Phase space compression of a positive muon beam in two spatial dimensions

TL;DR

This work addresses the challenge of producing high-brightness muon beams by demonstrating simultaneous two-dimensional phase-space compression in a cryogenic helium target under a strong magnetic field. The muCool scheme leverages a tailored electric-field configuration and a density gradient to compress muons in the transverse and longitudinal directions as they drift along the beam axis, aiming to produce keV-energy, sub-mm muon beams. Experimental time spectra show evidence of mixed compression, with quantitative agreement to GEANT4 simulations achieved after accounting for a beam-target misalignment; simulations project about 90% compression efficiency within ~5 microseconds and an overall chain efficiency on the order of 1.9×10^-5. This milestone validates the muCool approach and paves the way for vacuum extraction and further optimization toward ultra-bright muon sources for muSR and precision physics.

Abstract

We present the first demonstration of simultaneous phase space compression in two spatial dimensions of a positive muon beam, the first stage of the novel high-brightness muon beam under development by the muCool collaboration at the Paul Scherrer Institute. The keV-energy, sub-mm size beam would enable a factor 10$^5$ improvement in brightness for precision muSR, and atomic and particle physics measurements with positive muons. This compression is achieved within a cryogenic helium gas target with a strong density gradient, placed in a homogeneous magnetic field, under the influence of a complex electric field. In the next phase, the muon beam will be extracted into vacuum.

Figures (9)

• Figure 1: The muCool scheme: A positive muon beam of 4 MeV kinetic energy is directed into a solenoid and brought to a stop in a helium gas target at cryogenic temperatures, where compression (cooling) occurs. The compressed muons are subsequently extracted with eV-level energies from the target through an orifice and re-accelerated to keV energies along the magnetic field. Upon reaching a ferromagnetic plate equipped with a small aperture, the muons are extracted into a field-free region. To give a flavor of the compression achievable with the muCool scheme, we include the expected output beam parameters from preliminary simulations (before the magnetic shield) PhD_Sakurai2023, to be compared with the beam parameters of the High Intensity Muon Beam (HIMB) aiba2021scienceeichlerIMPACTConceptualDesign2022.
• Figure 2: (Top): Sketch of the muCool target geometry with the magnetic field $\vec{B}$ and electric field $\vec{E}$, featuring a transverse component $\vec{E}_T$ in the $xy$-plane at 45$^\circ$ with respect to the $x$-axis and longitudinal components $\vec{E}_L$ in $\pm z$-direction pointing to the target mid-plane. The vertical temperature gradient is also indicated. The simulated muon trajectories demonstrate fast simultaneous compression in transverse ($y$) and longitudinal ($z$) directions. The color scale represents the time relative to the muon entering the target. (Bottom, Left) Simulation of the muon trajectories projected onto the $xy$-plane demonstrating compression in the $y$-direction while drifting in the $x$-direction toward the tip of the target. The dashed circle indicates the initial position of the muons at time $t\approx 0$, just after slowing down in the target. (Bottom, Right) Simulation of the muon trajectories projected onto the $xz$-plane demonstrating compression in the $z$-direction while the muons drift in the $x$-direction.
• Figure 3: (Left) Picture of the Kapton foil, which, when folded, forms the top, bottom, and lateral walls of the target. The maximum positive voltage (HV) applied to the central large electrode is distributed to the other electrodes through two voltage dividers composed of SMD resistors. (Right) Picture of the helium gas target. The Kapton foil is folded and glued around the target frame to seal the target.
• Figure 4: (Top) Placement of the scintillators (positron detectors) around the target projected onto the $xy$-plane (Left) and the $xz$-plane (Right). Each bottom detector is paired with a top detector to form a telescope. (Middle) Simulated position-dependent detection efficiencies projected onto the $xy$-plane for the various positron detectors. These detection probabilities were obtained by requiring coincidences between top-bottom detector pairs and including the shielding from a massive copper collimator between the detector pairs (not shown in the picture). The dashed black circles indicate the initial muon stop distribution. (Bottom) Similar to (Middle) but projected on the $xz$-plane. The dashed black rectangles indicate the initial muon stop distribution.
• Figure 5: Measured time spectra in T1, T2 and L2 coincidences for a target with 10 mbar pressure, $T_\mathrm{top}=23.1$ K, $T_\mathrm{bottom}=6.6$ K, HV = +4.99 kV and 5 T B-field. The red curves represent the simulation at design conditions. They have been normalized to match the data as described in the main text. The black curves are simulations that assume a misalignment between target and B-field (beam) axes as in Fig. \ref{['sim_tilt']} (Right). Each black curve is fitted to the data using two free parameters: a normalization factor (amplitude) and an additional flat (muon-correlated) background.