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DOE OSTI2024

Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss function calculation. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing the Hutchinson Trace Estimation (HTE) method. Starting with the second-order high-dimensional PDEs, which are ubiquitous in scientific computing, HTE is applied to transform the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach not only alleviates the computational bottleneck via Taylor-mode automatic differentiation but also significantly reduces memory consumption from the Hessian matrix to an HVP’s scalar output. We further showcase HTE’s convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with the Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variability and variance among dimensions. We further extend the application of HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Curse of dimensionality↗

DOE OSTI2025

Quantitative phase retrieval and characterization of magnetic nanostructures via Lorentz (scanning) transmission electron microscopy

Magnetic materials phase reconstruction using Lorentz transmission electron microscopy (LTEM) measurements have traditionally been achieved using longstanding methods such as off-axis holography (OAH) fast-Fourier transform technique and the transport-of-intensity equation (TIE). The increase in access to processing power alongside the development of advanced algorithms have allowed for phase retrieval of nanoscale magnetic materials with greater efficacy and resolution. Specifically, reverse-mode automatic differentiation (RMAD) and the extended electron ptychography iterative engine (ePIE) are two recent developments of phase retrieval that can be applied to analyzing micro-to-nano- scale magnetic materials. This work evaluates phase retrieval using TIE, RMAD, and ePIE in simulations of Permalloy (Ni 80 Fe 20 ) nanoscale islands, or nanomagnets. Extending beyond simulations, we demonstrate total phase retrieval and image reconstructions of a NiFe nanowire using OAH and RMAD in LTEM and ePIE in Lorentz-mode-4D scanning transmission electron microscopy experiments and determine the saturation magnetization through corroborations with micromagnetic modeling. Finally, we demonstrate the efficacy of these methods in retrieving the total phase and highlight its use in characterizing and analyzing the proximity effect of the magnetic nanostructures.

Lorentz transmission electron microscopy↗

DOE OSTI2022

Measurements of the Higgs boson inclusive and differential fiducial cross-sections in the diphoton decay channel with pp collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A measurement of inclusive and differential fiducial cross-sections for the production of the Higgs boson decaying into two photons is performed using 139 fb –1 of proton-proton collision data recorded at $\sqrt{s}$ = 13 TeV by the ATLAS experiment at the Large Hadron Collider. The inclusive cross-section times branching ratio, in a fiducial region closely matching the experimental selection, is measured to be 67 ± 6 fb, which is in agreement with the state-of-the-art Standard Model prediction of 64 ± 4 fb. Extrapolating this result to the full phase space and correcting for the branching ratio, the total cross-section for Higgs boson production is estimated to be 58 ± 6 pb. In addition, the cross-sections in four fiducial regions sensitive to various Higgs boson production modes and differential cross-sections as a function of either one or two of several observables are measured. All the measurements are found to be in agreement with the Standard Model predictions. The measured transverse momentum distribution of the Higgs boson is used as an indirect probe of the Yukawa coupling of the Higgs boson to the bottom and charm quarks. In addition, five differential cross-section measurements are used to constrain anomalous Higgs boson couplings to vector bosons in the Standard Model effective field theory framework.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗

DOE OSTI2022

Understanding the Impacts of Support–Polymer Interactions on the Dynamics of Poly(ethyleneimine) Confined in Mesoporous SBA-15

