Polarized electrons play an important role in high-energy and nuclear physics, and their properties have also been exploited in ultrafast electron microscopy. Currently, gallium arsenide crystals illuminated by circular polarized infrared laser light are commonly used for generating polarized electrons. However, the achievable accelerating voltage and the gradient of these electrostatic sources limit the beam quality and quantity. A solution could be to combine gallium arsenide photocathodes with radio-frequency electron guns, which are capable of accelerating beams with significantly higher gradients and voltage. Here we report the successful operation of a gallium arsenide photocathode in a superconducting radio-frequency gun. Our findings are relevant for future sources of polarized electrons.

Numerical investigations of linear and nonlinear stages of quasi-interchange instability in a cylindrical tokamak geometry with a flat q-profile in the core region are conducted using eigenvalue and initial value codes, respectively. It is found that there exists a dependent relationship between the central plasma pressure p(0) (of the initial pressure profile) and the dominant harmonic of the quasi-interchange instability. As p(0) increases, m = n > 1 mode would be dominant in the linear stage and even in the nonlinear stage, where m and n are the poloidal and toroidal mode number, respectively. In addition, with p(0) increasing, the fast growth of other harmonics is inevitable and will deeply affect the evolution of m=n dominant quasi-interchange instability.

There are numerous instabilities present in charged particle beams that undergo exponential growth and reach saturation. In various applications, such as free-electron lasers or micro-bunching light sources, achieving saturation is desirable. Conversely, there are applications where these instabilities are utilized as linear broad-band amplifiers for signals embedded in the charged beam. In the latter scenario, the saturation of an instability induces non-linear distortions in the imprinted signal, thereby limiting the useful range of such amplifiers. Accurate evaluation of these instabilities necessitates a complete and comprehensive modeling approach that includes shot noise within the beam. Unfortunately, such modeling is not always feasible or practical. In this paper, we introduce a methodology utilizing the frequency and bandwidth of the instability as key parameters. Through this, we derive an estimation for the range of linear instability growth. Our derivation is conducted in a model-independent manner, making it applicable to a broad spectrum of instabilities. To validate our approach, we employ established and thoroughly benchmarked simulations with a free electron laser (FEL) code as well as self-consistent 3-dimensional simulation of plasma-cascade instability using code SPACE.

Microscopic, or short-wavelength, instabilities are known for drastic reduction of the beam quality and strong amplification of the noise in a beam. Space charge and coherent synchrotron radiation are known to be the leading causes for such instabilities. In this paper we present rigorous 3D theory of such instabilities driven by the space-charge forces. We define the condition when our theory is applicable for an arbitrary accelerator system with 3D coupling. Finally, we derive a linear integral equation describing such instability and identify conditions when it can be reduced to an ordinary second order differential equation.

