Implications of a 20-Hz Booster cycle-rate for Slip-stacking

We examine the potential impacts to slip-stacking from a change of the Booster cycle-rate from 15- to 20-Hz. We find that changing the Booster cycle-rate to 20-Hz would greatly increase the slip-stacking bucket area, while potentially requiring greater usage of the Recycler momentum aperture and additional power dissipation in the RF cavities. In particular, the losses from RF interference can be reduced by a factor of 4-10 (depending on Booster beam longitudinal parameters). We discuss the aspect ratio and beam emittance requirements for efficient slip-stacking in both cycle-rate cases. Using a different injection scheme can eliminate the need for greater momentum aperture in the Recycler.Comment: Fermilab Technical Memo 2587-AP

Integrable RCS as a proposed replacement for Fermilab Booster

Integrable optics is an innovation in particle accelerator design that potentially enables a greater betatron tune spread and damps collective instabilities. An integrable rapid-cycling synchrotron (RCS) would be an effective replacement for the Fermilab Booster, as part of a plan to reach multi-MW beam power at 120 GeV for the Fermilab high-energy neutrino program. We provide an example integrable lattice with features of a modern RCS - dispersion-free drifts, low momentum compaction factor, superperiodicity, chromaticity correction, bounded beta functions, and separate-function magnets.Comment: arXiv admin note: substantial text overlap with arXiv:1703.0095

Comparing the orthogonal and homotopy functor calculi

Goodwillie's homotopy functor calculus constructs a Taylor tower of approximations to F, often a functor from spaces to spaces. Weiss's orthogonal calculus provides a Taylor tower for functors from vector spaces to spaces. In particular, there is a Weiss tower associated to the functor which sends a vector space V to F evaluated at the one-point compactification of V. In this paper, we give a comparison of these two towers and show that when F is analytic the towers agree up to weak equivalence. We include two main applications, one of which gives as a corollary the convergence of the Weiss Taylor tower of BO. We also lift the homotopy level tower comparison to a commutative diagram of Quillen functors, relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.Comment: 28 pages, sequel to Capturing Goodwillie's Derivative, arXiv:1406.042

Dynamical Stability of Slip-stacking Particles

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.Comment: Supplemental Material appended to pape

Wavefront error sensing

A two-step approach to wavefront sensing for the Large Deployable Reflector (LDR) was examined as part of an effort to define wavefront-sensing requirements and to determine particular areas for more detailed study. A Hartmann test for coarse alignment, particularly segment tilt, seems feasible if LDR can operate at 5 microns or less. The direct measurement of the point spread function in the diffraction limited region may be a way to determine piston error, but this can only be answered by a detailed software model of the optical system. The question of suitable astronomical sources for either test must also be addressed