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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.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Microgrid Assisted Design for Remote Areas

In this work, we present a three-stage multiobjective mixed-integer linear programming (MILP) for the optimal expansion planning and operation of isolated multienergy microgrids in remote areas. By selecting the optimal distributed generators (DGs) and energy storage systems (ESSs) mix selection, siting, sizing, and scheduling in the remote microgrid, the proposed model is targeted to minimize the annualized total cost of microgrids while enhancing the performance of the system, i.e., minimizing the voltage deviations and line power loss. To represent the electricity and heat flow between generation resources and various electrical, heating, and cooling loads in the isolated microgrid, linearized power flow, and heat flow constraints are employed in the proposed optimization model. The available capacity of DGs and ESSs are modeled as discrete constants instead of continuous variables for practical purpose. Numerical simulation results on a remote microgrid consisting of DGs, ESSs, and various loads validate the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗
DOE OSTI2024

Small-scale signatures of primordial non-Gaussianity in k-nearest neighbour cumulative distribution functions

ABSTRACT Searches for primordial non-Gaussianity in cosmological perturbations are a key means of revealing novel primordial physics. However, robustly extracting signatures of primordial non-Gaussianity from non-linear scales of the late-time Universe is an open problem. In this paper, we apply k-Nearest Neighbour cumulative distribution functions, kNN-CDFs, to the quijote-png simulations to explore the sensitivity of kNN-CDFs to primordial non-Gaussianity. An interesting result is that for halo samples with $M_\mathrm{ h}\langle 10^{14}$ M$_\odot$ $h^{-1}$, the kNN-CDFs respond to equilateral PNG in a manner distinct from the other parameters. This persists in the galaxy catalogues in redshift space and can be differentiated from the impact of galaxy modelling, at least within the halo occupation distribution (HOD) framework considered here. kNN-CDFs are related to counts-in-cells and, through mapping a subset of the kNN-CDF measurements into the count-in-cells picture, we show that our results can be modelled analytically. A caveat of the analysis is that we only consider the HOD framework, including assembly bias. It will be interesting to validate these results with other techniques for modelling the galaxy–halo connection, e.g. (hybrid) effective field theory or semi-analytical methods.

Coulton, William R. (ORCID:0000000212973673)↗
DOE OSTI2019

A cloud computing approach to massively-parallel distributed stochastic optimization with application to geomechanical reservoir characterization

Many search strategies used to optimize parameters during hydrologic model calibration are inherently limited in that simulations must be performed sequentially in order for the algorithm to converge. As a result, the overall time required to reach a solution increases linearly with the number of steps necessary. In contrast, sampling strategies that attempt to approximate the posterior distribution of the parameters do not require the model simulations to be run in sequence and therefore invite the use of a massively parallel approach across heterogeneous computing environments. We apply a cloud computing methodology to this problem where a head node running on Amazon Web Services continuously produces candidate models that are distributed to arbitrary compute environments to run the simulation, in our case Clemson’s Palmetto cluster computer. Thus the time required to obtain a sufficient number of samples to produce an adequate approximation of the posterior distribution of the parameters is limited by the number of available compute sites. Monte Carlo sampling of the posterior space would be duplicative and inefficient, thus we combine Latin hypercube methods with genetic algorithms to ensure that no large regions of the parameter space are left unexplored, and that high probability regions are investigated thoroughly. We independently assess the fit to different types of data sets without the need to construct a single objective function. Sets of Pareto optimal models are particularly valuable when the quality and information content of data is poorly known or conceptual model errors exist in our simulation. We illustrate our approach for a problem where in situ strain data are used to calibrate the parameters of an oil reservoir in the Avant oil field in Oklahoma. We use well injection and shut-in to stress a deep (500m) confined formation, and observe the geomechanical response using borehole strainmeters installed in the shallow subsurface (30m). These data were then used to calibrate the poroelastic properties of the reservoir and caprock along with the geometry of an elliptic channel associated with the formation. Using our approach we are able to identify issues with model error as well as substantial tradeoffs that occur within the parameters.

inversion, stochastic, geomechanics, poroelastic, ↗
DOE OSTI2024

An economic perspective of the circular bioeconomy in the food and agricultural sector