Coherent electron cooling (CeC) is a novel technique for rapidly cooling high-energy, high-intensity hadron beam. Plasma cascade amplifier (PCA) has been proposed for the CeC experiment in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Cooling rate of CeC experiment with PCA has been predicted in 3D start-to-end CeC simulations using code SPACE. INTRODUCTION The Department of Energy (DOE) has selected BNL as the site for the future Electron-Ion Collider (EIC). Strong hadron cooling is essential to attain the luminosity required by the EIC design. CeC [1-3] is the most promising technique for the rapid cooling of high-energy high-intensity hadron beams in the EIC. A general CeC scheme consists of three main sections, the modulator, the amplifier, and the kicker. In the modulator, hadrons co-propagate with the electrons and induce density modulation by attracting surrounding electrons. The density modulation is then amplified in the second section of CeC, the amplifier. In the kicker, the electron beam interacts with the hadrons, correcting their energies towards the nominal value, which results in cooling of the hadron beam. Several CeC schemes have been proposed with different implementations of the CeC amplifier, including the highgain free electron laser (FEL) amplifier [3], the microbunching instability (MBI) amplifier [4], and the PCA [5]. In this paper, we present simulation studies of the PCA-based CeC. Working principle of PCA is the new plasma cascade instability (PCI) [6-7] occurring in electron beams propagating along a straight trajectory. Figure 1 shows the layout of a PCA-based CeC system, where solenoids are used to modulate the transverse size of the electron beam and to excite the PCI amplifying the density modulation induced by hadrons in the modulator. Our simulation tool is the SPACE code [8], a parallel, relativistic, three-dimensional (3D), electromagnetic (EM) Particle-in-Cell (PIC) code, which has been used in the simulation studies for the mitigation effect by beam induced plasma [9], the modulation process in CeC [10-13], the cooling performance of CeC with FEL amplifier [14-17] and the sensitivity study of PCA [18]. SIMULATION SETUP The setup in the simulation study is based on the CeC experiment at BNL RHIC. Figure 2 shows the layout of the CeC system installed at BNL RHIC. The CeC section includes a 3-meter modulator, an 8-meter 4-cell PCA and a 3-meter kicker. The lengths of the PCA cells are 1.8 m, 2.2 m, 2.2 m, and 1.8 m. Figure 3 presents the simulated evolution of transverse root mean square (RMS) size of the electron beam in the modulator, the PCA and the kicker. The electron beam parameters used in the simulations are listed in Table 1 and are relevant to the CeC experiment at BNL RHIC. A transverse Kapchinsky-Vladimirsky (KV) distribution has been applied to the electron beam in the simulations. Note that the KV emittance is 4 times of the traditionally defined RMS emittance. Figure 1: Schematic of a CeC system with the PCA. Figure 2: PCA-based CeC system installed at BNL RHIC. The electron beam is generated in a 1.25 MV superconducting radio frequency (SRF) photo-electron gun, accelerated to 14.56 MeV, and merged to co-propagate with the 26.5 GeV/u ion beam circulating in RHIC’s yellow ring. ___________________________________________ * Work supported by Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy. † jma1@bnl.gov 12th Int. Particle Acc. Conf. IPAC2021, Campinas, SP, Brazil JACoW Publishing ISBN: 978-3-95450-214-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2021-WEPAB265 MC5: Beam Dynamics and EM Fields D09 Cooling, Emittance Manipulation, Bunch Compression WEPAB265 3261 C on te nt fr om th is w or k m ay be us ed un de rt he te rm s of th e C C B Y 3. 0 lic en ce (© 20 21 ). A ny di st ri bu tio n of th is w or k m us tm ai nt ai n at tr ib ut io n to th e au th or (s ), tit le of th e w or k, pu bl is he r, an d D O I

Solenoids are frequently used for focusing low-energy beams. In this paper, we show how they can serve as multipurpose diagnostics tools to measure various beam parameters, including energy, emittance, the second moments of the transverse distribution, and the beam position and angle with respect to the solenoid’s axis. The energy measurement is based on rotation of the plane of the transverse motion, as opposed to generating dispersion with a dipole. Measurement of the beam trajectory with respect to the solenoid axis is done by analyzing the beam orbit downstream of the solenoid while varying its current. The second moments are calculated by analyzing the beam image on a profile monitor while accounting for the beam rotation caused by the solenoid. We describe in detail the corresponding procedures and the experimental results of these measurements.

