Momentum Deviation Research Articles

Analysis of off-momentum nonlinear driving terms for enlarging off-momentum dynamic apertures

Due to scattering, particles in a ring may have large momentum deviations, which will change their dynamics, potentially resulting in particle losses. Optimization of off-momentum nonlinear dynamics is, therefore, important for increasing beam lifetime. When analyzing off-momentum dynamics using the approach of resonance driving terms (RDTs), chromatic RDTs are usually used, which denote the deviations from on-momentum dynamics. In this paper, instead of using chromatic RDTs, we propose using off-momentum RDTs to analyze off-momentum dynamics, which is a more direct way. As in the case of on-momentum dynamics, the nonlinear driving terms for off-momentum particles include off-momentum RDTs and off-momentum amplitude-dependent tune shifts, which are calculated based on off-momentum linear optics. Similar to the analysis of on-momentum dynamics in our previous work [B. Wei , ], we study the fluctuation or variation of off-momentum RDTs along the longitudinal position, which is very effective for analyzing and optimizing off-momentum dynamic apertures (DAs). Similar results are obtained for the off-momentum case: (i) minimizing the element-by-element average of the RDTs is more effective than minimizing one-turn RDTs in enlarging DAs and (ii) minimizing the average of lower-order RDTs helps reduce higher-order RDTs. Published by the American Physical Society 2024

Gravitational orbital Hall effect of vortex light in Lense–Thirring metric

Vortex light, characterized by an intrinsic orbital angular momentum aligned with its propagation direction, is described through vortex electromagnetic waves. Similar to the gravitational spin Hall effect (SHE), vortex light is expected to exhibit intrinsic orbital angular momentum dependent trajectories and deviations from the null geodesic plane when propagating through a gravitational field, a phenomenon termed the gravitational orbital Hall effect (OHE). In this work, we model the vortex light as vortex Laguerre–Gaussian electromagnetic wave packets and analyze its motion by solving covariant Maxwell equations within the Lense–Thirring metric. Our findings reveal that the trajectory of vortex light with an intrinsic orbital angular momentum deviates from the null geodesic in two ways. It deviates both perpendicular to, and within, the null geodesic plane. This behavior contrasts with the gravitational SHE, where spin-polarized light primarily deviates perpendicular to the null geodesic plane. Moreover, the relationship between the deviation and intrinsic orbital angular momentum differs significantly from that between the deviation and spin. These results suggest a unique interaction between intrinsic orbital angular momentum and gravity, distinct from the spin-gravity coupling, indicating that the gravitational OHE of light might not be precisely predicted by merely substituting spin with intrinsic orbital angular momentum in the gravitational SHE of light.

Interaction-enhanced nesting in spin-fermion and Fermi-Hubbard models

The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, QN, connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from QN is given by χ−1∝|Δq|. Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a χ−1∝|Δq|2 dependence yields a robust finite-T scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the (t−t′) Hubbard model and found that at large U/t>5.5 before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by χ−1∝|Δq|2. Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024

Implementing dispersion measurement as part of scanning proton therapy commissioning and quality assurance

Introduction. Dispersion in an accelerator quantifies the deviation of the proton trajectory when there is a momentum deviation. We present for the first time a safe method of measuring dispersion in the clinic, using a scintillator detector and the momentum deviations within a spill. This is an important accelerator quantity as we found that this is the reason behind the large dose fluctuation in our absolute dosimetry measurement. Methods. Dispersions are measured for nine energies in a Hitachi ProBeat system at three locations (isocenter and at two profile monitors) and at two gantry angles (0 and 90 degrees) by first measuring the spot position and momentum drift within a spill. The spot position drift is measured by the XRV-4000 at the isocenter, and by the two profile monitors located at 0.57 and 2.27 m from the isocenter. The momentum drift is calculated from the intra-spill range drift which is measured using the Ranger accessory. The dispersion at isocenter and its gradient are calculated using the weighted least square regression on the measured dispersions at the three locations. A constraint is formulated on the dispersion and its gradient to ensure minimal intra-spill spot position deviation around the isocenter. Results. The measured intra-spill range and spot positional drift at isocenter are less than and respectively. The momentum spread calculated from the range drift are less than 0.08%. The dispersion at the isocenter ranged from to and the zero-crossing happens upstream of isocenter for all energies. 2 of the 9 energies (168.0 and 187.5 MeV) violated the constraint and has an intra-spill spot positional deviation greater than within from the isocenter. Conclusion. This measurement is recommended as part of commissioning and annual quality assurance for accelerator monitoring and to ensure intra-spill spot deviations remain low.

