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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Incommensurate Antiferromagnetic Order in the Fe-substituted Bi-2201 Cuprate in the Heavily Overdoped Regime

Elastic neutron scattering experiments showed incommensurate antiferromagnetic peaks in 5% Fe-substituted Bi-2201 cuprate in the non-superconducting heavily overdoped regime. Here, the incommensurability δ ∼ 0.21 is comparable to that observed in Fe-substituted Bi-2201 in the overdoped regime. [Hiraka et al., Phys. Rev. B 81, 144501 (2010).] The magnetic correlation length is comparable between the overdoped and non-superconducting heavily overdoped regimes. It is plausible that incommensurate antiferromagnetic order is induced and stabilized by Fe in the heavily overdoped regime, which suggests a robust antiferromagnetic correlation beyond the superconducting dome in the phase diagram.

Bi-2201↗
DOE OSTI2022

Land management explains major trends in forest structure and composition over the last millennium in California’s Klamath Mountains

Significance We provide the first assessment of aboveground live tree biomass in a mixed conifer forest over the late Holocene. The biomass record, coupled with local Native oral history and fire scar records, shows that Native burning practices, along with a natural lightning-based fire regime, promoted long-term stability of the forest structure and composition for at least 1 millennium in a California forest. This record demonstrates that climate alone cannot account for observed forest conditions. Instead, forests were also shaped by a regime of frequent fire, including intentional ignitions by Native people. This work suggests a large-scale intervention could be required to achieve the historical conditions that supported forest resiliency and reflected Indigenous influence.

Knight, Clarke A.↗
DOE OSTI2020

Active electrochemical interfaces stabilized through self-organized potential oscillations

Some electrochemical systems are known to have higher average efficiency when operated under an oscillatory regime. Given the compromise between activity and stability, the stability of electrochemical interfaces in a self-organized, oscillatory state must be taken into account. Here we evaluate the electro-oxidation of methanol and formic acid on platinum under regular and oscillatory conditions, and study the stability by following the Pt dissolution rates in situ with a stationary probe rotating disk electrode (SPRDE) coupled to an inductively coupled plasma mass spectrometer (ICP-MS). Generally speaking, as the electro-oxidation reaction proceeds, the platinum dissolution rate increases considerably. To guarantee Pt stability, the potential must be kept below 1.0 V vs. RHE. Interestingly, no dissolution is detectable when the electrode potential undergoes temporary self-organization, ensuring a stable and active interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Effects of equilibrium pressure on plasma response to RMPs in a spherical tokamak

This study presents a comprehensive analysis of the equilibrium pressure on the plasma response to resonant magnetic perturbations (RMPs) in the spherical tokamak (ST) MAST-U, employing both single-fluid and MHD-kinetic hybrid models (implemented via the MARS-F/K codes). As a key finding, the study identifies two different pressure-driven eigenmodes, exhibiting Sturmian property, that affect the Troyon no-wall limits for the onset of the n = 1 and n = 2 ( n is the toroidal mode number) ideal external kink instabilities as well as the corresponding plasma response to the applied RMP. With increasing equilibrium pressure, the plasma response to RMPs is significantly enhanced in the ST plasma, particularly in the high-pressure regime where kinetic effects strongly stabilize the external kink instability. The Troyon no-wall limit divides the plasma response into two regions: well below the limit, the response amplitudes and trends (versus pressure) are similar between the fluid and kinetic models; as the equilibrium pressure approaches the Troyon limit, the kinetic model predicts significant amplification of the RMP field, up to 30 times for cases considered. A relatively weak dependence of the optimal coil phasing on the equilibrium pressure is computed in this ST plasma, similar to the trend obtained for the conventional aspect ratio devices. These findings underscore the importance of incorporating kinetic effects in accurate prediction of the plasma response to RMPs in high-pressure ST tokamak plasmas and provide a theoretical basis for optimizing RMP-based control of the edge-localized modes in future ST devices.

RMP↗
DOE OSTI2024

Pressure-stabilized fixed-stress iterative solutions of compositional poromechanics

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the discrete saddle point matrix never appears in the fixed-stress approach. This observation reconciles previous results regarding the pressure stability of the splitting method. Using examples of compositional poromechanics with application to geological CO sequestration, we see that solutions obtained using the fixed-stress scheme with a low order finite element-finite volume discretization which is not inherently inf-sup stable can exhibit the same pressure oscillations obtained with the corresponding fully implicit scheme. Moreover, pressure jump stabilization can effectively remove these spurious oscillations in the fixed-stress setting, while also improving the efficiency of the scheme in terms of the number of iterations required at every time step to reach convergence.