Transforming the agri-food system from a “take-make-waste”, or linear production system, to a circular bioeconomy that reduces, recycles, recovers, reuses, and regenerates wastes and transitions from fossil to biobased fuels and products is being hailed as critical for meeting a growing population’s food and fuel needs in environmentally sustainable ways. While a transformation towards a circular bioeconomy is an appealing strategy to achieve multiple environmental goals, we argue that this strategy needs to go beyond a techno-centric focus and adopt an economic value-based lens to balance the desire for circularity with its costs, benefits, and distributional effects on society. This perspective analyzes the mechanisms that sustain the existing linear economy and proposes a novel social cost-benefit framework to determine the optimal level and path to circularity. We present five critical pathways to achieve a sustainable circular bioeconomy in a market economy consisting of decentralized decision-makers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Oblique propagation and temperature effects on the resonant right-hand ion beam instability

The resonant right-hand instability (RHI) is often the dominant mode driven by reflected ions upstream of Earth’s quasi-parallel bow shock. In the tradition of Peter Gary, this paper further explores the right-hand instability using numerical solutions of the plasma dispersion relation and non-linear kinetic simulations, with parameters inspired by observations from NASA’s Magnetospheric Multiscale (MMS) mission. Agreement is found between the ion distributions in the particle-in-cell simulations and Magnetospheric Multiscale spacecraft data, which show the gyrophase bunching characteristic of the instability. The non-linear structures created by right-hand instability tend to be stronger when the plasma beta is lower. These structures have sizes of around 100 to 200 ion inertial lengths perpendicular to the magnetic field, presenting planet-sized disturbances to the magnetosphere. 2d and 3D hybrid particle-in-cell simulations show that modes with a range of propagation angles oblique to the magnetic field are excited, providing a ground to understand previous statistical studies of observed foreshock waves.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments

A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in reference two. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized* data are perfect; 2. Normality: The prior and posterior PDF are normal; and 3. Linearity: The model is linear. In this work we outline how the framework in 1 could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in 1 to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implement- ing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS, and the stochastic method, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Frequency-Nadir-Constrained Unit Commitment for Low-Inertia, High-IBR Island Power Systems [Slides]

The process of energy decarbonization in island power systems is accelerated due to the swift integration of inverter-based renewable energy resources (IBRs). The unique features of such systems, including rapid frequency changes resulting from potential generation outages or imbalances due to the unpredictability of renewable power, pose a significant challenge in maintaining the frequency nadir without external support. This paper presents a unit commitment (UC) model with data-driven frequency nadir constraints, including either frequency nadir or minimum inertia requirements, helping to limit frequency deviations after significant generator outages. The constraints are formulated using a linear regression model that takes advantage of real-world, year-long generation scheduling and dynamic simulation data. The efficacy of the proposed UC model is verified through a year-long simulation in an actual island power system using historical weather data. The alternative minimum inertia constraint, derived from actual system operation assumptions, is also evaluated. Findings demonstrate that the proposed frequency nadir constraint notably improves the system's frequency nadir under high photovoltaic (PV) penetration levels, albeit with a slight increase in generation costs, when compared to the alternative minimum inertia constraint.

14 SOLAR ENERGY↗
DOE OSTI2022

A detailed analysis of the dynamics of fast neutrino flavor conversions with scattering effects

We calculate the dynamics of fast neutrino flavor conversions with Boltzmann collisions of neutrino scatterings in a homogeneous system. We find the enhancement or suppression of the flavor conversions in various setups of the collision terms. We analyze the mechanism of fast flavor conversions based on the motion of polarization vectors in the cylindrical coordinate analogous to a pendulum motion. The phases of the all the polarization vectors synchronize in the linear evolution phase, and the phase deviation from the Hamiltonian governs the neutrino flavor conversions. In a non-linear regime of flavor conversions, the collision terms induce a spiral motion of the polarization vector and gradually make the phase space smaller. The collision terms align all of the polarization vectors, and the flavor conversions eventually settle into equilibrium when the distributions of neutrinos become isotropic. Though our current analysis does not fully clarify the non-linear phenomena of fast flavor conversions, the framework of the pendulum motion gives a new insight into this complicated phenomenon that will be helpful in further studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Development of machine learning framework for interface force closures based on bubble tracking data