Evidence that uniform momentum zones originate from roughness sublayer structure interactions in fully rough channel turbulence

Fully rough wall-sheared turbulence is composed of an inner and outer layer, the former occupied by sinuous structures sustained by the well-known autonomous inner cycle, the latter occupied by inclined parcels of momentum deviations relative to the average. The outer-layer structures are also known as uniform momentum zones (UMZs), where the presence of successive UMZs manifests instantaneously with a distinct ‘staircase’ pattern in streamwise velocity. Direct numerical simulation (DNS) of fully rough channel turbulence was recently used to interpret UMZs as wakes originating from antecedent bluff-body-like interactions within the inner layer (Anderson & Salesky, J. Fluid Mech., vol. 906, 2020, A8). Wake-scaling arguments agreed precisely with instantaneous results from DNS. Foremost among these results was evidence that the instantaneous wall-normal gradient of streamwise velocity exhibited scaling of ${\sim }x_3^{-1/2}$ , where $x_3$ is wall-normal location; this is in contrast to logarithmic scaling, which requires the wall-normal gradient of streamwise velocity to scale as ${\sim }x_3^{-1}$ . Herein, wake-scaling arguments have been advanced and compared against results from wall-modelled large-eddy simulation (LES). New results from the ‘bottom up’ wake-scaling arguments agree with LES results, such that the shear associated with the instantaneous staircase-like streamwise velocity follows a clear trend. We have leveraged conditional sampling during LES – predicated upon instantaneous low-frequency, high-magnitude surface stress values known to correspond to large-scale inertial-layer coherence – to further assess the predictive value of the wake-scaling arguments. Model results compare favourably.

Energy-varying beam extraction assisted by large momentum deviation and charge exchange

Two energy-varying beam extraction schemes for energy sweeping compact rapid cycling therapy are discussed. One is one-turn (fast) extraction of a ${\mathrm{C}}^{6+}$ bunch from a fast-cycling hadron driver accelerator assisted by an off-momentum bump orbit, in which a combination of a kicker and a septum magnet are fired at a desired timing (or energy). The other is energy sweeping extraction, in which a ${\mathrm{C}}^{5+}$ bunch delivered from the laser ablation ion source is injected and accelerated in the barrier bucket up to the final energy. A fraction of the trapped ${\mathrm{C}}^{5+}$ ions is continuously released from the bucket on the way to the final energy to form a coasting beam over an expected time (or energy) region, and the beam drifts inward in the large flat momentum dispersion region. The drifting ${\mathrm{C}}^{5+}$ beam hits the stripper carbon foil located at the front of the bending magnet and near the inner surface of the vacuum chamber in the large flat dispersion region and is converted to a ${\mathrm{C}}^{6+}$ beam. The combination of the enhanced bending radius and septum magnet allows easy ${\mathrm{C}}^{6+}$ beam extraction by the single septum magnet downstream.

Arclike variable bunch compressors

Electron bunch compressors formed of achromat arcs have a natural advantage over the more commonly used chicane compressors in that linearisation of the longitudinal phase space is of the correct sign to compensate for the curvature imprinted by rf acceleration. Here we extend the utility of arc compressors to enable variation of the longitudinal compaction within a fixed footprint. We also show that this variability can be achieved independently order-by-order in momentum deviation. The technique we employ consists of additional dipoles, leading to the advantageous property that variability can be achieved without incurring significant penalty in terms of chromatic degradation. We show this by comparison to an alternative system where additional quadrupoles are utilised to enable variation of momentum compaction. Each of these alternative approaches are being considered in the context of an upgrade of the MAX IV linac, Sweden, to enable a soft X-ray free-electron laser (FEL) in addition to its existing functions.

