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DOE OSTI2024

On gauge amplitudes first appearing at two loops

We study scattering amplitudes in massless non-abelian gauge theory where all outgoing gluons have positive helicity. It has been argued recently by Costello that for a particular fermion representation (8 fundamentals plus one antisymmetric-tensor representation in SU(N)) the one-loop amplitudes vanish identically. We show that this vanishing leads to previously-observed identities among one-loop color-ordered partial amplitudes. We then turn to two loops, where Costello has computed the all-plus amplitudes for this theory, as rational functions of the kinematics for any number of gluons using the celestial chiral algebra (CCA) bootstrap. We show that in dimensional regularization, these two-loop amplitudes are not rational, and they are not even finite as ϵ → 0. However, the finite remainder for four gluons agrees with the formula by Costello. In addition, we provide a mass regulator for the infrared-divergent loop integrals; with this regulator, the CCA bootstrap formula is recovered exactly. Finally, we use the CCA bootstrap to compute the double-trace terms in the theory at two loops for an arbitrary number of gluons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Plasma self-driven current in tokamaks with magnetic islands

Magnetic island perturbations may cause a reduction in plasma self-driven current that is needed for tokamak operation. A novel effect on tokamak self-driven current revealed by global gyrokinetic simulations is due to magnetic-island-induced 3D electric potential structures, which have the same dominant mode numbers as that of the magnetic island, whereas centered at both the inner and outer edge of the island. The non-resonant potential islands are shown to drive a current through an efficient nonlinear parallel acceleration of electrons. In large aspect ratio (large-A) tokamak devices, this new effect can result in a significant global reduction of the electron bootstrap current when the island size is sufficiently large, in addition to the local current loss across the island region due to the pressure profile flattening. It is shown that there exists a critical magnetic island width for large-A tokamaks beyond which the electron bootstrap current loss is global and increases rapidly with the island size. As such, this process may introduce a size limit for tolerable magnetic islands in large-A tokamak devices in the context of steady state operation. On the other hand, the current loss caused by magnetic islands in low-A tokamaks such as spherical tokamak (ST) NSTX/U is minor. The reduction of the axisymmetric current by magnetic islands scales with the square of island width. However, the loss of the current is mainly local to the island region, and the pace of current loss as the island size increases is substantially slower compared to large-A tokamaks. In particular, the bootstrap current reduction in STs is even smaller in the reactor-relevant high-β p regime where neoclassical tearing modes are more likely to develop.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

On gauge amplitudes first appearing at two loops

Dixon, Lance J↗

DOE OSTI2026

A Tutorial on Bayesian analysis of linear shock compression data

Gas gun and other shock compression experiments often produce shock wave velocity measurements that are linearly associated with particle velocity. Traditionally, this empirical relationship is quantified with a single Hugoniot curve that is estimated using least squares regression. However, for downstream modeling and simulation tasks, it is often more useful to have multiple Hugoniot curves in the pressure–volume plane that are consistent with the data. We employ Bayesian uncertainty quantification methods as a framework for propagating measurement uncertainty through to model parameters and predictions. Specifically, this Tutorial shows how to sample multiple Hugoniot curves in the pressure–volume plane that are consistent with the shock wave-particle velocity measurements in a two-step Bayesian approach. First, we obtain an analytical expression for the posterior distribution of the linear model parameters using Bayesian linear regression. Second, we propagate samples from the posterior distribution through the Rankine–Hugoniot equations to yield Hugoniot curves in the pressure–volume plane. The procedure is demonstrated with publicly available data on argon, copper, and nickel, and compared against bootstrapping and linear regression. The Bayesian procedure is shown to be interpretable, computationally inexpensive, and less sensitive than an alternative bootstrapping approach to the removal of the point in the copper dataset that has the largest particle velocity. As a Tutorial on Bayesian methodology for the shock compression community, we provide several derivations and explanations that make this paper self-contained, and make all code and data available at github.com/llnl/BALSCD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Fast ion studies in the extended high-performance high β P plasma on EAST

