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At least 1,171 records · Page 65

Advancements in Constitutive Model Calibration: Leveraging the Power of Full‐Field DIC Measurements and In Situ Load Path Selection for Reliable Parameter Inference

Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.

Bayesian optimal experimental design↗

Noise resilience of variational quantum compiling

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e. the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effective Field Theory Analysis of CDMSlite Run 2 Data

CDMSlite Run 2 was a search for weakly interacting massive particles (WIMPs) with a cryogenic 600 g Ge detector operated in a high-voltage mode to optimize sensitivity to WIMPs of relatively low mass from 2 - 20 GeV/$c^2$. In this article, we present an effective field theory (EFT) analysis of the CDMSlite Run 2 data using an extended energy range and a comprehensive treatment of the expected background. A binned likelihood Bayesian analysis was performed on the recoil energy data, taking into account the parameters of the EFT interactions and optimizing the data selection with respect to the dominant background components. Energy regions within 5$\sigma$ of known activation peaks were removed from the analysis. The Bayesian evidences resulting from the different operator hypotheses show that the CDMSlite Run 2 data are consistent with the background-only models and do not allow for a signal interpretation assuming any additional EFT interaction. Consequently, upper limits on the WIMP mass and coupling-coefficient amplitudes and phases are presented for each EFT operator. These limits improve previous CDMSlite Run 2 bounds for WIMP masses above 5 GeV/$c^2$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Novel Framework for Optimizing Ramping Capability of Hybrid Energy Storage Systems

Hybrid Energy Storage System has been widely applied in aerospace, electric vehicle, and microgrid applications. The advantages are that they include complimentary technologies with both high power and energy capabilities. HESS have the potential to be useful to the bulk power systems, for example to increase the value of energy produced by variable generation resource through enabling participation in ancillary service markets. Actualizing the benefits of HESSs requires optimizing the combined ramping capability of aggregated HESS resources. To provide quality ancillary service, source of HESSs locating at multiple sites of variable generation resource must be optimally sized and cohesively controlled. Optimizing aggregated resources can be formulated as an optimization problem. Successfully solving this problem not only requires using effective solution methods but also depends on accurately and rapidly setting the necessary parameters in the problem formula. This article proposes a novel framework with double-layer structure to solve the optimization problem of aggregating ramping capability. Program developed on the upper layer focuses on solving the optimization of aggregating ramping capability among multiple HESSs and is compatible with most existing optimization algorithms. Program on lower layer of the framework targets at optimizing the local control of a single HESS based on a thorough analytics of HESS operation strategy presented in this article. Result of local optimization is also provided to upper layer program for updating the parameters in formula of optimization problem. Real time hardware-in-the-loop test is conducted to verify the performance of the optimization framework developed. The work presented is expected to provide guidance for implementing this framework in practical operation.

Luo, Yushen↗

Large gradients via correlation in random parameterized quantum circuits

Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Here, examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover's algorithm based on the quantum alternating operator ansatz. In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward $\mathcal{O}\left({2}^{n/2}\right)$, the optimal oracle complexity of quantum unstructured search.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

3D small-gain formula allowing strong focusing and harmonic lasing for a ring-based x-ray free electron laser oscillator

We present a detailed derivation of a formula for the small-gain calculation for an x-ray free electron laser oscillator (XFELO) based on a medium-energy (3–4 GeV) storage ring. We found harmonic lasing and strong focusing are essential for this beam energy range. Taking the small-signal low-gain formula developed by Kim and his colleagues, we modified it in such a way that the gain can be calculated without the “no focusing approximation,” and a strong focusing can be applied, as well as harmonic lasing. In this formula, the gain is represented as a product of two factors with one of them depending only on the harmonic number, undulator period, and gap. Using this factor, we show that it is favorable to use harmonic lasing to achieve hard x-ray FEL working in the small-signal low-gain regime with the medium-energy electron beam. Our formula also allows FEL optimization by varying the vertical gradient of the undulator, the vertical dispersion, and the horizontal and vertical focusing, independently. As an example, we applied this formula to study the feasibility of an XFELO option for the National Synchrotron Light Source II (NSLS-II) upgrade. Since a quite high peak current is required for the FEL, collective effects of beam dynamics in medium-energy synchrotrons significantly affect the electron beam parameters. We carried out a multiparameter optimization taking collective effects into account. Note, even though our example is for a ring-based XFELO at 3 to 4 GeV, the formula and, in particular, the approach developed here may be applied to other types of FELs. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