By incorporating the longitudinal electric field reduction due to finite transverse beam size into the Poisson equation and solving the Hill's equation with time-dependent plasma frequency, we investigate how the amplification of a Plasma-Cascade Amplifier (PCA) depends on the spatial frequency of the density modulation. INTRODUCTION E A new type of amplifier, plasma cascade amplifier (PCA) has been proposed for a coherent electron cooling (CeC) system [1-3]. Previously, the 1D model for PCA assumes that the transverse distribution of the density perturbation in the electrons is uniform and consequently, the plasma frequency does not depend on the wavelength of the perturbation [1]. This assumption is valid if the longitudinal wavelength of the initial perturbation in the beam frame is much shorter than the transverse width of perturbation. In this work, we explore the PCI gain at long wavelength by assuming the perturbation in electrons’ density has nonuniform transverse profile. Specifically, we solve the 3D Poisson equation for given charge distribution (longitudinal sinusoidal, transversely Gaussian or Beer-can), average the electric field over the transverse plane and then apply it to 1-D Vlasov equation. Similar to the previous calculation in [1], the Vlasov equation can be reduced to a Hill’s equation but the plasma frequency now depends on the longitudinal wavelength of the density perturbation in the electrons. By numerically solving the Hill’s equation, we obtain the gain of a PCA as a function of spatial frequency, k . EQUATION OF MOTION For 1-D analysis, we treat each electron as a charge disc with certain charge distribution and consequently the evolution of the electrons' density perturbation in the beam frame are determined by the linearized 1-D Vlasov equation, f z, v , t + v f z, v , t + v f z, v , t = 0, (1) where v is the longitudinal velocity of the electrons, z is the longitudinal position along the bunch, v = − , , (2) is the longitudinal acceleration due to the longitudinal electric field E z, t , e is the absolute value of the charge of an electron and f z, v , t is the density perturbation of the electrons in the longitudinal phase space and f v is the unperturbed distribution of electrons. The longitudinal electric field due to density perturbation is determined by the Poisson equation ∇ ⋅ E = − , , , , (3) where n r, z,θ, t is the local spatial density perturbation of the electrons. For the next step, we will try to solve Eq. (3) and since there is no operation in time t for Poisson equation, we will omit t from the variables in the bracket for now and will put it back when we solve the coupledPoisson-Vlasov equation system. If we assume that the spatial distribution of the electron beam has cylindrical symmetry and define n r, z = ρ z f r , (4) Eq. (3) becomes r φ r, z + φ r, z = − ρ z f r , (5) where φ r, z is the electric potential, f r is the transverse surface density of electrons in unit of m and ρ z is perturbation of electron line density in unit of m . Multiplying both sides of Eq. (5) by e and integrating over z yields φ + φ − k φ = f r , (6) with φ k, r = e φ r, z dk ∞∞ , (7) f r = − f r e ρ z dz ∞∞ = − f r ρ k , (8) and ρ k = e ρ z dz ∞∞ . (9) The solution of Eq. (6) can be written as φ r = c I kr + c K kr + ′ ′ ⋅ f ξ dξ, (10) where I x and K x are the modified Bessel functions. By applying the following boundary conditions, φ ∞ = 0 and lim → φ r ≠ ∞, the coefficient, c and c can be determined as c = 0, (11) and c = − ξI kξ ⋅ ∞ f ξ dξ. (12) Inserting Eq. (11) and Eq. (12) into Eq. 10 leads to ___________________________________________ * Work supported by Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy. † gawang@bnl.gov 12th Int. Particle Acc. Conf. IPAC2021, Campinas, SP, Brazil JACoW Publishing ISBN: 978-3-95450-214-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2021-WEPAB031 WEPAB031 C on te nt fr om th is w or k m ay be us ed un de rt he te rm s of th e C C B Y 3. 0 lic en ce (© 20 21 ). A ny di st ri bu tio n of th is w or k m us tm ai nt ai n at tr ib ut io n to th e au th or (s ), tit le of th e w or k, pu bl is he r, an d D O I 2672 MC4: Hadron Accelerators

In this paper we describe a new microbunching instability occurring in charged particle beams propagating along a straight trajectory. The nature of these exponentially growing plasma oscillations gave the reason for its name: plasma-cascade instability. Such instability can strongly amplify longitudinal microbunching originating from the beam's shot noise, even to the point of saturation. Resulting random density and energy microstructures can drastically reduce beam quality. Conversely, such instability can drive novel high-power sources of broadband radiation or can be used as a broadband amplifier. We discovered this phenomenon in a search for such amplifier in the coherent electron cooling scheme [Phys. Rev. Lett. 102, 114801 (2009)] without separation of electron and hadron beams. In this paper we present a brief analytical theory of this new phenomenon, detailed numerical studies, the results of experimental demonstration as well as control of the longitudinal plasma-cascade instability.

