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Quantum Theory of Surface Lattice Resonances
The collective interactions of nanoparticles arranged in periodic structures give rise to high‐ in‐plane diffractive modes known as surface lattice resonances. Although these resonances and their broader implications have been extensively studied within the framework of classical electrodynamics and linear response theory, a quantum optical theory capable of describing the dynamics of these structures, especially in the presence of material nonlinearities beyond ad hoc few‐mode approximations, is largely missing. To this end, we consider a lattice of metallic nanoparticles coupled to the electromagnetic field and derive the quantum input–output relations within the electric dipole approximation. As applications, we analyze coupling between the nanoparticle array and external quantum emitters, and show how the formalism extends to molecular optomechanics, where the high ‐factors of SLRs enable coupling to collective vibrational modes. We further consider arrays composed of saturable excitonic emitters, demonstrating how emitter nonlinearities can be used to switch the SLR condition between electronic transitions. Using a perturbative approach that accounts for population dynamics, we show how these effects can be probed in pump–probe experiments and give rise to nonlinear phase‐matching phenomena. Our work provides a microscopic framework for modeling SLRs interacting with quantum emitters without phenomenological descriptions of the electromagnetic environment.
Space Charge Driven Emittance Growth and the Effect of Octupoles in IOTA
The Integrable Optics Test Accelerator (IOTA) at Fermilab is a small machine dedicated to a broad frontier accelerator physics program. An important aspect of this program is to investigate the potential benefits of the resonance free tune spread achievable with integrable optics to store and accelerate high intensity proton beams for which space charge is significant. In this context, a good understanding of proton beam emittance growth and particle loss mechanisms is essential. Assuming nominal design parameters, simulations show that for a bunched beam, the bulk of emittance growth takes place immediately following injection, typically within tens of turns. We attempt to account for this growth using a simplified RMS mismatch theory; some of its limitations and possible improvements are briefly discussed. We then compare theoretical predictions to simulations performed using the PIC code pyORBIT. Further exploring ways to mitigate emittance growth and reduce particle loss, we compare two beam matching strategies: (1) matching at the injection point (2) matching at the center of the nonlinear (octupole) insertion region where $\beta_x = \beta_y$. To observe how nonlinearity affects emittance growth and whether it dominates growth due to mismatch, we track two different distributions. Finally, we explore the potential of using octupoles in a quasi-integrable configuration to mitigate growth using a variety of initial distributions both at reduced and full intensities.
JuTrack: A Julia package for auto-differentiable accelerator modeling and particle tracking
Efficient accelerator modeling and particle tracking are key for the design and configuration of modern particle accelerators. In this work, we present JuTrack, a nested accelerator modeling package developed in the Julia programming language and enhanced with compiler-level automatic differentiation (AD). With the aid of AD, JuTrack enables rapid derivative calculations in accelerator modeling, facilitating sensitivity analyses and optimization tasks. Here we demonstrate the effectiveness of AD-derived derivatives through several practical applications, including sensitivity analysis of space-charge-induced emittance growth, nonlinear beam dynamics analysis for a synchrotron light source, and lattice parameter tuning of the future Electron-Ion Collider (EIC). Through the incorporation of automatic differentiation, this package opens up new possibilities for accelerator physicists in beam physics studies and accelerator design optimization.
Second-harmonic generation in nonlinear plasmonic lattices enhanced by quantum emitter gain medium
In this work, we report on a theoretical study of second-harmonic generation (SHG) in plasmonic nanostructures interacting with two-level quantum emitters (QEs) under incoherent energy pump. We generalize the driven-dissipative Tavis–Cummings model by introducing the anharmonic surface plasmon-polariton (SPP) mode coupled to QEs and examine physical properties of corresponding SPP-QE polariton states. Our calculations of the SHG efficiency for strong QE-SPP coupling demonstrate orders of magnitude enhancement facilitated by the polariton gain. We further discuss time-domain numerical simulations of SHG in a square lattice comprising Ag nanopillars coupled to QEs utilizing a fully vectorial nonperturbative nonlinear hydrodynamic model for conduction electrons coupled to Maxwell–Bloch equations for QEs. The simulations support the idea of gain enhanced SHG and show orders of magnitude increase in the SHG efficiency as the QEs are tuned in resonance with the lattice plasmon mode and brought above the population inversion threshold by incoherent pumping. By varying pump frequency and tuning QEs to a localized plasmon mode, we demonstrate further enhancement of the SHG efficiency facilitated by strong local electric fields. The incident light polarization dependence of the SHG is examined and related to the symmetries of participating plasmon modes.
