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Beam-beam interactions pose substantial challenges in the design and operation of circular colliders, significantly affecting their performance. In particular, the weak-strong simulation approach is pivotal for investigating single-particle dynamics during the collider design phase. This paper evaluates the limitations of existing models in weak-strong simulations, noting that while they accurately account for energy changes due to slingshot effects, they fail to incorporate longitudinal coordinate changes (z variation). To address this gap, we introduce two novel transformations that enhance Hirata’s original framework by including both z variation and slingshot effect-induced energy changes. Through rigorous mathematical analysis and extensive weak-strong simulation studies, we validate the efficacy of these enhancements in achieving a more precise simulation of beam-beam interactions. Our results reveal that although z variation constitutes a higher-order effect and does not substantially affect the emittance growth rate within the specific design parameters of the Electron-Ion Collider, the refined model offers improved accuracy, particularly in scenarios involving the interaction between beam-beam effects and other random diffusion processes, as well as in simulations incorporating realistic lattice models.

In the local crabbing scheme for Electron Ion Collider interaction region, beam rotation is initiated by one set of crab cavities at a high beta region with near 90 deg phase advance to the interaction point (IP), and ceased by an identical set of cavities on the symmetrically opposite side. The fundamental mode of all crab cavities is designed to apply a momentum kick to the particle bunches to complete this half cycle of rotation in the horizontal plane, meanwhile the electromagnetic (EM) field can be expanded into a series of harmonics. Despite the lowest dipole mode, higher harmonics cause instabilities during beam operation and loss of particles. We used SimTrack, which is the 6-d symplectic element-by-element tracking code developed at Brookhaven National Laboratory in 2015, to study the threshold of each higher-order harmonic multipolar mode with the criteria of maintaining a dynamic aperture of 6 σ or greater for the Hadron Storage Ring (HSR). In this paper, we showed the threshold for each higher harmonic multipole and their comparison with the multipole strength for the current crab cavity design.

We present an update on the design of the Interaction Region (IR) for the the Electron Ion Collider (EIC) being built at Brookhaven National Laboratory (BNL). The EIC will collide high energy and highly polarized hadron and electron beams with a center of mass energy up to 140 GeV with luminosities of up to 10^34 /cm^2/s. The IR, located at RHIC's IR6, is designed to meet the requirements of the nuclear physics community as outlined in [1]. A second IR is technically feasible but not part of the project.The magnet apertures are sufficiently large to allow desired collision products to reach the far-forward detectors; the electron magnet apertures in the rear direction are chosen to be large enough to pass the synchrotron radiation fan. In the forward direction the electron apertures are large enough for non-Gaussian tails.The paper discusses a number of recent recent changes to the design. The machine free region was recently increased from 9 to 9.5 m to allow for more space in the forward direction for the detector. The superconducting magnets on the forward side now operate at 1.9 K, which helps crosstalk and space issues.

Objective This study aimed to investigate the use intention and influencing factors of telerehabilitation in people with rehabilitation needs. Methods This cross-sectional survey recruited a total of 183 participants with rehabilitation needs from May 2022 to December 2022. Sociodemographic and medical data were collected by a structured questionnaire. The factors influencing the use intention of telerehabilitation were measured by the extended Unified Theory of Acceptance and Use of Technology (UTAUT) model. Multiple hierarchical regression analyses were performed. Results A total of 150 valid questionnaires were included for analysis. The results indicated that the use intention of telerehabilitation was overall high in people with rehabilitation needs. Health condition ( β  = −0.21, p  = 0.03), performance expectancy ( β  = 0.21, p  = 0.01), facilitating conditions ( β  = 0.25, p  = 0.03), perceived trust ( β  = 0.25, p  < 0.01), and self-efficacy ( β  = 0.19, p  = 0.04) were significant factors influencing the use intention of telerehabilitation. Conclusion Overall, the use intention of telerehabilitation is high in individuals with rehabilitation needs. Health conditions, performance expectancy, facilitating conditions, perceived trust, and self-efficacy are important factors influencing the use intention of telerehabilitation in individuals with rehabilitation needs.