Interfacial force closures in the two-fluid model play a critical role for the predictive capabilities of void fraction distribution. However, the practices of interfacial force modeling have long been challenged by the inherent physical complexity of the two-phase flows. The rapidly expanding computational capabilities in the recent years have made high-fidelity data from the interface-captured direct numerical simulation become more available, and hence potential for data-driven interfacial force modeling has prevailed. In this work, we established a data-driven modeling framework integrated to the HZDR multiphase Eulerian-Eulerian framework for computational fluid dynamics simulations. The data-driven framework is verified in a benchmark problem, where a feedforward neural network managed to capture the non-linear mapping between bubble Reynolds number and drag coefficient and reproduce the void distribution resulting from the baseline model in the test case. The second focus is on utilizing the bubble tracking data set to form a closure for the bubble drag in the turbulent bubbly flow, in which the drag coefficient is set to be correlated with the bubble Reynolds number and the Eötvös number. Pseudo-steady state filtering in the Frenet Frame was carried out to obtain the drag coefficient from the turbulent bubbly flow data. The performance of the data-driven drag model is also examined through a case study, where improvement of model’s prediction near-wall is regarded necessary. In conclusion, discussion and further plans of investigation are provided.

42 ENGINEERING↗
DOE OSTI2024

Parallel interior-point solver for block-structured nonlinear programs on SIMD/GPU architectures

Here, we investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive operations: the evaluation of the derivatives and the solution of the associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both operations using two levels of parallelism. First, we distribute the computations on multiple processes using coarse parallelism. Second, each process uses SIMD/GPU accelerators locally to accelerate the operations using fine-grained parallelism. The KKT system is reduced by eliminating the inequalities and the state variables from the corresponding equations. We demonstrate our method's capability on the supercomputer Polaris, a testbed for the future exascale Aurora system. Each node is equipped with four GPUs, a setup amenable to our two-level approach. Our experiments on the stochastic optimal power flow problem show that the reduction method is 50x faster than the sparse linear solver HSL MA57 running in serial on the CPU, and 6x faster than Pardiso running in parallel on CPU on the same number of processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Simulation of dilatancy-controlled gas migration processes in saturated bentonite using a coupled multiphase flow and elastoplastic H 2 M model

Dilatancy-controlled gas flow in preferential pathways plays a key role in the safety analysis of radioactive waste repositories. This is particularly the case for bentonite, an often-preferred barrier material. Gas flow in preferential pathways is characterized by localization and spontaneous behavior, which is challenging to simulate in numerical models due to strong hydro-mechanical coupling. To analyze a laboratory experiment in the framework of the DECOVALEX-2023 project, this study introduced a new approach of combining continuous modelling methods with spatial material properties derived from material heterogeneities and experimental observations. The proposed model utilized hydro-mechanical spatial distributions, namely Young's modulus and gas entry pressure, and elastoplasticity combined with a linear swelling model. A conceptual strain-dependent permeability approach simulated dilatancy-controlled gas flow based on hydro-mechanical coupling. To test the effectiveness of the presented approach, a gas injection test in a compacted, saturated bentonite sample was simulated using the open-source code OpenGeoSys 5.8 and compared with experimental observations. The presented methodology is capable of simulating localized gas flow in preferential pathways. The spatial distributions of Young's modulus and gas entry pressure affect the swelling pressure, relative permeability and, in combination with the strain-dependent permeability model, also the intrinsic permeability.

42 ENGINEERING↗
DOE OSTI2021

Stochastic pre-event preparation for enhancing resilience of distribution systems

Extreme weather events are the common causes for power supply interruptions and power outages in electrical distribution systems. Improving the distribution system and enhancing its resilience is becoming crucial due to the increased frequency of extreme weather events. Preparation and allocation of multiple flexible resources, such as mobile resources, fuel resources, and labor resources before extreme weather events can mitigate the effects of extreme weather events and enhance the resilience of power distribution systems. Here, in this paper, a two-stage stochastic mixed-integer linear programming (SMILP) is proposed to optimize the preparation and resource allocation process for upcoming extreme weather events, which leads to faster and more efficient post-event restoration. The objective of the proposed two-stage SMILP is to maximize the served load and minimize the operating cost of flexible resources. The first stage in the optimization problem selects the amounts and locations of different resources. The second stage considers the operational constraints of the distribution system and repair crew scheduling constraints. The proposed stochastic pre-event preparation model is solved by a scenario decomposition method, Progressive Hedging (PH), to ease the computational complexity introduced by a large number of scenarios. Furthermore, to show the impact of solar photovoltaic (PV) generation on system resilience, three types of PV systems are considered during a power outage and the resilience improvements with different PV penetration levels are compared. Numerical results from simulations on a large-scale (more than 10,000 nodes) distribution feeder have been used to validate the effectiveness and scalability of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Rapidity-dependent spin decomposition of the nucleon