Downhole Sensing and Event-Driven Sensor Fusion for Depth-of-Cut Based Autonomous Fault Response and Drilling Optimization

Achieving robust and efficient drilling is a critical part of reducing the cost of geothermal energy exploration and extraction. Drilling performance is often evaluated using one or more of three key metrics: depth of cut (DOC), rate of penetration (ROP), and mechanical specific energy (MSE). All three of these quantities are related to each other. DOC refers to the depth a bit penetrates into rock during drilling. This is an important quantity for estimating bit behavior. ROP is the simply the DOC multiplied by the rotational rate, and represents how quickly the drill bit is advancing through the ground. ROP is often the parameter used for drilling control and optimization. Finally, MSE provides insight into drilling efficiency and rock type. MSE calculations rely on ROP, drilling force, and drilling torque. Surface-based sensors at the top of the drill are often used to measure all these quantities. However, top-hole measurements can deviate substantially from the behavior at the bit due to lag, vibrations, and friction. Therefore, relying only on top-hole information can lead to suboptimal drilling control. In this work, we describe recent progress towards estimating ROP, DOC, and MSE using down-hole sensing. We assume down-hole measurements of torque, weight-on-bit (WOB). Our hypothesis is that these measurements can provide more rapid and accurate measures of drilling performance. We show how a multi-layer perceptron (MLP) machine learning algorithm can provide rapid and accurate performance when evaluated on experimental data taken from Sandia’s Hard Rock Drilling Facility. In addition, we implement our algorithms on an embedded system intended to emulate a bottom-hole-assembly for sensing and estimation. Our experimental results show that DOC can be estimated accurately and in real-time. These estimates when combined with measurements for rotary speed, torque, and force can provide improved estimates for ROP and MSE. These results have the potential to enable better drilling assessment, improved control, and extended component lifetimes.

15 GEOTHERMAL ENERGY↗

Control-inspired design and power optimization of an active mechanical motion rectifier based power takeoff for wave energy converters

Ocean waves have high energy density and are persistent and predictable. Yet, converting wave energy to a useable form remains challenging. A significant hurdle is the oscillatory nature of waves resulting in the alternating loads, which necessitate the use of rectification at some stage of the energy conversion. This research effort presents a novel design of active mechanical motion rectifier (AMMR) for the power takeoff (PTO), which provides enhanced controllability and better power performance when compared to passive mechanical motion rectifiers (MMR). Inspired by transistors used in synchronous electrical rectifiers, the proposed design uses controllable electromagnetic clutches in the mechanical transmission to allow active engagement-disengagement control; thus, rectifying the oscillatory motion into a unidirectional rotation for high energy conversion efficiency and allowing the generator in unidirectional rotation to control the bidirectional wave capture structure for maximizing the power output. A semi-analytical computational approach is developed to efficiently evaluate the optimal power achieved using the proposed AMMR-based PTO and active control. It is found that the AMMR-based PTO design yields a higher optimal power than the previous passive MMR design across the wave spectrum. The influences of generator inertia and reactive power are discussed. Furthermore, the effects of control parameters on the power output and the optimal trajectories are analyzed. Wave tank tests with the AMMR prototype demonstrated the effectiveness of AMMR based PTO design and validated the numerical analysis.

