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

Area of Science:

• Particle Physics
• Accelerator Physics
• Materials Science

Background:

• Future multi-TeV muon colliders need advanced methods for muon production, accumulation, and acceleration.
• The Low Emittance Muon Accelerator (LEMA) concept uses a 45 GeV positron beam impacting a target for muon pair production.
• High positron beam intensity poses challenges for target energy dissipation and maintenance.

Purpose of the Study:

• To develop a theoretical approach for predicting temperature increase, thermal gradients, and thermomechanical stress on targets.
• To analyze the impact of high-intensity 45 GeV positron bunches on target materials.
• To establish criteria for preventing target damage and ensuring operational reliability.

Main Methods:

• Monte Carlo simulations to assess heat deposition from single positron bunches on targets.
• Development of a theoretical model to simulate target temperature response to rapid positron pulse sequences (ps to hundreds of seconds).
• Theoretical estimation of induced thermomechanical stresses and application of safety factors (e.g., Christensen safety factor) to predict crack formation.

Main Results:

• Quantified heat deposition for Beryllium and Graphite targets based on beam size and positron bunch intensity.
• Modeled temperature increases and thermal gradients across target materials under high-flux conditions.
• Provided a framework for estimating thermomechanical stress and identifying operational limits for target materials.

Conclusions:

• The study provides a crucial theoretical foundation for designing robust targets for high-intensity positron beams in future muon colliders.
• Understanding and mitigating thermal and mechanical stresses is essential for maintaining target integrity and enabling collider operation.
• The developed models and criteria aid in selecting appropriate target materials and optimizing beam parameters to prevent damage.