Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Damping”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Representation of the Convectively Coupled Kelvin Waves in Modern Reanalysis Products

Abstract This study aims to deepen our understanding of the destabilization mechanisms and the mean-state modulation of the convectively coupled Kelvin waves (CCKWs) while testing simple models for CCKWs. We examine CCKW precipitation, vertical structure, and energetics in four modern reanalyses: the fifth version of ECMWF Reanalysis (ERA5), NASA Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), the second version of the NCEP Climate Forecast System Reanalysis (CFSR), and the Japanese 55-year Reanalysis (JRA-55). The CCKW precipitation signal strength in the wavenumber–frequency domain and the geographical distribution of CCKW precipitation variability are reasonably represented in all reanalyses, although they commonly underestimate the amplitude of CCKW precipitation. Despite considerable interreanalysis differences in the vertical structure of temperature and diabatic heating anomalies, the eddy available potential energy (EAPE) generation within the CCKWs is found to be associated with the second baroclinic mode whereas the first baroclinic mode damps CCKW EAPE in three out of four reanalyses. Geographically, strong CCKW activity occurs in the areas of high mean-state sea surface temperature (SST), where the second mode EAPE generation is higher, mainly due to a stronger stratiform heating and a tighter wave–convection coupling. Our results are supportive of the simple models for CCKWs in which CCKWs are destabilized within the second baroclinic mode component.

Meteorology & Atmospheric Sciences↗
DOE OSTI2021

ENSO Dynamics in the E3SM-1-0, CESM2, and GFDL-CM4 Climate Models

We report that this study examines historical simulations of ENSO in the E3SM-1-0, CESM2, and GFDL-CM4 climate models, provided by three leading U.S. modeling centers as part of the Coupled Model Intercomparison Project phase 6 (CMIP6). These new models have made substantial progress in simulating ENSO’s key features, including: amplitude; timescale; spatial patterns; phase-locking; spring persistence barrier; and recharge oscillator dynamics. However, some important features of ENSO are still a challenge to simulate. In the central and eastern equatorial Pacific, the models’ weaker-than-observed subsurface zonal current anomalies and zonal temperature gradient anomalies serve to weaken the nonlinear zonal advection of subsurface temperatures, leading to insufficient warm/cold asymmetry of ENSO’s sea surface temperature anomalies (SSTA). In the western equatorial Pacific, the models’ excessive simulated zonal SST gradients amplify their zonal temperature advection, causing their SSTA to extend farther west than observed. The models underestimate both ENSO’s positive dynamic feedbacks (due to insufficient zonal wind stress responses to SSTA) and its thermodynamic damping (due to insufficient convective cloud shading of eastern Pacific SSTA during warm events); compensation between these biases leads to realistic linear growth rates for ENSO, but for somewhat unrealistic reasons. The models also exhibit stronger-than-observed feedbacks onto eastern equatorial Pacific SSTAs from thermocline depth anomalies, which accelerates the transitions between events and shortens the simulated ENSO period relative to observations. Implications for diagnosing and simulating ENSO in climate models are discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

The Dependence of Mean Climate State on Shortwave Absorption by Water Vapor

Abstract State-of-the-art climate models exhibit significant spread in the climatological value of atmospheric shortwave absorption (SWA). This study investigates both the possible causes and climatic impacts of this SWA intermodel spread. The intermodel spread of global-mean SWA largely originates from the intermodel difference in water vapor shortwave absorptivity. Hence, we alter the water vapor shortwave absorptivity in the Community Earth System Model, version 1, with the Community Atmosphere Model, version 4 (CESM1-CAM4). Increasing the water vapor shortwave absorptivity leads to a reduction in global-mean precipitation and a La Niña–like cooling over the tropical Pacific. The global-mean atmospheric energy budget suggests that the precipitation is suppressed as a way to compensate for the increased SWA. The precipitation reduction is driven by the weakened surface winds, stabilized planetary boundary layer, and surface cooling. The La Niña–like cooling over the tropical Pacific is attributed to the zonal asymmetry of climatological evaporative damping efficiency and the low cloud enhancement over the eastern basin. Complementary fixed SSTs simulations suggest that the latter is more fundamental and that it primarily arises from atmospheric processes. Consistent with our experiments, the CMIP5/6 models with a higher global-mean SWA tend to produce tropical Pacific toward a more La Niña–like mean state, highlighting the possible role of water vapor shortwave absorptivity for shaping the mean-state climate patterns.