Plasma cascade amplifier (PCA) is an advanced design of amplifier for the coherent electron cooling (CeC) experiment in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Woking principle of PCA is the new plasma cascade micro bunching instability occurring in electron beams propagating along a straight trajectory. PCA is cost effective as it does not require separating electron and hadron beams. SPACE, a parallel, relativistic 3D electromagnetic Particle-in-Cell (PIC) code, has been used for simulation studies of PCA. INTRODUCTION CeC [1-3] is a promising technique for the rapid cooling of high-energy high-intensity hadron beams. A CeC system consists of three main sections: the modulator, the amplifier, and the kicker. In the modulator, hadrons induce density modulation in the electron beam through Coulomb force. The density modulation is then amplified in the amplifier. In the kicker, the electron beam interacts with the hadrons, correcting their energies towards the nominal value, which results in cooling of the hadron beam. There are various implementations of the CeC amplifier. In this paper, we present simulation studies of the PCA [4]. Working principle of PCA is the new plasma cascade instability (PCI) [5-6] occurring in electron beams propagating along a straight trajectory. Figure 1 illustrates the layout of a CeC system with the PCA, where solenoids are used to focus the electron beam transversely. As a result, the plasmas frequency is modulated to excite the PCI, and to amplify the density modulation induced by hadrons in the modulator. Figure 1: Layout of a CeC system with the PCA. We have used the SPACE code [7] for simulation studies. SPACE is a parallel, relativistic, three-dimensional (3D), electromagnetic (EM) Particle-in-Cell (PIC) code, which has been used in the simulation studies for the mitigation effect by beam induced plasma [8], the modulation process in CeC [9-12], and the cooling performance of CeC with free electron laser (FEL) amplifier [13-16]. The SPACE code simulation results have been benchmarked with the analytical solution to the modulator problem [17]. PERIODIC PCA We have performed simulations of 4-cell periodic PCA to study the performance of PCA. Electron beam parameters in the simulations are listed in Table 1 and are relevant to the CeC experiment at BNL RHIC. A transverse Kapchinsky-Vladimirsky (KV) distribution has been applied to the electron beam in the simulation study. Note that the KV emittance is 4 times of the traditionally defined root mean square (RMS) emittance. Table 1: Electron Beam Parameters for Periodic PCA Beam energy, γ 28.5

We present a new type of longitudinal microbunching instability entitled ’Plasma-Cascade Instability’. This instability could occur in beams propagating along a straight section with external focusing elements. We present a theoretical description of this instability as well as self-consistent 3D simulations. Finally, we present results of experimental observation of Plasma-Cascade Instability at frequencies up to 10 THz using SRF linear accelerator built for Coherent electron Cooling experiment *.

