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This Letter presents the first complete six dimensional phase space measurement of a beam in an accelerator. The measurement was made on the Spallation Neutron Source Beam Test Facility. The data reveal previously unknown correlations in the six dimensional phase space distribution that are not visible in lower dimensionality measurements. The correlations are shown to be intensity dependent.

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We present a particle core model study of the space charge effect on high intensity synchrotron beams, with specific emphasis on the Proton Storage Ring (PSR) at Los Alamos National Laboratory. Our particle core model formulation includes realistic lattice focusing and dispersion. We transport both matched and mismatched beams through real lattice structure and compare the results with those of an equivalent uniform-focusing approximation. The effects of lattice structure and finite momentum spread on the resonance behavior are specifically targeted. Stroboscopic maps of the mismatched envelope are constructed and show high-order resonances and stochastic effects that dominate at high mismatch or high intensity. We observe the evolution of the envelope phase-space structure during a high intensity PSR beam accumulation. Finally, we examine the envelope-particle parametric resonance condition and discuss the possibility for halo growth in synchrotron beams due to this mechanism.

The Snowmass'21 Implementation Task Force has been established to evaluate the proposed future accelerator projects for performance, technology readiness, schedule, cost, and environmental impact. Corresponding metrics has been developed for uniform comparison of the proposals ranging from Higgs/EW factories to multi-TeV lepton, hadron and ep collider facilities, based on traditional and advanced acceleration technologies. This report documents the metrics and processes, and presents evaluations of future colliders performed by Implementation Task Force.