The uncertainty property of electromagnetic field in optical thin microcavity

The uncertainty property of electromagnetic field in thin microcavity is exactly derived in this paper. The intensity of the electromagnetic field at the center of thin microcavity is indeterminate while other positions intensity are determinate. The product of the deviation of momentum and the deviation of position at the center of thin microcavity is larger than a certain constant. By introducing the energy quantization condition (E=Nħω), we verify this constant has the same physical dimension as Planck’s constantħ and the value is an integral multiple of Planck’s constant, the integer is the smallest volume element at the center of thin microcavity. Furthermore, the perimeter of the smallest volume element is an integer multiple of the wavelength of the incident electromagnetic wave, which satisfies the assumption of DE Broglie matter wave. Our results are the first to find that the uncertainty property of electromagnetic field in thin microcavity and further derived the quantum uncertainty principle through the quantization of energy.

ESCORT: Energy sweep compact rapid cycling hadron therapy

The Energy Sweep Compact Rapid Cycling Hadron driver for future cancer therapies based on the induction synchrotron concept is described. This fast cycling synchrotron that allows the energy sweep beam scanning. Assuming a 1.5 T bending magnet, the ring can deliver heavy ions of 430 MeV/u at 10 Hz. A beam fraction is dropped from the barrier bucket at the desired timing and the increasing negative momentum deviation of this beam fraction becomes enough large for the fraction to fall in the electrostatic septum extraction gap, which is placed at the large D(s) region. The programmed energy sweeping extraction makes spot scanning beam irradiation on a cancer area in depth possible.

Assessing safety conditions in underground excavations after a methane-air mixture explosion

A technique for evaluation of shock wave impulse after a methane-air mixture explosion is elaborated. The numerical model developed in previous studies has been verified in the laboratory by using laser initiation of explosives and measuring the pressure impulses of explosion products on a ballistic pendulum. To evaluate the mechanical impulse the functional correlations between its magnitude, the swing angle, and the pendulum characteristics have been derived analytically. The reliability of experimental results is ensured by calibrating the sensor that measures the pendulum swing angle and estimating the impulse measurement errors caused by specifics of angle measurements by a digital voltmeter, pendulum axis friction, and the pauses between measurements. Testing the developed technique to evaluate the shock wave impact showed satisfactory consistency of experimental and theoretical results with the momentum deviation below 9%, which confirms model applicability and correct reproducibility of the shock wave propagation process.

Collision detection algorithm for collaborative robots considering joint friction

This article proposes a collision detection algorithm without external sensors that can detect potential collisions in man–robot interaction. The algorithm is based on a modified first-order momentum deviation observer that also takes friction into account. The collision detection algorithm uses joint angles, angular velocities, and torques during the detection process, without any need to consider angular acceleration. The algorithm also uses an accurate friction model that is based on a Stribeck model with second-order Fourier series compensation. The friction model is applied in advance so that compensation can be made in real time during collision detection. Identification data are filtered through a first-order low-pass filter to reduce high-frequency noise. In order to verify the algorithm, a simulation and experiment were carried out using a collaborative robot experimental platform. The results confirmed that collisions can be detected by setting appropriate threshold values. Different possible responses can be implemented according to different response strategies, with the ultimate arbiter being that collision forces are kept strictly within ordinary human tolerances. This makes sure that safety can be preserved in man–robot interaction processes.

Uncertainty Principle on 3-Dimensional Manifolds of Constant Curvature

We consider the Heisenberg uncertainty principle of position and momentum in 3-dimensional spaces of constant curvature $K$. The uncertainty of position is defined coordinate independent by the geodesic radius of spherical domains in which the particle is localized after a von Neumann-L\"uders projection. By applying mathematical standard results from spectral analysis on manifolds, we obtain the largest lower bound of the momentum deviation in terms of the geodesic radius and $K$. For hyperbolic spaces, we also obtain a global lower bound $\sigma_p\geq |K|^\frac{1}{2}\hbar$, which is non-zero and independent of the uncertainty in position. Finally, the lower bound for the Schwarzschild radius of a static black hole is derived and given by $r_s\geq 2\,l_P$, where $l_P$ is the Planck length.