The brand new non-magnetized bunched beam electron cooler (LEReC) has been built to provide luminosity improvement for the Beam Energy Scan II (BES-II) physics program at the Relativistic Heavy Ion Collider (RHIC). The LEReC accelerator includes a photocathode DC gun, a laser system, a photocathode delivery system, magnets, beam diagnostics, an SRF booster cavity, and a set of Normal Conducting RF cavities to provide sufficient flexibility to tune the beam in the longitudinal phase space. This highcurrent high-power accelerator was successfully commissioned in the period of March -September 2018. Beam quality suitable for cooling has been achieved which led to the first demonstration of bunched beam electron cooling of hadron beams in April 2019. In this paper we discuss achieved results and experience learned during commissioning. INTRODUCTION A new, state of the art, electron accelerator for cooling low energy RHIC hadron beams (LEReC) was built and is being commissioned at BNL. The purpose of LEReC is to provide luminosity improvement for the RHIC operation at low energies to search for the QCD critical point (Beam Energy Scan Phase-II physics program) [1-2]. Unlike all electron coolers to date, LEReC uses bunched electron beams accelerated to the required energies using RF cavities [3]. To achieve efficient cooling, the electron beam must not only be optimized for low transverse emittance but, more importantly, for low energy spread. The LEReC accelerator includes a photocathode DC gun with a high power laser system, magnets, beam diagnostics, an SRF booster cavity, and a set of normal conducting RF cavities to provide sufficient flexibility to tune the beam in the longitudinal phase space. LEReC uses a DC photocathode gun similar to the one used at the Cornell University [4]. The gun itself was built by the Cornell University. The gun tests with beam started in 2017 when it operated up to 10 mA average current [5]. Electron beams are generated by illuminating a multi-alkali (CsK2Sb or NaK2Sb) photocathode [6] with green light (532 nm) from a high-power fiber laser [7] by utilizing sophisticated laser transport and stabilization [8]. To optimize operational time and minimize the cathode exchange time three multi-cathode carriers were built. Each cathode carrier, which can hold up to 12 pucks of photocathodes, is attached to the gun in a 10-11 Torr-scale vacuum (for details of design see [9]). Figure 1: Layout of the LEReC accelerator. The red contour box indicates DC gun test area. The layout of LEReC is shown in Fig. 1. The 350-400 keV electron beam from the gun is transported via a 704 MHz SRF booster cavity and a 2.1 GHz 3rd harmonic linearizer normal conductive cavity. Electron beams can be accelerated to maximum kinetic energy of 2.6 MeV. The electron bunch is ballistically stretched to the required bunch length in the transport line. The accumulated energy ___________________________________________ * Work supported by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy † dkayran@bnl.gov 10th Int. Particle Accelerator Conf. IPAC2019, Melbourne, Australia JACoW Publishing ISBN: 978-3-95450-208-0 doi:10.18429/JACoW-IPAC2019-MOPRB085 MC1: Circular and Linear Colliders A19 Electron-Hadron Colliders MOPRB085 769 Co nt en tf ro m th is w or k m ay be us ed un de rt he te rm so ft he CC BY 3. 0 lic en ce (© 20 19 ). A ny di str ib ut io n of th is w or k m us tm ai nt ai n at tri bu tio n to th e au th or (s ), tit le of th e w or k, pu bl ish er ,a nd D O I

The SPACE code is a parallel, relativistic, three-dimensional, electromagnetic, particle-in-cell code developed for the simulations of beam dynamics and interactions. The SPACE code can perform simulations with various beam distributions, different types of boundary conditions, and flexible beam line, as well as provide sufficient processing routines for data analyses and visualization. Self-consistent, highly resolved and realistic simulations were performed using the SPACE code to study the coherent electron cooling (CeC) experiment with two types of amplifiers, the free electron laser (FEL) and plasma-cascade micro-bunching amplifiers.

Interaction of hadrons with electron beam in a modulator is an important part of coherent electron cooling (CeC), a novel cooling method for hadron beams. Being an untested technique, the CeC is undergoing a proof-of-principle test at Brookhaven National Laboratory (BNL). Simulation of this process for a realistic electron beam propagating through a realistic quadrupole beamline constitutes a very challenging problem. We successfully used the code SPACE for these simulations and obtained accurate dependences of the modulation process on the position and velocity of ions. We obtained good numerical convergence of simulations and performed verification tests using theoretical predications available for a uniform infinite plasma with K - 2 velocity distribution. In this paper, we describe simulation methods and results, and report our findings for the CeC modulator in the BNL experiment.

Highly resolved numerical simulations of the modulator, the first section of the proposed coherent electron cooling (CEC) device, have been performed using the code SPACE. The beam parameters for simulations are relevant to the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Numerical convergence has been studied using various numbers of macro-particles and mesh refinements of computational domain. A good agreement of theory and simulations has been obtained for the case of stationary and moving ions in uniform electron clouds with realistic distribution of thermal velocities. The main result of the paper is the prediction of modulation processes for ions with reference and off-reference coordinates in realistic Gaussian electron bunches with quadrupole field.