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

The design of the electron-ion collider (EIC) at Brookhaven National Laboratory is well underway, aiming at a peak electron-proton luminosity of 10e+34 cm^-1·sec^-1. This high luminosity, the wide center-of-mass energy range from 29 to 141 GeV (e-p) and the high level of polarization require innovative solutions to maximize the performance of the machine, which makes the EIC one of the most challenging accelerator projects to date. The complexity of the EIC will be discussed, and the project status and plans will be presented.

The Electron-Ion Collider (EIC) presently under construction at Brookhaven National Laboratory will collide polarized high energy electron beams with hadron beams with luminosities up to 10^34cm^{-2}s^{-1} in the center mass energy range of 20-140 GeV. Preliminary beam-beam simulations resulted in an optimum working point of (.08, .06) in the Electron Storage Ring (ESR). However, during the ESR polarization simulation study this working point was found to be less than optimal for electron polarization. In this article, we present beam-beam simulation results in a wide range tune scan to search for optimal ESR design tunes that are acceptable for both beam-beam and polarization performances.

This note presents key findings for the ESR main magnet dipole power supplies (PS), where we find the current ripple specification to be close to or beyond the state-of-the-art. These specifications originate from beam-beam considerations, with the requirement to limit the ripple-induced hadron emittance growth to below 10%/hour. Beam dynamics that drive this PS ripple specification arise from the beam motions at the Interaction Point (IP). The frequency of the motions can be separated into "low", compared to the betatron frequency, and "high", i.e. around the betatron frequency and harmonics. In terms of the driving frequency, "low" implies ƒ<<ƒ₀v_x,y and "fast" means ƒ≈{ƒ₀v_x,y, ƒ₀(1-v_x,y, etc.}, where ƒ₀=1/T₀=78.2 kHz is the revolution frequency, and v_x,y are the fractional parts of the betatron tunes. Frequencies higher than ƒ₀/2 will be folded back due to the particles sampling the field once per turn. To provide flexibility for future lattice adjustments and working point variations, we do not consider the tunes as fixed. Instead, we assume a certain margin and allow them to potentially fall within the range of 0.1<v_x,y<0.5. In other words, the high-frequency region spans approximately from 8kHz to 40 kHz. Consequently,, we definte the dipole PS ripple in two distinct frequency ranges: the low-frequency range of [1-8000] Hz and the high-frequency range of [8-40] kHz. For the physics effects we analyzed in this note, there is no distinction between the ripple (which can be approximately reproduced in the frequency domain) and the random noise if both have some power within the frequency bandwidth of interest. Therefore, while we will use the term "ripple" for short, it should always be understood that we are referring to "ripple plus noise." Except for the lower end of the low-frequency range, the impact of the rippling PS current on the beam will be considerably reduced due to the eddy currents induced in the walls of the vacuum chamber. We will account for this effect in the PS ripple specifications to follow. The remaining sections of this note are structure as follows: Section II outlines the beam-beam physics requirements for the positional stability of the beam at the IP. Section III describes the anticipated shielding effect of the eddy currents induced in the vacuum chamber. Section IV derives the ripple requirement for the low-frequency range by propagating the closed orbit ripple resulting from the rippling dipoles to the IP (relevant lattice simulation results are summarized in the Appendix). In Section V, we present the analytical criterion for the ripple in the high-frequency range by considering resonant oscillations of the electron beam around a stable closed orbit near the betatron frequency. Finally, Section VI provides a summary of our findings and discusses related work.

The Electron-Ion Collider is gearing up for "Critical Decision 2", theproject baseline with defined scope, cost and schedule.Lattice designs are beingfinalized, and preliminary component design is being carried out. Beam dynamicsstudies such as dynamic aperture optimization, instability and polarizationstudies, and beam-beam simulations are continuing in parallel. We report onthe latest developments and the overall status of the project, and presentthe plans for future activities.

In this paper, we present the effects of linear transverse-longitudinal coupling on beam size at the interaction point (IP) of a collider with a local crab crossing scheme, when time-dependent transverse deflection (crab kicks) and dispersive orbit intertwine near IP. The analytic propagation formula and the closed orbit form of the crab dispersion and momentum dispersion are derived. The nonzero momentum dispersion at crab cavities and the nonideal phase from crab cavities to IP are detailed with the derived propagation formula to predict the beam size distortion at IP with or without the beam-beam interaction. The linear results are compared with nonlinear simulation using the weak-strong beam-beam code.