Crystalline collimators can potentially considerably improve the cleaning performance of the presently used collimator systems using amorphous collimators. A crystal-based collimation scheme which relies on the channeling particle deflection in bent crystals has been proposed and extensively studied both theoretically and experimentally. However, since the efficiency of particle capture into the channeling regime does not exceed ninety percent, this collimation scheme partly suffers from the same leakage problems as the schemes using amorphous collimators. To improve further the cleaning efficiency of the crystal-based collimation system to meet the requirements of the FCC, we suggest here a double crystal-based collimation scheme, to which the second crystal is introduced to enhance the deflection of the particles escaping the capture to the channeling regime in its first crystal. The application of the effect of multiple volume reflection in one bent crystal and of the same in a sequence of crystals is simulated and compared for different crystal numbers and materials at the energy of 50 TeV. To enhance also the efficiency of use of the first crystal of the suggested double crystal-based scheme, we propose: the method of increase of the probability of particle capture into the channeling regime at the first crystal passage by means of fabrication of a crystal cut and the method of the amplification of nonchanneled particle deflection through the multiple volume reflection in one bent crystal, accompanying the particle channeling by a skew plane. We simulate both of these methods for the 50 TeV FCC energy.

Hamiltonian dynamics has been applied to study the slip-stacking dynamics. The canonical-perturbation method is employed to obtain the second-harmonic correction term in the slip-stacking Hamiltonian. The Hamiltonian approach provides a clear optimal method for choosing the slip-stacking parameter and improving stacking efficiency. The dynamics are applied specifically to the Fermilab Booster-Recycler complex. The dynamics can also be applied to other accelerator complexes.

An in-vacuum undulator (IVU) provides a means to reach high-brilliance x rays in medium energy storage rings. The development of short period undulators with low phase errors creates the opportunity for an unprecedented brilliant light source in a storage ring. Since the spectral quality from cryogenic permanent magnet undulators (CPMUs) has surpassed that of IVUs, NdFeB or PrFeB CPMUs have been proposed for many new advanced storage rings to reach high brilliance x-ray photon beams. In a low emittance ring, not only the performance of the undulator but also the choice of the lattice functions are important design considerations. Optimum betatron functions and a zero-dispersion function shall be provided in the straight sections for IVU/CPMUs. In this paper, relevant factors and design issues for IVUs and CPMUs are discussed together with many technological challenges in short period undulators associated with beam induced–heat load, phase errors, and the deformation of support girders.

The efficiency of a free-electron laser can be enhanced by the phase jump method. The method utilizes the phase-shifting chicanes in the drift sections between the undulator segments. By applying appropriate phase jumps, the microbunched electron beam can decelerate and radiate coherently beyond the initial saturation, enabling further energy transfer to the optical beam. This article presents a new physics model for the phase jump method, and supports it with numerical simulations. Based on the electron dynamics in the longitudinal phase space, the model describes the energy extraction mechanism, and addresses the selection criteria for the phase jump magnitude. While the ponderomotive bucket is stationary, energy can be extracted from electrons outside the bucket. With the aid of the new model, a comparison is made between the phase jump method and undulator tapering. The model also explores the potential of the phase jump method to suppress the growth of synchrotron sidebands in the optical spectrum.

An extensive experimental study is performed to confirm fundamental resonance bands of an intense hadron beam propagating through an alternating gradient linear transport channel. The present work focuses on the most common lattice geometry called “FODO” or “doublet” that consists of two quadrupoles of opposite polarities. The tabletop ion-trap system “S-POD” (Simulator of Particle Orbit Dynamics) developed at Hiroshima University is employed to clarify the parameter-dependence of coherent beam instability. S-POD can provide a non-neutral plasma physically equivalent to a charged-particle beam in a periodic focusing potential. In contrast with conventional experimental approaches relying on large-scale machines, it is straightforward in S-POD to control the doublet geometry characterized by the quadrupole filling factor and drift-space ratio. We verify that the resonance feature does not essentially change depending on these geometric factors. A few clear stop bands of low-order resonances always appear in the same pattern as previously found with the sinusoidal focusing model. All stop bands become widened and shift to the higher-tune side as the beam density is increased. In the space-charge-dominated regime, the most dangerous stop band is located at the bare betatron phase advance slightly above 90 degrees. Experimental data from S-POD suggest that this severe resonance is driven mainly by the linear self-field potential rather than by nonlinear external imperfections and, therefore, unavoidable at high beam density. The instability of the third-order coherent mode generates relatively weak but noticeable stop bands near the phase advances of 60 and 120 degrees. The latter sextupole stop band is considerably enhanced by lattice imperfections. In a strongly asymmetric focusing channel, extra attention may have to be paid to some coupling resonance lines induced by the Coulomb potential. Our interpretations of experimental data are supported by theoretical predictions and systematic multiparticle simulations.