Supported amines are a promising class of CO 2 sorbents offering large uptake capacities and fast uptake rates. Additionally, among supported amines, poly(ethyleneimine) (PEI) physically impregnated in the mesopores of SBA-15 silica is widely used. Within these composite materials, the chain dynamics and morphologies of PEI strongly influence the CO 2 capture performance, yet little is known about chain and macromolecule mobility in confined pores. Here, we probe the impact of the support–PEI interactions on the dynamics and structures of PEI at the support interface and the corresponding impact on CO 2 uptake performance, which yields critical structure–property relationships. The pore walls of the support are grafted with organosilanes with different chemical end groups to differentiate interaction modes (spanning from strong attraction to repulsion) between the pore surface and PEI. Combinations of techniques, such as quasi-elastic neutron scattering (QENS), 1 H T 1 –T 2 relaxation correlation solid-state NMR, and molecular dynamics (MD) simulations, are used to comprehensively assess the physical properties of confined PEI. We hypothesized that PEI would have faster dynamics when subjected to less attractive or repulsive interactions. However, we discover that complex interfacial interactions resulted in complex structure–property relationships. Indeed, both the chain conformation of the surface-grafted chains and of the PEI around the surface influenced the chain mobility and CO 2 uptake performance. By coupling knowledge of the dynamics and distributions of PEI with CO 2 sorption performance and other characteristics, we determine that the macroscopic structures of the hybrid materials dictate the first rapid CO 2 uptake, and the rate of CO 2 sorption during the subsequent gradual uptake stage is determined by PEI chain motions that promote diffusive jumps of CO 2 through PEI-packed domains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Augmenting subspace optimization methods with linear bandits

In this work, we consider the framework of methods for unconstrained minimization that are, in each iteration, restricted to a model that is only a valid approximation to the objective function on some affine subspace containing an incumbent point. These methods are of practical interest in computational settings where derivative information is either expensive or impossible to obtain. Recent attention has been paid in the literature to employing randomized matrix sketching for generating the affine subspaces within this framework. We consider a relatively straightforward, deterministic augmentation of such a generic subspace optimization method. In particular, we consider a sequential optimization framework where actions consist of one-dimensional linear subspaces and rewards consist of (approximations to) the magnitudes of directional derivatives computed in the direction of the action subspace. Reward maximization in this context is consistent with maximizing lower bounds on descent guaranteed by first-order Taylor models. This sequential optimization problem can be analysed through the lens of dynamic regret. We modify an existing linear upper confidence bound (UCB) bandit method and prove sublinear dynamic regret in the subspace optimization setting. We demonstrate the efficacy of employing this linear UCB method in a setting where forward-mode algorithmic differentiation can provide directional derivatives in arbitrary directions and in a derivative-free setting. For the derivative-free setting, we propose SS-POUNDers, an extension of the derivative-free optimization method POUNDers that employs the linear UCB mechanism to identify promising subspaces. Our numerical experiments suggest a preference, in either computational setting, for employing a linear UCB mechanism within a subspace optimization method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Apparatus and methods of detecting transient discharge modes and/or closed loop control of pulsed systems and method employing same

A system and method for differentiating between different modes of pulsed electrical discharges via of an amplitude to time (ATC) conversion circuit is described. A bipolar ATC circuit is used to add together the positive and negative portions of an attenuated and filtered signal derived either from the voltage or current of a pulse. Alternatively, a unipolar ATC circuit may be employed. The resulting processed signal is compared against a reference voltage to generate an output signal that is active for the amount of time that the processed signal exceeds the reference voltage. Discharge mode is determined based on three factors: did a pulse occur, if a pulse occurred when did the pulse start relative to the original pulse event, and what is the duty cycle of the pulse. Subsequent pulse generated may be controlled accordingly.

Fitzpatrick, Joseph F.↗

DOE OSTI2021

Measurement of the Z boson differential production cross section using its invisible decay mode (Z$\nu\bar{\nu}$) in proton-proton collisions at $\sqrt{s}=$ 13 TeV

Measurements of the total and differential fiducial cross sections for the Z boson decaying into two neutrinos are presented at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV. The data were collected by the CMS detector in 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. In these measurements, events are selected containing an imbalance in transverse momentum and one or more energetic jets. The fiducial differential cross section is measured as a function of the Z boson transverse momentum. The results are combined with a previous measurement of charged-lepton decays of the Z boson. The measured total fiducial cross section for events with Z boson transverse momentum greater than 200 GeV is $ {3000}_{-170}^{+180} $ fb.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