Comprehending and optimizing fast ion behaviors is critical for the enhancement of performance in Experimental Advanced Superconducting Tokamak (EAST). This study explores the potential benefits of several factors that can improve the fast ion confinement. First, experiments show the change in the direction of the NBI2 from counter-I p to co-I p leads to a significant reduction in fast ion losses. TRANSP/NUBEAM simulation and tomography results based on fast-ion D-alpha measurements reveal that after the neutral beam injection (NBI) upgrade, the beam ion prompt loss is reduced by approximately 50%. Second, the upgraded ion cyclotron resonant frequency (ICRF) antenna at the N-port features twice the coupling resistance of the original antennas at EAST. This improved ICRF power coupling has enhanced the synergistic heating effect of NBI + ICRF, where the ICRF wave field accelerates beam ions at the harmonics. Experiments demonstrate that NBI + ICRF synergistic not only enhances plasma neutron yield and β P , but also accelerates beam ions to hundreds of keV. Further, the electron density and the neutral beam voltage have been optimized to reduce the fast ion slowing-down time and beam ion losses. Experimental and simulation results indicate that increasing the electron density reduces beam ion losses and enhances the bootstrap current fraction. While higher beam voltage results in a slight decrease in beam power absorption, it can increase the fraction of bootstrap current. With the understanding of these optimization of fast ion confinement, experiments have demonstrated fully non-inductive operation at high density (n e /n G ∼ 0.67, β P ∼ 3.1, β N ∼ 2.1, H 98,y2 ∼ 1.2) even without the support of co-I p beam NBI2. This investigation presents a potential regime to enhance fast ion confinement and extend performance in the high β P plasma for future experiments.

EAST tokamak↗

DOE OSTI2025

Understanding the formation of a low-pressure pedestal in the presence of a strong internal transport barrier in DIII-D high β p plasmas

As a promising scenario for fusion reactors, the high poloidal-beta (β P ) scenario is characterized by a strong large radius internal transport barrier (ITB), which significantly enhances the overall confinement quality and the bootstrap current fraction for fully non-inductive operation. It is frequently observed that in the presence of a strong ITB, the pedestal height is lower and is accompanied by small edge localized modes (ELMs), which further improves the compatibility of a high performance core with an edge solution. A mechanism for the formation of the low pedestal is proposed in this paper. It is found that the strong ITB creates an off-axis bootstrap current to clamp the local safety factor q, and thus the magnetic shear in the outer core/pedestal region is increased. Gyrokinetic simulations with the CGYRO code show that the higher magnetic shear brings the experimental profiles into the range where the growth rate of drift-wave instabilities and thus transport is higher, and therefore a lower pedestal gradient is expected. Here, the combination of low pedestal and high magnetic shear further enhances the turbulent transport across the whole pedestal, consistent with power balance analysis. Such a positive feedback mechanism ultimately results in a lower pressure pedestal as observed in experiments. Under such a low pedestal, linear simulations with BOUT++ predict the growth rates of peeling–ballooning modes to be lower across the whole toroidal mode number spectra, and the nonlinear BOUT++ simulation exhibits lower saturated fluctuation intensity as well, consistent with the experimentally observed lower ELM size.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Current ramp-up studies for NSTX-U in support of the development of non-inductive current ramp-up scenarios in STs

The Spherical Tokamak (ST) is a low-aspect-ratio tokamak projected to enable simultaneous operation at high normalized toroidal beta and high bootstrap current fraction. However, a compact ST reactor cannot be built with a full-sized solenoid. The remaining current required for sustained operation must be ramped up non-inductively. Sustained 100% non-inductive current drive at the MA level has not yet been demonstrated on an ST. Non-inductive current ramp-up is therefore a more challenging objective that the NSTX-U research program aims to address. In support of this development, free-boundary TRANSP simulations have been used to develop a current ramp-up scenario in which a significant fraction of the current is driven non-inductively by a combination of neutral-beam and bootstrap current drive. The resulting discharge has properties favorable for non-inductive current drive, such as a low normalized internal plasma inductance of approximately 0.45, a minimum safety factor exceeding 2, and a slightly reversed-shear q-profile. In these discharges, the plasma current ramps to 900 kA within 250 ms in an L-mode configuration, with varying electron density and density profiles. These discharges should be suitable for next-step NSTX-U experiments aimed at generating a robust L-mode fiducial scenario with low central solenoid flux consumption, which could be progressively improved as new NSTX-U experimental discharges are developed.

