Bunch Population Research Articles

On the effect of the maximal proper acceleration in the inertia

The effect of a hypothetical maximal proper acceleration on the mass of a charged particle is investigated in the context of particle accelerators. In particular, it is shown that maximal proper acceleration implies an increase in the kinetic energy of the particle being accelerated with respect to the relativistic energy. Such an increase in kinetic energy leads to a reduction of the luminosity of the bunches with respect to the expected luminosity in the relativistic models of the bunches. This relative loss in luminosity is of the order 10 −3 to 10 −5 for the Large Hadron Collider (LHC) bunches and can be of order up to 10 −3 for certain laser-plasma accelerator facilities. Although the effect is small, it increases with the square of the bunch population.

Non-monotonic dependence of heat loads induced by electron cloud on bunch population at the LHC

Electron cloud effects are among the main performance limitations for the operation of the Large Hadron Collider with 25 ns bunch spacing. Electrons impacting on the beam screens of the superconducting magnets induce a significant heat load reaching values close to the full cooling capacity available from the cryogenic system in some LHC sectors. To better understand this performance limitation, numerical simulations with the PyECLOUD code were performed to study the dependence of the heat load on different beam and machine parameters, in particular the bunch population, which is foreseen to be considerably increased with the impending HL-LHC upgrade. The simulations predict a complex, non-monotonic behavior of the heat load with bunch population which has important implications in defining the upgrade of the cryogenic system required for coping with HL-LHC beam intensities. An in-depth analysis of the simulation results shows that the non-monotonic dependence of the heat load on the bunch population is driven by an interplay between the spectrum of the impacting electrons and the shape of the Secondary Electron Yield curve. Experimental data were collected at the LHC during normal operation and dedicated experiments in order to validate the simulation model and confirm the expected non-monotonic behavior. The simulation results are found to reproduce very well the measurement data.

Autofocusing drift tube linac envelopes

To date, beam dynamics studies and design of combined zero degree drift tube linac (DTL) structures (Kombinierte Null Grad Struktur; KONUS) have only been carried out in multiparticle codes. Quantities such as the beam envelopes are obtained by averaging over particles, whose tracking is computationally intensive for large bunch populations. Tune computations, which depend on this average, are burdensome to obtain. This has motivated the implementation of a simulation of KONUS DTLs in the code transoptr, whose Hamiltonian treatment of beam dynamics enables the integration of energy gain from the longitudinal electric field on axis while simultaneously elaborating the field in transverse directions to obtain the linear optics. The code also features an in-built space charge capability. The evolution of the beam matrix including longitudinal optics is computed in a reference Frenet-Serret frame through the time-dependent DTL cavity fields. This enables fast envelope simulations for DTLs, resulting in a variable energy sequential tune optimization capability. The implementation methodology and optimization techniques, applicable for any combination of DTL tanks and bunchers, is outlined. Comparisons with the code lorasr, in addition to beam-based $E/A$ measurements of a DTL are presented.

Multifold bunch splitting in a high-intensity medium-energy proton synchrotron

Bunch splitting is an RF manipulation method of changing the bunch structure, bunch numbers and bunch intensity in a high-intensity synchrotron that serve as the injector for a particle collider. An efficient way to realize bunch splitting is to use the combination of different harmonic RF systems, such as the two-fold bunch splitting of a bunch with a combination of fundamental harmonic and higher harmonic RF systems. The two-fold bunch splitting and three-fold bunch splitting methods have been experimentally verified and successfully applied in the CERN PS. In this paper, a generalized multifold bunch splitting method is given. The five-fold bunch splitting method using specially designed multi-harmonic RF systems was studied and tentatively applied to the medium-stage synchrotron (MSS), the third accelerator of the injector chain of the Super Proton-Proton Collider (SPPC), to mitigate the pileup effects and collective instabilities of a single bunch in the SPPC. The results show that the five-fold bunch splitting is feasible and both the bunch population distribution and longitudinal emittance growth after the splitting are acceptable, e.g., a few percent in the population deviation and less than 10% in the total emittance growth. Intensity-related effects and beam feedback issues during the splitting process have also been addressed.