A Generalized Approach to Photon Avalanche Upconversion in Luminescent Nanocrystals
Photon avalanching nanoparticles (ANPs) exhibit extremely nonlinear upconverted emission valuable for subdiffraction imaging, nanoscale sensing, and optical computing. Avalanching has been demonstrated with Tm 3+ -, Pr 3+ -, or Nd 3+ -doped nanocrystals, but their emission is limited to a few wavelengths and materials. Here, we utilize Gd 3+ -assisted energy migration to tune the emission wavelengths of Tm 3+ -sensitized ANPs and generate highly nonlinear emission from Eu 3+ , Tb 3+ , Ho 3+ , and Er 3+ ions. The upconversion intensities of these spectrally discrete ANPs scale with nonlinearity factor s = 10-17 under 1064 nm excitation at power densities as low as 7 kW cm -2 . This strategy for imprinting avalanche behavior on remote emitters can be extended to fluorophores adjacent to ANPs, as here we demonstrate with CdS/CdSe/CdS core/shell/shell quantum dots. ANPs with rationally designed energy transfer networks provide the means to transform conventional linear emitters into a highly nonlinear ones, expanding the use of photon avalanching in biological, chemical, and photonic applications.
Imposing strong correlated energy spread on relativistic bunches with transverse deflecting cavities
We demonstrate a novel scheme for imposing or removing large energy chirp on relativistic electron bunches. This method relies on the transverse-to-longitudinal mixing accomplished with a set of transverse deflecting cavities. The working principles of the new concept are explained using the first-order matrix formalism in the approximation of the linear single-particle dynamics. The scheme demonstrates versatility regarding the average beam energy and, hence, positioning along the accelerator beam line. The performance of the scheme is numerically investigated with the elegant particle-tracking code. It is shown that the associated nonlinear effects causing emittance deterioration for the extreme quantities of the total energy spread can be effectively compensated by optimization of the Twiss parameters while relying on the eigenemittance analysis. The impact of the longitudinal space charge effects on the beam dynamics in the proposed scheme is also investigated.
Compensating slice emittance growth in high brightness photoinjectors using sacrificial charge
Achieving maximum electron beam brightness in photoinjectors requires detailed control of the 3D bunch shape and precise tuning of the beam focusing. Even in state-of-the-art designs, slice emittance growth due to nonlinear space charge forces and partial nonlaminarity often remains non-negligible. In this work, we introduce a new means to linearize the transverse slice phase space: a sacrificial portion of the bunch’s own charge distribution, formed into a wavebroken shock front by highly nonlinear space charge forces within the gun, whose downstream purpose is to dynamically linearize the desired bunch core. We show that linearization of an appropriately prepared bunch can be achieved via strongly nonlaminar focusing of the sacrificial shock front, while the inner core focuses laminarly. This leads to a natural spatial separation of the two distributions: a dense core surrounded by a diffuse halo of sacrificial charge that can be collimated. Multiobjective genetic algorithm optimizations of the ultracompact x-ray free electron laser injector employ this concept, and we interpret it with an analytic model that agrees well with the simulations. In simulation, we demonstrate a final bunch charge of 100 pC, peak current ∼ 30 A, and a sacrificial charge of 150 pC (250 pC total emitted from cathode) with normalized emittance growth of < 20 nm rad due to space charge. This implies a maximum achievable brightness approximately an order of magnitude greater than existing free electron laser injector designs. Published by the American Physical Society 2024
Final Physics Design of Proton Improvement Plan-II at Fermilab
This paper presents the final physics design of the Proton Improvement Plan-II (PIP-II) at Fermilab, focusing on the linear accelerator (Linac) and its beam transfer line. We address the challenges in longitudinal and transverse lattice design, specifically targeting collective effects, parametric resonances, and space charge nonlinearities that impact beam stability and emittance control. The strategies implemented effectively mitigate space charge complexities, resulting in significant improvements in beam quality—evidenced by reduced emittance growth, lower beam halo, decreased loss, and better energy spread management. This comprehensive study is pivotal for the PIP-II project's success, providing valuable insights and approaches for future accelerator designs, especially in managing nonlinearities and enhancing beam dynamics.