A Nonlocal Magneto-curvature Instability in a Differentially Rotating Disk

A global mode is shown to be unstable to nonaxisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic fields where local standard magnetorotational instability (MRI) becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global domain and are Alfvén-continuum-driven unstable modes. As its mode structure and relative dominance over MRI are inherently determined by the global spatial curvature as well as the flow shear in the presence of a magnetic field, we call it the magneto-curvature (magneto-spatial-curvature) instability. Consistent with the linear analysis, as the field strength is increased in the nonlinear simulations, a transition from MRI-driven turbulence to a state dominated by global nonaxisymmetric modes is obtained. This global instability could therefore be a source of nonlinear transport in accretion disks at a higher magnetic field than predicted by local models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Decoupled Active and Reactive Power Control without PLL Requirement for Differential Buck Converter

This paper presents a decoupled active and reactive power control for the differential buck converter. This control does not require phase locked loop (PLL) for synchronization. Also, it achieves active and reactive power control in a simple single control loop structure. The differential buck converter has the capability to compensate the double line frequency power ripple without relying on additional hardware. Particularly, the Common Mode (CM) operation is used for active double line frequency power ripple absorption. Whereas, the Differential Mode (DM) operation is used as an active and reactive power exchanging port between the converter and the grid at the point of common coupling (PCC). The motivation behind this paper proposal are: (i) to avoid PLL induced instabilities, especially, when connecting the differential buck converter with weak grid, and (ii) direct active and reactive power control for the differential buck in a single loop control. The theoretical analyses are verified with a 5 kW converter with only 50 μF decoupling capacitor connected to a weak grid.

Khan, Ahmad↗

DOE OSTI2021

Measurement of the inclusive and differential Higgs boson production cross sections in the leptonic WW decay mode at $\sqrt{s} =$ 13 TeV

Measurements of the fiducial inclusive and differential production cross sections of the Higgs boson in proton-proton collisions at $ \sqrt{s} $ = 13 TeV are performed using events where the Higgs boson decays into a pair of W bosons that subsequently decay into a final state with an electron, a muon, and a pair of neutrinos. The analysis is based on data collected with the CMS detector at the LHC during 2016–2018, corresponding to an integrated luminosity of 137 fb$^{−1}$. Production cross sections are measured as a function of the transverse momentum of the Higgs boson and the associated jet multiplicity. The Higgs boson signal is extracted and simultaneously unfolded to correct for selection efficiency and resolution effects using maximum-likelihood fits to the observed distributions in data. The integrated fiducial cross section is measured to be 86.5 ± 9.5 fb, consistent with the Standard Model expectation of 82.5 ± 4.2 fb. No significant deviation from the Standard Model expectations is observed in the differential measurements.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

First Muon Neutrino on Argon Cross Section Measurements With an Off-Axis Beam

While over ninety years have passed since neutrinos were first predicted in 1930 by Wolfgang Pauli, much about them is still unknown [20]. How many types of neutrinos there are, how precisely neutrinos change flavor, and how neutrinos interact with various types of matter are largely unanswered questions that have implications for fields beyond particle physics, such as cosmology and astrophysics. The final question can be answered partially by differential cross section measurements, two of which constitute the primary result of this thesis. The NeUtrinos at the Main Injector (NuMI) Beam at Fermilab in Batavia, IL provides a source of muon neutrinos and muon antineutrinos to the MicroBooNE experiment, an 85 ton liquid argon time projection chamber (LArTPC). The technology allows for high precision particle tracking and energy reconstruction that can be used to make cross section measurements. Necessary work for making these measurements for which the author of this thesis made an essential contribution is presented in detail in References [21] [22] [11] [23]. The measurement presented in this thesis is made with 2.187e20 Protons on Target (POT), the standard metric for an amount of beam exposure, of data when the beam was in forward horn current mode. Single-differential cross section measurements in terms of muon candidate kinetic energy and direction are made, and their statistical fits with simulation are 5.8 (12 d.o.f.) and 11.4 (10 d.o.f.), respectively. This indicates that the muon kinematics for muon neutrino and muon antineutrino charged-current (CC) events primarily in the energy range [0-3] GeV can be trusted for oscillation experiments, including DUNE, because of the agreement to within the associated systematic and statistical uncertainties between the measurement and the model in every bin of both single-differential cross sections. This result adds to the corresponding result for the Booster Neutrino Beam (BNB) because it covers a completely different energy region than that measurement, a double-differential cross section in terms of muon momentum and direction [14]. This result contributes to reducing the uncertainty in near-far event rate comparisons in long baseline neutrino experiments and also adds to existing knowledge of the neutrino-nucleus interaction by describing the outgoing muon kinematics in interactions of muon neutrinos and muon antineutrinos. This result is the first-ever measurement of differential cross sections of muon neutrinos and muon antineutrinos in liquid argon made with an off-axis beam.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Parity-doublet coherence times in optically trapped polyatomic molecules