Kim, Hanjun↗
DOE OSTI2022

Understanding the Drivers of Atlantic Multidecadal Variability using a Stochastic Model Hierarchy

The relative importance of ocean and atmospheric dynamics in generating Atlantic Multidecadal Variability (AMV) remains an open question. Comparisons between climate models with SLAB and fully-dynamic (FULL) ocean components are often used to explore this question, but cannot reveal how individual ocean processes generate these differences. We build a hierarchy of physically interpretable stochastic models to investigate the contribution of two upper-ocean processes to AMV: the role of seasonal variation and mixed-layer entrainment. This interpretability arises from the stochastic model’s simplified representation of sea surface temperature (SST), considering only the local upper ocean response to white-noise atmospheric forcing and its impact on surface heat exchange. We focus on understanding differences between SLAB and FULL non-eddy resolving pre-industrial control simulations of the Community Earth System Model 1 (CESM), and estimate the stochastic model parameters from each respective simulation. Despite its simplicity, the stochastic model reproduces temporal characteristics of SST variability in the SPG, including reemergence, seasonal-to-interannual persistence and power spectra. Furthermore, unrealistically persistent SST of the CESM-SLAB ocean simulation is reproduced in the equivalent stochastic model configuration where the mixed-layer depth (MLD) is constant. The stochastic model also reveals that vertical entrainment primarily damps SST variability, thus explaining why SLAB exhibits larger SST variance than FULL. Here, the stochastic model driven by temporally stochastic, spatially coherent forcing patterns reproduces the canonical AMV pattern. However, the amplitude of low-frequency variability remains underestimated, suggesting a role for ocean dynamics beyond entrainment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗
DOE OSTI2024

Bulk Viscosity in Dense Nuclear Matter

NEUTRON star mergers are an extreme environment where, within milliseconds, the cold, dense matter in neutron stars is dramatically heated to some of the hottest temperatures encountered in astrophysics. Matter in neutron star mergers is located solidly in the interior of the QCD phase diagram, and therefore, the observation and simulation of these mergers provides an opportunity to learn about the strong interaction at a set of densities and temperatures that compliment those obtained in relativistic heavy-ion collisions. Matter during the merger of two neutron stars is far from hydrostatic equilibrium, allowing for the study of not only the equation of state of dense matter, but of transport properties as well. Perhaps the most likely transport property to play a role in neutron star mergers is the bulk viscosity, which acts to resist changes in density. Furthermore, the bulk viscosity of matter at high densities has long been anticipated to damp oscillations in isolated neutron stars, and the study of its role in neutron star mergers is just beginning.

Harris, Steven P.↗
DOE OSTI2020

Physics and applications of quantum dot lasers for silicon photonics

Abstract Photonic integrated circuits (PICs) have enabled numerous high performance, energy efficient, and compact technologies for optical communications, sensing, and metrology. One of the biggest challenges in scaling PICs comes from the parasitic reflections that feed light back into the laser source. These reflections increase noise and may cause laser destabilization. To avoid parasitic reflections, expensive and bulky optical isolators have been placed between the laser and the rest of the PIC leading to large increases in device footprint for on-chip integration schemes and significant increases in packaging complexity and cost for lasers co-packaged with passive PICs. This review article reports new findings on epitaxial quantum dot lasers on silicon and studies both theoretically and experimentally the connection between the material properties and the ultra-low reflection sensitivity that is achieved. Our results show that such quantum dot lasers on silicon exhibit much lower linewidth enhancement factors than any quantum well lasers. Together with the large damping factor, we show that the quantum dot gain medium is fundamentally dependent on dot uniformity, but through careful optimization, even epitaxial lasers on silicon can operate without an optical isolator, which is of paramount importance for the future high-speed silicon photonic systems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