Raman, Roger [Univ. of Washington, Seattle, WA (Un↗

DOE OSTI2025

Comment on "An implementation of neural simulation-based inference for parameter estimation in ATLAS''

The paper titled "An implementation of neural simulation-based inference for parameter estimation in ATLAS" by the ATLAS collaboration (arXiv:2412.01600v1 [hep-ex]) describes the implementation of neural simulation-based inference for a measurement analysis performed by ATLAS. The uncertainties in the analysis arising from the finiteness of the simulated datasets are estimated using a novel double-bootstrapping technique described in that work. In the present comment, it is claimed and demonstrated, using a toy example, that the double-bootstrapping technique does not actually capture the aforementioned uncertainties.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Code associated with "Assessing the Effect of a Deep-Rooted Grass on Belowground Carbon Storage in Cultivated Land: Insights from a Multi-Site US Study"

R code associated with "Assessing the Effect of a Deep-Rooted Grass on Belowground Carbon Storage in Cultivated Land: Insights from a Multi-Site US Study" These scripts can be used to analyze the accompanying dataset: https://doi.org/10.5281/zenodo.16620529. (1) resampling_functions.R : Creates functions for resampling data for nonparametric bootstrapping (2) bootstrap_depth_profiles.R : Applies resampling functions to the dataset (3) gapfill_masscalcs.R : Prepares data for equivalent mass calculations (4) get_14C_EM.R : Applies soilR to obtain the 14C end member for mixing model calculations (5) mass_aggregate.R : Performs equivalent mass and mass weighted averaging calculations.

Carbon↗

DOE OSTI2024

MONKES: a fast neoclassical code for the evaluation of monoenergetic transport coefficients in stellarator plasmas

Abstract MONKES is a new neoclassical code for the evaluation of monoenergetic transport coefficients in stellarators. By means of a convergence study and benchmarks with other codes, it is shown that MONKES is accurate and efficient. The combination of spectral discretization in spatial and velocity coordinates with block sparsity allows MONKES to compute monoenergetic coefficients at low collisionality, in a single core, in approximately one minute. MONKES is sufficiently fast to be integrated into stellarator optimization codes for direct optimization of the bootstrap current and to be included in predictive transport suites. The code and data from this paper are available at https://github.com/JavierEscoto/MONKES/ .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Modeling resistive-inductive evolution of currents in Wendelstein 7-X

This research investigates the temporal evolution of the toroidal plasma current in the Wendelstein 7-X (W7-X) stellarator under different heating, fueling, and current drive scenarios. The THRIFT code has been modernized and its predictions of the evolution of the toroidal current have been compared against experimentally measured currents in W7-X. Good agreement is found with respect to the characteristic timescale between experimentally measured and simulated toroidal currents. The total bootstrap current is under-predicted owing to the applicability of the BOOTSJ model for the plasma collisionalities in question. Edge plasma resistivity is found to play an important role in the asymptotic behavior of the evolution of the current, indicating a possible limitation of the minimum plasma temperature when applying this model. Simulations of ECCD and heating power steps show THRIFT is capable of capturing the dynamical evolution of the current in response to changes in current sources. Future uses of THRIFT include validating and benchmarking other non-inductive current models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

On unitarity of the hypergeometric amplitude

The hypergeometric amplitude is a one-parameter deformation of the Veneziano amplitude for four-point tachyon scattering in bosonic string theory that is consistent with S-matrix bootstrap constraints. In this article we construct a similar hypergeometric generalization of the Veneziano amplitude for type-I superstring theory. We then rule out a large region of the (r, m 2 , D) parameter space as non-unitary, and establish another large subset of the (r, m 2 , D) parameter space where all of the residue’s partial wave coefficients are positive. We also analyze positivity in various limits and special cases. As a corollary to our analysis, we are able to directly demonstrate positivity of a wider set of Veneziano amplitude partial wave coefficients than what has been presented elsewhere.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Tracking discontinuities in parameter space

We develop a geometric framework in Feynman-parameter space to determine constraints on the sequential discontinuities of Feynman integrals. Our method is based on tracking the deformation of the integration contour as external kinematics are analytically continued. This procedure imposes powerful constraints on the analytic structure of Feynman integrals, providing crucial inputs for their bootstrap. We demonstrate the usefulness of this framework by applying it to integrals in dimensional regularization, with higher propagator powers, and to examples with non-uniform transcendental weight. The method is illustrated with several one- and two-loop calculations.