Luminosity optimization and leveling in the Super Proton–Proton Collider

The design luminosity and the beam energy scale in the future Super Proton–Proton Collider (SPPC) are unprecedented. In this article, different luminosity and leveling scenarios are studied to see if the luminosity design goal is feasible. The luminosity in a collider can be optimized by a group of machine parameters including beam emittance, number of bunches, bunch population, beta functions at the interaction point (IP), colliding mode (such as head-on or crossing, round or flat optics) and their changes during the colliding process. The beam–beam effects, event pileup and machine turnaround time have direct impact on the luminosity. Different measures or scenarios by taking the above factors are studied. When crab cavities are not available, the flat optics is studied to recover the luminosity lost due to a large crossing angle. The luminosity patterns during the physics run and averaged luminosities are given for different luminosity schemes. One can compare the performance potential and the technical difficulties among the schemes. The difference between the round optics and flat optics in the case of no crab cavities is presented. SPPC has a very high performance in the averaged luminosity. Flexible luminosity optimization and leveling schemes are available to enhance the physics performance. The flat optics as a backup plan in the case of no crab cavities does help to improve the luminosity compared with the round optics.

Electron flux and pressure dynamic in the LHC vacuum pilot sector as a function of beam parameters and beam pipe properties

The Large Hadron Collider (LHC) is affected by the electron cloud (EC) phenomenon that can provoke beam instabilities, detrimental heat loads and pressure increases in the vacuum system. An innovative dedicated system called vacuum pilot sector (VPS) provides a continuous monitoring of the electron flux and of the pressure signals thanks to electron pickup and vacuum gauges. The VPS system is installed in a room temperature, field-free part of the LHC storage ring. Several technical surfaces, such as ex situ nonevaporable getter (NEG), amorphous carbon coating and copper, are simultaneously tested. The main outcomes of this study show that the EC signals have: (1) a linear dependence upon the number of bunches and upon the bunch population in the multipacting regime, (2) a multipacting threshold at a given bunch population, (3) a reduction under beam conditioning, (4) a strong dependence on the filling pattern and beam energy. The comparison between different surfaces shows that amorphous carbon coating reduces drastically the EC buildup, thanks to its low secondary electron yield (SEY) and photoelectron yield (PY), while copper and ex situ NEG coated surfaces suffer of EC multipacting, even after several months of operation. The multipacting rate coefficients are higher for copper than for ex situ NEG, as predicted from the SEY estimation. Other detailed experimental observations are discussed in this paper.

Nanometric muon beam emittance from e+ annihilation on multiple thin targets

The production of a low emittance muon beam is interesting for muon collider projects. In such context we study the production of positive and negative muon beams at 22 GeV, from ${e}^{+}$ beam-vs-fixed target collisions, with a very small transverse and longitudinal emittance of $25\text{ }\text{ }\ensuremath{\pi}\text{ }\mathrm{nm}\text{ }\mathrm{rad}$ and $3\ifmmode\times\else\texttimes\fi{}1\text{ }\text{ }\ensuremath{\pi}\text{ }\mathrm{mm}\text{ }\mathrm{GeV}$, respectively. In order to cope with the small conversion efficiency of positrons into muon pairs and the divergence of the beams, we connect thin targets by a quadrupole-only transport line common to three beams (${\ensuremath{\mu}}^{+}$, ${\ensuremath{\mu}}^{\ensuremath{-}}$, and ${e}^{+}$) at two different energies ($\ensuremath{\mu}$ at 22 GeV and ${e}^{+}$ at 44 GeV), where the line is specially designed to match the muon beam phase space over $\ifmmode\pm\else\textpm\fi{}5%$ energy spread and to mitigate the effect of multiple scattering with the targets on all beams. The transport line allows us to use a larger fraction of target material, increasing the muon population by a factor of 10 per positron bunch and splitting the power deposition over 20 to 40 targets, while keeping the muon beam emittance equal or similar to one from a single thin target of 1% of a radiation length. It might be possible to integrate this line into an accumulator ring in order to increase the muon bunch population over hundreds of positron bunches.

Estimation of longitudinal bunch characteristics in the LHC using Schottky-based diagnostics

The Large Hadron Collider (LHC) Schottky monitors have been designed to measure various parameters of relevance to beam quality, namely tune, momentum spread, and chromaticity. In this work, we present how this instrument can be used to estimate longitudinal bunch characteristics, such as longitudinal bunch profile or synchrotron frequency distribution. Under the assumption of bunched beams with no intrabunch coherent motion, we start by deriving the relation between the distribution of synchrotron amplitudes within the bunch population and the longitudinal bunch profile from probabilistic principles. Subsequently, we fit the cumulative power density of acquired Schottky spectra with the underlying distribution of synchrotron amplitudes. Finally, the result of this fit is used to reconstruct the bunch profile using the derived model. The results obtained with this method are verified by comparison with longitudinal profile measurements from the LHC wall current monitors.