MBARI-WEC September and October 2022 Field Data

This data is needed to simulate a model of the MBARI-WEC (Monterey Bay Aquarium Research Institute, Wave Energy Converter device) in a simulation environment (e.g. Gazebo) for 56 observation dates in the time between September and October 2022, and to compare the simulation outputs to the corresponding field data of the physical MBARI-WEC. There were 50 observations chosen in Sept and 6 observations in Oct. To help understand terms below, a summary of the system can be found at the github link in the downloads section below. The Gazebo MBARI-WEC model is also provided, should users wish to simulate using this platform. There are 4 *mat files included. ................................................................................................................................................................................................................................... Spectrum and Simulation Inputs: September2022_spectrum_siminputs.mat and October2022_spectrum_siminputs.mat has data needed for simulation inputs in table format. These include the ocean spectrum for an observation and operating parameters of the MBARI-WEC during that observation. They are organized as rows representing an observation and columns representing data. For example, for the September *mat there are 50 rows. The first 7 columns are Datetime, sig_waveheight, peak_period, mean_period, heaveconedoor_status, pistonpos_mean, and scale_factor: - Datetime is the date and time the observation occurred in PST - sig_waveheight is the significant wave height of the ocean spectrum during that observation in meters - peak_period is the peak period of the ocean spectrum during that observation in seconds - mean_period is the mean period of the ocean spectrum during that observation in seconds - heaveconedoor_status is the status of the heave cone doors where 0 represents the doors are open and 1 represents they are closed - pistonpos_mean is the mean position of the PTO ram (piston) in meters - scale_factor is an additional factor of 0.5 --1.4 applied to a default damping relationship The next columns are data needed to represent the ocean spectrum. First are the frequencies [Hz] labeled as "f0-f38", then the variance density [m2/Hz] labeled as "vardens0-vardens38". October2022_spectrum_siminputs.mat follows as a similar format as above, but includes a larger amount of ocean spectrum frequencies and variance density elements. ................................................................................................................................................................................................................................... Field data: The field data is found in MBARIWEC_septdata.mat and MBARIWEC_octdata.mat for the observations of September and October, respectively. These contain data in a struct format. The struct contains the following fields for each observation: PC_BattCurr, PC_LoadCurr, PC_RPM, PC_Voltage, SC_Range, SC_Velocity, DateTime, where: - PC_BattCurr is the current flowing to or from the onboard batteries in Amps - PC_LoadCurr is the current flowing to the load dump in Amps - PC_RPM is the electric/hydraulic motor shaft speed (directly coupled) in RPM - PC_Voltage is the bus voltage at the power converter in Volts - SC_Range is the PTO ram (piston) position in meters where 0 is fully retracted and 2.03 is fully extended - SC_Velocity is the PTO ram (piston) velocity in meters/sec - DateTime is the date and time of the sampled field data in each observation in PST - Electric Power is equal to: PC_Voltage*(PC_BattCurr + PC_LoadCurr) in Watts For example, upon loading MBARIWEC_octdata.mat, the aforementioned fields would be loaded, each with {6x1} cells for the 6 observations chosen in October. Within the first cell of e.g. SC_Range would be sampled data representing the field data of the MBARIWEC PTO piston position for say, one hour, of the first October observation. The corresponding field DateTime would...