16 TIDAL AND WAVE POWER↗

Group structure selection with random forests

Choosing an appropriate group structure for multigroup transport is far from an exact science. For some applications, one blindly uses a group structure developed years ago by forgotten methods. Furthermore, one sometimes uses the same group structure for a variety of problems, even if the group structure was originally developed with a certain application in mind. In this work, we create optimized group structures with simulated annealing for critical assembly test problems and apply a random forest regressor with bagging to choose the best group structure based on parameters of the different test problems. The optimized group structures were generated using a simulated annealing optimizer for several simple, spherical, and unreflected problems. The optimization was performed to minimize a cost function that included fission rate, absorption rate, leakage, and k{sub eff}. A random forest regressor was then trained on a set of International Criticality Safety Benchmark Evaluation Project inputs and used to select one of these six group structures. The trained machine learning model chose the best group structure 65% of the time, and one of the three best 89% of the time. Furthermore, it decreased the L2 error over all test problems by a factor of 25 when compared to the standard Los Alamos 70-group structure. In other words, the model chose group structure that were far more appropriate for the test problems than the traditional LANL group structure. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Automation and control of laser wakefield accelerators using Bayesian optimization

Laser wakefield accelerators promise to revolutionize many areas of accelerator science. However, one of the greatest challenges to their widespread adoption is the difficulty in control and optimization of the accelerator outputs due to coupling between input parameters and the dynamic evolution of the accelerating structure. Here, we use machine learning techniques to automate a 100 MeV-scale accelerator, which optimized its outputs by simultaneously varying up to six parameters including the spectral and spatial phase of the laser and the plasma density and length. Most notably, the model built by the algorithm enabled optimization of the laser evolution that might otherwise have been missed in single-variable scans. Subtle tuning of the laser pulse shape caused an 80% increase in electron beam charge, despite the pulse length changing by just 1%.

43 PARTICLE ACCELERATORS↗

The DESC stellarator code suite Part 3: Quasi-symmetry optimization

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to automatic differentiation, which efficiently provides exact derivative information. A Gauss–Newton trust-region optimization method uses second-order derivative information to take large steps in parameter space and converges rapidly. With just-in-time compilation and GPU portability, high-dimensional stellarator optimization runs take orders of magnitude less computation time with DESC compared to other approaches. This paper presents the theory of the DESC fixed-boundary local optimization algorithm along with demonstrations of how to easily implement it in the code. Example quasi-symmetry optimizations are shown and compared to results from conventional tools. Three different forms of quasi-symmetry objectives are available in DESC, and their relative advantages are discussed in detail. In the examples presented, the triple product formulation yields the best optimization results in terms of minimized computation time and particle transport. This paper concludes with an explanation of how the modular code suite can be extended to accommodate other types of optimization problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical Investigation of Butterfly Valve Performance in Variable Valve Sizes, Positions and Flow Regimes

Reliability and efficiency of valves are necessary for precise control and sufficient heat-flow to heat application plants for the integrated energy systems of nuclear power plants (NPPs). Strategic Management Analysis Requirement and Technology (SMART) valves’ ability to control flow and assess environmental parameters stands out for these requirements. Their ability to sustain the downstream flow rate, prevent reverse flow, and maintain pressure in the heat transport loop is much more efficient with the integration of sensors and intelligent algorithms. For assessing valve performance and monitoring, mechanical design and operating conditions are two important parameters. In this study, the butterfly valves of three different sizes are simulated with water and steam using STAR-CCM+ in various flow regimes and positions to analyze performance parameters to strategize an automated control system for efficiently balancing the heat–transport network. Also, flow behavior is studied using velocity and pressure fields for valve–body geometry optimization. It can be observed, through performance parameters, that the valves are suitable for operation between 30° and 90° positions with significantly low loss coefficients and high flow coefficients, and the performance parameters follow a certain pattern in both water and steam flow in each scenario.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Toward a scalable robust security-constrained optimal power flow using a proximal projection bundle method

Robust security-constrained optimal power flow (rSCOPF) aims to find the worst-case contingencies of alternating current optimal power flow (ACOPF) in power systems. With the rise of GPU architectures on the upcoming supercomputer architectures, optimization algorithms that rely on sparse linear algebra and indefinite linear systems are becoming increasingly hard to solve efficiently (e.g. interior-point method). To address this we revisit a maximin optimization formulation of the rSCOPF and the single-level mixed-integer semidefinite programming (MISDP) reformulation, which is obtained by taking the Lagrangian relaxation of the inner minimization ACOPF problem. In this paper, we focus on the development of a proximal projection bundle method (PPBM) for solving continuous relaxation node subproblems of the MISDP problem, based primarily on the well-known alternating direction method of multipliers. Cutting planes reminiscent of bundle method ideas are also applied in coordination with updates of the proximal parameter. The cutting-plane method can generate a large number of linear inequalities, leading to a large scale but decomposable quadratic programming (QP) subproblem that is amenable to GPUs. We present the numerical results on the IEEE 30, 57, 118, and 300-bus systems by using our PBMM method. We discuss the main computational bottleneck of our method, which is the time taken to solve each iteration of a QP subproblem instance of the PPBM, and how GPU architectures can accelerate this solution process.

