with high energy acceptance and low angular divergence, is extracted and driven to a target system in order to produce muon pairs near the kinematic threshold. However, this scheme requires an intensity of the impinging positron beam so high that the energy dissipation and the target maintenance are crucial aspects to be investigated. Both peak temperature rises and thermomechanical shocks are related to the beam spot size at the target for a given material: these aspects are setting a lower bound on the beam spot size itself. The purpose of this paper is to provide a fully theoretical approach to predict the temperature increase, the thermal gradients, and the induced thermomechanical stress on targets, generated by a sequence of 45 GeV positron bunches.A case study is here presented for Beryllium and Graphite targets. We first discuss the Monte Carlo simulations to evaluate the heat deposited on the targets after a single bunch of 3 × 1011 positrons for different beam sizes. Then a theoretical model is developed to simulate the temperature increase of the targets subjected to very fast sequences of positron pulses, over different timescales, from ps regime to hundreds of seconds. Finally a simple approach is provided to estimate the induced thermomechanical stresses in the target, together with simple criteria to be fulfilled (i.e., Christensen safety factor) to prevent the crack formation mechanism.