Muon production and accumulation from positrons on target

In this paper we investigate the production of a muon beam by positrons on target. We describe the characteristics of the muon beam as produced by different target configurations. We present an optics for the muon accumulator ring, discussing how it fulfils the large energy acceptance requirement and the high order chromaticity correction at the target, as well as other parameters relevant to enhance the muon bunch quality. We discuss the muon beam dynamics through the ring for the configuration of the single-pass LEMMA scheme, and the optimization study performed with the goals of maximizing the muon bunch population and minimizing its emittance.

Measurement and modeling of electron-cloud-induced betatron tune shifts at the Cornell Electron-Positron Storage Ring test accelerator

We report on extensive measurements at the Cornell Electron-Positron Storage Ring of electron-cloud-induced betatron tune shifts for trains of positron bunches at 2.1 and 5.3 GeV with bunch populations ranging between $0.64\ifmmode\times\else\texttimes\fi{}{10}^{10}$ and $9.6\ifmmode\times\else\texttimes\fi{}{10}^{10}$. Measurements using a witness bunch with variable distance from the end of the train and variable bunch population provide information on cloud decay and cloud pinching during the bunch passage. We employ Monte Carlo simulations of the reflection and absorption of synchrotron radiation photons to determine the pattern of absorption sites around the circumference of the storage ring. The Geant4 simulation toolkit is used to model the interactions of the photons with the beampipe wall and determine the production energy and location distributions of the photoelectrons which seed the electron cloud. An electron cloud buildup model based on fitted ring-averaged secondary-yield properties of the vacuum chamber predicts tune shifts in good agreement with the measurements.

Potential of a laser-driven source of characteristic γ-rays for fast detection and identification of nuclear materials

Active interrogation of special nuclear materials (SNM) represents the most promising detection technique in combating their illicit trafficking and diverted use. Among the many interrogation approaches under investigation, the one based on photoinduced fission relies on large prompt and delayed radiation signatures. Pulsed induction (tens of ns) of photofission, in particular, enables to distinguish between prompt and delayed radiation emission, providing additional signatures to identify fissile materials. As the probing radiation, 6- to 7-MeV characteristic γ-rays produced by the 19F(p,αγ)16O reaction are of particular interest; in fact, they have energy sufficient to induce fission in SNM, but insufficient to create significant radioactivity via photonuclear activation, especially in lighter elements. In this study, the feasibility of a pulsed source of characteristic γ-rays based on the interaction of laser-accelerated protons with a fluorine-rich target is assessed. For practical applications, proton energies above 2 MeV, a bunch population of the order of 1014 particles or higher, and a laser repetition rate of the order of 10 Hz are of interest. The development of ultrahigh-power table-top lasers could greatly contribute to the deployment of this kind of interrogation source for a variety of operations.

Longitudinal density monitor for the LHC

The longitudinal density monitor (LDM) is primarily intended for the measurement of the particle population in nominally empty rf buckets. These so-called satellite or ghost bunches can cause problems for machine protection as well as influencing the luminosity calibration of the LHC. The high dynamic range of the system allows measurement of ghost bunches with as little as 0.01% of the main bunch population at the same time as characterization of the main bunches. The LDM is a single-photon counting system using visible synchrotron light. The photon detector is a silicon avalanche photodiode operated in Geiger mode, which allows the longitudinal distribution of the LHC beams to be measured with a resolution of 90 ps. Results from the LDM are presented, including a proposed method for constructing a 3-dimensional beam density map by scanning the LDM sensor in the transverse plane. In addition, we present a scheme to improve the sensitivity of the system by using an optical switching technique.

Time evolution of the luminosity of colliding heavy-ion beams in BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider

We have studied the time evolution of the heavy ion luminosity and bunch intensities in the Relativistic Heavy Ion Collider (RHIC), at BNL, and in the Large Hadron Collider (LHC), at CERN. First, we present measurements from a large number of RHIC stores (from Run 7), colliding 100 GeV/nucleon Au beams without stochastic cooling. These are compared with two different calculation methods. The first is a simulation based on multi-particle tracking taking into account collisions, intrabeam scattering, radiation damping, and synchrotron and betatron motion. In the second, faster, method, a system of ordinary differential equations with terms describing the corresponding effects on emittances and bunch populations is solved numerically. Results of the tracking method agree very well with the RHIC data. With the faster method, significant discrepancies are found since the losses of particles diffusing out of the RF bucket due to intrabeam scattering are not modeled accurately enough. Finally, we use both methods to make predictions of the time evolution of the future Pb beams in the LHC at injection and collision energy. For this machine, the two methods agree well.

