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DOE OSTI2020

Very-Low-Frequency transmitters bifurcate energetic electron belt in near-earth space

Very-Low-Frequency (VLF) transmitters operate worldwide mostly at frequencies of 10–30 kilohertz for submarine communications. While it has been of intense scientific interest and practical importance to understand whether VLF transmitters can affect the natural environment of charged energetic particles, for decades there remained little direct observational evidence that revealed the effects of these VLF transmitters in geospace. Here we report a radially bifurcated electron belt formation at energies of tens of kiloelectron volts (keV) at altitudes of ~0.8–1.5 Earth radii on timescales over 10 days. Using Fokker-Planck diffusion simulations, we provide quantitative evidence that VLF transmitter emissions that leak from the Earth-ionosphere waveguide are primarily responsible for bifurcating the energetic electron belt, which typically exhibits a single-peak radial structure in near-Earth space. Since energetic electrons pose a potential danger to satellite operations, our findings demonstrate the feasibility of mitigation of natural particle radiation environment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Bifurcation-driven vertical plasma displacement

This paper considers vertical plasma motion resulting from plasma current decay during the disruption event. The presented filament-based model describes the motion in the ideal wall limit as an adiabatically slow evolution of the plasma equilibrium. Here, the equilibrium exhibits a pitchfork bifurcation when the decaying plasma current passes a critical value determined by the external magnetic field. This bifurcation affects the disruption-induced mechanical loads on the first wall.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Kinetic-ballooning-bifurcation in tokamak pedestals across shaping and aspect-ratio

We use a new gyrokinetic threshold model to predict a bifurcation in tokamak pedestal width-height scalings that depends strongly on plasma shaping and aspect-ratio. The bifurcation arises from the first and second stability properties of kinetic-ballooning-modes that yields wide and narrow pedestal branches, expanding the space of accessible pedestal widths and heights. The wide branch offers potential for edge-localized-mode-free pedestals with high core pressure. For negative triangularity, low-aspect-ratio configurations are predicted to give steeper pedestals than conventional-aspect-ratio. Both wide and narrow branches have been attained in tokamak experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Neural operator transformers capture bifurcating drift-wave turbulence in fusion plasma simulations

Self-consistent modeling of turbulence-driven transport is critical for optimizing confinement in magnetically confined fusion plasmas, such as tokamaks and stellarators. In particular, capturing the long-term co-evolution of turbulence, flow, and background plasma profiles remains computationally challenging. Direct numerical simulation of these multiscale, highly nonlinear processes is often demanding and impractical for real-time control or design optimization. To address this bottleneck, we investigate transformer-based neural operator partial differential equation surrogates for emulating the dynamics of drift-wave turbulence bifurcation mediated by zonal flows, using the modified Hasegawa–Wakatani (MHW) model as a prototypical system. We find that the finetuned neural operator model has excellent performance in capturing the multi-spatiotemporal-scales of MHW turbulence bifurcation and is robust to testing on rare and out-of-distribution dynamics. Specifically, we demonstrate that a single unified model accurately predicts both quasi-steady-state turbulence and a wide range of dynamical transition processes, such as nonlinear saturation, spontaneous suppression of turbulence, and the emergence of macroscopic zonal flows, over time horizons vastly exceeding the local turbulence correlation time. This computationally efficient approach establishes a strong foundation for fast, AI-based modeling of complex, multiscale phenomena in magnetized fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Bifurcation from L-mode to internal transport barrier triggered by a magnetic island in tokamak plasmas

Magnetic islands are believed to be responsible for triggering the internal transport barrier (ITB) around the rational surface and hence improves confinement in magnetic confinement fusion plasma, for more than two decades. Although some recent theoretical or modelling works support this hypothesis, the direct experimental demonstration on the ITB triggered by a magnetic island is still missing. Here, we report the first experimental observation that the increase in the magnetic island width triggers the bifurcation of the plasma transport state from a low confinement mode (L-mode) to an ITB mode in tokamak plasma. At medium island widths, the bifurcation appears with a dithering phase, i.e. plasma transitions from L-mode to ITB or vice versa quasi-periodically. As the island width further increases, the dithering ITB transitions into a steady ITB. The electron temperature gradient inside the ITB increases with island width. The trigger of the ITB and further enhancement of the ITB performance are also demonstrated by locking the island via applying a resonant magnetic perturbation field. The reduction of density fluctuations in the ITB region is observed and indicates turbulence suppression during ITB formation. These findings offer new insights for understanding ITB formation and robust ITB control.

internal transport barrier↗

DOE OSTI2021

Experimental Observation of Magnetic Island Heteroclinic Bifurcation in Tokamaks

We report empirical observations of magnetic island heteroclinic bifurcation for the first time. This behavior is observed in interacting coupled 2/1 tearing modes in the core of a DIII-D tokamak plasma. Poincaré maps constrained by measured magnetic amplitudes and phasing show bifurcation from heteroclinic to homoclinic topology in the 2/1 island as the 4/2 relative amplitude (R 4/2 ) decreases. Initially, the local electron temperature peak in the 2/1 island splits, consistent with two O points. As R 4/2 decreases a single peak forms, consistent with one O point. Lastly, these call for developing tearing stability theory and control solutions for heteroclinic islands in tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1975

Bifurcation and collapse analysis of stringer and ring-stringer stiffened cylindrical shells with cutouts

Results for cylindrical configurations using the STAGS computer program were presented. Discontinuities were imposed upon the shell's skin by incorporating symmetrical cutout openings. In addition, the surface is stiffened with both stringer and ring-stringer arrangements. The cutout problem has been shown to be highly nonlinear for smooth surface shells, but it was found that bifurcation and collapse loads are close when one is considering stiffened skin configurations. In order to arrive at this conclusion, it was necessary to evaluate the following: (1) comparison between smeared and discrete stiffener theory for linear solutions, (2) numerical finite difference convergence as directed toward buckling determination, (3) collapse load results with the various skin stiffeners. A linear bifurcation study relating to stiffening effects around cutout areas present within stringer and ring-stringer shell surfaces was included. Comparisons were made between a variety of geometric positions considering cutout frame and thickened skin additions.