42 ENGINEERING↗
DOE OSTI2021

Characteristics of Ultralow Aspect Ratio Toroidal Plasmas and Non-Solenoidal Startup and Edge Stability Studies at Near-Unity Aspect Ratio (Final Report)

This grant supported a long-term research and development program to explore the physics and technology of spherical tokamak (ST) plasma behavior at near-unity aspect ratio ( A ). The PEGASUS Toroidal Experiment is a university-scale ( R ) ~ 0.40 m, α ~ .35 m, I p ≤ 0.3 MA, B T ≤ 0.15 T) experiment that accesses A → 1, to provide large values of the normalized plasma current, I N = I p /α B T , or equivalently the toroidal field utilization factor I p / I TF . The research activities focused on: 1) developing the technique of Local Helicity Injection (LHI) as a viable means of initiating and growing an ST plasma without the use of a central solenoid; 2) exploring the equilibrium and stability properties of spherical tokamak plasmas at extremely low aspect ratio; and 3) obtaining new insights in the properties of the enhanced confinement H-mode regime at A ~ 1. The initial (Phase I) facility employed a unique high-stress central solenoid Ohmic for current drive and heating with simple magnet current waveforms. A subsequent major upgrade (Phase II) offered more flexible control of the plasma evolution along with a powerful LHI system for plasma initiation, heating and sustainment. The LHI technique consists of injection of high-density current streams into vacuum toroidal and vertical magnetic fields. These streams become unstable and support magnetic reconnection to allow the system to relax into a tokamak-like magnetic configuration. This program focused on: 1) development of electron current sources that provide sufficiently high injection currents in the challenging edge plasma region; 2) validation of theoretical limits to achievable I p arising from magnetic helicity and energy conservation plus absolute limits arising from relaxation to a minimal energy states; 3) tests of a power balance model to describe the evolution of the plasma current I p (t); and 4) study of magnetic fluctuations and their role in the I p evolution. This culminated in the production of toroidal currents of I p ≥ 0.2 MA with only ~8 kA of injected current. Operation with Ohmic induction alone in Phase I created plasmas with soft limits on the achievable I p and field utilization ( I p / I TF ~ 1) due to the onset of large low-order (2/1 or 3/2) internal resonant tearing modes. With the expanded capabilities in Phase II operation, methods employed to mitigate those modes and achieve I p / I TF > 1 were: 1) I TF ramp-downs; 2) non-solenoidal startup via LHI; and 3) extremely low I TF Ohmic operations assisted by LHI current injector pre-ionization. Extensive use of LHI-driven startup and drive for non-solenoidal operation produced favorable current profiles to stably operate tokamak plasmas with unprecedentedly high I N = I p / aB T ~ 15 and I p / I TF > 2. With strong reconnection-driven anomalous ion heating, this in turn provided access to tokamak plasmas with B t up to 100%, a world record 2 times higher than that previously achieved in advanced or spherical tokamaks. This high B t regime had a large fraction (~50%) of the plasma volume in a region of an absolute minimum- B configuration. The MHD stability limit in this regime was the ideal external kink mode without a stabilizing wall. These results provided the first demonstration of access to tokamak plasmas with very high B t , high i N , high elongation κ, and low internal inductance ℓ i , and as such served as a proof-ofprinciple for access to this long-sought ST regime. The naturally low B T needed for stability at A ≤ 1.2 reduces the L-H mode power threshold, P LH , so that H-mode plasmas were achieved with Ohmic heating alone. The power threshold for the transition to the H-mode regime was found to be 10× the accepted values from the ITER international scaling, confirming initial trends indicated by experiments on MAST and NSTX, and suggesting that the physics behind this transition is not yet fully understood. The density dependence of the transition and the observed insensitivity to whether the plasma is bounded by a limiter or magnetic divertor are consistent with the recent FM 3 model. Multiple unstable toroidal magnetic modes were measured during ELM (Edge Localized Mode) crashes, with generally lower toroidal mode numbers than seen at higher A , which was attributed to the larger peeling mode instability drive at low A . First-ever edge current profile measurements through an ELM crash showed current-carrying filaments were generated, as seen in ELM simulations and in electromagnetic blob transport theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The stability of subducted glaucophane with the Earth’s secular cooling

