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26 records · Page 2

Polynomial approximation of Poincare maps for Hamiltonian system

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Froeschle, Claude

Nonlinear simulations of GAEs in NSTX-U

A set of nonlinear simulations has been performed in order to study the nonlinear evolution of unstable global Alfvén eigenmodes in the National Spherical Torus Experiment-Upgrade (NSTX-U). Results of the single toroidal mode number, n, simulations are compared with a full nonlinear simulation (all toroidal harmonics included). In single-n simulations, the conservation of two integrals of motion of a particle in a cyclotron resonance with a monochromatic wave is demonstrated, resulting in a one-dimensional evolution of the particle distribution in (E,μ,pϕ) phase-space. Nonlinear simulations (both single-n and full nonlinear) show a significant redistribution of the resonant fast ions, especially in the pitch parameter. Thus, the changes in the resonant particle's parallel and perpendicular energies can be several times larger than the total particle energy change, with only a small fraction transferring into the excitation of the mode itself. This implies that even a relatively small amplitude mode can significantly modify the beam distribution in the resonant region. For the NSTX-U case considered, the single-n simulation results are close to full nonlinear simulation only for the most unstable mode, in which case the saturation amplitudes and changes in the fast ion distribution are comparable. In contrast, peak amplitudes of subdominant modes in all-n simulations are smaller by a factor of 3–10 compared to single-n runs due to the flattening of the beam ion distribution by the fastest growing mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Dynamics of McMillan mappings II. axially symmetric map

Here, in this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device potentially capable of mitigating collective space charge forces, some of its fundamental properties have not been described yet. The main goal of our work is to close this gap and understand the limitations and potentials of this device. It is worth mentioning that the McMillan axially symmetric map provides the first-order approximations of dynamics for a general linear lattice plus an arbitrary thin lens with motion separable in polar coordinates. Therefore, advancements in its understanding should give us a better picture of more generic and not necessarily integrable round beams. In the first part of the article, we classify all possible regimes with stable trajectories and find the canonical action-angle variables. This provides an evaluation of the dynamical aperture, Poincaré rotation numbers as functions of amplitudes, and thus determines the spread in nonlinear tunes. Also, we provide a parameterization of invariant curves, allowing for the immediate determination of the map image forward and backward in time. The second part investigates the particle dynamics as a function of system parameters. We show that there are three fundamentally different configurations of the accelerator optics causing different regimes of nonlinear oscillations. Each regime is considered in great detail, including the limiting cases of large and small amplitudes. In addition, we analyze the dynamics in Cartesian coordinates and provide a description of observable variables and corresponding spectra.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Measurement of C P Violation Observables in D + → K − K + π + Decays

A search for violation of the charge-parity ( C P ) symmetry in the D + → K − K + π + decay is presented, with proton-proton collision data corresponding to an integrated luminosity of 5.4 fb − 1 , collected at a center-of-mass energy of 13 TeV with the LHCb detector. A novel model-independent technique is used to compare the D + and D − phase-space distributions, with instrumental asymmetries subtracted using the D s + → K − K + π + decay as a control channel. The p value for the hypothesis of C P conservation is 8.1%. The C P asymmetry observables A C P | S ϕ π + = ( 0.95 ± 0.4 3 stat ± 0.2 6 syst ) × 10 − 3 and A C P | S K ¯ * 0 K + = ( − 0.26 ± 0.5 6 stat ± 0.1 8 syst ) × 10 − 3 are also measured. These results show no evidence of C P violation and represent the most sensitive search performed through the phase space of a multibody decay. © 2024 CERN, for the LHCb Collaboration 2024 CERN

Aaij, R. (ORCID:0000000305331952)

Storm-Time Variability of Terrestrial Hydrogen Exosphere: Kinetic Simulation Results