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Temperature Effects on Droplet Oscillation Decay with Application to Fuel Property Measurement

Observation of oscillation decay in droplets has been shown to be an effective approach in determining physical properties such as viscosity and surface tension for emerging biofuels using μl quantities. Herein this work extends the approach to higher temperatures relevant to fuel injection conditions for internal combustion engines. Experiments are conducted that use high-resolution strobed imaging of moving, heated, μm-sized, fuel droplets to capture shape oscillation decay through image processing and analysis. Two fuels are investigated, iso-butanol and a primary reference fuel (PRF 84), which is a mixture of iso-octane and n-heptane. A piezoelectric droplet generator is used to generate a continuous train of single droplets, which are given an initial perturbation and subsequently undergo damped oscillations, captured using strobed imaging. Surface tension and viscosity calculated at four different temperatures ranging from 30°C-55°C using the frequency and decay time associated with the fundamental mode are found to be within ~ 10% of reference values obtained from the literature. Complementary numerical simulations are performed that utilize a volume-of-fluid approach to track transient droplet oscillation phenomena along with heat and mass transfer in a 2D axisymmetric domain. Simulations, where droplet size and temperature can be independently varied, capture an expected decrease in oscillation frequency and increase in decay time, with increase in fuel temperature. The simulations are further used to study the relative contribution to deviations in surface tension and viscosity predictions due to heat and mass transfer from the droplet, as well as viscous effects violating the inviscid flow assumption in the droplet oscillation theory. Mass loss effects are found to be negligible. Temperature change due to heat transfer is found to have the next highest sensitivity, particularly for the more volatile PRF 84, which has a lower viscosity and associated Ohnesorge number. For isobutanol, which has a higher viscosity and Ohnesorge number, viscous effects contribute the most to deviation in fuel property predictions.

09 BIOMASS FUELS↗
DOE OSTI2020

Regional-Scale 3D Ground-Motion Simulations of M w 7 Earthquakes on the Hayward Fault, Northern California Resolving Frequencies 0–10 Hz and Including Site-Response Corrections

Large earthquake ground-motion simulations in 3D Earth models provide constraints on site-specific shaking intensities but have suffered from limited frequency resolution and ignored site response in soft soils. In this work we report new regional-scale 3D simulations for moment magnitude 7.0 scenario earthquakes on the Hayward Fault, northern California with SW4. Simulations resolved significantly broader band frequencies (0–10 Hz) than previous studies and represent the highest resolution simulations for any such earthquake to date. Seismic waves were excited by a kinematic rupture following Graves and Pitarka (2016) and obeyed wave propagation in a 3D Earth model with topography from the U.S. Geological Survey (USGS) assuming a minimum shear wavespeed, VSmin, of 500 m/s. We corrected motions for linear and nonlinear site response for the shear wavespeed, VS, from the USGS 3D model, using a recently developed ground-motion model (GMM) for Fourier amplitude spectra . At soft soil locations subjected to strong shaking, the site-corrected intensities reflect the competing effects of linear amplification by low V S material, reduction of stiffness during nonlinear deformation, and damping of high frequencies. Sites with near-surface V S of 500 m/s or greater require no linear site correction but can experience amplitude reduction due to nonlinear response. Averaged over all sites, we obtained reasonable agreement with empirical ergodic median GMMs currently used for seismic hazard and design ground motions (epsilon less than 1), with marked improvement at soft sedimentary sites. At specific locations, the simulated shaking intensities show systematic differences from the GMMs that reveal path and site effects not captured in these ergodic models. Results suggest how next generation regional-scale earthquake simulations can provide higher spatial and frequency resolution while including effects of soft soils that are commonly ignored in scenario earthquake ground-motion simulations.

