The Relativistic Heavy Ion Collider (RHIC) was designed for head-on collisions in the Interaction Regions. However, RHIC operation in recent years necessitated crossing angles to limit collisions to a narrow longitudinal vertex region, which created operating conditions with a large Piwinski angle (LPA). The angles were implemented by adjusting the shunt currents of four dipoles, the D0 and DX magnets, near the IP. The longitudinal bunch profile often deviates from Gaussian due to the utilization of high-order RF cavities, adding complexity to calculating luminosity reduction with crossing angle. This paper introduces two methods for implementing crossing angles, discusses resultant aperture concerns, conducts numerical calculations of luminosity reduction, and compares these findings with experimental observations.

The Electron Ion Collider design strategy for reaching unprecedented luminosities and detection capabilities involves collision of flat bunches at a relatively large crossing angle. Effective head-on collisions are restored using crab cavities, which introduce a correlation of the particles' transverse coordinates with their longitudinal positions in the bunch, or crab dispersion. The collision geometry is further complicated by a tilt of the Electron Storage Ring plane with respect to that of the Hadron Storage Ring. In addition, the interaction point is placed inside the field of a detector solenoid. Reaching the design luminosity requires precise control of the 6D bunch distribution at the IP accounting for all of the aforementioned design features. This paper describes correction of the detector solenoid effect on the beam optics of the Hadron Storage Ring using a combination of local and global skew quadrupoles.

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) will use swap-out injection scheme for the Electron Storage Ring (ESR) to overcome limitations in polarization lifetime. However, the pursuit of highest luminosity with the required $28~\mathrm{nC}$ electron bunches encounters stability challenges in the Rapid Cycling Synchrotron (RCS). One method is to inject multiple RCS bunches into a same ESR bucket. In this paper we perform simulation studies investigating proton emittance growth and electron emittance blowup in this injection scheme. Mitigation strategies are explored. These findings promise enhanced EIC stability and performance, shaping potential future operational improvements.

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.

We study coherent transverse beam oscillations in the EIC electron storage ring (ESR), to specify the tolerance for high-frequency ripple of the magnet power supplies. To avoid unacceptable proton emittance growth from the oscillating beam-beam kick from the electrons, the amplitude of these oscillations at the proton betatron frequency needs to be limited to about 1e-4 fraction of the beam size at the interaction point. We show that the oscillations potentially caused by the ESR magnet dipole power supply ripple could be substantial, but still tolerable, if we account for the eddy current shielding in the vacuum chamber. Beam size oscillations, potentially caused by the rippling quadrupole magnet power supplies are also studied and appear manageable.

The EIC electron storage ring has very tight tolerances for the amplitude of electron beam position and size oscillations at the interaction point. The oscillations at the proton betatron frequency and its harmonics are the most dangerous because they could lead to unacceptable proton emittance growth from the oscillating beam-beam kick from the electrons. To estimate the amplitude of these oscillations coming from the magnet power supply current ripple we need to accurately account for the eddy current shielding by the copper vacuum chamber with 4-mm thick wall. At the frequencies of interest, the skin depth is a small fraction of the wall thickness, so the commonly used single-pole expressions for eddy current shielding transfer function do not apply. In this paper we present new (to the best of our knowledge) analytical formulas that adequately describe the shielding for this frequency range and chamber geometry and discuss the implications for the power supply ripple specifications at high frequency.

The Electron Ion Collider (EIC), to be constructed at Brookhaven National Laboratory, will collide polarized high-energy electron beams with hadron beams, achieving luminosities of up to 1e+34 cm^−2 s^−1 in the center-mass energy range of 20-140 GeV. Crab cavities are employed to compensate for the geometric luminosity loss caused by a large crossing angle of 25 mrad in the interaction region. The phase noise in crab cavities will induce a significant emittance growth for the hadron beams in the Hadron Storage Ring (HSR). Various models have been utilized to study the effects of crab cavity phase noise. In this article, we present our numerical simulation results using a weak-strong beam-beam model. In addition to horizontal emittance growth, we also observed vertical emittance growth resulting from both crab cavity noises and beam-beam interaction. The tolerance for crab cavity phase noise was determined and compared with analytical predictions.

The Electron Ion Collider (EIC), to be constructed at Brookhaven National Laboratory, will collide polarized high-energy electron beams with hadron beams, achieving luminosities up to 1e+34 cm^−2 s^−1 in the center-mass energy range of 20-140 GeV. The current fractional design tunes for the Hadron Storage Ring (HSR) are (0.228, 0.210) to mitigate the effects of synchro-betatron resonances. In this article, based on a strong-strong beam-beam simulation model, we carried out a wide range tune scan for the HSR to search for optimum working points. We found a good tune space around (0.735, 0.710), which is close to the working point (0.695, 0.685) of the polarized proton operation of the Relativistic Heavy Ion Collider (RHIC). We plan to further estimate the dynamic aperture and polarization with this working point.

The Electron Ion Collider (EIC), to be constructed at Brookhaven National Laboratory, will collide polarized high-energy electron beams with hadron beams, achieving luminosities up to 1e+34 cm^−2 s^−1 in the center-mass energy range of 20-140 GeV. The Hadron Storage Ring (HSR) of the EIC will utilize the arcs of the Relativistic Heavy Ion Collider (RHIC) and construct new straight sections connecting the arcs. In this article, we will examine all available skew quadrupoles currently in the HSR lattice and explore possible schemes for future global betatron coupling correction with RHIC-like decoupling feedback system. The effects of detector solenoids and quadrupole rolls are estimated at injection and stored energies. We also studied the decoupling requirements for generating and maintaining large transverse emittance ratio beams in the HSR.

