Transverse Space Research Articles

Electron beam transverse phase space tomography using nanofabricated wire scanners with submicrometer resolution

Characterization and control of the transverse phase space of high-brightness electron beams is required at free-electron lasers or electron diffraction experiments for emittance measurement and beam optimization as well as at advanced acceleration experiments. Dielectric laser accelerators or plasma accelerators with external injection indeed require beam sizes at the micron level and below. We present a method using nano-fabricated metallic wires oriented at different angles to obtain projections of the transverse phase space by scanning the wires through the beam and detecting the amount of scattered particles. Performing this measurement at several locations along the waist allows assessing the transverse distribution at different phase advances. By applying a novel tomographic algorithm the transverse phase space density can be reconstructed. Measurements at the ACHIP chamber at SwissFEL confirm that the transverse phase space of micrometer-sized electron beams can be reliably characterized using this method.

Single-shot measurement of transverse second moments using the projection method

We introduce a diagnostic for measuring the transverse phase space (TPS) and transverse second moments of a particle beam in a single shot. The diagnostic consists of a slit followed by a simple projection beam line to project the TPS onto an imaging screen. The beam line is composed of a skew quadrupole magnet followed by a normal quadrupole magnet with an imaging screen at the end. The skew quadrupole generates a coupling between the initial $x$ and the final $y$, while the normal quadrupole removes the correlation between the initial $x$ and the initial ${x}^{\ensuremath{'}}$. Thus, the initial $(x,{x}^{\ensuremath{'}})$ is mapped onto the final $(x,y)$. The slit is needed before the projection beam line to remove the initial $(y,{y}^{\ensuremath{'}})$ contribution from the final $(x,y)$ image on the screen. We present simulation studies and a demonstration of the diagnostic with an experiment performed at Argonne Wakefield Accelerator facility. We also discuss the method's limitations.

Self-consistent numerical approach to track particles in free electron laser interaction with electromagnetic field modes

In this paper we present a novel approach to FEL simulations based on the decomposition of the electromagnetic field in a finite number of radiation modes. The evolution of each mode amplitude is simply determined by energy conservation. The code is developed as an expansion of the General Particle Tracer framework and adds important capabilities to the suite of well-established numerical simulations already available to the FEL community. The approach is not based on the period average approximation and can handle long-wavelength waveguide FELs as it is possible to include the dispersion effects of the boundaries. Futhermore, it correctly simulates lower charge systems where both transverse and longitudinal space charge forces still play a significant role in the dynamics. For free-space FEL interactions, a source dependent expansion approximation can be used to limit the number of transverse modes required to model the field profile and speed up the calculation of the system evolution. Three examples are studied in detail including a single pass FEL amplifier, the high efficiency TESSA266 scenario and a THz waveguide FEL operating in the zero-slippage regime.

Kundt spacetimes in the Einstein-Gauss-Bonnet theory

We systematically investigate the complete class of vacuum solutions in the Einstein-Gauss-Bonnet gravity theory which belong to the Kundt family of non-expanding, shear-free and twist-free geometries (without gyratonic matter terms) in any dimension. The field equations are explicitly derived and simplified, and their solutions classified into three distinct subfamilies. Algebraic structures of the Weyl and Ricci curvature tensors are determined. The corresponding curvature scalars directly enter the invariant form of equation of geodesic deviation, enabling us to understand the specific local physical properties of the gravitational field constrained by the EGB theory. We also present and analyze several interesting explicit classes of such vacuum solutions, namely the Ricci type III spacetimes, all geometries with constant-curvature transverse space, and the whole pp-wave class admitting a covariantly constant null vector field. These exact Kundt EGB gravitational waves exhibit new features which are not possible in Einstein's general relativity.

