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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The Effect of the Degree of Premixedness on Self-Excited Combustion Instability

The use of lean, premixed fuel and air mixtures is a common strategy to reduce NO x emissions in gas turbine combustors. However, this strategy causes an increased susceptibility to self-excited instability, which manifests as fluctuations in heat release rate, flow velocity, and combustor acoustics that oscillate in-phase in a feedback loop. Here, this study considers the effect of the level of premixedness on the self-excited instability in a single-nozzle combustor. In this system, the fuel can be injected inside the nozzle to create a partially-premixed mixture or far upstream to create a fully-premixed mixture, varying the level of premixedness of the fuel and air entering the combustor. When global equivalence ratio is held constant, the cases with higher levels of premixing have higher instability amplitudes. High-speed CH* chemiluminescence imaging shows that the flame for these cases is more compact and the distribution of the heat release rate oscillations is more concentrated near the corner of the combustor in the outer recirculation zones. Rayleigh index images, which are a metric for the relative phase of pressure and heat release rate oscillations, suggest that vortex rollup in the corner region is primarily responsible for determining instability characteristics when premixedness is varied. This finding is further supported through analysis of local flame edge dynamics.

42 ENGINEERING↗
DOE OSTI2025

Oceanic mixing and waves in the presence of a suspended canopy

Large-eddy simulations are analysed to determine the influence of suspended canopies, such as those formed in macroalgal farms, on ocean mixed layer (OML) deepening and internal wave generation. In the absence of a canopy, we show that Langmuir turbulence, when compared with wind-driven shear turbulence, results in a deeper OML and more pronounced internal waves beneath the OML. Subsequently, we examine simulations with suspended canopies of varying densities located in the OML, in the presence of a background geostrophic current. Intensified turbulence occurs in the shear layer at the canopy’s bottom edge, arising from the interaction between the geostrophic current and canopy drag. Structures resembling Kelvin–Helmholtz (KH) instability emerge as the canopy shear layer interacts with the underlying stratification, radiating internal waves beneath the OML. Both intensified turbulence and lower-frequency motions associated with KH-type structures are critical factors in enhancing mixing. Consequently, the OML depth increases by up to a factor of two compared with cases without a canopy. Denser canopies and stronger geostrophic currents lead to more pronounced KH-type structures and internal waves, stronger turbulence and greater OML deepening. Additionally, vertical nutrient transport is enhanced as the OML deepens due to the presence of the canopy. Considering that the canopy density investigated in this study closely represents offshore macroalgal farms, these findings suggest a mechanism for passive nutrient entrainment conducive to sustainable farming. Overall, this study reveals the intricate interactions between the suspended canopy, turbulent mixing and stratification, underscoring their importance in reshaping OML characteristics.

Bo, Tong (ORCID:0000000260300561)↗
DOE OSTI2023

Models of resistive wall tearing mode disruptions

Disruptions are a serious issue in tokamaks. In a disruption, the thermal energy is lost by means of an instability which could be a resistive wall tearing mode (RWTM). During precursors to a disruption, the plasma edge region cools, causing the current to contract. Model sequences of contracted current equilibria are given, and their stability is calculated. A linear stability study shows that there is a maximum value of edge q a ≈ 3 for RWTMs to occur. Further, this also implies a minimum rational surface radius normalized to plasma radius from RWTMs to be unstable. Nonlinear simulations are performed using a similar model sequence derived from an equilibrium reconstruction. There is a striking difference in the results, depending on whether the wall is ideal or resistive. With an ideal wall, the perturbations saturate at moderate amplitude, causing a minor disruption without a thermal quench. With a resistive wall, there is a major disruption with a thermal quench, if the edge q a ≤ 3. There is a sharp transition in nonlinear behavior at q a = 3. This is consistent with the linear model and with experiments. If disruptions are caused by RWTMs, then devices with highly conducting walls, such as the International Tokamak Experimental Reactor will experience much milder, tolerable, disruptions than presently predicted.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A numerical study of particle jetting in a dense particle bed driven by an air-blast

