For a single hadron bunch in a circular accelerator at zero chromaticity, without multiturn wakes and without electron clouds and other beams, only one transverse collective instability is possible, the mode-coupling instability (TMCI). For sufficiently strong space charge (SC), the instability threshold of the wake-driven coherent tune shift normally increases linearly with the SC tune shift, as independently concluded by several authors using different methods. This stability condition has, however, a very strange feature: at strong SC, it is totally insensitive to the number of particles. Thus, were it correct, such a beam with sufficiently strong SC, being stable at some intensity, would remain stable at higher intensity, regardless of how much higher. This paper suggests a resolution of this conundrum: while SC suppresses the TMCI, it introduces head-to-tail convective amplifications, which could make the beam even less stable than without SC, even if all the coherent tunes are real, i.e., all the modes are stable in the conventional absolute meaning of the word. This is done using an effective new method of analysis of the beam’s transverse spectrum for arbitrary space charge and wake fields. Two new types of beam instabilities are introduced: the saturating convective instability and the absolute-convective instability.

A study of the optimization of iron dominated dipole magnets with pole face widths comparable or less than the gap size, i.e., low aspect ratio (AR), is conducted using both theoretical and computational approaches. This regime of magnet design is particularly relevant in the context of laser plasma accelerators (LPA) due to unique beam parameters and geometric constraints, namely large energy spreads and the requirement for large apertures to accommodate drive laser passage. The breakdown of commonly employed approximations and rules of thumb in typical $\mathrm{AR}\gg 1$ magnet design is examined. A library of generalized, optimized pole face geometries is provided to expedite optimization of future magnets. Finally, this methodology is used to design an electromagnetic chicane which has been fabricated, validated, and is currently in use in an x-ray free electron laser driven LPA experiment at LBNL.

Top-up operation was recently introduced at the European Synchrotron Radiation Facility (ESRF) to provide constant beam current to the beam line users. This mode of operation involves frequent injections that can be the source of significant perturbations on the stored beam. Beam lines running experiments with a timescale longer than the injection period may be impacted by such perturbations. The ESRF storage ring injection systems and layout were not designed to allow for transparent injection, i.e., without visible perturbations on the stored beam. These perturbations are driven directly or indirectly by rapidly pulsing elements, the effect of which cannot be corrected by standard methods such as feedback loops. Major efforts were put into the development of mitigation measures at the ESRF. Depending on the source of perturbation different approaches were used. They all contribute to the achievement of transparent injections and unperturbed continuous data acquisition for the beam lines. After a review of the ESRF injection systems, these developments and the resulting reduction of the injection perturbations are described in this paper.

Charge state evolution of the projectile ions while traversing through the solid target medium has been explored using the radiative electron capture process. The measured centroid energies of the convoluted radiative electron capture peak structures have been used to determine the mean K-shell binding energies and mean charge state of the projectile ions. It has been observed that the mean charge states of present measurements are lower than the earlier measurements done using the characteristic ${\mathrm{K}}_{\alpha }$ x-ray transitions. The difference is due to the capture of target electrons in the inner-shell vacancies, created during the collision process, of projectile ions. Further, the measured mean charge states are compared with the empirical predictions. A significant discrepancy between experimental and theoretical values has been observed, which is attributed to the multielectron capture by projectile ions due to nonradiative electron capture process from the exit surface while exiting from the foil. The significant variation between mean charge state values obtained from different tools provides a clear indication of the dynamic nature of the charge-changing mechanism at different regions (entrance surface, bulk, and exit surface) of the ion-solid interaction. The present results can be used to validate the departure between the theory and experiment on the charge state dependent stopping powers.

Ambient mechanical vibrations could cause significant detuning in superconducting accelerating cavities, disturbing the acceleration regime. The mechanical damper, first developed at Laboratori Nazionali di Legnaro, Istituto Nazionale di Fisica Nucleare by A. Facco [Mechanical mode damping in superconducting low $\beta$ resonators, in Proceedings of the Eighth Workshop on RF Superconductivity, SRF’97, Abano Terme (Padova), Italy, 1997 (JACoW, Geneva, 1997)], dissipates the kinetic energy of vibrations due to friction. The study of damping efficiency, corresponding to the maximum cavity detuning, is addressed in this paper. The mechanism of the damper parameters impacting on the maximum cavity detuning at a given excitation is investigated. An analytical model of the damper has been derived to predict the nonlinear response. Numerical results from simulations in ANSYS confirmed the model over a wide range of excitation. An experimental demonstration has been conducted successfully on a test bench. Online measurements taken on the ISAC-II superconducting linac at TRIUMF further verify the analytical model.