Differential and Algebraic Geometry↗

DOE OSTI2025

Recurrent features of amplitudes in planar $\mathcal{N}$ = 4 super Yang-Mills theory

The planar three-gluon form factor for the chiral stress tensor operator in planar maximally supersymmetric Yang-Mills theory is an analog of the Higgs-to-three-gluon scattering amplitude in QCD. The amplitude (symbol) bootstrap program has provided a wealth of high-loop perturbative data about this form factor, with results up to eight loops available. The symbol of the form factor at L loops is given by words of length 2L in six letters with associated integer coefficients. In this paper, we analyze this data, describing patterns of zero coefficients and relations between coefficients. We find many sequences of words whose coefficients are given by closed-form expressions which we expect to be valid at any loop order. Moreover, motivated by our previous machine-learning analysis, we identify simple recursion relations that relate the coefficient of a word to the coefficients of particular lower-loop words. These results open an exciting door for understanding scattering amplitudes at all loop orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Relations between anomalous dimensions in the Regge limit

We extend the recent formalism developed for computing rapidity anomalous dimension of form factors using unitarity to the problem of high-energy near forward scattering. By combining the factorization of 2 → 2 scattering in the effective field theory (EFT) for Glauber operators with definite signature amplitudes, we derive an expression that relates anomalous dimensions (including Regge trajectories) to cut amplitudes, leading to significant computational simplifications. We demonstrate this explicitly by computing the one and two-loop Regge trajectories. Our formalism can also be used to bootstrap anomalous dimensions of operators not related by symmetries. As an example, we show that the full anomalous dimensions (including both the Regge pole and cut pieces) of the two Glauber exchange anti-symmetric octet operator, can be determined from the anomalous dimension of the single Glauber exchange operator. Many other such relations exist between other color channels at each order in α.

Effective Field Theories↗

DOE OSTI2025

A universal inequality on the unitary 2D CFT partition function

We prove the conjecture proposed by Hartman, Keller and Stoica (HKS) [1]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension $\frac{c}{12}$ + ϵ and below the twist $\frac{c}{12}$ is universal in the large c limit for all β L β R ≠ 4π 2 . The technique of the proof allows us to derive a one-parameter (with parameter α ∈ (0, 1]) family of universal inequalities on the unitary 2D CFT partition function with general central charge c ⩾ 0, using analytical modular bootstrap. We derive an iterative equation for the domain of validity of the inequality on the (β L , β R ) plane. The infinite iteration of this equation gives the boundary of maximal-validity domain, which depends on the parameter α in the inequality.

AdS-CFT Correspondence↗

DOE OSTI2024

Holography and Regge phases with U(1) charge

Abstract We use holography to study the large spinJlimit of the spectrum of low energy states with chargeQunder a U(1) conserved current in CFTs ind> 2 dimensions, with a focus ond= 3 andd= 4. ForQ= 2, the spectrum of such states is known to be universal and properly captured by the long-distance limit of holographic theories, regardless of whether the CFT itself is holographic. We study in detail the holographic description of such states atQ> 2, by considering the contribution to the energies ofQscalar particles coming from single photon and graviton exchange in the bulk of AdS; in some cases, scalar exchange and bulk contact terms are also included. For a range of finite values ofQandJ, we numerically diagonalize the Hamiltonian for such states and examine the resulting spectrum and wavefunctions as a function of the dimension ∆ of the charge-one operator and the central charges$$ {c}_{\mathcal{T}} $$ c T ,$$ {c}_{\mathcal{J}} $$ c J of the stress tensor and U(1) current, finding multiple regions in parameter space with qualitatively different behavior. We discuss the extension of these results to the regime of parametrically large chargeQ, as well as to what extent such results are expected to hold universally, beyond the limit of holographic CFTs. We compare our holographic computations to results from the conformal bootstrap for the 3dO(2) model atQ= 3 andQ= 4 and find excellent agreement.

Physics↗

DOE OSTI2024

Bounding irrelevant operators in the 3d Gross-Neveu-Yukawa CFTs

We perform a numerical bootstrap study of scalar operators in the critical 3d Gross-Neveu-Yukawa models, a family of conformal field theories containing N Majorana fermions in the fundamental representation of an O(N) global symmetry. We compute rigorous bounds on the scaling dimensions of the next-to-lowest parity-even and parity-odd singlet scalars at N = 2, 4, and 8. All of these dimensions have lower bounds greater than 3, implying that there are only two relevant singlet scalars and placing constraints on the RG flow structure of these theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