We revisit the two-dimensional Fourier transform of generalized parton distributions (GPDs) at nonzero skewness. At 𝜂 = 0 it reduces to the standard impact-parameter density, while at 𝜂 ≠ 0 it is an off-forward amplitude that we interpret as a genuine parton–nucleon correlation. Its overall strength (the transverse-plane integral of the density) is fixed by the GPD at the kinematic point 𝑡 =−𝑐 𝜂 =−4⁢𝜂 2 ⁢𝑚$^{2}_{𝑁}$/(1 − 𝜂 2 ) and decreases monotonically with the rapidity gap Δ⁢𝑦 = ln⁡[(1+𝜂)/(1−𝜂)] = 2 artanh⁡(𝜂). This rapidity dependence implies rapidity-modified Ji identities that connect helicity, orbital, and total angular momenta of the correlation in closed form. To quantify these effects, we construct leading-twist quark and gluon GPDs in a string-based conformal framework: conformal moments are parametrized by linear open- and closed-string Regge trajectories with slopes constrained by parton distribution functions (PDFs), hadron/glueball spectroscopy, and form-factor data, and GPDs are reconstructed over the full (𝑥,𝜂,𝑡) domain by Mellin-Barnes inversion with next-to-leading order evolution. We find qualitative agreement (and fair quantitative agreement within quoted uncertainties) for several moments and selected nonsinglet 𝑥-space channels at 𝜇 = 2 GeV when compared with lattice QCD, while we also identify channels with visible tension and discuss likely sources (PDF priors and 𝑡-slope systematics).

Gauge-gravity dualities↗
DOE OSTI2022

Exploiting non-linear scales in galaxy–galaxy lensing and galaxy clustering: A forecast for the dark energy survey

ABSTRACT The combination of galaxy–galaxy lensing (GGL) and galaxy clustering is a powerful probe of low-redshift matter clustering, especially if it is extended to the non-linear regime. To this end, we use an N-body and halo occupation distribution (HOD) emulator method to model the redMaGiC sample of colour-selected passive galaxies in the Dark Energy Survey (DES), adding parameters that describe central galaxy incompleteness, galaxy assembly bias, and a scale-independent multiplicative lensing bias Alens. We use this emulator to forecast cosmological constraints attainable from the GGL surface density profile ΔΣ(rp) and the projected galaxy correlation function wp, gg(rp) in the final (Year 6) DES data set over scales $r_p=0.3\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$. For a $3{{\ \rm per\ cent}}$ prior on Alens we forecast precisions of $1.9{{\ \rm per\ cent}}$, $2.0{{\ \rm per\ cent}}$, and $1.9{{\ \rm per\ cent}}$ on Ωm, σ8, and $S_8 \equiv \sigma _8\Omega _m^{0.5}$, marginalized over all halo occupation distribution (HOD) parameters as well as Alens. Adding scales $r_p=0.3\!-\!3.0\, h^{-1} \, \mathrm{Mpc}$ improves the S8 precision by a factor of ∼1.6 relative to a large scale ($3.0\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$) analysis, equivalent to increasing the survey area by a factor of ∼2.6. Sharpening the Alens prior to $1{{\ \rm per\ cent}}$ further improves the S8 precision to $1.1{{\ \rm per\ cent}}$, and it amplifies the gain from including non-linear scales. Our emulator achieves per cent-level accuracy similar to the projected DES statistical uncertainties, demonstrating the feasibility of a fully non-linear analysis. Obtaining precise parameter constraints from multiple galaxy types and from measurements that span linear and non-linear clustering offers many opportunities for internal cross-checks, which can diagnose systematics and demonstrate the robustness of cosmological results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Quantifying a partial polyamorphic transition in a cerium-based metallic glass during cooling

Cerium-based metallic glasses are prototype polyamorphous systems with pressure-induced polyamorphic transitions extensively reported. Cooling typically has a similar effect on materials as compression with regard to reducing volume. However, previous studies show dramatically different behavior of Ce-based metallic glasses between cooling and compression, whose origin remains unclear. Here, using in situ low-temperature synchrotron high-energy x-ray diffraction, the structural evolution of a Ce68Al10Cu20Co2 metallic glass is accurately determined and analyzed by a structure factor and a reduced pair distribution function (PDF) during cooling from 298 to 83 K. An unusually large linear thermal expansion coefficient is revealed, which is associated with both continuous but inconsistent structural changes between the two subpeaks of the first atomic shell in terms of average bond lengths and coordination numbers. These phenomena are suggested to be attributed to a gradual 4f electron delocalization of only a minimal amount (∼2.6% at 83 K) of Ce atoms by quantitative analysis of the PDF data. However, a previously expected global polymorphic transition from a low-density amorphous state to a high-density amorphous state with an abrupt volume collapse is not observed. Moreover, electrical resistivity also shows a continuous increase during cooling without any sharp change. It is clarified that cryogenic temperatures could facilitate but are not powerful enough alone to trigger a global polymorphic transition in the Ce68Al10Cu20Co2 metallic glass, suggesting a wide distribution of its local atomic environment.