We introduce a 1D planar static model to elucidate the underlying mechanism of large ion current losses in the vacuum convolute and the inner magnetically insulated transmission line (MITL) of the $Z$ machine. We consider $\mathbf{E}\times \mathbf{B}$ electron flow, parallel to the electrodes, and ion motion across the vacuum gap, for given voltage $V$, gap distance $d$, anode magnetic field $B_a$, and vacuum electron current $\mathrm{\Delta }I$. This model has been introduced and solved before by Desjarlais [Phys. Rev. Lett. 59, 2295 (1987)] for the applied magnetic field ion diode. Here we apply it to convolute and inner MITL ion losses of $Z$, relaxing the fix magnetic flux condition of that reference. In the absence of ions we show that the electron vacuum flow must be close to the anode if its current exceeds the value given by the local flow impedance, implying high electric fields there. We then introduce space charge limited ion emission from the anode, neglecting the magnetic force on ions. We obtain the solution of the steady state equations for two special cases: (a) when both the electric potential and the electric field are zero inside the gap, and there is a layer of electrons not carrying current that neutralizes the ion charge between the virtual and the electrode cathode, making that region electric field free, and (b) when the electric field is zero inside the gap, but the potential is not, and zero electron charge between that point and the physical cathode. For case (a) we obtain an ion current density which we conjecture is the maximum attainable for any electron charge distribution in the electron current carrying layer, given $V,d,B_a,\mathrm{\Delta }I$ an ion species. We obtain the enhancement factor for both cases with respect to the ion-only Child-Langmuir ion current density, and show that it can be significantly larger than that of the electron saturated flow case. Furthermore, imposing electron current conservation as the flow enters the inner MITL from the four outer MITLs, we recover the well-known dependence $j_{\mathrm{ion}}\sim V^{3/2}/d^2$, where voltage and gap are taken near the joining point of those outer MITLs. The implications and limitations of the proposed model are discussed.

In this work we provide an in-depth analysis of mechanisms which mitigate the hose instability in the blowout regime in plasma-wakefield accelerators. We show by means of theory and three-dimensional particle-in-cell simulations that the mitigation mechanisms related to a beam energy spread are effective for parameters as used in major plasma-wakefield accelerator experiments and for various beam energies, beam current profiles, and types of hosing seed. In addition, we establish the theoretical principles for the reduction of the initial hosing seed in tapered vacuum-to-plasma transitions and derive respective analytic predictions which are successfully benchmarked against particle-in-cell simulations. We also investigate the possibility to facilitate efficient and stable acceleration of witness beams in the blowout regime. This work therefore provides a deepened understanding for the methods that allow for the mitigation of hosing, a crucial prerequisite to facilitate stable acceleration of high quality beams in plasma-wakefield accelerators.

We describe a benchmark study of collective and nonlinear dynamics in the Advanced Photon Source storage ring. A 1-mm long bunch was assumed in the calculation of wakefield and element by element particle tracking with distributed wakefield components along the ring was performed in an elegant simulation. Although the accurate prediction of nonlinear beam dynamics with collective effects is extremely challenging, the simulations agree well with experimental measurements.

Recently studies are started on the application of volume reflection of particles in crystals for the steering beams (for extraction and collimation of a circulating beam in accelerators). Volume reflection is more efficient than channeling, but requires amplification of the deflection angle by applying multicrystals. The report discusses two new applications of multicrystals made like multistrip structures: (i) the property of effective deflection of particle beam was used to protect the septum magnets of the U-70 in the process of extraction of the proton beam with energy of 50 GeV; (ii) the possibility of generation of gamma radiation was studied in the secondary electron beam with energy of 7 GeV. In both cases, promising preliminary data were obtained.

We present a fusion-oriented pulsed power module M-50, which is based on the linear transformer driver (LTD) and magnetically insulated inductive voltage adder (MIVA) technologies. The module M-50, which consists of 50 identical LTD cavities connected in series, is one of the 60 modules of a fusion-scale pulsed power facility. M-50 is a comprehensive test bed for LTD integration and engineering validation. Each cavity consists of 32 bricks and has an output capability of $90\mathrm{kV}/1.0\mathrm{MA}/120\mathrm{ns}$ to the matched load. The output power of the 50 cavities is added with a MIVA, whose operation impedance is approximately matched to both source and load. Therefore, it has a nominal output capability of $4.5\mathrm{MV}/1.0\mathrm{MA}/120\mathrm{ns}$ to $4.5\mathrm{\Omega }$ resistive load. The module is divided into five groups, and each group has ten cavities in series. The inner stalk of the MIVA is divided into five main straight segments. Conical transitions are employed to connect adjacent straight segments. The output end of M-50 is shrunk and connected a ring-cathode diode, whose cathode and anode radii are identical to those of a 12-m-long transmission line in the fusion facility. In this paper, the general concept of the fusion accelerator, the physical design, engineering design and development progress of M-50 are described for the first time.

