Transverse Dynamics Research Articles

Nucleon Energy Correlators.

We introduce the concept of the nucleon energy correlators, a set of novel objects that encode the microscopic details of a nucleon, such as the parton angular distribution in a nucleon, the collinear splitting to all orders, as well as the internal transverse dynamics of the nucleon. The nucleon energy correlators complement the conventional nucleon or nucleus tomography, but without introducing the nonperturbative fragmentation functions or the jet clustering algorithms. We demonstrate how the nucleon energy correlators can be measured in the lepton-nucleon deep inelastic scattering. The predicted distributions display a fascinating phase transition between the perturbative and nonperturbative regime. In the perturbative phase, a polar angle version of the Bjorken scaling behavior is predicted. We discuss its possible applications and expect it to aggrandize the physics content at the electron ion colliders with a far-forward detector.

NMR Relaxation by Redfield equation in a spin system [formula omitted

The Redfield master equation was solved analytically for a nuclear system with spin I=7/2. Using the irreducible tensor operator basis, the solutions of each density matrix element were computed. The experimental setup consisted of the 133Cs nuclei of the cesium-pentadecafluorooctanoate molecule in a lyotropic liquid crystal sample in the nematic phase at room temperature. Experimental longitudinal and transverse magnetization dynamics of the 133Cs nuclei were monitored, and the theoretical approach was used to generate valuable mathematical expressions with the highest accuracy through numerical procedures. This methodology can be extended to other nuclei with minimal difficulties.

Onset of collective excitations in the transverse dynamics of simple fluids.

A thorough analysis of the transverse current autocorrelation function obtained by molecular dynamics simulations of a dense Lennard-Jones fluid reveals that even such a simple system is characterized by a varied dynamical behavior with changing length scale. By using the exponential expansion theory, we provide a full account of the time correlation at wavevectors Q between the upper boundary of the hydrodynamic region and Q_{p}/2, with Q_{p} being the position of the main peak of the static structure factor. In the Q range studied, we identify and accurately locate the wavevector at which shear wave propagation starts to take place, and show clearly how this phenomenon may be represented by a damped harmonic oscillator changing, in a continuous way, from an overdamped to an underdamped condition. The decomposition into exponential modes allows one to convincingly establish not only the crossover related to the onset of transverse waves but, surprisingly, also the existence of a second pair of modes equivalent to another oscillator that undergoes, at higher Q values, a similarly smooth over to underdamped transition.

Reference values and functional descriptions of transverse plane spinal dynamics during gait based on surface topography

Spinal dynamics during gait have been of interest in research for many decades. Based on respective previous investigations, the pelvis is generally expected to be maximally forward rotated on the side of the reference leg at the beginning of each gait cycle and to reach its maximum counterrotation approximately at the end of the reference leg’s stance phase. The pelvic–upper-thoracic-spine coordination converges towards an anti-phase movement pattern in high velocities during ambulation. The vertebral bodies around the seventh thoracic vertebra are considered to be an area of transition during human ambulation where no or at least little rotary motion can be observed. The respective cranial and caudal vertebrae meanwhile are expected to rotate conversely around this spinal point of intersection. However, these previous assumptions are based on scarce existing research, whereby only isolated vertebrae have been analyzed contemporaneously. Due to huge methodological differences in data capturing approaches, the results are additionally hardly comparable to each other and involved measurement procedures are often not implementable in clinical routines. Furthermore, none of the above-mentioned methods provided reference data for spinal motion during gait based on an appropriate number of healthy participants. Hence, the aim of this study was to present such reference data for spinal rotary motion of every vertebral body from C7 down to L4 and the pelvis derived from surface topographic back shape analyses in a cohort of 201 healthy participants walking on a treadmill at a given walking speed of 5 km/h. Additionally, the spine‘s functional movement behavior during gait should be described in the transverse plane based on data derived from this noninvasive, clinically suitable measurement approach and, in conclusion, the results shall be compared against those of previous research findings derived from other measurement techniques. Contrary to the previous functional understanding, the area of the mid-thoracic spine was found to demonstrate the largest amplitude of rotary motion of all investigated vertebrae and revealed an approximately counterrotated movement behavior compared to the rotary motion of the pelvis. In both directions, spinal rotation during gait seemed to be initiated by the pelvis. The overlying vertebrae followed in succession in the sense of an ongoing movement. Therefore, the point of intersection was not statically located in a specific anatomical section of the spine. Instead, it was found to be dynamic, ascending from one vertebra to the next from caudal to cranial in dependence of the pelvis’s rotation initiation.