The blueschist to eclogite transition is one of the major geochemical–metamorphic processes typifying the subduction zone, which releases fluids triggering earthquakes and arc volcanism. Although glaucophane is an index hydrous mineral for the blueschist facies, its stability at mantle depths in diverse subduction regimes of contemporary and early Earth has not been experimentally determined. Here, we show that the maximum depth of glaucophane stability increases with decreasing thermal gradients of the subduction system. Along cold subduction geotherm, glaucophane remains stable down ca. 240 km depth, whereas it dehydrates and breaks down at as shallow as ca. 40 km depth under warm subduction geotherm or the Proterozoic tectonic setting. Our results imply that secular cooling of the Earth has extended the stability of glaucophane and consequently enabled the transportation of water into deeper interior of the Earth, suppressing arc magmatism, volcanism, and seismic activities along subduction zones.

58 GEOSCIENCES↗
DOE OSTI2022

Stability in integrable nonlocal nonlinear equations

Recently a variety of nonlocal integrable systems has been introduced that besides fields located at particular space-time points simultaneously also contain fields that are located at different, but symmetrically related, points. Here we investigate different types of soliton solutions with regard to their stability against linear perturbations obtained for the nonlocal version of the Hirota/nonlinear Schrödinger equation and the so-called Alice and Bob versions of the Korteweg-de Vries and Bousinesq equations. In this work, we encounter different types of scenarios: Solition solutions that are linearly stable or unstable and also solutions that change their stability properties depending on the parameter regime they are in.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Machine-learning-enabled on-the-fly analysis of RHEED patterns during thin film deposition by molecular beam epitaxy

Thin film deposition is a fundamental technology for the discovery, optimization, and manufacturing of functional materials. Deposition by molecular beam epitaxy (MBE) typically employs reflection high-energy electron diffraction (RHEED) as a real-time in situ probe of the growing film. However, the state-of-the-art for RHEED analysis during deposition requires human observation. Here, we present an approach using machine learning (ML) methods to monitor, analyze, and interpret RHEED images on-the-fly during thin film deposition. In the analysis workflow, RHEED pattern images are collected at one frame per second and featurized using a pretrained deep convolutional neural network. The feature vectors are then statistically analyzed to identify changepoints; these changepoints can be related to changes in the deposition mode from initial film nucleation to a transition regime, smooth film deposition, and in some cases, an additional transition to a rough, islanded deposition regime. The feature vectors are additionally analyzed via graph analysis and community classification. The graph is quantified as a stabilization plot, and we show that inflection points in the stabilization plot correspond to changes in the growth regime. The full RHEED analysis workflow is termed RHAAPsody and includes data transfer and output to a visual dashboard. We demonstrate the functionality of RHAAPsody by analyzing the precaptured RHEED images from epitaxial depositions of anatase TiO2 on SrTiO3(001) and show that the analysis workflow can be executed in less than 1 s. Our approach shows promise as one component of ML-enabled real-time feedback control of the MBE deposition process.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Study of Alfvén eigenmode stability in Quasi-Poloidal Stellarator (QPS) plasma using a Landau closure model

The aim of this study is to analyze the linear stability of Alfvén eigenmodes (AE) in the QPS device heated by a tangential neutral beam injector (NBI). The analysis is performed using the gyro-fluid code FAR3d, that solves the reduced MHD equations for the thermal plasma coupled with moments of the kinetic equation for the energetic particles (EP). The AE stability is calculated in several operational regimes of the tangential NBI: EP β between 0.001 and 0.1, EP energy between 12 and 180 keV and different radial locations of the beam. The analysis is performed for vacuum and finite β equilibria as well as QPS configurations with two and three periods. The EP β threshold in the vacuum case is 0.001 and the AE frequency is lower as the energy of the EP population decreases. Toroidal Alfvén eigenmodes with f = 80–120 kHz and elliptical AE between f = 120–350 kHz are triggered between the middle-outer plasma region ($r/a \gt 0.5$). The AE stability improves in the simulations with finite β equilibria and three period configurations with respect to the vacuum case with two periods because the continuum gaps are slender, leading to a higher threshold of the EP β, above 0.03 for the AEs triggered by the helical mode families. Helical effects are not strong enough to destabilize Helical Alfvén eigenmodes, the AEs with the largest growth rates are triggered by the n = 1 and n = 2 toroidal families.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Borehole breakout modeling in arkose and granite rocks