The 3-GeV rapid cycling synchrotron (RCS) of the Japan Proton Accelerator Research Complex (J-PARC) is now in the final beam commissioning phase, aiming for a design output beam power of 1 MW. With a series of injector linac upgrades in 2013 and 2014, RCS developed a high-intensity beam test, and launched 1-MW beam tuning in October 2014. The most important issues in realizing such a high-power continuous beam operation are to control and minimize beam loss for maintaining machine activations within permissible levels. In RCS, numerical simulation was successfully utilized along with experimental approaches to isolate the mechanism of beam loss and find its solution. By iteratively performing actual beam experiments and numerical simulations, and also by several hardware improvements, we have recently established a 1-MW beam operation with very low fractional beam loss of a couple of ${10}^{-3}$. In this paper, our recent efforts toward realizing such a low-loss high-intensity beam acceleration are presented as a follow-up of our previous article, H. Hotchi et al. Phys. Rev. ST Accel. Beams 12, 040402 (2009), in which the initial beam commissioning status of RCS has been reported.

The image displacement instability (IDI) has been measured on the 20 MeV Axis I of the dual axis radiographic hydrodynamic test facility and compared to theory. A 0.23 kA electron beam was accelerated across 64 gaps in a low solenoid focusing field, and the position of the beam centroid was measured to 34.3 meters downstream from the cathode. One beam dynamics code was used to model the IDI from first principles, while another code characterized the effects of the resistive wall instability and the beam break-up (BBU) instability. Although the BBU instability was not found to influence the IDI, it appears that the IDI influences the BBU. Because the BBU theory does not fully account for the dependence on beam position for coupling to cavity transverse magnetic modes, the effect of the IDI is missing from the BBU theory. This becomes of particular concern to users of linear induction accelerators operating in or near low magnetic guide fields tunes.

We analytically examine the bunching factor spectrum of a relativistic electron beam with sinusoidal energy structure that then undergoes an echo-enabled harmonic generation (EEHG) transformation to produce high harmonics. The performance is found to be described primarily by a simple scaling parameter. The dependence of the bunching amplitude on fluctuations of critical parameters is derived analytically, and compared with simulations. Where applicable, EEHG is also compared with high gain harmonic generation (HGHG) and we find that EEHG is generally less sensitive to several types of energy structure. In the presence of intermediate frequency modulations like those produced by the microbunching instability, EEHG has a substantially narrower intrinsic bunching pedestal.

Synchronized proton acceleration by ultraintense slow light (SASL) in low-density targets has been studied in application to fabricated carbon nanotube films. Proton acceleration from low-density plasma films irradiated by a linearly polarized femtosecond laser pulse of ultrarelativistic intensity was considered as result of both target surface natural contamination by hydrocarbons and artificial volumetric doping of low-density carbon nanotube films. The 3D particle-in-cell simulations confirm the SASL concept [A. V. Brantov et al., Synchronized Ion Acceleration by Ultraintense Slow Light, Phys. Rev. Lett. 116, 085004 (2016)] for proton acceleration by a femtosecond petawatt-class laser pulse from realistic low-density targets with a hydrogen impurity, quantify the characteristics of the accelerated protons, and demonstrate a significant increase of their energy compared with the proton energy generated from contaminated ultrathin solid dense foils.

The interrelation between the accelerating gradient and the transformer ratio in the collinear wakefield accelerator has been analyzed. It has been shown that the high transformer ratio and the high efficiency of the energy transfer from the drive bunch to the witness bunch can only be achieved at the expense of the accelerating gradient. Rigorous proof is given that in best cases of meticulously shaped charge density distributions in the drive bunch, the maximum accelerating gradient falls proportionally to the gain in the transformer ratio. Conclusions are verified using several representative examples.

Following a successful commissioning period, the multiturn extraction (MTE) at the CERN Proton Synchrotron (PS) has been applied for the fixed-target physics programme at the Super Proton Synchrotron (SPS) since September 2015. This exceptional extraction technique was proposed to replace the long-serving continuous transfer (CT) extraction, which has the drawback of inducing high activation in the ring. MTE exploits the principles of nonlinear beam dynamics to perform loss-free beam splitting in the horizontal phase space. Over multiple turns, the resulting beamlets are then transferred to the downstream accelerator. The operational deployment of MTE was rendered possible by the full understanding and mitigation of different hardware limitations and by redesigning the extraction trajectories and nonlinear optics, which was required due to the installation of a dummy septum to reduce the activation of the magnetic extraction septum. This paper focuses on these key features including the use of the transverse damper and the septum shadowing, which allowed a transition from the MTE study to a mature operational extraction scheme.

