This study investigates how target geometry and material influence pion and muon production from an 8 GeV proton beam, in support of target-system design for a muon collider demonstrator. A 2 m long, 0.7 m radius solenoid with a 5 T peak magnetic field is used to capture secondary particles, with the target positioned at its center. We examine how variations in target radius, length, and material affect secondary-beam yield and emittance at the solenoid exit. In parallel, we evaluate temperature rise within the target to assess material limitations and guide future work on thermal and structural survivability. The results provide initial intuition for optimizing both particle yield and target durability in muon collider front-end systems.
Muon colliders offer a promising path forward in high-energy physics, but their feasibility relies heavily on producing intense muon beams with high efficiency. Since muons originate from pion decays, and pions are created when protons strike a fixed target, the design of that target becomes a central component in maximizing secondary-particle yield. This work investigates how variations in target geometry and material affect pion and muon production, as well as the resulting beam quality, within a solenoidal capture system.
Flair, the graphical user interface of FLUKA [1] [2], provides built-in scoring cards for energy deposition, fluence, current, etc… However, extracting more detailed particle information often requires custom user routines. For this work, understanding the spatial distribution and momentum of particles exiting the target was essential. To achieve this, two user routines were realized: mgdraw.f and fluscw.f. These routines rely on pre-defined FLUKA variables, so learning their structure and data flow was a key milestone in enabling advanced and customized particle tracking beyond default scoring capabilities.
Moreover, user routines can be applied beyond particle tracking. They can also be used to define custom magnetic field configurations or to build user-defined particle sources within a simulation, using magfld.f and source.f, respectively. Flair does not provide a straightforward way to define a solenoidal magnetic field directly. To address this limitation, two approaches were explored to reproduce the solenoidal field: the first using an axial magnetic field approximation, and the second by generating a field map in G4beamline and importing it into Flair.
For the first approach, magfld.f was developed to implement the axial magnetic field approximation, derived from Biot-Savart, of a 5 T solenoidal field, EQ. 1. [3]
Where L is the length of the solenoid, R is the radius of the solenoid, and z and r are the axial and radial positions.
Although this method provides a reasonable estimate close to the beamline axis, its accuracy decreases significantly away from the axis. Moreover, integrating the effects of adjacent magnetic fields is challenging because the combined magnetic field approximation would need to be calculated manually.
The second approach offers a more comprehensive and flexible solution. It involves generating a magnetic field map using G4beamline, which produces over 4,000 data points describing the 5 T solenoidal field. A custom Python script was then developed to reformat this data for compatibility with Flair’s MGNDATA card, which reads in field points manually. Because FLUKA relies on strict Fortran-based input formatting, even minor spacing inconsistencies can cause read failures, requiring careful attention to detail during data preparation. Utilizing G4beamline has the advantage of automatically accounting for fringe fields in the magnetic configuration, and it simplifies the inclusion of additional magnetic sources, as it directly computes the resultant magnetic field distribution. FIG. 1 shows the magnetic field maps produced by the two methods.
Target design is an optimization problem that involves geometry, material choice and the placement of the target relative to the proton beam. The goal is to maximize the yield of pion and muon while limiting damage and extending the target life span. This study focuses on how changes in target radius, length, and material affect secondary beam yield and quality, quantified through mechanical emittance. In addition, we examine the temperature rise in the target to understand material limitations and identify potential failure thresholds. Temperature changes are reported as ∆T (K) per bunch, assuming 10 13 protons per bunch.
The simulation setup consists of an 8 GeV proton beam striking a target positioned at the center of a 2 m, 5 T solenoid, where the field is strongest and provides efficient capture of high-transverse-momentum pions and muons. Each simulation uses 100,000 primary protons. Results are presented in two parts: geometry and material.
To study the effects of target radius and length on the secondary beam, a graphite target was used for all simulations in this subsection. We first examine how changing the radius influences secondary-beam production while keeping the length fixed at 40 cm, approximately one interaction length in graphite. When comparing targets of different radii, the beam spot size increases modestly as the radius grows. The corresponding emittance differences remain minor and fall within the level of statistical variation expected from Monte Carlo-based simulations. FIG. 2a summarizes the total number of pions and muons detected at the end of the solenoid, along with their emittances, for target radii ranging from 0.3 to 2.1 cm. Because all simulations were generated using the same random seed and therefore the same sequence of primary particle histories, the statistical uncer
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