bundle method↗

Optimization of the moderators in the STS preliminary design

This report details the results for an optimization of the dimensions of the moderators in the preliminary design of the Spallation Neutron Source Second Target Station (STS). This study uses the optimization algorithms of Dakota and an unstructured mesh model for the moderators in MCNP. More details on the unstructured mesh model and the automated mesh generation can be found in [3]. Parallel to this effort, the same moderator geometries have been optimized using a constructive solid geometry (CSG) MCNP model. More details on this model and its results can be found in [4]. Three optimal designs are selected for each moderator: one that is optimized for maximum peak brightness, one for maximum time-integrated brightness, and one for a combination of peak and time-integrated brightness. The backbone of the optimization work flow is provided by Dakota. For each set of design parameters requested by Dakota, a new solid geometry is automatically built in Creo and SpaceClaim, and subsequently exported to Attila4MC to generate an unstructured mesh geometry for MCNP. After the MCNP calculation is finished, the objective function (e.g., brightness metric) is returned to Dakota. After the new design has been evaluated, a result-file is written, and Dakota proposes the next set of design parameters to be evaluated. The loop continues until a specified convergence criterion has been met. The design parameters of the cylindrical (upper) moderator include the hydrogen radius, the premoderator thickness (top, bottom, radial), the beryllium radius and the horizontal position of the moderator. The crucial design choice is the hydrogen radius. A radius of 62 mm is shown to provide the maximum time-integrated brightness. The maximum peak brightness occurs with a radius of 40 mm. A combined (middle) design, which balances peak and time-integrated brightnesses, is obtained with a hydrogen radius of 50 mm. The premoderator thicknesses and the beryllium radius are slightly larger in the design optimized for time-integrated brightness than in the design optimized for peak brightness. The sensitivity to these two parameters is relatively small close to the optimal configurations. The hydrogen vessel and vacuum vessel wall thicknesses are dependent on the radius of the liquid hydrogen due to structural integrity requirements. The increased wall thicknesses for larger vessels significantly penalize the time-integrated brightness, with the maximum obtainable value reduced by more than 10% relative to earlier studies which used fixed vessel wall thicknesses. The impact of the variable wall thicknesses is much less for the peak brightness and combined brightness designs. The design parameters of the tube (lower) moderator selected for the optimization are the tube length, the annular premoderator thickness, the beryllium radius and the horizontal position of the moderator. The tube length is the crucial parameter and is chosen large (210 mm) and small (125 mm) in the designs optimized for time-integrated and peak brightness respectively. A combined optimal design has a tube length of 170 mm. The premoderator thickness and the beryllium radius are chosen larger in the design optimized for time-integrated brightness.

42 ENGINEERING↗

Sensitivity analysis applied to SiC failure probability in TRISO modeled with BISON