We study the design and spin performance of a polarized electron Booster. This booster will accelerate polarized electrons from 200 MeV to 3 GeV. We examine the polarization transmission of the existing NSLS-II Booster design as well as a modified AGS-Booster lattice using an 8-fold symmetric design and increasing the betatron tune to 7.85 to avoid all intrinsic spin resonances.

One of the challenges of designing the Electron-Ion Collider (EIC) is to mitigate beam-induced heating due to the intense electron and hadron beams. Heating of the Electron Storage Ring (ESR) vacuum chamber components is mainly due to beam-induced resistive wall loss and synchrotron radiation. For the Hadron Storage Ring (HSR) components, heating is mainly due to resistive wall loss because of the large radial offset, electron cloud formation, and heat conduction from room temperature to cryo-components. In this paper, we provide an update on the beam-induced heating and thermal analysis for some EIC vacuum chamber components including the RF-fingers module of HSR cryogenic interconnect assembly. In addition, we provide simulation update for the HSR snake BPM, and abort kicker along with the change in ESR vacuum chamber profile. Similar analysis for other HSR and ESR components are available in Ref.~\cite{sangroulalocalized_NAPAC22, sangroula2023beam}. Our approach for thermal analysis involves calculating resistive wall losses using CST, evaluating heat loss due to synchrotron radiation and electron cloud formation and incorporating these losses into ANSYS for finding the temperature distribution.

The Electron-Ion Collider (EIC) utilizes the existing Relativistic Heavy Ion Collider (RHIC) rings as a Hadron Storage Ring (HSR) with some modifications. However, this presents significant challenges, primarily due to beam-induced Resistive Wall (RW) heating resulting from a larger radial offset and shorter EIC bunches (up to 10 times shorter than RHIC). Additionally, the formation of an electron cloud further complicates matters. To address these issues and operate the HSR effectively, this paper focuses on the RW heating and thermal analysis of the EIC HSR beam screen. Our approach involves the insertion of a copper-coated stainless steel beam screen with cooling channels and longitudinal slots. We conducted a detailed thermal analysis, assessing piecewise RW losses around the beam screen's profile due to an offset beam, employing the 3D commercial code CST. These losses, along with realistic boundary conditions, were then integrated into another code, ANSYS, to determine the thermal distribution.

The Rapid Cyclotron Synchrotron (RCS) is an acceleration ring designed for boosting the electron energy from 400 MeV after the LINAC to 1 GeV prepared for injection into the Electron Storage Ring (ESR). Operating in a pulsed mode at 1 Hz, the RCS accelerates four consecutive bunches with dipole magnet ramping rapidly at each injection. Rapid ramping of the magnetic field induces eddy currents, causing delays and high harmonic effects which are detrimental to low-energy electron bunches. To mitigate this, cost-effective multi-turn coils with specific patterns are proposed. These coils, powered by eddy currents from main dipole field ramping, generate counter fields to cancel selected high harmonic components. This paper explores the coil pattern selection process.

The Electron Ion Collider (EIC) hadron storage ring (HSR) requires a beam screen made of 75 μm copper layer on top of a 1 mm thick 316LN stainless steel sheet. The eddy currents produced by the dynamic fields at the beam screens of the transition jump quadrupoles will increase the field response delay. The field response curve depends on the thickness and Residual Resistivity Ratio (RRR) value of the copper layer. Manufacturing variances of thickness and RRR in the beam screens of the gamma transition quadrupole will result in different field response delays. This paper summarizes the effects from the beam screens on transition crossing. From the varying delays, the beta-wave and eta-wave may exceed typical RHIC values. The effectiveness of the jump will be estimated using simulations of the existing RHIC lattice.

In order to prevent emittance growth during long stores of the proton beam at the future Electron-Ion Collider (EIC), we need to have some mechanism to provide fast cooling of the dense proton beams. One promising method is coherent electron cooling (CeC), which uses an electron beam to both ``measure'' the positions of protons within the bunch and then apply energy kicks which tend to reduce their longitudinal and transverse actions. In this work, we discuss the underlying physics of this process. We then discuss simulations which constrain the electrons to move only longitudinally in order to perform fast optimizations and long-term tracking of the bunch evolution, and benchmark these results against fully 3D codes. Additionally, we discuss practical challenges, including the necessity of a high-quality electron beam and sub-micron alignment of the electrons and protons.

A new high-luminosity Electron-Ion Collider (EIC) is being developed at BNL. Beam collisions occur at IP-6, involving two rings: the Electron Storage Ring (ESR) and the Hadron Storage Ring (HSR). The vacuum system of both rings is newly developed and impedance optimization is progressing. Beam-induced heating and thermal analysis are performed for both rings to manage and control thermal distribution. The study explores collective effects across the Rapid Cycling Synchrotron (RCS), ESR, and HSR using simulated single bunch wakefields. Discussions encompass impedance analysis, collective effects and beam interactions, and the impact of ion and electron clouds on beam dynamics.

Collective wakefield and beam-beam effects play an important role in accelerator design and operation. These effects can cause beam instability, emittance growth, and luminosity degradation, and warrant careful study during accelerator design. In this paper, we report on the development of a computational capability that combines both short and long range wakefield models and a strong-strong beam-beam simulation model. Applications to the EIC will be discussed.