Fourier-Limited Attosecond Pulse from High Harmonic Generation Assisted by Ultrafast Magnetic Fields

One of the main constraints for reducing the temporal duration of attosecond pulses is the attochirp inherent to the process of high-order harmonic generation (HHG). Though the attochirp can be compensated in the extreme-ultraviolet using dispersive materials, this is unfeasible toward x-rays, where the shortest attosecond or even sub-attosecond pulses could be obtained. We theoretically demonstrate that HHG driven by a circularly polarized infrared pulse while assisted by an strong oscillating ultrafast intense magnetic field enables the generation of few-cycle Fourier-limited few attosecond pulses. In such a novel scenario, the magnetic field transversally confines the ionized electron during the HHG process, analogously to a nanowire trapping. Once the electron is ionized, the transverse electron dynamics is excited by the magnetic field, acting as a high-energy reservoir to be released in the form of phase-locked spectrally wide high-frequency harmonic radiation during the electron recollision with the parent ion. In addition, the transverse breathing dynamics of the electron wavepacket, introduced by the magnetic trapping, strongly modulates the recollision efficiency of the electronic trajectories, thus the attosecond pulse emissions. The aftermath is the possibility of producing high-frequency (hundreds of eV) attosecond isolated few-cycle pulses, almost Fourier limited. The isolated intense magnetic fields considered in our simulations, of tens of kT, can be produced in finite spatial volumes considering structured beams or stationary configurations of counter-propagating state-of-the-art multi-terawatt/petawatt lasers.

Ultra-high phase-locked harmonic generation from magnetic transversal confinement of electrons

The technological refinements on high-power laser systems of Petawatt class unveil scenarios for light-matter interaction beyond the laser-plasma perspective. In this contribution we explore the possibility of assisting high-harmonic generation (HHG) with the strong magnetic field associated with one of those intense sources. Recently, there has been an interest in developing schemes to employ intense laser beams to define spatial volumes in which strong magnetic fields are found isolated from the electric field. In this conditions, the magnetic field can be used to assist the harmonic generation from atoms from standard drivers. We demonstrate that, using the proper interaction geometry, the magnetic field confines the transversal dynamics of the con-tinuum electrons allowing, on one side, to enhance the efficiency of the electron rescattering that produces the harmonic radiation and, on the other side, to excite the electron transverse dynamics and to convert this energy into phase-locked harmonic photons of few hundreds of eV.

Simulating quasi-integrable optics with space charge in the IBEX Paul trap

The intensity frontier has called for new initiatives in hadron accelerator design in order to accommodate space charge dominated beams. Octupoles are often used to damp beam instabilities caused by space charge, however the insertion of octupole magnets leads to a nonintegrable lattice which reduces the area of stable particle motion. One proposed solution is Quasi-Integrable optics (QIO), where the octupoles are inserted between sections of a specific lattice insertion called a T-insert. An octupole with a strength that scales as 1/β 3(s) is applied in the drift region, where the horizontal and vertical beta functions are equal, to create a time independent octupole field. This leads to a lattice with a time-independent Hamiltonian which is robust to small perturbations. IBEX is a Paul trap which allows the transverse dynamics of a collection of trapped particles to be studied, mimicking the propagation through multiple quadrupole lattice periods, whilst remaining stationary in the laboratory frame. In order to test QIO at the IBEX experiment, it has recently undergone an upgrade to allow for the creation of octupole fields. We present our design of the IBEX experiment upgrade along with simulation results of our proposed experiment to test QIO with space charge.

A Methodology for Extracting the Physical Parameters of Soil-Foundation-Pier Systems from Dynamic Tests

The paper presents a methodology for the identification of the physical parameters of a model describing the transverse dynamics of soil-foundation-pier systems founded on piles, starting from results of dynamic experimental tests. In detail, the procedure exploits the identified state-space models of the systems obtained from results of dynamic tests through consolidated identification techniques available in the literature. The procedure permits to compute the physical parameters of the real system (e.g. masses, pier stiffness matrix, and soil-foundation impedance) by directly comparing the components of the analytical and identified stiffness, mass and damping matrices; the latter extracted from the identified state-space models. The proposed approach allows the direct definition of the numerical model that best fits the experimental data, and permits the identification of the soil-foundation compliance. Firstly, the dynamics of the analytical model, which includes the frequency-dependent behaviour of the soil-foundation system through the introduction of a lumped parameter model, is formulated adopting the continuous-time first-order state-space form. Then, an identification strategy of the physical parameters of a soil-foundation-pier system is proposed, starting from the discrete-time state-space model identified from dynamic tests. The procedure allows the identification of the soil-foundation system compliance through experimental tests.

