A: The Fermilab accelerator complex delivers intense high-energy proton beams to a variety of fixed-target scientific programs, including a flagship long-baseline neutrino program. With the advent of the Deep Underground Neutrino Experiment (DUNE) and Long Baseline Neutrino Facility (LBNF) program there is strong motivation for a 2.4 MW beam power upgrade of the Fermilab proton facility. We show the Fermilab proton facility can achieve 2.4 MW with a new rapid-cycling synchrotron (RCS) to replace the Fermilab Booster and we provide a comprehensive technical analysis of the RCS-based facility design. Past design efforts and operational experience at the Fermilab Booster, J-PARC RCS, and Oak Ridge SNS are leveraged to provide strong empirical precedent for the design. We provide a parametric study of slip-stacking accumulation, RCS extraction energy, space-charge limits, beampipe aperture, eddy current heating, injection foil heating, and lattice optics. The 2.4 MW benchmark for the long baseline neutrino program is achieved independently of a previously proposed multi-GeV linac program, but we assess the impact the linac upgrade would have on RCS performance.

We study the stability of particles in slip-stacking configuration, used to nearly double proton beam intensity at Fermilab. We introduce universal area factors to calculate the available phase space area for any set of beam parameters without individual simulation. We find perturbative solutions for stable particle trajectories. We establish Booster beam quality requirements to achieve 97% slip-stacking efficiency. We show that slip-stacking dynamics directly correspond to the driven pendulum and to the system of two standing-wave traps moving with respect to each other.

Criterion for a companion matrix to have a certain number of flat portions on the boundary of its numerical range is given. The criterion is specialized to the cases of 3 × 3 and 4 × 4 matrices. In the latter case, it is proved that a 4 × 4 unitarily irreducible companion matrix cannot have 3 flat portions on the boundary of its numerical range. Numerical examples are given to illustrate the main results.

Abstract-Electron cloud beam instabilities are an important consideration in virtually all high-energy particle accelerators and could pose a formidable challenge to forthcoming highintensity accelerator upgrades. Dedicated tests have shown beampipe coatings dramatically reduce the density of electron cloud in particle accelerators. In this work, we evaluate the performance of titanium nitride, amorphous carbon, and diamond-like carbon as beampipe coatings for the mitigation of electron cloud in the Fermilab Main Injector. Altogether our tests represent 2700 ampere-hours of proton operation spanning five years. Three electron cloud detectors, retarding field analyzers, are installed in a straight section and allow a direct comparison between the electron flux in the coated and uncoated stainless steel beampipe. We characterize the electron flux as a function of intensity up to a maximum of 50 trillion protons per cycle. Each beampipe material conditions in response to electron bombardment from the electron cloud and we track the changes in these materials as a function of time and the number of absorbed electrons. Contamination from an unexpected vacuum leak revealed a potential vulnerability in the amorphous carbon beampipe coating. We measure the energy spectrum of electrons incident on the stainless steel, titanium nitride and amorphous carbon beampipes. We find the electron cloud signal is highly sensitive to stray magnetic fields and bunch-length over the Main Injector ramp cycle. We conduct a complete survey of the stray magnetic fields at the test station and compare the electron cloud signal to that in a field-free region.