We study coherent synchrotron radiation by electrons in the Frenet-Serret coordinate system with a constant curvature $1/\rho$. Based on the Hamiltonian in the Courant-Synder theory of particle accelerators, we find in general that the transverse force is essentially the Lorentz force but with a substitution of the transverse magnetic field $B_{x,y}\to (1+x/\rho )B_{x,y}$, where $x$ and $y$ are the transverse positions. The curvature term provides us a key to derive the point-charge wakefield explicitly in terms of the incomplete elliptic integrals of the first and second kind, resulting in a steady-state theory of the coherent synchrotron radiation in two-dimensional free space.

Electron cyclotron resonance ion sources based charge breeders (ECR-CB) are fundamental devices for Isotope Separation On Line (ISOL) facilities aiming at postaccelerating radioactive ion beams (RIBs). Presently, low intensity RIBs do not allow a conventional tuning of the ECR-CB: as a consequence, it has to be set with a stable 1+ pilot beam first, switching then to the radioactive one without changing any parameter; this procedure is usually called “blind tuning.” Besides having different masses, pilot and radioactive beams can also differ in terms of the rms transverse emittance ${\epsilon }_{\mathrm{rms}}$ and/or longitudinal energy spread $\mathrm{\Delta }E$, so the choice of a given pilot beam can determine the overall performances of the final breeding stage. This paper shows a numerical study of how the capture efficiency of the PHOENIX charge breeder is affected by the aforementioned beam paramaters: the analysis reveals the two-step nature of the process, highlighting the role of the injection optics and the plasma capture capability in the overall performances of this device. The simulations predict highest efficiency for ${\epsilon }_{\mathrm{rms}}<5\pi \mathrm{mm}\mathrm{mrad}$ and $\mathrm{\Delta }E<5\mathrm{eV}$ in a optimum energy range between 2 and 6 eV, thus giving important information on the possibility of blindly tuning an ECR-CB. No isotopical effects were observed, while it clearly came out the necessity to improve the $1+$ beam characteristics with a rf beam cooler prior to the injection into an ECR-CB.

Nowadays, designs for ring-based light sources use multibend lattices for achieving a very small emittance of around 100 pmrad. In this type of storage ring, the chromaticity correcting sextupoles generally have greater strengths than those used in typical third-generation light sources. Therefore, controlling lattice nonlinearity such as amplitude-dependent tune shift (ADTS) is important for enabling stable operations and smooth beam commissioning. As the strength of the sextupoles increases, their higher-order terms contribute significantly to ADTS, rendering well-known lowest-order formulas inadequate for describing tune variations at large horizontal amplitudes. In response, we have derived explicit expressions of ADTS up to the fourth order in sextupole strength based on the canonical perturbation theory, assuming that the amplitude of a vertical betatron oscillation is smaller compared with the horizontal one. The new formulas express the horizontal and vertical betatron tune variations as functions of the action variables: $J_x$ and $J_y$ up to $O(J_x^2)$ and $O(J_y)$. The derived formulas were applied to a five-bend achromat lattice designed for the SPring-8 upgrade. By comparing the calculated results with the tracking simulations, we found that (1) the formulas accurately express ADTS around a horizontal amplitude of $\sim 10\mathrm{mm}$ and (2) the nonlinear terms of the fourth order in sextupole strength govern the behaviors of circulating electrons at large horizontal amplitudes. In this paper, we present explicit expressions of fourth-order formulas of ADTS and provide some examples to illustrate their effectiveness.

Longitudinal instabilities are one of the main limitations in the CERN Super Proton Synchrotron (SPS) to reach the beam parameters required for the High Luminosity LHC project. In preparation to the SPS upgrade, possible remedies are studied by performing macroparticle simulations using the machine impedance model obtained from electromagnetic simulations and measurements. To benchmark the impedance model, the results of simulations are compared with various beam measurements. In this study, the reactive part of the impedance was probed by measuring the quadrupole frequency shift with intensity, obtained from bunch length oscillations at mismatched injection into the SPS. This method was applied over many last years to follow up the evolution of the SPS impedance, injecting bunches with the same bunch length. A novel approach, giving significantly more information, consists in varying the injected bunch length. The comparison of these measurements with macroparticle simulations allowed us to test the existing model, identify some missing SPS impedance and to obtain its possible dependence on frequency.

Higher order modes (HOMs) may affect beam stability and refrigeration requirements of superconducting proton linacs such as the Superconducting Proton Linac, which is studied at CERN. Under certain conditions beam-induced HOMs can accumulate sufficient energy to destabilize the beam or quench the superconducting cavities. In order to limit these effects, CERN considers the use of coaxial HOM couplers on the cutoff tubes of the 5-cell superconducting cavities. These couplers consist of resonant antennas shaped as loops or probes, which are designed to couple to potentially dangerous modes while sufficiently rejecting the fundamental mode. In this paper, the design process is presented and a comparison is made between various designs for the high-beta SPL cavities, which operate at 704.4 MHz. The rf and thermal behavior as well as mechanical aspects are discussed. In order to verify the designs, a rapid prototype for the favored coupler was fabricated and characterized on a low-power test-stand.