The existence of a deep borehole in the Earth’s crust disturbs the local stresses and creates a stress concentration that may result in breakout and damage to the borehole. Maintaining wellbore integrity mitigates environmental impacts such as groundwater contamination, gas leakage to the atmosphere, and fluid spills and seepage at the surface. In this paper, the stability of deep boreholes (5 km) is examined by laboratory experiments and numerical models in the context of nuclear waste disposal in Israel. Two rock types in southern Israel are considered: the crystalline basement (granite) and the Zenifim Formation (arkose). A series of room-temperature triaxial rock deformation experiments were conducted at different confining pressures. This mechanical characterization was then used to parameterize the elastic properties and damage behavior of the rocks. This facilitated modeling the stability of the deep boreholes by two different formulations of damage rheology: a dynamic-oriented formulation used to model deformation immediately after the creation of the open hole and a quasi-static formulation used to model longer stress corrosion regime. The calibrated modeling results indicate greater stability with Zenifim arkose than the crystalline granite for deep borehole conditions despite the granite having a greater triaxial compressive strength. Dissipation associated with dilation and porous compaction in the arkose during deformation plays a significant stabilizing role in the borehole compared to crystalline rocks. These results suggest that common strength-based borehole stability assessment may lead to inaccurate predictions. Three-dimensional modeling of bottom-hole stress conditions and the effects of transient borehole geometry show conventional two-dimensional analysis may not be conservative when predicting borehole damage.

58 GEOSCIENCES↗
DOE OSTI2020

Effect of nickel on the kinematic stability of retained austenite in carburized bearing steels – In-situ neutron diffraction and crystal plasticity modeling of uniaxial tension tests in AISI 8620, 4320 and 3310 steels

The presence of kinematically metastable retained austenite in the microstructure of bearing components can significantly affect the macro and micro-mechanical material response. In the present work, the influence of Ni on the stability of the retained austenite within three different grades of high carbon bearing steel using in-situ neutron diffraction is investigated. For the first time, the results show that presence of Ni increases the stability of the austenite in the elastic regime whereas the transformation rate remains unaffected. Crystal plasticity finite element (CPFE) modeling was used to study the deformation in these three steels and shows that the predominant factor causing the difference in mechanical behavior of these steels is the austenite stability. Finally, the elastic and plastic response of the matrix martensite was found to be identical among all specimens while the austenite demonstrates similar elastic behavior but remarkably different stabilities under monotonic loading.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Enhanced ferroelectricity in ultrathin films grown directly on silicon

Ultrathin ferroelectric materials could potentially enable low-power logic and nonvolatile memories. As ferroelectric materials are made thinner, however, the ferroelectricity is usually suppressed. Size effects in ferroelectrics have been thoroughly investigated in perovskite oxides—the archetypal ferroelectric system. Perovskites, however, have so far proved unsuitable for thickness scaling and integration with modern semiconductor processes. In this paper we report ferroelectricity in ultrathin doped hafnium oxide (HfO 2 ), a fluorite-structure oxide grown by atomic layer deposition on silicon. We demonstrate the persistence of inversion symmetry breaking and spontaneous, switchable polarization down to a thickness of one nanometre. Our results indicate not only the absence of a ferroelectric critical thickness but also enhanced polar distortions as film thickness is reduced, unlike in perovskite ferroelectrics. This approach to enhancing ferroelectricity in ultrathin layers could provide a route towards polarization-driven memories and ferroelectric-based advanced transistors. This work shifts the search for the fundamental limits of ferroelectricity to simpler transition-metal oxide systems—that is, from perovskite-derived complex oxides to fluorite-structure binary oxides—in which ‘reverse’ size effects counterintuitively stabilize polar symmetry in the ultrathin regime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Data efficiency and extrapolation trends in neural network interatomic potentials