In this work, the particle jetting behavior in a blast-driven dense particle bed is studied at early times. Four-way coupled Euler–Lagrange simulations are performed using a high-order discontinuous Galerkin spectral element solver coupled with a high-order Lagrangian particle solver, wherein the inter-particle collisions are resolved using a discrete element method collision model. Following the experiments of Rodriguez et al. [“Formation of particle jetting in a cylindrical shock tube,” Shock Waves 23(6), 619–634 (2013)] and the simulations of Osnes et al. [“Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell,” Shock Waves 28(3), 451–461 (2018)], the simulations are performed in a quasi-two-dimensional cylindrical geometry (Hele-Shaw cell). Parametric studies are carried out to assess the impact of the coefficient of restitution and the strength of the incident shock on the particle jetting behavior. The deposition of vorticity through a multiphase (gas–particle) analog of Richtmyer–Meshkov instability is observed to play a crucial role in channeling the particles into well-defined jets at the outer edge of the particle bed. This is confirmed by the presence of vortex pairs around the outer jets. Furthermore, the effect of the relaxation of the relative velocity between the two phases on the vorticity generation is explored by analyzing the correlation between the radial velocity of particles and the radial velocity of the gas at the particle location.

42 ENGINEERING↗
DOE OSTI2021

Dynamics of filaments during the edge-localized mode crash on NSTX

Edge localized modes (ELMs) are routinely observed in H-mode plasma regimes of the National Spherical Torus Experiment (NSTX). Due to the explosive nature of the instability, only diagnostics with high temporal and spatial resolution could provide a detailed insight into the dynamics associated with the ELMs. Gas-puff imaging at NSTX provides 2D measurements of the magnetic field aligned fluctuations (e.g., ELM filaments) in the scrape-off layer and at the plasma edge with 2.5 μs temporal and 10 mm optical resolution. A novel analysis technique was developed to estimate the frame-by-frame velocities and the spatial parameters of the dominant structures associated with the ELMs. The analysis was applied to single ELM events to characterize the ELM crash dynamics and then extended to a database of 159 ELM events. Statistical analysis was performed in order to find the characterizing dynamics of the ELM crash. The results show that on average, an ELM crash consists of a filament with a circular cross section, which is propelled outward with a characterizing peak radial velocity of ~3.3 km/s. The radial velocity was found to be linearly dependent on the distance of the filament from the separatrix, which has never been seen before. The ELM filament is characterized by propagation in the ion-diamagnetic direction poloidally with a peak velocity of 11.4 km/s. The ELM crash lasts for approximately 100 μs until the radial propulsion settles back to the pre-ELM level. Furthermore, the experimental findings were compared with analytical theory. Two possible mechanisms were identified for explaining the observations: the curvature interchange model and the current–filament interaction model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Dynamics of filaments during the edge-localized mode crash on NSTX

Edge localized modes (ELMs) are routinely observed in H-mode plasma regimes of the National Spherical Torus Experiment (NSTX). Due to the explosive nature of the instability, only diagnostics with high temporal and spatial resolution could provide a detailed insight into the dynamics associated with the ELMs. Gas-puff imaging (GPI) at NSTX provides 2D measurements of the magnetic field aligned fluctuations (e.g. ELM filaments) in the scrape-off layer and the at the plasma edge with 2.5 us temporal and 10 mm optical resolution.A novel analysis technique was developed to estimate the frame-by-frame velocities and the spatial parameters of the dominant structures associated with the ELMs. The analysis was applied to single ELM events to characterize the ELM crash dynamics, and then extended to a database of 169 ELM events.Statistical analysis was performed in order to find the characterizing dynamics of the ELM crash. The results show that on average an ELM crash consists of a filament with a circular cross-section which is propelled outwards with a characterizing peak radial velocity of ~3.3 km/s. The radial velocity was found to be linearly dependent on the distance of the filament from the separatrix, which has never been seen before. The ELM filament is characterized by propagation in the ion-diamagnetic direction poloidally with a peak velocity of 11.4 km/s. The ELM crash lasts for approximately 100us until the radial propulsion settles back to the pre-ELM level. The experimental findings were compared with analytical theory. Two possible mechanisms were identified for explaining the observations: the curvature interchange model and the current-filament interaction model.