Diagnostics of nonlinear beam dynamics has become more important for the LHC as it advances into increasingly challenging regimes of operation, as well as for the High Luminosity LHC where machine nonlinearities will have a significantly larger impact. Limitations of traditional excitation methods at top energy, in particular due to machine protection, have pushed the development of safe alternative methods using ac dipoles to characterize the nonlinear content of the LHC. One of the methods that has been proposed is the dynamic aperture under forced oscillation of ac dipoles. This new observable has the potential to help characterize relative changes in the nonlinear content of the machine, improve the understanding of the nonlinear models by comparing to simulations, validate nonlinear optics corrections, and give a qualitative lower bound estimate on the free dynamic aperture. This paper presents the first experimental demonstration of forced dynamic aperture measurements under forced oscillations performed using the LHC ac dipoles, and discusses the benefits of forced dynamic aperture measurements in circular colliders.

When a superconducting radiofrequency cavity is cooled through its critical temperature, ambient magnetic flux can become “frozen in” to the superconductor, resulting in degradation of the quality factor. This is especially problematic in applications where quality factor is a cost driver, such as in the cw linac for LCLS-II. Previously, it had been unknown how to prevent flux from being trapped during cooldown in bulk niobium cavities, but recent R&D studies showed near-full flux expulsion can be achieved through high temperature heat treatment and cooling cavities through the superconducting transition with a spatial thermal gradient over the surface. In this paper, we describe the first accelerator implementation of these procedures, in cryomodules that are currently being produced for LCLS-II. We compare the performance of cavities under different conditions of heat treatment and thermal gradient during cooldown, showing a substantial improvement in performance when both are applied, enabling cryomodules to reach and, in many cases, exceed a $Q_0$ of $\sim 3\times {10}^{10}$.

A time-of-flight device was developed to characterize wavelength distribution and uniformity of a cold neutron beam. This device is very compact—the distance of flight is 60 cm—but achieves very high resolution—the intrinsic resolution $\mathrm{\Delta }\lambda /\lambda =2.4\times {10}^{-3}$ at $\lambda =0.89\mathrm{nm}$. The time-of-flight device is composed of a fixed slit, a disk rotating up to 216 Hz, and a neutron detector with a thin spherical conversion layer with the chopper slit in its focus. The device accepts the complete angular divergence of the initial neutron beam. The efficiency of neutron detection is constant over the detector area. Systematic corrections caused by neutron scattering in air are minimized due to the reduction of the time-of-flight length. Measurements have been performed on the beamline of the GRANIT experiment at ILL (part of the H172 beamline) on level C, and the first order diffraction peak of the crystal monochromator used for the GRANIT beamline was found to be at $\lambda =0.8961(11)\mathrm{nm}$, and having a width of $\sigma =0.0213(13)\mathrm{nm}$.

The advent of circular accelerators based on superconducting magnets has revolutionized the field of beam dynamics, with particle motion turning from linear to nonlinear due to unavoidable high-order field errors generated by the ring magnets. Nonlinear dynamics was already well mastered, e.g., in the close field of celestial mechanics as similar problems had been considered and successfully tackled. Hence, several results were available to aid comprehension of the behavior of charged particle beams under the influence of nonlinear forces. Here, we discuss how concepts derived from the theory of dynamical systems, linked with the fundamental Kolmogorov–Arnold–Moser theory and Nekhoroshev theorem, can be successfully applied to the analysis of nonlinear motion of charged particles in a circular accelerator. Based on these ideas, an innovative method to measure the extent of the phase-space region within which bounded motion occurs is presented, which has been successfully tested for the first time at the CERN LHC.

At the ion accelerator HELIS at the LPI, the neutron yield is investigated from a deuteron-deuteron (DD) reaction in a deuterated Pd target, during an irradiation of its surface by a 20 keV deuterium (D) ion beam. The measurements of the neutron flux in the D beam direction are performed in dependence on the target angle $\beta$ with respect to the D beam axis using a multichannel detector based on ${\mathrm{He}}^3$ counters. A significant anisotropy in the neutron yield is observed, and it was higher by a factor of 2 at $\beta =0$ compared to that at $\beta =\pm 30°$. The possible reasons for the anisotropy, including D ion channeling, are discussed. The orientation effect of increasing the relative probability of the DD reaction in Pd due to channeling was investigated by computer simulations using the bcm-2.0 code. The numerically obtained 20 keV D trajectories allow calculating the flux density of channeled D in dependence on the penetration depth and angle of incidence. The enhanced D flux density between crystal planes at a zero incident angle with respect to (200) Pd planes allows a qualitative explanation of the increase of the neutron yield in the DD reaction.