Efficient Fourier transforms for transverse momentum dependent distributions

Hadron production at low transverse momenta in semi-inclusive deep inelastic scattering can be described by transverse momentum dependent (TMD) factorization. This formalism has also been widely used to study the Drell–Yan process and back-to-back hadron pair production in e+e− collisions. These processes are the main ones for extractions of TMD parton distribution functions and TMD fragmentation functions, which encode important information about nucleon structure and hadronization. One of the most widely used TMD factorization formalism in phenomenology formulates TMD observables in coordinate b⊥-space, the conjugate space of the transverse momentum. The Fourier transform from b⊥-space back into transverse momentum space is sufficiently complicated due to oscillatory integrands that it requires a careful and computationally intensive numerical treatment in order to avoid potentially large numerical errors. Within the TMD formalism, the azimuthal angular dependence is analytically integrated and the two-dimensional b⊥ integration reduces to a one-dimensional integration over the magnitude b⊥. In this paper we develop a fast numerical Hankel transform algorithm for such a b⊥-integration that improves the numerical accuracy of TMD calculations in all standard processes. Libraries for this algorithm are implemented in Python 2.7 and 3, C++, as well as FORTRAN77. All packages are made available open source. Program summaryProgram Title: Fast Bessel Transform (FBT)CPC Library link to program files:http://dx.doi.org/10.17632/65zkb53z8d.1Developer’s repository link:http://github.com/UCLA-TMD/OgataLicensing provisions: MITProgramming language: Python 2/3, C++, FORTRAN77Nature of problem: In order to perform extractions of transverse momentum distribution functions, numerical Hankel transforms must be performed from b⊥-space to momentum space. However, these numerical Hankel transforms are a huge bottleneck in these extractions, making these extractions extremely computationally intensive.Solution method: We develop a numerical Hankel transform algorithm by optimizing Ogata quadrature formula. This algorithm improves the performance of these numerical Hankel transforms by nearly an order of magnitude.

An ultra-compact x-ray free-electron laser

In the field of beam physics, two frontier topics have taken center stage due to their potential to enable new approaches to discovery in a wide swath of science. These areas are: advanced, high gradient acceleration techniques, and x-ray free electron lasers (XFELs). Further, there is intense interest in the marriage of these two fields, with the goal of producing a very compact XFEL. In this context, recent advances in high gradient radio-frequency cryogenic copper structure research have opened the door to the use of surface electric fields between 250 and 500 MV m−1. Such an approach is foreseen to enable a new generation of photoinjectors with six-dimensional beam brightness beyond the current state-of-the-art by well over an order of magnitude. This advance is an essential ingredient enabling an ultra-compact XFEL (UC-XFEL). In addition, one may accelerate these bright beams to GeV scale in less than 10 m. Such an injector, when combined with inverse free electron laser-based bunching techniques can produce multi-kA beams with unprecedented beam quality, quantified by 50 nm-rad normalized emittances. The emittance, we note, is the effective area in transverse phase space (x, p x /m e c) or (y, p y /m e c) occupied by the beam distribution, and it is relevant to achievable beam sizes as well as setting a limit on FEL wavelength. These beams, when injected into innovative, short-period (1–10 mm) undulators uniquely enable UC-XFELs having footprints consistent with university-scale laboratories. We describe the architecture and predicted performance of this novel light source, which promises photon production per pulse of a few percent of existing XFEL sources. We review implementation issues including collective beam effects, compact x-ray optics systems, and other relevant technical challenges. To illustrate the potential of such a light source to fundamentally change the current paradigm of XFELs with their limited access, we examine possible applications in biology, chemistry, materials, atomic physics, industry, and medicine—including the imaging of virus particles—which may profit from this new model of performing XFEL science.

PERFORMANCE ANALYSIS OF HIGH STEEL TUBE LATTICE SUPPORT SYSTEM IN TYPHOON AREA

Research on safety of high steel tube lattice support systems in typhoon areas is still in the preliminary stage. The purpose of this paper is to study the overall buckling and overturning stability of the high steel tube lattice support systems in typhoon area. By constructing the spatial finite element model of the high steel tube lattice support system via MIDAS Civil, the optimal design of the steel tube lattice support system is carried out through the analysis of the main influencing parameters. The stability of steel pipe lattice support system is calculated theoretically, and the optimal design of steel pipe lattice support system is studied by finite element numerical method in Typhoon area. The calculation results show that Critical buckling load coefficient increases with the increase in diameter of the steel tube when the δ/d ratio of steel pipe structure is fixed. The critical load factor of the six-limb support system is slightly larger than that of the four-limb support system. When the transverse space of the support system is from 5 m to 7 m, stability increases rapidly. The best stability of the support system is obtained when the transverse space is approximately 7 m. The diagonal brace can significantly improve the stability of the steel tube lattice falsework.