Modeling microbunching from shot noise using Vlasov solvers

Unlike macroparticle simulations, which are sensitive to unphysical statistical fluctuations when the number of macroparticles is smaller than the bunch population, direct methods for solving the Vlasov equation are free from sampling noise and are ideally suited for studying microbunching instabilities evolving from shot noise. We review a 2D (longitudinal dynamics) Vlasov solver we have recently developed to study the microbunching instability in the beam delivery systems for X-ray FELs and present an application to FERMI@Elettra. We discuss, in particular, the impact of the spreader design on microbunching.

Vlasov solver for longitudinal dynamics in beam delivery systems for x-ray free electron lasers

Direct numerical methods for solving the Vlasov equation offer some advantages over macroparticle simulations, as they do not suffer from the consequences of the statistical fluctuations inherent in using a number of macroparticles smaller than the bunch population. Unfortunately, these methods are more time consuming and generally considered impractical in a full 6D phase space. However, in a lower-dimension phase space they may become attractive if the beam dynamics is sensitive to the presence of small charge-density fluctuations and a high resolution is needed. In this paper we present a 2D Vlasov solver for studying the longitudinal beam dynamics in single-pass systems of interest for x-ray FELs, where characterization of the microbunching instability stemming from self-field amplified noise is of particular relevance.

A preliminary assessment of the electron-cloud effect for the FNAL main injector upgrade

We present results from a preliminary assessment, via computer simulations, of the electron-cloud (EC) density for the FNAL Main Injector upgrade at injection energy. Assuming a peak value for secondary emission yield δmax = 1.3, we find a threshold value of the bunch population, Nb,th≃ 1.25 ×1011, beyond which the EC density ρe reaches a steady-state level that is ∼104 times larger than for Nb<Nb,th, essentially neutralizing the beam, and leading to a tune shift ∼0.05. Our investigation is limited to a field-free region and to a dipole magnet region, both of which yield similar results for both Nb,th and the steady-state value of ρe. Possible dynamical effects from the EC on the beam, such as emittance growth and instabilities, remain to be investigated separately.

Maps for coupled electron and ion clouds in accelerators

Electron clouds sometimes limit accelerator performance by their appearance when the circulating bunch population exceeds a threshold value. Dynamical models of cloud buildup, and of the phase transition from ``cloud off'' to ``cloud on'', are enhanced when simple coupling between electron and ion clouds is included. Maps are then capable of reproducing the first order phase transitions sometimes seen in practice. They also predict that hysteresis, period doubling, and chaotic phenomena may be observed.

Possible scenarios for the LHC luminosity upgrade

We discuss here of the possible scenarios to upgrade the LHC luminosity beyond nominal value of 10 34 cm −2 s −1 . The first step along this way consist in pushing the accelerator parameters to the ultimate performance: by increasing to 1.7 10 11 the bunch population, a peak luminosity of 2.3×10 34 cm −2 s −1 should be eventually made available. To go beyond, a considerable improvement of the LHC parameters, such as β * , beam intensity, bunch length, number of circulating bunches is required. Finally, the upgrade of the injector complex and of the injection energy is another important ingredient to increase both peak and integrated luminosity up to an order of magnitude above the nominal value.

Muon acceleration in FFAG rings

Muon acceleration from 6 or 10 to 20 GeV in fixed-field alternating gradient (FFAG) rings is considered. The novel physics issues associated with non-scaling FFAG machines, namely the very acceleration process and the crossing of transverse imperfection resonances are addressed. These FFAG machines are essentially strong-focusing rings with a dispersion small enough to keep muons over the full momentum range inside the same magnet aperture. We consider two cases: (i) A Modified FODO Ring with about a metre long straight sections, enough to house normal-conducting RF cavities at about 200 MHz and (ii) A Doublet Ring with a few metres long straight sections, enough for super-conducting RF cavities also at about 200 MHz. Parameters are derived for the lattice and RF system of an electron model. It accelerates electrons from about 10–20 MeV and allows one to study the critical issues of non-scaling FFAGs. For both a full machine and a model, lattice parameters such as magnet type and dimension, spacing, and number of cells are presented. The consequences of misaligned magnets are studied by simulation. Practical RF system design issues, e.g. RF power, and the limit on the bunch population due to beam loading are estimated.

Beam-beam limit in e+e- circular colliders.

Beam-beam effects limit the luminosity of circular colliders. Once the bunch population exceeds a threshold, the luminosity increases at a slower rate. This phenomenon is called the beam-beam limit. Onset of the beam-beam limit has been analyzed with various simulation methods based on the weak-strong and strong-strong models. We have observed that an incoherent phenomenon is mainly concerned in the beam-beam limit. The simulation have shown that equilibrium distributions of the two colliding beams are distorted from Gaussians when the luminosity is limited. The beam-beam limit is estimated to be xi approximately 0.1 for a B factory with damping time of several thousand turns.