correlation↗
DOE OSTI2025

Taylor limit studies for local helicity injection plasma startup

Solenoid-free tokamak startup techniques can simplify the design and reduce the cost of tokamak-based fusion energy systems. The newly commissioned Pegasus-III spherical tokamak provides a dedicated platform for developing a scalable solenoid-free startup approach. Local helicity injection (LHI) is one promising technique being developed on Pegasus-III, which uses compact edge current sources to drive open field line current I inj that is redistributed via helicity-conserving instabilities to initiate tokamak plasmas. These instabilities relax the system toward a minimum energy state described by Taylor relaxation theory. This relaxation process imposes a global current limit for LHI plasmas, referred to as the Taylor limit I TL ⁠, which can dictate the plasma current I p evolution. Experiments on Pegasus and Pegasus-III show that increasing this limit leads to more effective utilization of the available helicity input and higher I p plasmas. Initial Pegasus-III experiments have verified the expected I TL $\varpropto$ ( I inj B T ) 1/2 scaling holds for B T and I inj up to 0.3 T on axis and 12 kA ⁠, respectively. Additionally, data from different injector arrays show that the width of the injector aperture directly alters I TL and can be leveraged for future injector design optimization. Throughout these scaling studies, discharges were overdriven at I p = I TL by providing excess helicity input. Intermittent bursts of n = 1 magnetic activity consistent with large-scale reconnection events occurred more often as the system was increasingly overdriven leading to a flattening of the λ = μ 0 J ∥ / |B| profile, where J ∥ is the parallel current density.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Divertor characterization and access to dissipative divertor conditions in negative triangularity discharges in DIII-D

Reduced radial transport, short midplane-to-target parallel connection lengths, and a strong effect of cross-field drifts were responsible for the high densities required for detachment in strong negative triangularity (NT) configurations in DIII-D. Dissipative divertor conditions were achieved in NT discharges at different triangularity, injected power, plasma current, and toroidal field direction. Differences between negative and positive triangularity (PT) discharges are analyzed in this paper to understand the requirements for access to detached divertor conditions: power balance, geometry, radial transport and effect of cross-field particle drifts. Parametric dependencies of access to detachment on plasma current and power flowing into the scrape-off layer remained similar in negative and PT and impurity seeding was observed to reduce the density needed to detach by up to 30% at the expense of core impurity dilution. The impact of triangularity on core-edge integration was tested varying bottom triangularity at fixed top triangularity. The high density needed to detach was not intrinsic to the NT edge as shapes with positive lower triangularity and negative upper triangularity were able to detach at lower upstream densities while maintaining an ELM-free NT edge. Confinement degradation at deeper detachment levels was however observed in all NT shapes, often associated with radiation instabilities.

detachment↗
DOE OSTI2022

A BOUT++ extension for full annular tokamak edge MHD and turbulence simulations

For tokamak edge plasma simulation, a plasma simulation framework BOUT++ employs a dual coordinate system to simulate moderate-n and high-n plasma instability with reasonable computational cost, where n is the toroidal mode number. This coordinate system however limits the computational domain to the toroidal wedge (full torus divided into N parts in the toroidal direction) for computational efficiency and the use of flute-ordering approximation in the field solver calculating the flow potential from the vorticity which may not be valid for low-n modes. Improving numerical treatment of low-n modes is however indispensable to address simulations of low-n current-driven edge localized mode (ELM), ELM control by resonant magnetic perturbations (RMPs), edge turbulence with RMPs and so on. In this work, BOUT++ is extended to simulate the interplay between $n=0$, low-n and high-n plasma components in a full annular tokamak edge domain through hybrid modeling of the flow potential and the vorticity. Low-n modes of flow potential are calculated in an orthogonal flux surface coordinate and high-n modes in the dual coordinate system separately in Fourier space. Finally, the proposed scheme can capture an interplay between $n=1$ global modes and high-n turbulence during pedestal collapse in a full annular torus domain with a circular cross section.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Assessment of vertical stability for negative triangularity pilot plants