Uncertainty relations for a particle confined in a finite square well potential

In order to specify the uncertainty relation for a particle confined in a finite square well potential we derived the standard deviation of momentum and that of position It is shown that has a peak as a function of the well width and both and have a dip in contrast to the case of the particle confined in an infinite square well potential. We clarified that of the particle occupying the ground state exists in the finite range as a function of the well width and the potential-barrier height, but a particle confined in an infinite square well potential has a constant In addition, we found that the values of for excited states diverge in a certain range of well widths, where the energy level of the confined particle exceeds the potential barrier.

Effects of optical phonon interaction on dynamical valley polarization in graphene

The present report is concerned with the dynamical behavior of [Formula: see text]-electronic valley states, under the interaction with transverse zone-boundary optical phonons, in graphene. It is assumed that the phonons are thermal and obey the Bose–Einstein distribution, while the [Formula: see text]-electrons are initially prepared in an experimentally realizable particular valley state. In our study, we take the view that such a mixture is completely described by a time-dependent density operator which is then determined, to the second-order of perturbation, from the governing Schrödinger equation. Employing the density operator so calculated, an analytical expression for the valley polarization, as a function of time, phonon frequency and temperature, is obtained. The results, accompanying with illustrative figures, reveal that the [Formula: see text]-electrons, through the elastic exchange of energy with phonons, change the valley states periodically with characteristics that strongly depend upon the temperature. It is in particular shown that as the temperature is raised, the time-averaged valley polarization approaches zero, as expected. Our calculations also show that the amplitude of valley oscillations is solely determined by the temperature and phonon frequency: an increase in the temperature enlarges the amplitudes in contrast to the phonon frequency which does the reverse. Along these lines, moreover, we demonstrate that the frequency of valley oscillations is determined by the electronic momentum deviation from the valley states, along with the phonon frequency.

Analytical approach to chromatic correction in the final focus system of circular colliders

A conventional final focus system in particle accelerators is systematically analyzed. We find simple relations between the parameters of two focus modules in the final telescope. Using the relations, we derive the chromatic Courant-Snyder parameters for the telescope. The parameters are scaled approximately according to $({L}^{*}/{\ensuremath{\beta}}_{y}^{*})\ensuremath{\delta}$, where ${L}^{*}$ is the distance from the interaction point to the first quadrupole, ${\ensuremath{\beta}}_{y}^{*}$ the vertical beta function at the interaction point, and $\ensuremath{\delta}$ the relative momentum deviation. Most importantly, we show how to compensate its chromaticity order by order in $\ensuremath{\delta}$ by a traditional correction module flanked by an asymmetric pair of harmonic multipoles. The method enables a circular Higgs collider with 2% momentum aperture and illuminates a path forward to 4% in the future.

Timing the Market with a Combination of Moving Averages

AbstractA combination of simple moving average trading strategies with several window lengths delivers a greater average return and skewness as well as a lower variance and kurtosis compared with buying and holding the underlying asset using daily returns of value‐weighted US decile portfolios sorted by market size, book‐to‐market, momentum, and standard deviation as well as more than 1000 individual US stocks. The combination moving average (CMA) strategy generates risk‐adjusted returns of 2% to 16% per year before transaction costs. The performance of the CMA strategy is driven largely by the volatility of stock returns and resembles the payoffs of an at‐the‐money protective put on the underlying buy‐and‐hold return. Conditional factor models with macroeconomic variables, especially the market dividend yield, short‐term interest rates, and market conditions, can explain some of the abnormal returns. Standard market timing tests reveal ample evidence regarding the timing ability of the CMA strategy.