58 GEOSCIENCES↗
DOE OSTI2024

Measurement of Stability Diagram at IOTA at Fermilab

Nonlinear focusing elements can enhance the stability of particle beams in high-energy colliders by means of Landau Damping, through the tune spread which is introduced. We propose an experiment at Fermilab’s Integrable Optics Test Accelerator (IOTA) to investigate the influence of nonlinear focusing elements on the transverse stability of the beam. In this experiment, we employ an anti-damper, an active transverse feedback system, as a controlled mechanism to induce coherent beam instability. By utilizing the anti-damper, we can examine the impact of the nonlinear focusing element on the beam’s transverse stability. The stability diagram, a tool used to determine the system’s stability, will be measured using a recently demonstrated method at the LHC. This measurement is carried out experimentally by selecting specific threshold gains and measuring them for a range of phases. The stability diagram is represented by gei¿ on the complex plane. The experiment at IOTA adds insight towards the stability diagram measurement method by supplying a reduced machine impedance, to investigate the impedance’s effect on the stability diagram, as well as a larger range of phase measurements.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

An Overview of RF Systems for the EIC

The Electron Ion Collider (EIC) to be constructed at Brookhaven National Laboratory in the USA will be a complex system of accelerators providing high luminosity, high polarization, variable center of mass energy collisions between electrons and protons or ions. To achieve this a variety of RF systems are required. They must provide for capture, formation and storage of Ampere-class beams in the electron and hadron storage rings (ESR and HSR), fast acceleration of high-charge polarized electron bunches in the rapid cycling synchrotron (RCS), provision of cold high current electron bunches in the high-energy cooler ERL and precise high-gradient crabbing of electrons and hadrons either side of the interaction point. The challenges include strong HOM damping in the storage ring cavities and cooler ERL, very high fundamental mode power in the ESR and cooler injector, extremely stable low-noise operation of the crab cavities, mitigation of transient beam loading from gaps, and operating over a wide range of energies and beam currents. We describe the high-level system parameters and principal design choices made and progress on the R&D plan to develop these state of the art systems.

Rimmer, R. A.↗
DOE OSTI2021

3D Tracking of a Single Electron in IOTA

High-resolution observations of single-particle dynamics have potential as a powerful tool in the diagnostics, tuning and design of storage rings. We are presenting the results of experiments with single electrons that were conducted at Fermilab’s IOTA ring to explore the feasibility of this approach. A set of sensitive, high-resolution digital cameras was used to detect the synchrotron radiation emitted by an electron, and the resulting images were used to reconstruct the time evolution of oscillation amplitudes in all three degrees of freedom. From the evolution of the oscillation amplitudes, we deduce transverse emittances, momentum spread, damping times, beam energy and estimated residual-gas density and composition. To our knowledge, this is the first time that the dynamics of a single particle in a storage ring has been tracked in all three dimensions. We discuss farther development of a single particle diagnostics that may allow reconstruction of its turn-by-turn coordinates over macroscopic periods of time facilitating ultra-precise lattice diagnostics and direct benchmarking of tracking codes.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Beam Dynamics Study in a Dual Energy Storage Ring for Ion Beam Cooling

A dual energy storage ring designed for beam cooling consists of two closed rings with significantly different energies: the cooling and damping rings. These two rings are connected by an energy recovering superconducting RF structure that provides the necessary energy difference. In our design, the RF acceleration has a main linac and harmonic cavities both running at crest that at first accelerates the beam from low energy E_{L} to high energy E_{H} and then decelerates the beam from E_{H} to E_{L} in the next pass. The purpose of the harmonic cavities is to extend the bunch length in a dual energy storage ring as such a longer bunch length may be very useful in a cooling application. Besides these cavities, a bunching cavity running on zero-crossing phase is used outside of the common beamline to provide the necessary longitudinal focusing for the system. In this paper, we present a preliminary lattice design along with the fundamental beam dynamics study in such a dual energy storage ring.