Recent studies of TWINS Lyman-α observations have reported an increase in geocoronal column brightness during geomagnetic storms, indicating enhanced exospheric hydrogen atom density (NH). This suggests a complex role of exospheric neutrals in determining storm-time magnetosphere dynamics and their energy release through charge-exchange processes. We developed a Model for Analyzing Terrestrial Exosphere (MATE) to investigate storm-time exospheric behaviors and their physical drivers. MATE traces test hydrogen atoms backward in time from locations in the exosphere to a nominal exobase altitude of 500 km, employing Newtonian mechanics with gravitational force. The model then calculates the phase-space densities (PSDs) of test hydrogen atoms at the exobase using the Maxwellian distribution with physics-based exobase conditions from the TIMEGCM upper atmosphere model. MATE maps PSDs at the exobase to the exosphere using Liouville’s Theorem under collisionless assumptions and derives NH by integrating the PSDs across velocity space. We conducted MATE simulation before, during, and after a minor geomagnetic storm from 12 to 18 June 2008, and compared the model results with NH estimates from the TWINS geocorona data. MATE reproduces storm-time density enhancements soon after the minimum Dst is reached, matching well with a general trend of TWINS NH estimates. The results suggest that upper atmospheric heating during a geomagnetic storm increases the number of ballistic and escaping hydrogen atoms entering the exosphere from the exobase, thereby boosting NH. However, the magnitude of modeled NH mismatches the TWINS NH estimates. The potential mechanisms of this density discrepancy include the physics excluded in the MATE model — such as neutralneutral collisions, neutral-plasma charge exchange, solar radiation pressure, and photoionization — as well as the higher exobase hydrogen density of TIMEGCM compared to typical empirical values, which will be addressed in future.

Hyunju K Connor

Qualitative simulation for process modeling and control

A qualitative model is developed for a first-order system with a proportional-integral controller without precise knowledge of the process or controller parameters. Simulation of the qualitative model yields all of the solutions to the system equations. In developing the qualitative model, a necessary condition for the occurrence of oscillatory behavior is identified. Initializations that cannot exhibit oscillatory behavior produce a finite set of behaviors. When the phase-space behavior of the oscillatory behavior is properly constrained, these initializations produce an infinite but comprehensible set of asymptotically stable behaviors. While the predictions include all possible behaviors of the real system, a class of spurious behaviors has been identified. When limited numerical information is included in the model, the number of predictions is significantly reduced.

Dalle Molle, D. T.

Phase-Space Energization of Ions in Oblique Shocks

Examining energization of kinetic plasmas in phase space is a growing topic of interest, owing to the wealth of data in phase space compared to traditional bulk energization diagnostics. Via the field-particle correlation (FPC) technique and using multiple means of numerically integrating the plasma kinetic equation, we have studied the energization of ions in phase space within oblique collisionless shocks. The perspective afforded to us with this analysis in phase space allows us to characterize distinct populations of energized ions. In particular, we focus on ions that reflect multiple times off the shock front through shock-drift acceleration, and how to distinguish these different reflected populations in phase space using the FPC technique. We further extend our analysis to simulations of three-dimensional shocks undergoing more complicated dynamics, such as shock ripple, to demonstrate the ability to recover the phase-space signatures of this energization process in a more general system. This work thus extends previous applications of the FPC technique to more realistic collisionless shock environments, providing stronger evidence of the technique's utility for simulation, laboratory, and spacecraft analysis.

Plasma astrophysics

Measurement of top-quark pair production in association with charm quarks in proton–proton collisions at √s = 13 TeV with the ATLAS detector

Inclusive cross-sections or top-quark pair production in association with charm quarks are measured with proton-proton collision data at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 140 fb -1 , collected with the ATLAS experiment at LHC between 2015 and 2018. The measurements are performed by requiring one or two charged leptons (electrons and muons), two b-tagged jets, and at least one additional jet in the final state. A custom flavor-tagging algorithm is employed for the simultaneous identification of b-jets and c-jets. In a fiducial phase space that replicates the acceptance of the ATLAS detector, the cross-sections for $t\bar{t}$ + ≥ 2c and $t\bar{t}$ + 1c production are measured to be $1.28^{+0.27}_{-0.24}$ pb and $6.4^{+1.0}_{-0.9}$ pb, respectively. The measurements are primarily limited by uncertainties in the modeling of inclusive $t\bar{t}$ and $t\bar{t}$ + $b\bar{b}$ production, in the calibration of the flavor-tagging algorithm, and by data statistics. Cross-section predictions from various $t\bar{t}$ simulations are largely consistent with the measured cross-section values, though all underpredict the observed values by 0.5 to 2.0 standard deviations. In a phase-space volume without requirements on the $t\bar{t}$ decay products and the jet multiplicity, the cross-section ratios of $t\bar{t}$ + ≥ 2c and $t\bar{t}$ + 1c to total $t\bar{t}$ + jets production are determined to be (1.23 ± 0.25)% and (8.8 ± 1.3)%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS