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

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

The JPL Phase B interferometer testbed

Future NASA missions with large optical systems will require alignment stability at the nanometer level. However, design studies indicate that vibration resulting from on-board disturbances can cause jitter at levels three to four orders of magnitude greater than this. Feasibility studies have shown that a combination of three distinct control layers will be required for these missions, including disturbance isolation, active and passive structural vibration suppression, and active optical pathlength compensation. The CSI technology challenge is to develop these design and control approaches that can reduce vibrations in the optical train by a factor of 1000 to 10,000. The focus of the paper is on describing the Phase B Testbed structure and facility, as the experimental results are included in other papers presented at this same conference

Derivatives of rational inner functions: geometry of singularities and integrability at the boundary

We analyze the singularities of rational inner functions on the unit bidisk and study both when these functions belong to Dirichlet-type spaces and when their partial derivatives belong to Hardy spaces. We characterize derivative $H^{\mathfrak{p}}$ membership purely in terms of contact order, a measure of the rate at which the zero set of a rational inner function approaches the distinguished boundary of the bidisk. We also show that derivatives of rational inner functions with singularities fail to be in $H^{\mathfrak{p}}$ for $\mathfrak{p}\ge\frac{3}{2}$ and that higher non-tangential regularity of a rational inner function paradoxically reduces the $H^{\mathfrak{p}}$ integrability of its derivative. We derive inclusion results for Dirichlet-type spaces from derivative inclusion for $H^{\mathfrak{p}}$. Using Agler decompositions and local Dirichlet integrals, we further prove that a restricted class of rational inner functions fails to belong to the unweighted Dirichlet space.Comment: 56 pages, 2 figure