Dhital, B.↗
DOE OSTI2022

The European ERL Roadmap

Following the European Strategy process in 2019, five Roadmap Panels were set up to prepare the technologies needed for future accelerators and colliders: high-field magnets, SRF, muon colliders, plasma wakefield accelera-tors and Energy Recovery Linacs (ERLs). The ERL Roadmap Panel, consisting of ERL experts from around the world, first developed an overview of current and future ERLs. From this it was possible to carry out a gap analysis to see what R&D would be needed, from which the roadmap could be developed. The European ERL Roadmap [1] focused on three main aspects: 1) the con-tinuation and development of facility programs for which no additional funds are needed, S-DALINAC in Darm-stadt and MESA in Mainz; 2) technology development for room-temperature HOM damping and twin-axis SRF cavities; 3) the timely upgrade of bERLinPro for 100 mA current and the construction of PERLE at Orsay as a dedi-cated 10 MW power multi-turn facility. The roadmap entails a vision of a future energy frontier electron-positron and electron-hadron collider and describes a high-quality ERL program for 4.4K SRF technology at high Q0.

Hutton, A.↗
DOE OSTI2022

Simulation Studies of Intra-Train, Bunch-by-Bunch Feedback Systems at the International Linear Collider

The International Linear Collider (ILC) is a proposed electron-positron collider targeting collision energies from 250 GeV to 1 TeV. With design luminosities of order 10³⁴ cm²s⁻¹, a beam-based, intra-train feedback system would be required near the Interaction Point (IP) to provide nanometre-level stabilisation of the beam overlap in the collisions. Here we present results from beam-tracking simulations of the 500 GeV ILC, including the impact of beam-trajectory imperfections on the luminosity, and the capability of the IP feedback system to compensate for them. Effects investigated include the position jitter introduced by the damping ring extraction kicker, short-range and long-range wakefields, and ground motion. The feedback system was shown to be able to correct for beam-beam offsets of up to 200 nm and stabilise the collision overlap to the nanometre level, within a few bunch crossings.

Ramjiawan, R. L.↗
DOE OSTI2024

Progress on the normal conducting magnets for the Electron-Ion Collider

The electron-ion collider (EIC) at Brookhaven National Laboratory (BNL) is designed to deliver a peak luminosity of 1e+34 1/cm2 1/sec. The EIC will take advantage of the existing Relativistic Heavy Ion Collider (RHIC) facility. Two additional rings will be installed: an electron storage ring (ESR) and a rapid cycling electron synchrotron ring (RCS).This paper presents an update on the normal conducting magnet designs required for both the ESR and RCS rings. The ESR will store polarized electron beams up to 18 GeV and utilizes a triplet of dipole magnets to increase the emittance at 5 GeV and generate excess bending to create additional radiation damping to allow a larger beam-beam tune shift. The RCS will accelerate single bunches of spin-polarized electrons at various energies from 5 GeV to 18 GeV, with a ramp rate of 100 ms and 1 Hz repetition rate. Both rings require dipole, quadrupole and sextupole magnets with different specifications.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Measurement of stability diagrams in the IOTA ring at Fermilab

Nonlinear focusing elements can enhance the stability of particle beams in high-energy colliders through Landau Damping, by means of the tune spread which is introduced. Here we discuss an experiment at Fermilab's Integrable Optics Test Accelerator (IOTA) which investigates the influence of nonlinear focusing elements, such as octupoles, on the beam’s transverse stability. In this experiment, we employ an anti-damper, an active transverse feedback system, as a controlled mechanism to induce coherent beam instability. By utilizing the anti-damper we can examine the impact of a nonlinear focusing element on the beam's transverse stability. The stability diagram, a tool used to determine the system's stability, is measured using a recently demonstrated method at the LHC. The experiment at IOTA adds insight towards this stability diagram measurement method by supplying a reduced machine impedance to investigate the machine impedance’s effect on the stability diagram, as well as by aiming to map out the full stability diagram by using a large phase range of the anti-damper. From this experiment in IOTA, we present the first results of stability diagram analysis with varying octupole currents.

43 PARTICLE ACCELERATORS↗