Abstract Negative triangularity (NT) tokamak configurations may be more susceptible to magneto-hydrodynamic instability, posing challenges for recent reactor designs centered around their favorable properties, such as improved confinement and operation free of edge-localized modes. In this work, we assess the vertical stability of plasmas with NT shaping and develop potential reactor solutions. When coupled with a conformal wall, NT equilibria are confirmed to be less vertically stable than equivalent positive triangularity (PT) configurations. Unlike PT, their vertical stability is degraded at higher poloidal beta. Furthermore, improvements in vertical stability at low aspect ratio do not translate to the NT geometry. NT equilibria are stabilized in PT vacuum vessels due to the increased proximity of the plasma and the wall on the outboard side, but this scenario is found to be undesirable due to reduced vertical gaps which give less spatial margin for control recovery. Instead, we demonstrate that informed positioning of passively conducting plates can lead to improved vertical stability in NT configurations on par with stability metrics expected in PT scenarios. An optimal setup for passive plates in highly elongated NT devices is presented, where plates on the outboard side of the device reduce vertical instability growth rates to 16% of their baseline value. For lower target elongations, integration of passive stabilizers with divertor concepts can lead to significant improvements in vertical stability. Plates on the inboard side of the device are also uniquely enabled in NT geometries, providing opportunity for spatial separation of vertical stability coils and passive stabilizers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Variability of MHD instabilities in benign termination of high-current runaway electron beams in the JET and DIII-D tokamaks

Benign termination, in which magnetohydrodynamic (MHD) instabilities deconfine runaway electrons (REs) following hydrogenic injections, is a promising strategy for mitigating dangerous RE loads after disruptions. Recent experiments on the Joint European Torus (JET) have explored this scenario at higher pre-disruptive plasma currents than are achievable on other devices, revealing challenges in obtaining benign terminations at I p ≥2.5 MA. This work analyzes the evolution of these high-current RE beams and their terminating MHD events using fast magnetic sensor measurements and EFIT equilibrium reconstructions for approximately 40 JET and 20 DIII-D tokamak discharges. On JET, unsuccessful non-benign terminations occur at low edge safety factor (q edge ≈ 2), and are preceded by intermittent, non-terminating MHD events at higher rational qedge. Trends in the internal inductance I i indicate more peaked RE current profiles in the high-I p non-benign population, which may hinder successful recombination through re-ionization of the companion plasma. In contrast, benign terminations on JET typically occur at higher q edge ≥3 and exhibit less peaked RE current profiles. DIII-D displays a broader range of terminating edge safety factors, again correlated with the measured values. Across both tokamaks, the RE current peaking is therefore found to determine which MHD instability boundary is encountered, a result confirmed by linear resistive MHD modeling with the CASTOR3D code. Measured growth rates are similar for benign and non-benign cases, indicating that ideal MHD timescales at low density after hydrogenic injection do not alone explain efficient RE deconfinement. Instead, non-benign cases are most readily characterized by their comparably lower overall MHD perturbation amplitudes δB. These observations suggest that the interplay between ideal and resistive dynamics governs the termination process, with implications for extrapolating benign RE termination to high-I p reactor scenarios.