Abstract Recently, key architectural advances have been proposed for neural network interatomic potentials (NNIPs), such as incorporating message-passing networks, equivariance, or many-body expansion terms. Although modern NNIP models exhibit small differences in test accuracy, this metric is still considered the main target when developing new NNIP architectures. In this work, we show how architectural and optimization choices influence the generalization of NNIPs, revealing trends in molecular dynamics (MD) stability, data efficiency, and loss landscapes. Using the 3BPA dataset, we uncover trends in NNIP errors and robustness to noise, showing these metrics are insufficient to predict MD stability in the high-accuracy regime. With a large-scale study on NequIP, MACE, and their optimizers, we show that our metric of loss entropy predicts out-of-distribution error and data efficiency despite being computed only on the training set. This work provides a deep learning justification for probing extrapolation and can inform the development of next-generation NNIPs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Investigating the role of edge neutrals in exciting tearing mode activity and achieving flat temperature profiles in LTX-β

Abstract We present observations, numerical simulations, and analysis from experiments in the Lithium Tokamak Experiment-Beta (LTX- β ) in which the electron temperature profile ( T e ( r )) shifts from flat to peaked and a tearing mode is also destabilized when the average density ( n e ave ) exceeds ∼10 19 m −3 . Flat T e ( r ) is obtained routinely in LTX- β , with a lithium coated, low-recycling first wall, once the external fueling is stopped and density decays [Boyle et al 2023 Nucl. Fusion 63 056020]. In the present experiment, flat T e profiles can be sustained while maintaining constant n e ave below a line averaged density threshold ( n e ave th ) of ∼10 19 m −3 . Above n e ave th , T e ( r ) shifts from flat to peaked and a tearing mode is destabilized. Due to low recycling, the achieved n e ave can be controlled precisely by external fueling and hence, a certain threshold of the edge neutral inventory from the external fueling is experimentally manifested through n e ave th . The goal of the present work is to investigate the role of edge neutrals in determining T e ( r ) and MHD stability in the unique low-recycling regime of LTX- β . Our hypothesis is that the peaking of T e ( r ) beyond n e ave th is due ultimately to the edge cooling by the cold neutrals beyond a critical fueling flux. At lower fueling flux, flat T e ( r ) results in broader pressure profile and lower resistivity, which in turn stabilizes the tearing mode. This hypothesis is supported by edge neutral density estimation by DEGAS 2 code. Mode analysis by singular value decomposition confirms the tearing mode structure to be m / n = 2/1 ( m and n being the poloidal and toroidal mode numbers). Linear tearing stability analysis with M3D-C1 predicts that plasmas with n e ave > 10 19 are highly susceptible to a n = 1 tearing mode. ORBIT simulations, however, confirmed that the tearing modes do not contribute to the loss of fast ions from neutral beam injection. This study shows for the first time that the neutral inventory at the edge could be one of the deciding factors for the achievability of the unique operation regime of flat T e ( r ) and the excitation of tearing activity that could be disruptive for the plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Overview of the ASDEX Upgrade results

After a 26-month vent ASDEX Upgrade (AUG) went back in operation with a newly designed upper W-divertor suitable for alternative divertor configurations (featuring in-vessel coils and cryo-pump). Parameter scans and an extensive set of measurements were obtained and their interpretation is ongoing. Prompted by the ITER wall change, dedicated experiments on non-boronized plasma startup were contrasted to that employing asymmetric and more symmetric boronizations. The asymmetric boronization proved to be as beneficial as the more symmetric one, which is in contrast to previous model calculations assuming perfect sticking of boron (measurements suggest sticking ≈ 0.3). In the startup phase also the impurity influxes at the outboard limiters were investigated contrasting the unboronized case featuring cold edges (low- Z radiation) to the boronized case, in which the lifetime of the boron layers could be estimated. Pedestal stability investigations revealed that the quasi-continuous exhaust (QCE) regime is obtained when ballooning modes are active in the vicinity of the separatrix and the global peeling-ballooning stability is high enough. Thus, at high enough shaping and high gas flux both can be achieved and QCE is a consequence. The closely related enhanced D-alpha (EDA) mode is not clearly distinguishable from QCE, e.g. the quasi-coherent mode characteristic for EDA also shows up in QCE. In QCE the impurity transport is behaving benign as could be measured for Ne with a novel analysis method making use of a comprehensive set of CXRS measurements. For high radiative fractions the regime of the X-point radiator (XPR) is accessible at AUG and the understanding of its access conditions and behaviour is further developed. Due to the localized radiative cooling at the X-point the XPR can be well diagnosed and thus controlled. For negative triangularity shapes, further experiments at increased shaping resulted in strongly heated L-mode plasmas avoiding ELMs. Two integrated modelling approaches towards ITER suggested that core W-accumulation will be no issue for ITER and that the fusion yield in ITER may be Q = 12 (i.e. ITPA20-IL scaling is too pessimistic). Further, investigations of the ITER ramp-down in AUG provide insights into maintaining position control. Various aspects of shattered pellet injection were investigated in AUG and one of the results show that with increasing Ne fraction the radiation during the current quench increases and the current decay becomes faster.