Measurements of a 2.1 MeV H- beam with an Allison scanner.

Transverse 2D phase space distributions of a 2.1 MeV, 5 mA H- beam are measured at the Proton Improvement Plan II Injector Test accelerator at Fermilab with an Allison scanner. This paper describes the design, calibration, and performance of the scanner along with the main results from beam measurements. Analyses of the recorded phase portraits are performed primarily in action-phase coordinates. The stability of the action under linear optics makes it easier to compare measurements taken under different beamline conditions. The amplitude of a single measured point ("pixel") is proportional to the phase density in the corresponding portion of the beam. When the Twiss parameters are calculated using only the high-phase density part of the beam, the pixel amplitude in the beam core is found to be decreasing approximately exponentially with action and to be phase-independent. Outside of the core, the amplitudes decrease with action at a slower rate than in the core. This "tail" comprises 10%-30% of the beam, with 0.1% of the total measured intensity extending beyond action 10-20 times larger than the rms emittance. The transition from the core to the tail is accompanied by the appearance of two "branches" that are separated in phase and extend beyond the core. A set of selected measurements shows that there is no measurable emittance dilution along the beamline; the beam parameters are practically constant over a 0.5 ms pulse; and scraping in various parts of the beamline is an effective way to decrease the transverse tails by removing the branches.

Bifurcation analysis of nonlinear Hamiltonian dynamics in the Fermilab Integrable Optics Test Accelerator

The Integrable Optics Test Accelerator (IOTA) is a novel storage ring at Fermi National Accelerator Laboratory designed (in part) to investigate the dynamics of beams in the presence of highly nonlinear transverse focusing fields that generate integrable single-particle motion with a large spread in the intrinsic betatron tunes. We describe how contemporary geometrical methods from the theory of integrable Hamiltonian systems may be used to locate all critical separatrixlike structures in the 4D transverse phase space, and to construct a complete analysis of the dynamical bifurcations of the system. Application of these techniques results in a global picture of the nominal on-energy transverse dynamics, revealing a rich diversity of accessible dynamical behavior. Similar techniques may be applied to future facilities that exploit the concept of nonlinear integrable optics.

Transverse phase space characterization in an accelerator test facility

We compare three techniques for characterising the transverse phase space distribution of the beam in CLARA FE (the Compact Linear Accelerator for Research and Applications Front End, at Daresbury Laboratory, UK): emittance and optics measurements using screens at three separate beamline locations; quadrupole scans; and phase space tomography. We find that where the beam distribution has significant structure (as in the case of CLARA FE at the time the measurements presented here were made) tomography analysis is the most reliable way to obtain a meaningful characterisation of the transverse beam properties. We present the first experimental results from four-dimensional phase space tomography: our results show that this technique can provide an insight into beam properties that are of importance for optimising machine performance.

From little string free energies towards modular graph functions

We study the structure of the non-perturbative free energy of a one-parameter class of little string theories (LSTs) of A-type in the so-called unrefined limit. These theories are engineered by N M5-branes probing a transverse flat space. By analysing a number of examples, we observe a pattern which suggests to write the free energy in a fashion that resembles a decomposition into higher-point functions which can be presented in a graphical way reminiscent of sums of (effective) Feynman diagrams: to leading order in the instanton parameter of the LST, the N external states are given either by the fundamental building blocks of the theory with N = 1, or the function that governs the counting of BPS states of a single M5-brane coupling to one M2-brane on either side. These states are connected via an effective coupling function which encodes the details of the gauge algebra of the LST and which in its simplest (non-trivial) form is captured by the scalar Greens function on the torus. More complicated incarnations of this function show certain similarities with so-called modular graph functions, which have appeared in the study of Feynman amplitudes in string- and field theory. Finally, similar structures continue to exist at higher instanton orders, which, however, also contain contributions that can be understood as the action of (Hecke) operators on the leading instanton result.