MHD instabilities↗
DOE OSTI2024

Highest fusion performance without harmful edge energy bursts in tokamak

The path of tokamak fusion and International thermonuclear experimental reactor (ITER) is maintaining high-performance plasma to produce sufficient fusion power. This effort is hindered by the transient energy burst arising from the instabilities at the boundary of plasmas. Conventional 3D magnetic perturbations used to suppress these instabilities often degrade fusion performance and increase the risk of other instabilities. This study presents an innovative 3D field optimization approach that leverages machine learning and real-time adaptability to overcome these challenges. Implemented in the DIII-D and KSTAR tokamaks, this method has consistently achieved reactor-relevant core confinement and the highest fusion performance without triggering damaging bursts. This is enabled by advances in the physics understanding of self-organized transport in the plasma edge and machine learning techniques to optimize the 3D field spectrum. The success of automated, real-time adaptive control of such complex systems paves the way for maximizing fusion efficiency in ITER and beyond while minimizing damage to device components.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Linking constituent phase properties to ductility and edge stretchability of two DP 980 steels

Two DP 980 steels were characterized with multiple methods to determine its microstructure characteristics, tensile properties and edge stretchability. The first (DP980-B) is a commercial grade DP980 steel produced by AK Steel, while the second (DP980-T) is a modification of the first one by a tempering process. Both contain two individual phases: ferrite and martensite with body centered cubic (BCC) and tetragonal (BCT) crystal structure respectively. ASTM standard tensile tests were performed for both materials, revealing that DP980-B has higher work hardening and larger total elongation than DP980-T. Standard hole piercing and subsequent hole expansion and extrusion tests were also performed. The critical hole expansion ratio (HER) of hole pierced sheet at different nominal clearances, on the other hand, show an opposite trend: the HER of DP980-T almost doubles that of DP980-B. This indicates the tensile ductility and edge stretchability are determined by different mechanisms due to different deformation modes. The ductility of sheet metal during uniaxial tension is determined by deformation instability, i.e. necking, due to less constraint at the region of deformation and fracture will occur quickly after necking. The contribution of post-necking deformation to the total elongation is insignificant for the high strength grades such as DP980 steels. The ductility during hole-expansion, however, is mainly determined by material fracture behavior that is dependent on phase property disparity and material intrinsic fracture parameters. With the individual phase properties for both DP steels determined by in situ tensile tests under high energy X-ray diffraction, the results show that DP980-T steel has lower property disparities between the two phases than DP980-B steel, due to the tempering process. This explains why the DP980-T steel has higher HER than DP980-B steel: lower phase disparity will lead to less local deformation during loading. The higher work hardening rate for DP980-B steel contributes to its higher uniform elongation compared with DP980-T steel based on the maximum load condition of deformation instability. An integrated finite element simulation framework for studying hole expansion is also presented here, based on the calculated individual phase properties from the combined high energy x-ray diffraction (HEXRD) and elastic plastic self-consistent modeling. The simulation results correlate well with the experimental results on the HER difference between the two materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe 4

The convergence of topology and correlations represents a highly coveted realm in the pursuit of new quantum states of matter. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order, not possible in quantum Hall and Chern insulator systems. Here, in this study, we report a new dual QSH insulator within the intrinsic monolayer crystal of TaIrTe 4 , arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe 4 demonstrates the QSH insulator, manifesting enhanced nonlocal transport and quantized helical edge conductance. After introducing electrons from charge neutrality, TaIrTe 4 shows metallic behaviour in only a small range of charge densities but quickly goes into a new insulating state, entirely unexpected on the basis of the single-particle band structure of TaIrTe 4 . This insulating state could arise from a strong electronic instability near the van Hove singularities, probably leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state. The observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands through CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism.

electronic devices↗
DOE OSTI2024

Effects of zero and reversed magnetic shear on resistive wall modes in a straight limiter tokamak with zero beta

Advanced tokamak scenarios often feature equilibriums with zero and reversed magnetic shear. To isolate and investigate their impacts on the resistive wall mode (RWM) instability analytically, we construct a series of cylindrical limiter equilibriums with different magnetic shear in the core and toward plasma edge, as a prototype of the configurations in advanced tokamak scenarios. Equilibriums with zero β are considered so that the analysis focuses on the current-driven RWMs. Analytical solutions for the n=1 resistive wall mode, derived from the reduced ideal magnetohydrodynamics (MHD) equations, consistently demonstrate key insights for both the core and the edge: the growth rate of RWMs is inversely proportional to the averaged magnetic shear when the safety factor at the edge (qa) is held constant. Specifically, an increase in positive averaged magnetic shear results in a decreased growth rate, whereas an increase in negative averaged magnetic shear leads to an increased growth rate. Furthermore, the influence of nqa on the mode's stability significantly surpasses the effects of magnetic shear changes previously discussed. These analytical calculation results provide a verification of NIMROD simulations.