Polyatomic molecules provide complex internal structures that are ideal for applications in quantum information science, quantum simulation and precision searches for physics beyond the standard model. A key feature of polyatomic molecules is the presence of parity-doublet states. These structures, which generically arise from the rotational and vibrational degrees of freedom afforded by polyatomic molecules, are a powerful feature to pursue diverse quantum science applications. Linear triatomic molecules contain ℓ-type parity-doublet states in the vibrational bending mode, which are predicted to exhibit robust coherence properties. Here we report optically trapped CaOH molecules prepared in ℓ-type parity-doublet states and realize a bare qubit coherence time of $T$$^{*}_{2}$, which is longer than the 0.36 s lifetime of the bending mode. We suppress differential Stark shifts by cancelling ambient electric fields using molecular spectroscopy and characterize parity-dependent trap shifts, which are found to limit the coherence time. Furthermore, the parity-doublet coherence times achieved in this work are a defining milestone for the use of polyatomic molecules in quantum science.

Quantum information↗

DOE OSTI2021

Structural insight into host plasma membrane association and assembly of HIV-1 matrix protein

Oligomerization of Pr55 Gag is a critical step of the late stage of the HIV life cycle. It has been known that the binding of IP6, an abundant endogenous cyclitol molecule at the MA domain, has been linked to the oligomerization of Pr55 Gag . However, the exact binding site of IP6 on MA remains unknown and the structural details of this interaction are missing. Here, we present three high-resolution crystal structures of the MA domain in complex with IP6 molecules to reveal its binding mode. Additionally, extensive Differential Scanning Fluorimetry analysis combined with cryo- and ambient-temperature X-ray crystallography and GNM-based transfer entropy calculations identify the key residues that participate in IP6 binding. Our data provide novel insights about the multilayered HIV-1 virion assembly process that involves the interplay of IP6 with PIP2, a phosphoinositide essential for the binding of Pr55 Gag to membrane. IP6 and PIP2 have neighboring alternate binding sites within the same highly basic region (residues 18–33). This indicates that IP6 and PIP2 bindings are not mutually exclusive and may play a key role in coordinating virion particles’ membrane localization. Based on our three different IP6-MA complex crystal structures, we propose a new model that involves IP6 coordination of the oligomerization of outer MA and inner CA domain’s 2D layers during assembly and budding.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Precision Measurement of the Microwave Dielectric Loss of Sapphire in the Quantum Regime with Parts-per-Billion Sensitivity