Generalized quasi-, Ioffe-time-, and pseudodistributions of the pion in the Nambu–Jona-Lasinio model

We analyze the generalized quasi, Ioffe-time, and pseudodistributions of the valence quarks in the pion at the quark model scale. We use the framework of the Nambu-Jona-Lasinio model and investigate the basic question of how fast the pion has to move to effectively reach the infinite momentum limit, where the approach can provide the information on the generalized parton distribution functions. We consider both the vector distributions and the transversity distributions, related to the spin densities. With the developed analytic expressions, we conclude that to effectively approach the infinite momentum limit in the Ioffe-time distributions for values of the Ioffe-time accessible in lattice QCD, one roughly needs the pion momenta of the order of $\ensuremath{\sim}3\text{ }\text{ }\mathrm{GeV}$. We explore polynomiality of the quasidistributions and study the generalized quasi form factors. The issue of separability of the transverse and longitudinal dynamics in the model is studied with the help of the generalized Ioffe-time distributions, with the conclusion that the breaking is not substantial, unless the momentum transfer $t$ is large. We also provide an estimate of the range of the Ioffe-time values needed to obtain the generalized parton distributions with a reasonable accuracy. Our model results, which are analytic or semianalytic, provide a valuable insight into the theoretical formalism and illustrate the intricate features of the investigated distributions.

Symplectic Foliation Structures of Non-Equilibrium Thermodynamics as Dissipation Model: Application to Metriplectic Nonlinear Lindblad Quantum Master Equation.

The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action. A novel symplectic thermodynamics and information geometry known as "Lie group thermodynamics" then explains foliation structures of thermodynamics. We then infer a geometric structure for heat equation from this archetypal model, and we have discovered a pure geometric structure of entropy, which characterizes entropy in coadjoint representation as an invariant Casimir function. The coadjoint orbits form the level sets on the entropy. By using the KKS 2-form in the affine case via Souriau's cocycle, the method also enables the Fisher metric from information geometry for Lie groups. The fact that transverse dynamics to these symplectic leaves is dissipative, whilst dynamics along these symplectic leaves characterize non-dissipative phenomenon, can be used to interpret this Lie group thermodynamics within the context of an open system out of thermodynamics equilibrium. In the following section, we will discuss the dissipative symplectic model of heat and information through the Poisson transverse structure to the symplectic leaf of coadjoint orbits, which is based on the metriplectic bracket, which guarantees conservation of energy and non-decrease of entropy. Baptiste Coquinot recently developed a new foundation theory for dissipative brackets by taking a broad perspective from non-equilibrium thermodynamics. He did this by first considering more natural variables for building the bracket used in metriplectic flow and then by presenting a methodical approach to the development of the theory. By deriving a generic dissipative bracket from fundamental thermodynamic first principles, Baptiste Coquinot demonstrates that brackets for the dissipative part are entirely natural, just as Poisson brackets for the non-dissipative part are canonical for Hamiltonian dynamics. We shall investigate how the theory of dissipative brackets introduced by Paul Dirac for limited Hamiltonian systems relates to transverse structure. We shall investigate an alternative method to the metriplectic method based on Michel Saint Germain's PhD research on the transverse Poisson structure. We will examine an alternative method to the metriplectic method based on the transverse Poisson structure, which Michel Saint-Germain studied for his PhD and was motivated by the key works of Fokko du Cloux. In continuation of Saint-Germain's works, Hervé Sabourin highlights the, for transverse Poisson structures, polynomial nature to nilpotent adjoint orbits and demonstrated that the Casimir functions of the transverse Poisson structure that result from restriction to the Lie-Poisson structure transverse slice are Casimir functions independent of the transverse Poisson structure. He also demonstrated that, on the transverse slice, two polynomial Poisson structures to the symplectic leaf appear that have Casimir functions. The dissipative equation introduced by Lindblad, from the Hamiltonian Liouville equation operating on the quantum density matrix, will be applied to illustrate these previous models. For the Lindblad operator, the dissipative component has been described as the relative entropy gradient and the maximum entropy principle by Öttinger. It has been observed then that the Lindblad equation is a linear approximation of the metriplectic equation.