Wan, Sui (ORCID:0009000464121677)↗
DOE OSTI2023

Nonlinear second order electromagnetic gyrokinetic theory for a tokamak plasma

The steep plasma pressure gradient that forms at the edge of the high confinement, H-mode regime of tokamak operation provides free energy to drive electromagnetic micro-instabilities that are widely believed to influence the transport processes in this so-called pedestal region. This high pressure gradient also provides a high current density (bootstrap current), known to influence ballooning mode stability and to be important for driving kink modes in the ideal magneto-hydrodynamic plasma model (so-called peeling-ballooning modes). Furthermore, efficient, steady state future tokamak power plants must operate with a large bootstrap current in the core and especially concerning spherical tokamaks, confinement will be influenced by electromagnetic turbulence. To accommodate these important situations, conventional electromagnetic gyrokinetic theory is extended to incorporate neoclassical effects in the equilibrium drives, allowing $B_{\vartheta} ~ B_0$ (B0 is the confining magnetic field, and $B_{\vartheta}$ is its poloidal component). This provides a global gyrokinetic model that self-consistently captures the consequences of large bootstrap current fractions on the equilibrium distribution functions.

kink modes↗
DOE OSTI2020

The Role of Multiscale Interaction in Tropical Cyclogenesis and Its Predictability in Near-Global Aquaplanet Cloud-Resolving Simulations

Tropical cyclogenesis (TCG) is a multiscale process that involves interactions between large-scale circulation and small-scale convection. A near-global aquaplanet cloud-resolving model (NGAqua) with 4-km horizontal grid spacing that produces tropical cyclones (TCs) is used to investigate TCG and its predictability. This study analyzes an ensemble of three 20-day NGAqua simulations, with initial white-noise perturbations of low-level humidity. TCs develop spontaneously from the northern edge of the intertropical convergence zone (ITCZ), where large-scale flows and tropical convection provide necessary conditions for barotropic instability. Zonal bands of positive low-level absolute vorticity organize into cyclonic vortices, some of which develop into TCs. A new algorithm is developed to track the cyclonic vortices. A vortex-following framework analysis of the low-level vorticity budget shows that vertical stretching of absolute vorticity due to convective heating contributes positively to the vorticity spinup of the TCs. A case study and composite analyses suggest that sufficient humidity is key for convective development. TCG in these three NGAqua simulations undergoes the same series of interactions. The locations of cyclonic vortices are broadly predetermined by planetary-scale circulation and humidity patterns associated with ITCZ breakdown, which are predictable up to 10 days. Whether and when the cyclonic vortices become TCs depend on the somewhat more random feedback between convection and vorticity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Uniform-density Bose-Einstein condensates of the Gross-Pitaevskii equation found by solving the inverse problem for the confining potential

Here, in this work, we consider a “reverse-engineering” approach to construct confining potentials that support exact, constant density kovaton solutions to the classical Gross-Pitaevskii equation (GPE) also known as the nonlinear Schr¨odinger equation (NLSE). In the one-dimensional case, the exact solution is the sum of stationary kink and anti-kink solutions, i.e. a kovaton, and in the overlapping region, the density is constant. In higher dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed out finite square well with minima also at the edges. When self-interactions are added, a term proportional to ±gψ*ψ gets added to the confining potential and ±gM, where M is the norm, gets added to the total energy. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of M (related to the number of particles in the BEC). Comparing the stability criteria from Derrick’s theorem and Bogoliubov-de Gennes analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass M for attractive interactions. However, the numerical analysis gives a much lower critical mass. The numerical analysis shows further that the initial instabilities violate the symmetry x → -x assumed by Derrick’s theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