Accelerator performance analysis of the Fermilab Muon Campus

Fermilab is dedicated to hosting world-class experiments in search of new physics that will operate in the coming years. The Muon g-2 Experiment is one such experiment that will determine with unprecedented precision the muon anomalous magnetic moment, which offers an important test of the Standard Model. We describe in this study the accelerator facility that will deliver a muon beam to this experiment. We first present the lattice design that allows for efficient capture, transport, and delivery of polarized muon beams. We then numerically examine its performance by simulating pion production in the target, muon collection by the downstream beam line optics, as well as transport of muon polarization. We finally establish the conditions required for the safe removal of unwanted secondary particles that minimizes contamination of the final beam.

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Figure 1

A schematic representation of the Muon Campus accelerator complex that is used by the Muon g-2 Experiment. Secondaries are produced on a target that then travel through the M2- and M3-line, which is designed to capture as many $3.1\mathrm{GeV}/c$ muons from pion decays as possible. The beam is injected into the DR wherein a kicker is used to remove the protons, the resulting muon beam is then extracted into the M4-line, and the muon beam is eventually transferred to the new M5-line that leads to the muon storage ring (enclosed in the MC1 hall). The M3-line, DR, and M4-line are also designed to be used for 8 GeV proton transport by the Mu2e Experiment [18]. The combined M2- and M3-line and M4-and M5-line lengths are 280 and 130 m respectively, along with the DR that has a circumference of 505 m. One should note that the horizontal alignment of the M3-line with the injection leg of the DR is achieved by two 9.25° bends and an additional 5° bend that is placed upstream of the AP30 straight section.

Figure 2

(a) A Schematic representation of the Muon Campus target station, where the positive pion (${\pi }^{+}$) and proton trajectories are shown in blue and pink respectively. (b) The optics functions are shown for the M2- and M3-line, where the lattice is designed to have a transverse acceptance of 40 mmmrad, and a narrow momentum acceptance of $\mathrm{\Delta }p/p=\pm 2\%$. The beam line has 120° phase-advance cells between $S=23.2\mathrm{m}$ and 35.6 m, 90° phase-advance cells between 65.4 and 143.1 m, and 72° phase-advance cells between 177.8 to 240.2 m. The point of intersection between M2 and M3 is at $\mathrm{S}=50.0\mathrm{m}$, the two 9.25° horizontal bending magnets are at $S=160.0\mathrm{m}$ and $S=174.0\mathrm{m}$, while injection to the DR occurs at $S=280.0\mathrm{m}$.

Figure 3

(a) The conceptual design for injection into the DR, where the beam direction is from right to left. (b) The conceptual design for extraction from the DR, where the beam direction is from right to left. (c) A distorted image of the DR that shows all focusing elements, where the large aperture injection quad (D3Q3) is shown in red, extraction quad (D2Q5) is shown in yellow, all other quads are shown in orange, and bends are shown in cyan. Injection and extraction beam lines are omitted for the sake of simplicity.

Figure 4

(a) The optics functions for the DR. (b) The optics functions for the M4-and M5-line, where the M5-line ends at the entrance of the muon storage ring. The lattice is designed to have a transverse acceptance of 40 mm-mrad and a narrow momentum acceptance of $\mathrm{\Delta }p/p=\pm 2\%$. The M5 begins at $S\approx 30.0\mathrm{m}$, a 27.1° horizontal bend string begins at $S= 46.5\mathrm{m}$ that provides the proper entry position into the muon storage ring, while a tunable final focus section using four quadrupole magnets begins at $S=119.8\mathrm{m}$ that provides optical matching to the storage ring.

Figure 5

The simulated performance along the M2- and M3-line, where the evolution of secondary particles is shown as a function of distance along the channel for different momentum acceptances. The dashed line shows the performance of pions when decays are not included. The final number of pions is $1.87\times {10}^{-5}$ per POT at the end of the channel ($S=280\mathrm{m}$), which is in agreement with our theoretical findings (triangle). One should note that $S=0$ is the same point as in Fig. 2.

Figure 6

The simulated performance along the DR, where the evolution of secondary particles is given as a function of the number of turns for different momentum acceptances. One should note that all pions decay to muons after the third turn.

Figure 7

The simulated performance along the M4-and M5-line, where the evolution of muons is given as a function of distance along the channel for different momentum acceptances.

Figure 8

The muon momentum distribution at the end of the Muon Campus, where the muons have an average momentum of $3.09\mathrm{GeV}/c$ with one standard deviation of 1.20%. The solid curve is a Gaussian distribution fit to the points.

Figure 9

The simulation results for the muon horizontal (${\mathrm{P}}_{\mathrm{x}}$), vertical (${\mathrm{P}}_{\mathrm{y}}$), and longitudinal (${\mathrm{P}}_{\mathrm{S}}$) polarizations: (a) at the end of M3-line, (b) after one turn in the DR, (c) after four turns in the DR, and (d) at end of the M5-line. The average muon beam polarization is $\sim 96\%$ and remains unchanged through the channel.

Figure 10

The tracking of muon and proton longitudinal distributions along the DR: (a) entering, (b) after one turn in, (c) after three turns in, and (d) after four turns in the DR. The separation of muon and proton bunches increases by 75 ns after each turn. This plot indicates that four revolutions are required to safely remove the proton contamination, because of the $\sim 180\mathrm{ns}$ rise time for the proton removal kicker magnets. One should note that the histograms are normalized so that the area sum is equal to 1.