A one-time sampling method for the real-time measurement of bunch-by-bunch three-dimensional positions in storage rings

Bunch-by-bunch (BbB) technique, which allows accelerator physicists to monitor beam information on finer timescales, is an efficient tool for studying longitudinal and transverse beam dynamics. However, the real-time measurement in BbB technique can only monitor one beam parameter, thus focusing only on the longitudinal phase or transverse positions of bunches. Therefore, to solve this issue, we put forward a one-time sampling method (OSM) to evaluate the longitudinal phase and transverse positions of bunches simultaneously, taking as one way of the real-time measurement for BbB three-dimensional (3D) positions. And we carried out related experiments in Hefei Light Source II and Shanghai Synchrotron Radiation Facility. As a result, experiments show that OSM obtains 12 μm of x-direction resolution, 10 μm of y-direction resolution, 0.57 ps of z-direction resolution at Hefei Light Source II, and 10 μm of x-direction resolution, 10 μm of y-direction resolution, 0.35 ps of z-direction resolution at Shanghai Synchrotron Radiation Facility. All these experimental results reveal that OSM is feasible to measure the BbB 3D positions.

Hybrid macroparticle algorithm for modeling space charge

A space charge algorithm is constructed that is a hybrid between envelope and multiparticle models. The transverse dynamics is simplified by tracking the transverse envelope of each macroparticle. The equations of motion are derived from the Hamiltonian-fluid formulation of the Vlasov Poisson system. A novel electrostatic self-field solver is derived that solves directly for the self-consistent on-axis potential and linear defocusing force, including longitudinal and beam pipe boundary conditions. The implementation of the algorithm, hyper3d, is presented. It is tested against the particle-in-cell code warp, using various configurations of a periodic focusing structure with rf cavities. The required number of macroparticles is reduced substantially compared to standard particle-tracking codes. This model is well adapted to cases where the transverse dynamics is linear and where the details of the longitudinal dynamics are the principal point of interest; an example is where a dc beam is converted to a bunched beam.

Experimental study of transverse effects in planar dielectric wakefield accelerating structures with elliptical beams

The main obstacle to the practical implementation of the dielectric wakefield acceleration (DWA) concept is the development of the beam breakup instability due to transverse dipole wakefields generated when the beam propagates off axis in the accelerating structure. One of the methods to suppress this instability is to elliptically shape the beam and accelerate it in a planar structure. Here, we report a detailed experimental investigation of the transverse dynamics of elliptical beams in planar dielectric structure with parameters mimicking future DWA modules. Both dipole and quadrupole wakefields' effects on beam stability and projected emittance were studied. This study has highlighted the importance of counteracting quadrupole wakefields in future DWA implementations.

Two local slip modes at the liquid–liquid interface over liquid-infused surfaces

A liquid–liquid interface (LLI) at liquid-infused surfaces (LISs) plays a significant role in promoting slip flow and reducing frictional drag. By employing the transverse many-body dissipative particle dynamics simulations, the behavior of local and effective slip at a flat LLI for shear flows over periodically grooved LISs has been studied. With increasing viscosity ratio between the working fluid and lubricant fluid, two local slip modes are identified. For a small viscosity ratio, the local slip length remains finite along the LLI, while a hybrid local slip boundary condition holds along the LLI for large viscosity ratios, i.e., the local slip length is finite near the groove edge and unbounded in the central region of the LLI. The vortical flow inside the groove can be enhanced by increasing viscosity ratio due to the change in the local slip mode from the finite state to the hybrid one. Moreover, the results suggest two scenarios for the variation of the effective slippage. For LISs with a large LLI fraction, the effective slip length increases significantly with increasing viscosity ratio, while for a small LLI fraction, the effective slippage is rather insensitive to the viscosity ratio. The underlying mechanism for the relationship between the effective slip length and the viscosity ratio for different LLI fractions is revealed based on the two slip modes. These results elucidate the effect of LLI on slip boundary conditions and might serve as a guide for the optimal design of LISs with enhanced slip properties.

Longitudinal dynamics in light-front holographic QCD and hadron spectroscopy

We demonstrate that the ’t Hooft equation and the light-front holographic Schrodinger equation are complementary to each other in governing ¨ the longitudinal and the transverse dynamics of color confinement in mesons (quark-antiquark) and baryons (quark-diquark). Together, they describe remarkably well the spectroscopic data for the light-light, heavy-light and heavy-heavy hadrons. In all hadrons, the transverse dynamics of confinement is controlled by the universal emerging hadronic scale of the light-front holography, κ ∼ 0.5 GeV, which, in heavy-heavy hadrons, coincides with the ’t Hooft coupling that governs the longitudinal confinement. This reflects the restoration of the rotational symmetry in the non-relativistic limit.