ASDEX Upgrade↗
DOE OSTI2024

Stability optimization of energetic particle driven modes in nuclear fusion devices: the FAR3d gyro-fluid code

The development of reduced models provide efficient methods that can be used to perform short term experimental data analysis or narrow down the parametric range of more sophisticated numerical approaches. Reduced models are derived by simplifying the physics description with the goal of retaining only the essential ingredients required to reproduce the phenomena under study. This is the role of the gyro-fluid code FAR3d, dedicated to analyze the linear and nonlinear stability of Alfvén Eigenmodes (AE), Energetic Particle Modes (EPM) and magnetic-hydrodynamic modes as pressure gradient driven mode (PGDM) and current driven modes (CDM) in nuclear fusion devices. Such analysis is valuable for improving the plasma heating efficiency and confinement; this can enhance the overall device performance. The present review is dedicated to a description of the most important contributions of the FAR3d code in the field of energetic particles (EP) and AE/EPM stability. FAR3d is used to model and characterize the AE/EPM activity measured in fusion devices as LHD, JET, DIII-D, EAST, TJ-II and Heliotron J. In addition, the computational efficiency of FAR3d facilitates performing massive parametric studies leading to the identification of optimization trends with respect to the AE/EPM stability. This can aid in identifying operational regimes where AE/EPM activity is avoided or minimized. This technique is applied to the analysis of optimized configurations with respect to the thermal plasma parameters, magnetic field configuration, external actuators and the effect of multiple EP populations. In addition, the AE/EPM saturation phase is analyzed, taking into account both steady-state phases and bursting activity observed in LHD and DIII-D devices. The nonlinear calculations provide: the induced EP transport, the generation of zonal structures as well as the energy transfer towards the thermal plasma and between different toroidal/helical families. Finally, FAR3d is used to forecast the AE/EPM stability in operational scenarios of future devices as ITER, CFETR, JT60SA and CFQS as well as possible approaches to optimization with respect to variations in the most important plasma parameters.

Alfv én Eigenmodes↗
DOE OSTI2022

Stability of exact solutions of the (2 + 1)-dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter κ

In this work, we consider the nonlinear Schrödinger equation (NLSE) in 2+1 dimensions with arbitrary nonlinearity exponent κ in the presence of an external confining potential. Exact solutions to the system are constructed, and their stability as we increase the 'mass' (i.e., the L 2 norm) and the nonlinearity parameter κ is explored. Here we observe both theoretically and numerically that the presence of the confining potential leads to wider domains of stability over the parameter space compared to the unconfined case. Our analysis suggests the existence of a stable regime of solutions for all κ as long as their mass is less than a critical value M*(κ). Furthermore, we find that there are two different critical masses, one corresponding to width perturbations and the other one to translational perturbations. The results of Derrick's theorem are also obtained by studying the small amplitude regime of a four-parameter collective coordinate (4CC) approximation. A numerical stability analysis of the NLSE shows that the instability curve M*(κ) versus κ lies below the two curves found by Derrick's theorem and the 4CC approximation. In the absence of the external potential, κ = 1 demarcates the separation between the blowup regime and the stable regime. In this 4CC approximation, for κ < 1, when the mass is above the critical mass for the translational instability, quite complicated motions of the collective coordinates are possible. Energy conservation prevents the blowup of the solution as well as confines the center of the solution to a finite spatial domain. We call this regime the 'frustrated' blowup regime and give some illustrations. In an appendix, we show how to extend these results to arbitrary initial ground state solution data and arbitrary spatial dimension d.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