Chen, Zhi↗
DOE OSTI2024

Test and Validate Distributed Coaxial Cable Sensors for in situ Condition Monitoring of Coal-Fired Boiler Tubes

This project aims to test, validate, and advance the technology readiness level (from TRL5 to TRL7) of a novel low-cost distributed stainless-steel/ceramic coaxial cable sensing (SSC-CCS) technology for in situ monitoring of the boiler tube temperature in existing coal-fired power plants. The novel SSC-CCS sensing technology and associated condition-based monitoring (CBM) software to be demonstrated in this project will lead to an improved understanding of the boiler tube failure mechanisms and a prognostic system to improve the overall performance, reliability, and flexibility of the nation’s coal-fired power plant fleet. A boiler tube monitoring system with distributed coaxial cable temperature sensors and a sensor acquisition system was constructed. The high-temperature coaxial cable sensor with a length of 1.3m was made by using a quartz tube (1mm inner diameter (ID) and 6mm outer diameter (OD)) to concentrically separate a 304 stainless-steel (SS) rod (1mm OD) and SS tube (7.94mm OD and 6.16mm ID). The sensor acquisition system includes a vector network analyzer (VNA), a radio frequency (RF) power amplifier, multiple switches and a USB hub. The distributed stainless-steel quartz coaxial cable sensor (SSQ-CCS) had a linear response to temperature with a resolution uncertainty of σ = 0.77℃. To withstand the harsh conditions of 3,300 steam pressures and 800℃ high temperatures, the sensor was shielded by a protective tube made of the same material as the boiler tube. The protection tube had an OD of 1.5 inches and a thickness of 0.25 inches. In the laboratory tests, the sensor showed good sensitivity and fast response. The drift was bounded between +0.33% and -0.67% during a test at 600℃ for 350 hours, indicating good stability of the sensor. A field test was conducted where four sensors were welded on four superheat tubes (SH-Ts) at a coal-fired power station over 400 days. Conventional thermocouples were welded to the superheater tubes alongside the coaxial cable sensors for the purpose of comparison. Two sensors were capable of distributed sensing, with three multiplexed sensing sections. The other two sensors were single section. During the 400-day test period, the power plant experienced startups and shutdowns. At the steady state operations, the temperature of the boiler tube is about 600℃ (1112°F). The sensors recorded the entire coal-firing processes (start-up, steady state, and shut-down) and the glitch event. A GSM modem and a Watchdog were added to the system to ensure reliable data recording. The GSM modem sent daily messages to plant managers and Clemson team to inform the status of the sensor system. If the system was not normally working, the Watchdog would reboot the system automatically. The new coaxial cable based distributed sensing technology has been proven to be successful in both laboratory and field tests. A comprehensive four-stage multi-physics computational framework has been developed to assist the design, optimization, installation, and operation of SSQ-CCS. With the consideration of various operation conditions, we predict the distributions of flue gas temperatures within coal-fired boilers, the temperature correlation between the boiler tube and SSQ-CCS, and the safety of SSQ-CCS. A conditional-based monitoring system is implemented as well. The computational framework developed in this work can guide the future operation of coal-fired plants and other power plants for the safety prediction of boiler operations.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2021

On the possibility of footprint compression with one lens in nonlinear accelerator lattice

Electromagnetic interaction of colliding beams along with other nonlinear fields often limits the beams' lifetimes and luminosities. Nonlinearities result in the spread of betatron frequencies (footprint) and, thus, may enhance dynamic diffusion of particles due to high order resonances. One of the possible ways to eliminate nonlinearities and overcome the corresponding difficulties is compensation of nonlinear forces, but, in practice, it is hardly possible to obtain exact linearity of the system. The compensation with a single nonlinear lens cannot cope with distributed nonlinearities, nonlinearities due to parasitic crossings, etc. Here, we present a method to compute parameters of nonlinear element (lens) that eliminates both the footprint and resonance strength without achieving full compensation.

43 PARTICLE ACCELERATORS↗