Creating exact multipolar fields with azimuthally modulated rf cavities

Radio-frequency cavities used in modern particle accelerators operate in ${\mathrm{TM}}_{m10}$-like modes composed of a single, dominant multipole of order $m$; $m=0$ modes are used for the longitudinal acceleration of a particle beam and $m\ensuremath{\ne}0$ modes for controlling transverse beam dynamics. The practical design of the latter, however, can be complex and require extensive analysis through the iteration of both approximate mathematical models and computationally expensive simulations to optimize the performance of the structure. In this paper we present a new, systematic method for designing azimuthally modulated rf cavities that support modes composed of any number and magnitude of user-specified transverse multipoles, either with or without a longitudinally accelerating component. Two case studies are presented of rf cavity designs that support modes composed of a longitudinally accelerating field in addition to a single transverse multipole, and designs that support modes composed of two transverse multipoles. We discuss generalizing the discoveries and conclusions from the two case studies to designing cavities that support modes composed of any number of multipoles. The theoretical work is verified with analysis of 3D simulations and experimental measurements are presented of a cavity operating in a 3 GHz mode that simultaneously longitudinally accelerates and transversely focuses a beam.

Rational endomorphisms of codimension one holomorphic foliations

Abstract We study dominant rational maps preserving singular holomorphic codimension one foliations on projective manifolds and that exhibit non-trivial transverse dynamics.

Experimental investigation of transverse quadrupolar beam oscillation in the Hefei Light Source-II storage ring

Research on the transverse beam dynamics issues and collective bunch behaviors in association with the higher-mode oscillation fields are important in analyzing beam properties and improving machine performance of particle accelerators. In this study, a simple effective excitation and detection scheme was developed to analyze the transverse quadrupole-mode beam oscillation in electron storage rings. Transverse quadrupole-mode beam oscillation was induced by the stripline transverse quadrupole kicker, and then, measured using the stripline beam position monitor in the Hefei Light Source-II storage ring. A spectrum analyzer was employed for the real-time detection of the excitation sidebands of the horizontal quadrupole-mode oscillation in both single-bunch and nominal multi-bunch operations. Additionally, the horizontal dipolar and quadrupolar kick factors are obtained as 6.992 × 1014 and −4.458 × 1014 V/mC with accuracy of 7.49% and 2.03%, respectively, for the single-bunch operation. The dipolar and quadrupolar kick factors in the nominal multi-bunch operation are −2.567 × 1013 and −2.344 × 1013 V/mC with accuracy of 3.53% and 4.91%, respectively. The experimental measurements thus validate the practicability and reliability of this scheme. Moreover, it is demonstrated that this excitation and detection method for the transverse quadrupole oscillation is valid for studying the properties of transverse higher-mode wakefields and related beam behaviors in storage ring light sources.

Early time behavior of spatial and momentum anisotropies in a kinetic approach to nuclear collisions

We derive a general formula for the early time dependence of a phase space distribution evolving according to the kinetic Boltzmann equation. Assuming that the early evolution of the system created in high-energy nuclear collisions can be described by kinetic theory, we calculate the scaling behaviors for the onset of various characteristics of the transverse dynamics. In particular, we show that the scaling behavior of the anisotropic flow coefficients v_n at early times does not depend on the details of the collision kernel or the system composition, while at the same time it differs from the prediction of fluid dynamics.

Manipulation of transverse emittances in circular accelerators by crossing nonlinear 2D resonances

Controlling nonlinear effects in the transverse dynamics of charged particle beams in circular accelerators opens new possibilities for controlling some of the beam properties. Beam splitting by crossing a stable 1D nonlinear resonance is part of the routine operation of the CERN Proton Synchrotron. The beam undergoes trapping and transport inside stable islands created in the horizontal plane to allow multi-turn extraction toward the Super Proton Synchrotron, where the beam is used for fixed-target experiments. This process acts only on the horizontal beam emittance, inducing a reduction of its initial value. In this paper, we present a generalization of this approach, in which both transverse planes are affected by the proposed technique. We will discuss in detail how to manipulate the transverse emittances by means of a controlled crossing of a 2D nonlinear resonance. The novel technique will be presented by discussing the theoretical analysis of a Hamiltonian model, as well as simulating the performance of the proposed manipulation using a more realistic nonlinear symplectic map.