Symmetries in A-type little string theories. Part II. Eisenstein series and generating functions of multiple divisor sums

We continue our study of symmetries of a class of little string theories of A-type, which are engineered by N parallel M5-branes probing a flat transverse space. Extending the analysis of the companion paper [1], we discuss the part of the free energy that is sensitive to the details of the \U0001d51eN−1 gauge structure, by computing explicit series expansions for the cases N = 2, 3, 4. Based on these examples, we find a class of functions that we conjecture to resum whole sectors in the instanton expansion of the free energy and which combine in a natural manner its modular properties as well as the gauge symmetry. These functions have previously been introduced in the literature as the generating functions of multi-divisor sums and in the case N = 2 can also be cast into the form of a generalised Eisenstein series. We use these resummed contributions to the free energy to perform a number of non-trivial consistency checks for our results.

CT evaluation of elbow congruity in dogs: radial incisure versus apical medial coronoid process fragmentation.

To compare elbow congruity in two cohorts of Labrador retrievers affected with either radial incisure or apex fragmentation of the medial coronoid process. Dogs were included if they had elbow lameness and a CT diagnosis of a fissure or fragmentation of the medial coronoid process occurring either along the radial incisure or at the coronoid apex. Radioulnar joint space was measured incrementally from the lateral to the medial coronoid process on transverse slice images. Axial radioulnar congruency was also measured at the apex and mid-coronoid in the dorsal plane and at the base of the coronoid in the sagittal plane. We studied 99 elbows (in 66 dogs) of which 56 had a fissure or fragmentation along the radial incisure and 43 had an apical fragment. No difference was found between the two groups at the different measuring points - with the exception of a transverse plane radioulnar joint space measurement in the radial incisure group that was smaller adjacent to the lateral coronoid process. Abnormal ulnar morphology in the radial incisure group could result in a fulcrum effect within the radioulnar joint, overloading the radial incisure and predisposing to osteochondral damage at this site.

Extended transfer matrix through aligned solenoidal fields using the traditional formalism

The traditional transfer matrix used in particle accelerators has been modified to easily take into account a non-zero angular canonical momentum, without the hard edge approximation of the field. To this end, we reformulate the transfer matrix based on an existing method, but by using both the explicit real transformation matrix in the Larmor frame of the 4D transverse phase space, and the real 4D transfer matrix of a solenoidal field in this frame and in the laboratory frame. This reformulation allows to clearly identify differences with the traditional matrix when performing analytic inter-comparisons. The implementation is also easier to perform. A comparison with computer simulation further illustrates its usefulness.

Mitigation of microbunching instability in x-ray free electron laser linacs

Author(s): Li, B; Qiang, J | Abstract: The microbunching instability seeded by small initial density modulation and driven by collective effects can cause significant electron beam quality degradation in next generation x-ray free electron lasers. A method exploiting longitudinal mixing derived from the natural transverse spread of the electron beam through a dispersive bending magnet was proposed to suppress this instability several years ago [Phys. Rev. Lett. 111, 054801 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.054801]. Instead of using bending magnets to introduce the transverse-to-longitudinal coupling, which will lead to an inconvenient deflection of the downstream beam line, in this paper, we propose a scheme to mitigate the microbunching instability by inserting a quadrupole magnet inside a bunch compressor of the accelerator. This results in transverse-to-longitudinal phase space mixing and large slice energy spread that can efficiently mitigate the growth of the microbunching instability through the major accelerator section. Finally, at the exit of the accelerator, a dogleg section is used to restore the emittance and slice energy spread before entering the undulator radiation section. Multiparticle simulations show that the transverse space charge, structure wakefield, and the coherent synchrotron radiation effects will have a relatively small impact on this scheme.

Development of a Pepper Pot probe to measure the Four-dimensional emittance of low energy beam of electron cyclotron resonance ion source at IMP

The ion beams extracted from an Electron Cyclotron Resonance (ECR) ion source always exist strong transverse coupling effect that is caused by the field of the axis mirror magnets and the extraction solenoid. In order to obtain the four-dimensional (4D) characteristic matrix with coupling elements, a Pepper Pot probe was developed and used to obtain the full 4D transverse phase space distribution of the low energy beam extracted from the ECR ion source at IMP. This paper describes the detailed design and image processing procedure of Pepper Pot probe, especially the analysis results verification compared to another type emittance meter. The first 4D transverse phase space distribution measurement data of oxygen beams from the LECR4 experimental platform are presented and discussed.