Final Physics Design of Proton Improvement Plan-II At Fermilab
This paper presents the final physics design of the Proton Improvement Plan-II (PIP-II) at Fermilab, focusing on the linear accelerator (Linac) and its beam transfer line. We address the challenges in longitudinal and transverse lattice design, specifically targeting collective effects, parametric resonances, and space charge nonlinearities that impact beam stability and emittance control. The strategies implemented effectively mitigate space charge complexities, resulting in significant improvements in beam quality -- evidenced by reduced emittance growth, lower beam halo, decreased loss, and better energy spread management. This comprehensive study is pivotal for the PIP-II project's success, providing valuable insights and approaches for future accelerator designs, especially in managing nonlinearities and enhancing beam dynamics.
Beam Losses and Emittance Growth Studies at the Record High Space-Charge in the Booster
Comprehensive studies of high intensity proton beams in the 0.4-8 GeV FNAL Booster synchrotron have revealed interesting nonlinear dynamics of the beam losses and emittance growth at the record high dQ_{SC}=0.6. We report the results of the studies and directions of further improvements to prepare the Booster to the era of even higher intensity operation with new 0.8 GeV PIP-II linac.
Resonant Emittance Mixing of Flat Beams in Plasma Accelerators
Linear colliders rely on high-quality flat beams to achieve the desired event rate while avoiding potentially deleterious beamstrahlung effects. Here, we show that flat beams in plasma accelerators can be subject to quality degradation due to emittance mixing. This effect occurs when the beam particles' betatron oscillations in a nonlinearly coupled wakefield become resonant in the horizontal and vertical planes. Emittance mixing can lead to a substantial decrease of the luminosity, the main quantity determining the event rate. In some cases, the use of laser drivers or flat particle beam drivers may decrease the fraction of resonant particles and, hence, mitigate emittance deterioration.
Emittance preservation for the electron arm in a single PWFA-LC stage using quasi-adiabatic plasma density ramp matching sections
Plasma-based acceleration (PBA) is being considered for a next generation linear collider (LC). In some PBA-LC designs for the electron arm, the extreme beam parameters are expected to trigger background ion motion within the witness beam, which can lead to longitudinally varying nonlinear focusing forces and result in an unacceptable emittance growth of the beam. To mitigate this, we propose to use quasi-adiabatic plasma density ramps as matching sections at the entrance and exit of each stage. We match the witness electron beam to the low density plasma entrance, where the beam initially has a large matched spot size so the ion motion effects are relatively small. As the beam propagates in the plasma density upramp, it is quasi-adiabatically focused, and its distribution maintains a non-Gaussian equilibrium distribution in each longitudinal slice throughout the process, even when severe ion collapse has occurred. This only causes small amounts of slice emittance growth. The phase mixing between slices with different betatron frequencies leads to additional projected emittance growth within the acceleration stage. A density downramp at the exit of an acceleration section can eliminate much of the slice and projected emittance growth as the beam and ion motion adiabatically defocuses and decreases, respectively. Simulation results from QuickPIC with Azimuthal Decomposition show that within a single acceleration stage with a 25 GeV energy gain, this concept can limit the projected emittance growth to only ∼2% for a 25 GeV, 100 nm emittance witness beam and ∼20% for a 100 GeV, 100 nm normalized emittance witness beam. The trade-off between the adiabaticity of the plasma density ramp and the initial ion motion at the entrance for a given length of the plasma density ramp is also discussed.