The radio-frequency quadrupole (RFQ) group at Peking University has built a window-type RFQ, operating at 162.5 MHz in continuous-wave (cw) mode. It is designed to accelerate a 50 mA deuteron beam from 50 keV to 1 MeV with a vane length of 1.809 m. The cavity was fabricated in two segments using 100% oxygen-free electronic (OFE) copper. Using an iterative assembly and measurement procedure for the precise alignment of the two segments, we reduced the assembly errors to within $\pm 0.05\mathrm{mm}$. The radio frequency (rf) measurements of the whole cavity show excellent rf properties, with the measured intrinsic Q-value of 8962, which equates to 96% of the simulated value for OFE copper. We also investigated field fluctuations caused by misalignment between the two segments, and studied their impact on the beam transmission using beam dynamics simulations. During field tuning, we compiled a set of unique tuning rules for the window-type RFQ. After tuning, the maximal field unflatness of the single quadrant is within $\pm 2\%$, and the asymmetry of the four quadrants is within $\pm 1\%$. During rf conditioning, the cw power of the cavity reached 55 kW within 32 hours, and we have recorded nearly seven hours of stable running at a cw power of 50 kW. The measured bremsstrahlung spectrum shows that the accelerator needs 49.9 kW to generate the intervane voltage of 60 kV, with a specific shunt impedance of $130.5\mathrm{k}\mathrm{\Omega }\mathrm{m}$. An ${\mathrm{H}}_2^{+}$ ion beam extracted from an electron cyclotron resonance ion source was used for the beam commissioning, because deuteron beam acceleration will bring a serious radiation field. We achieved stable and robust acceleration of about 1.5 mA cw ${\mathrm{H}}_2^{+}$ beam for one hour.

Choke-mode accelerating structures are higher-order-mode (HOM) damped structures that are relatively simple to fabricate and have low surface magnetic fields. $C$-band choke-mode accelerating structures have been successfully applied in free electron lasers. However, studies on $X$-band choke-mode structures for the main linac of the Compact Linear Collider (CLIC) currently remain at the theoretical design stage, and the high-gradient performance of a choke remains unknown. In this study, we designed and fabricated five different single-cell choke-mode accelerating structures and subjected them to high-gradient tests to study related radio frequency (rf) breakdown characteristics. High electrical field and small choke gap caused serious breakdowns in the choke, which mainly limited high-gradient performance. The choke-mode accelerating structure reached $121\mathrm{MV}/\mathrm{m}$ at a breakdown rate of $8.30\times {10}^{-4}$ per pulse per meter and a flat top pulse width of 250 ns. A new quantity proposed to give the high-gradient performance limitation of choke-mode accelerating structures due to rf breakdown. The new quantity was obtained from the summary of the high-gradient experiments and can be used as reference for high-gradient choke-mode accelerating structure design.

Bulk niobium is the most common material used in the fabrication of rf superconducting cavities for accelerators. Predicting and reducing the rf surface dissipation in these cavity structures is mandatory, since it has a tremendous cost impact on the large accelerator projects. In this paper the author hopes to demonstrate that sources of dissipation usually attributed to external causes (mainly flux trapping during cooldown and hydrides precipitates) are related to the same type of crystalline defects that affect the local superconducting properties and can be at the source of early vortex penetration at the surface. We also want to show how these types of defects can explain some of the discrepancies observed from other laboratories in niobium cavity doping experiments. Understanding the origin and the role of these defects could provide direction for improving material specifications as well as improving fabrication control from sheet material to completed cavity. In particular, we will demonstrate that dislocation entanglements, due to the fabrication damage layer, have the strongest impact for the pinning behavior of trapped flux, as well as hydrogen segregation in cavity niobium. The author wishes to present to the superconducting radio frequency (SRF) accelerator community the synthesis of experimental results scattered in the literature, completed with some personal results. The results of this effort provide a new perspective on recently published work in the domain of SRF cavity doping and sensitivity to trapped flux during cooldown. I will also try to draw whenever possible, some conclusions about other types of superconductors used for SRF applications including $\mathrm{Nb}/\mathrm{Cu}$ thin films and to discuss their possible change of behavior with field or frequency. I will concentrate on surface and material science aspects since the experimental results on rf cavities have already been treated elsewhere.