Searching for the Critical Point of Strongly Interacting Matter in Nucleus–Nucleus Collisions at CERN SPS

The search for experimental signatures of the critical point (CP) of strongly interacting matter is one of the main objectives of the NA61/SHINE experiment at CERN SPS. In the course of the experiment, a beam momentum and system size scan is performed. Local proton density fluctuations in transverse momentum space represent an order parameter of the chiral phase transition and are expected to scale according to a universal power-law in the vicinity of the CP; we probe their behavior through an intermittency analysis of the proton second scaled factorial moments (SSFMs) in transverse momentum space. Previous such analyses revealed power-law behavior in NA49 Si+Si collisions at 158$A$ GeV/$c$, with no intermittency observed in lighter or heavier NA49 & NA61/SHINE systems at the same energy. We now extend the analysis to NA61/SHINE Ar+Sc collisions at 150$A$ GeV/$c$, similar in size and baryochemical potential to NA49 Si+Si. We employ statistical techniques to subtract non-critical background and estimate statistical and systematic uncertainties. Subsequently, we use Monte Carlo simulations to assess the statistical significance of the observed intermittency effect.

Emittance study of the high intensity highly charged heavy ion beams extracted from electron cyclotron resonance ion source

According to the requirements of ion beams extracted from an electron cyclotron resonance ion source transverse phase space coupling research and the afterglow beam property effective measurement, a pepper pot type meter called PEMiL (Pepper Pot Emittance Meter in Lanzhou) has been designed, fabricated, and commissioned to obtain the emittance of high intensity highly charged heavy ion beams. The direct current beam emittance measurement results verify the coupling property caused by the semisolenoid field. This paper also describes the scheme of multiple exposure accumulation which was applied to measure the afterglow beam property, and the transverse phase space distribution of the oxygen afterglow beam which was measured for the first time is presented.

Numerical simulations of electron cloud build-up in circular accelerators in the presence of multimode distribution beams

Electron cloud effects have become one of the main performance limitations for circular particle accelerators operating with positively charged beams. Among other machines worldwide, the CERN Super Proton Synchrotron (SPS) as well as the Large Hadron Collider (LHC) are affected by these phenomena. Intense efforts have been devoted in recent years to improving the understanding of electron cloud (EC) generation with the aim of finding efficient mitigation measures. In a different domain of accelerator physics, non-linear resonances in the transverse phase space have been proposed as novel means of manipulating charged particle beams. While the original goal was to perform multi-turn extraction from the CERN Proton Synchrotron (PS), several other applications have been proposed. In this paper, the study of EC generation in the presence of charged particle beams with multimode horizontal distribution is presented. Such a peculiar distribution can be generated by different approaches, one of which consists in splitting the initial Gaussian beam distribution by crossing a non-linear resonance. In this paper, the outcome of detailed numerical simulations is presented and discussed.

A 0.3 THz Multi-Beam Extended Interaction Klystron Based on TM10,1,0 Mode Coaxial Coupled Cavity

A new conceive of high-order mode multi-beam Extended interaction Klystron (EIK) at the terahertz (THz) band is proposed. The interaction circuit based on the coaxial coupled cavity at ${\mathrm {TM}}_{\mathrm {10,1,0}} - 2\pi $ mode is designed and analyzed. Benefiting from the larger transverse space of the coaxial coupled cavity operating at high-order mode, multiple electron beams are formatted to reduce the current density of each electron beam. The crucial parameters associated with the interaction are determined by theoretical calculation and optimized by three-dimensional (3D) Particle-in-Cell (PIC) simulation. The results of theoretical analysis and PIC simulation demonstrate that the EIK operates at ${\mathrm {TM}}_{\mathrm {10,1,0}} - 2\pi $ mode without mode competition and self-oscillation. Driven by ten individual electron beams with the voltage of 20 kV, the current of 0.1 A and the current density of 318 A/cm2, the maximum gain of 48 dB is achieved at the center frequency of 300 GHz with a 3-dB gain bandwidth of 200 MHz. And the corresponding output power and efficiency are 312.5 W and 1.56 %. The results indicate that the proposed EIK is a practical approach to generate high power terahertz waves using the thermal beam with a low compression ratio.