Dependence of emittance on the length of an electron bunch during laser-plasma acceleration in guiding structures
We report a theoretical analysis and numerical simulation of the dynamics of transverse emittance of an electron bunch during its acceleration in wake fields generated by a laser pulse in a weakly nonlinear mode. Analytical expressions are obtained for the main factors affecting the emittance growth during acceleration and the case is considered when the characteristic transverse size of the injected bunch exceeds the matched radius determined by the focusing force at the injection point, the initial emittance and the electron bunch energy, and the resulting value of emittance is much larger than the initial one. The dynamics of the emittance growth during acceleration as a function of the length of the electron bunch is described, and the length of the bunch is found at which there occurs a complete phase mixing of betatron oscillations of electrons and the emittance increases to its maximum value determined by the bunch parameters and the focusing force at the injection point. Analytical expressions are in good agreement with the results of numerical simulation. (paper)
Storage ring nonlinear dynamics optimization with multi-objective multi-generation Gaussian process optimizer
Nonlinear beam dynamics optimization is essential in a low emittance storage ring design. Multi-objective optimization algorithms are needed in order to simultaneously optimize the dynamic aperture and the momentum aperture. In this study we demonstrate the application of a highly efficient stochastic optimization algorithm, the multi-generation Gaussian process optimizer (MG-GPO), to storage ring nonlinear dynamics optimization by successfully applying the method to the SPEAR3 upgrade lattice. It is shown that the new method, owing to its capability of selecting high rank candidates from a large number of trial solutions, converges significantly faster than the commonly used traditional algorithms, multi-objective genetic algorithms (MOGA) and particle swarm optimization (PSO).
Accelerator physics at NSLS-II: research accomplishments in 2020
NSLS-II accelerator physicists provide scientific support for user operations, as well as for improvements and developments of the accelerator systems. This work includes optimization of the NSLS-II performance with high beam current and low vertical emittance, improvement of the beam stability, development of new software tools for operations and beam studies. The accelerator physicists productively worked on a number of research activities such as the conceptual design of NSLS-II accelerator upgrade; design and optimization of advanced low-emittance lattices; development of novel methods to study nonlinear beam dynamics; ultrafast electron diffraction and microscopy. The physicists also contributed to the BNL electron-ion collider project, to the APS and ALS upgrade projects. Research accomplishments achieved in 2020, are summarized in this report.
Toward a systematic design theory for silicon solar cells using optimization techniques
This work is a first detailed attempt to systematize the design of silicon solar cells. Design principles follow from three theorems. Although the results hold only under low injection conditions in base and emitter regions, they hold for arbitrary doping profiles and include the effects of drift fields, high/low junctions and heavy doping concentrations of donor or acceptor atoms. Several optimal designs are derived from the theorems, one of which involves a three-dimensional morphology in the emitter region. The theorems are derived from a nonlinear differential equation of the Riccati form, the dependent variable of which is a normalized recombination particle current.
Degenerate parametric down-conversion facilitated by exciton-plasmon polariton states in a nonlinear plasmonic cavity
Abstract We study the effect of degenerate parametric down-conversion (DPDC) in an ensemble of two-level quantum emitters (QEs) coupled via near-field interactions to a single surface plasmon (SP) mode of a nonlinear plasmonic cavity. For this purpose, we develop a quantum driven-dissipative model capturing non-equilibrium dynamics of the system in which incoherently pumped QEs have transition frequency tuned near the second-harmonic response of the SPs. Considering the strong coupling regime, i.e. the SP-QE interaction rate exceeds system dissipation rates, we find a critical SP-QE coupling attributed to the phase transition between normal and lasing steady states. Examining fluctuations above the system’s steady states, we predict new elementary excitations, namely, the exciton-plasmon polaritons formed by the two-SP quanta and single-exciton states of QEs. The contribution of two-SP quanta results in the linear scaling of the SP-QE interaction rate with the number of QEs, o , as opposed to the o -scaling known for the Dicke and Tavis–Cummings models. We further examine how SP-QE interaction scaling affects the polariton dispersions and power spectra in the vicinity of the critical coupling. For this purpose, we compare the calculation results assuming a finite ensemble of QEs and the model thermodynamic limit. The calculated power spectra predict an interplay of coherent photon emission by QEs near the second-harmonic frequency and correlated photon-pair emission at the fundamental frequency by the SPs (i.e. the photonic DPDC effect).