Dielectric loss is known to limit state-of-the-art superconducting qubit lifetimes. Recent experiments imply upper bounds on bulk dielectric loss tangents on the order of 100 parts per billion but because these inferences are drawn from fully fabricated devices with many loss channels, these experiments do not definitely implicate or exonerate the dielectric. To resolve this ambiguity, we devise a measurement method capable of separating and resolving bulk dielectric loss with a sensitivity at the level of 5 ×10 –9 . The method, which we call the dielectric dipper, involves the in situ insertion of a dielectric sample into a high-quality microwave cavity mode. Smoothly varying the participation of the sample in the cavity mode enables a differential measurement of the dielectric loss tangent of the sample. The dielectric dipper can probe the low-power behavior of dielectrics at cryogenic temperatures and does so without the need for any lithographic process, enabling controlled comparisons of substrate materials and processing techniques. We demonstrate the method with measurements of sapphire grown by edge-defined film-fed growth (EFG) in comparison to high-grade sapphire grown by the heat-exchanger method (HEMEX). For EFG sapphire, we infer a bulk loss tangent of 63⁢(8) ×10 –9 and a substrate-air interface loss tangent of 15⁢(3) ×10 –4 (assuming a sample surface thickness of 3 nm). For a typical transmon, this bulk loss tangent would limit device quality factors to Q ≲20 ×10 6 , suggesting that bulk loss is likely the dominant loss mechanism in the longest-lived transmons on sapphire. We also demonstrate this method on HEMEX sapphire and bound its bulk loss tangent to be less than 19⁢(6) ×10 –9 . As this bound is about 3 times smaller than the bulk loss tangent of EFG sapphire, the use of HEMEX sapphire as a substrate would lift the bulk dielectric coherence limit of a typical transmon qubit to several milliseconds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Beyond Ohm's law: Bernoulli effect and streaming in electron hydrodynamics

Recent observations of nonlocal transport in ultraclean two-dimensional materials raised the tantalizing possibility of accessing hydrodynamic correlated transport of a many-electron state. However, it has been pointed out that nonlocal transport can also arise from impurity scattering rather than interaction. At the crux of the ambiguity is the focus on linear effects, i.e., Ohm's law, which cannot easily differentiate among different modes of transport. Furthermore we propose experiments that can reveal rich hydrodynamic features in the system by tapping into the nonlinearity of the Navier-Stokes equation. Three experiments we propose will each manifest a unique phenomenon that is well known in classical fluids: the Bernoulli effect, Eckart streaming, and Rayleigh streaming. Analysis of known parameters confirms that the proposed experiments are feasible and the hydrodynamic signatures are within reach of graphene-based devices. Experimental realization of any one of the three phenomena will provide a stepping stone to formulating and exploring the notions of nonlinear electron fluid dynamics with an eye to celebrated examples from classical nonlaminar flows, e.g., pattern formation and turbulence.

2-dimensional systems↗

DOE OSTI2023

Prevention of Dual-Mode Excitation in 9-Cell Cavities for LCLSII-HE

Dual-Mode Excitation, also referred to as mode-mixing, is a superposition of two fundamental pi modes in an SRF cavity. In 9-cell TESLA cavities used for the LCLSII-HE project, the two modes that are commonly excited are the pi mode (1300.2 MHz), and the 7/9 pi mode (1297.8 MHz). During vertical cavity qualification testing, only the pi mode is driven by the RF system. However, at high gradients, emitted power at the frequency of the 7/9 pi mode grows despite the RF system only powering the pi mode. When this happens, the RF power measurement system is unable to differentiate between the superimposed modes, and any data taken is invalid. The previous method of dealing with mode-mixing was to turn off power to the cavity, let both modes decay fully, then restore power. Because of the time-sensitive nature of this testing, this leads to underestimates of Q0 or any radiant field emission present in the cavity. The novel RF control solution prevents the 7/9 pi mode from being excited while not interfering with measurements of the fundamental pi mode. A second RF control system is connected to the cavity which drives the 7/9 pi mode. The loop phase for driving the 7/9 pi mode in self excited loop mode is determined then shifted by 180 degrees, thus providing a negative feedback to the undesired mode. Because this off-resonance power can be very small, on the order of milliwatts, it does not interfere with the high-power measurements of the fundamental pi mode. At Jefferson Lab, we are now able to test a cavity for the LCLSII-HE project with no problems from mode-mixing, which allows for CW processing of high-gradient multipacting and field emission.

Owen, Peter↗