Here, a sensitivity analysis on the failure probability of the Silicon Carbide (SiC) layer in tristructural isotropic (TRISO) nuclear fuel during transient conditions predicted by the BISON fuel performance code is performed. The principal goal of the analysis is to understand the most important parameters dictating SiC failure behavior in BISON during Reactivity Initiated Accidents (RIAs). SiC brittle fracture probability is modeled using Weibull statistics. A total of seven inputs related to SiC failure has been selected for the analysis, including the Weibull statistics parameters, elastic moduli for SiC and Pyrolitic Carbon (PyC) and SiC stress-free temperature. A 1D TRISO BISON model has been established for various reactivity insertions performed at the Nuclear Safety Research Reactor (NSRR). The principal advantage associated with the 1D TRISO model developed in this work is its computational efficiency. The Sobol variance decomposition method is used, and the sensitivity indices are presented for eight different values of the energy deposition. The results show that the two most important parameters impacting the predicted SiC failure probability are the Weibull modulus and the characteristic stress, and a co-variance amongst these parameters is obtained for low reactivity insertions. An additional new finding of this work is that the relative importance of Weibull parameters depends on the energy deposition, and thus reactivity, regime. For low energy depositions, two parameters are of influence on SiC failure probability, while for high energy depositions only one parameter impacts failure probability results. Moreover, optimization of the Weibull modulus and characteristic stress is performed by minimizing the RMSE between BISON failure probability predictions and experimental failure fractions for each energy deposition. This work also demonstrates the validity of the NSRR tests BISON simulations and of the respective sensitivity analysis results as conservative, yet indicative for slower transients characterized by lower deposited energies. Such verification is achieved through the partial extension of the analysis to a group Control Rod Withdrawal reproduced from a previous study. Another novel result of this analysis is that no single set of Weibull parameters can reproduce all reactivity insertion experimental failure results, which is related to the intrinsic nature of SiC failure properties, and a new range for the parameters is proposed to produce a failure probability envelope that encompasses the experimental fractions. Additionaly, this work proposes a new approach for future failure analysis with BISON, consisting in the use of Weibull parameters ranges, rather than fixed sets, along with failure envelopes generation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Optimizing the regularization in size-consistent second-order Brillouin-Wigner perturbation theory

Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter ($α$) was set to recover the exact dissociation limit of H 2 in a minimal basis set. Alternatively $α$ can be viewed as a regularization parameter, where each value of $α$ represents a valid variant of BW-s2, which we denote as BW-s2($α$). In this work, we semi-empirically optimize $α$ for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the ab initio parameterization of BW-s2 and MP2. We demonstrate that the optimal $α$ parameter ($α$ = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2($α$) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2($α$) is iterative $\mathcal{O}$($N^5$), this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-amplifier Sensing Charge-coupled Devices for Next Generation Spectroscopy

We present characterization results and performance of a prototype Multiple-Amplifier Sensing (MAS) silicon charge-coupled device (CCD) sensor with 16 channels potentially suitable for faint object astronomical spectroscopy and low-signal, photon-limited imaging. The MAS CCD is designed to reach sub-electron readout noise by repeatedly measuring charge through a line of amplifiers during the serial transfer shifts. Using synchronized readout electronics based on the Dark Energy Spectroscopic Instrument CCD controller, we report a read noise of 1.03 e$^{−}$ rms pix$^{−1}$ at a speed of 26 μs pix$^{−1}$ with a single-sample readout scheme where charge in a pixel is measured only once for each output stage. At these operating parameters, we find the amplifier-to-amplifier charge transfer efficiency (ACTE) to be >0.9995 at low counts for all amplifiers but one for which the ACTE is 0.997. This charge transfer efficiency falls above 50,000 electrons for the read-noise optimized voltage configuration we chose for the serial clocks and gates. The amplifier linearity across a broad dynamic range from ∼300 to 35,000 e$^{−}$ was also measured to be ±2.5%. We describe key operating parameters to optimize on these characteristics and describe the specific applications for which the MAS CCD may be a suitable detector candidate.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

IOTA Experiment for Proton Pulse Compression at Extreme Space-Charge

The longitudinal compression of high-intensity, space-charge-dominated proton bunches is a critical requirement for future proton-driven muon colliders. We propose a proton bunch compression experiment at the Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab to investigate optimal radio-frequency (RF) cavity parameters and lattice configurations. IOTA is a compact, fixed-energy storage ring dedicated to beam physics Research and Development and capable of circulating a 2.5 MeV proton beam under extreme space-charge conditions. Using the ImpactX code with its 3D space-charge solver, simulations indicate that the bunch length can be rapidly reduced by at least a factor of two without appreciable degradation of transverse beam quality--even in the strong space-charge regime. However, longitudinal defocusing due to the space-charge remains a significant challenge in short-pulsed intense proton bunches, and the optimization of compression under these conditions is discussed.

Simons, B. D. [Northern Illinois U.]↗