Explicit symplectic orbit and spin tracking method for electric storage ring

We develop a symplectic charged particle tracking method for phase space coordinates and polarization in all electric storage rings. Near the magic energy, the spin precession tune is proportional to the fractional momentum deviation ${\ensuremath{\delta}}_{m}$ from the magic energy, and the amplitude of the radial and longitudinal spin precession is proportional to $\ensuremath{\eta}/{\ensuremath{\delta}}_{m}$, where $\ensuremath{\eta}$ is the electric dipole moment for an initially vertically polarized beam. The method can be used to extract the electron electric dipole moment of a charged particle by employing narrow band frequency analysis of polarization around the magic energy.

Compact hadron driver for cancer therapies using continuous energy sweep scanning

A design of a compact hadron driver for future cancer therapies based on the induction synchrotron concept is presented. To realize a slow extraction technique in a fast-cycling synchrotron, which allows energy sweep beam scanning, a zero momentum-dispersion $D(s)$ region and a high flat $D(s)$ region are necessary. The proposed design meets both requirements. The lattice has two-fold symmetry with a circumference of 52.8 m, a 2-m dispersion-free straight section, and a 3-m-long large flat dispersion straight section. Assuming a 1.5-T bending magnet, the ring can deliver heavy ions ($200\text{ }\text{ }\mathrm{MeV}/\mathrm{u}$) at 10 Hz. A beam fraction is dropped from the barrier bucket at the desired timing, and the increasing negative momentum deviation of this beam fraction becomes large enough for the fraction to fall in the electrostatic septum extraction gap, which is placed at the large $D(s)$ region. The programmed energy sweep extraction enables scanning beam irradiation on a cancer site in depth without an energy degrader, avoiding the production of secondary particles and the degradation of emittance. Details of the lattice parameters and computer simulations for slow extraction are discussed. An example extraction scenario is presented. Qualities of the spilled beam such as emittance and momentum spread are discussed, as well as necessary functions and parameters required for the extraction system.

Symplectic maps and chromatic optics in particle accelerators

We have applied the nonlinear map method to comprehensively characterize the chromatic optics in particle accelerators. Our approach is built on the foundation of symplectic transfer maps of magnetic elements. The chromatic lattice parameters can be transported from one element to another by the maps. We introduce a Jacobian operator that provides an intrinsic linkage between the maps and the matrix with parameter dependence. The link allows us to directly apply the formulation of the linear optics to compute the chromatic lattice parameters. As an illustration, we analyze an alternating-gradient cell with nonlinear sextupoles, octupoles, and decapoles and derive analytically their settings for the local chromatic compensation. As a result, the cell becomes nearly perfect up to the third-order of the momentum deviation.

Changes in electrical activation modify the orientation of left ventricular flow momentum: novel observations using echocardiographic particle image velocimetry.

Changes in electrical activation sequence are known to affect the timing of cardiac mechanical events. We aim to demonstrate that these also modify global properties of the intraventricular blood flow pattern. We also explore whether such global changes present a relationship with clinical outcome. We investigated 30 heart failure patients followed up after cardiac resynchronization therapy (CRT). All subjects underwent echocardiography before implant and at follow-up after 6+ months. Left ventricular mechanics was investigated at follow-up during active CRT and was repeated after a temporary interruption <5 min later. Strain analysis, performed by speckle tracking, was used to assess the entity of contraction (global longitudinal strain) and its synchronicity (standard deviation of time to peak of radial strain). Intraventricular fluid dynamics, by echographic particle image velocimetry, was used to evaluate the directional distribution of global momentum associated with blood motion. The discontinuation of CRT pacing reflects into a reduction of deformation synchrony and into the deviation of blood flow momentum from the base-apex orientation with the development of transversal flow-mediated haemodynamic forces. The deviation of flow momentum presents a significant correlation with the degree of volumetric reduction after CRT. Changes in electrical activation alter the orientation of blood flow momentum. The long-term CRT outcome correlates with the degree of re-alignment of haemodynamic forces. These preliminary results suggest that flow orientation could be used for optimizing the biventricular pacing setting. However, larger prospective studies are needed to confirm this hypothesis.