Palazotto, A. N.↗

NASA NTRS1980

Hydroelastic effects in the aorta bifurcation zone

The mechanical behavior of the vessels and blood is mathematically analyzed at the point of aortic bifurcation using a homogeneous single layer channel as a model of the aorta. Allowance is made for the fact that the aortic intima is considerably less rigid than the other layers. For analysis of blood flow in the major arteries, the blood is treated as a viscous Newtonian fluid whose movements are described by Navier-Stokes equations and a continuity equation. Blood flow dynamics at the aortic bifurcation are discussed on the basis of the results.

Volmir, A. S.↗

NASA NTRS1985

Hopf bifurcation in the presence of symmetry

Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.

Golubitsky, M.↗

NASA NTRS1988

A numerical study of bifurcations in a barotropic shear flow

In the last few years, more and more evidence has emerged suggesting that transition to turbulence may be viewed as a succession of bifurcations to deterministic chaos. Most experimental and numerical observations have been restricted to Rayleigh-Benard convection and Taylor-Couette flow between concentric cylinders. An attempt is made to accurately describe the bifurcation sequence leading to chaos in a 2-D temporal free shear layer on the beta-plane. The beta-plane is a locally Cartesian reduction of the equations describing the dynamicss of a shallow layer of fluid on a rotating spherical planet. It is a valid model for large scale flows of interest in meteorology and oceanography.

Huerre, P.↗

NASA NTRS1989

The route to chaos in thermal convection at infinite Prandtl number. I - Some trajectories and bifurcations

The question of whether or not thermal convection in the earth's mantle is chaotic is addressed. It is suggested that the high Prandtl number/high Raleigh number thermal convection associated with mantle convection is chaotic. To test this hypothesis, the route to chaos in a fluid with infinite Prandtl number is examined, using the Saltzman (1962) equations and the Lorenz (1963) equations. It is concluded that thermal convection at infinite Prandtl number becomes chaotic by means of symmetry-breaking pitchfork bifurcations and the appearance of Hopf bifurcations which produce unstable periodic orbits.

Stewart, Cheryl A.↗

NASA NTRS1989

Bifurcating families of periodic traveling waves in rarefied plasmas

A necessary condition for the existence of undamped spatially periodic traveling waves near spatially uniform equilibria is derived. When the necessary condition is satisfied, a bifurcation analysis of Berstein-Greene-Kruskal modes is used to construct branches of such waves with wavelength equal to the fundamental wavelength. Expansions of the bifurcating potential for these waves are derived, and the reconstruction of the distribution function is discussed.

Holloway, James Paul↗

NASA NTRS1990

Intraseasonal oscillations in the extratropics - Hopf bifurcation and topographic instabilities

A potential vorticity model in a beta-channel is used to analyze the resonant response of equivalent-barotropic flow to topography in the presence of a forced zonal jet with arbitrary meridional structure. The nonlinear dynamics near different resonances is studied considering both wave-wave and wave-zonal flow interactions. It is shown that Hopf bifurcations from stationary to periodic flows are possible due to the nonlinear instability of nonzonal, topographically forced flow. Low-frequency, finite-amplitude oscillations arise due to a combination of two factors: (1) nonlinear wave-wave interactions, which tend to reduce the Rossby wave frequency; and (2) wave-zonal flow interactions, which reflect the importance of wave momentum transport in shifting the westerly jet and of the topographic form drag. The physical mechanism of atmospherically realistic Hopf bifurcations depends crucially on the meridional profile of the mean zonal flow giving rise to a dipole-shaped resonance.

Jin, F.-F.↗

NASA NTRS1991

Equilibria, stability and bifurcations of rotating columns of fluid subjected to planar disturbances

Long gyrostatically rotating drops bonded by surface tension are amenable to conventional bifurcation analysis and newer, computer-aided analytical methods, and therefore are useful prototypes of three-dimensional drops. A study is conducted by setting aside instability to Rayleigh's axisymmetric mode and investigating the effects of translationally symmetric (planar) disturbances. The disadvantage of employing single-coordinate representation of drop shapes close to break-up is brought out. It is shown that a family of symmetric two-lobed shapes bifurcates from the main family of perfectly cylindrical shapes when the rotation rate reaches a critical value, in accord with the linearized hydrodynamic analysis of Hocking.

Benner, R. E., Jr.↗

NASA NTRS1992

Cellular instability in rapid directional solidification - Bifurcation theory

Merchant and Davis performed a linear stability analysis on a model for the directional solidification of a dilute binary alloy valid for all speeds. The analysis revealed that nonequilibrium segregation effects modify the Mullins and Sekerka cellular mode, whereas attachment kinetics has no effect on these cells. In this paper, the nonlinear stability of the steady cellular mode is analyzed. A Landau equation is obtained that determines the amplitude of the cells. The Landau coefficient here depends on both nonequilibrium segregation effects and attachment kinetics. This equation gives the ranges of parameters for subcritical bifurcation (jump transition) or supercritical bifurcation (smooth transition) to cells.

Braun, R. J.↗

NASA NTRS1992

Some Aspects of Bifurcation Structure of Laminar Flow in Curved Ducts

A bifurcation study is made of laminar flow in curved ducts. The problem is formulated in a curvilinear coordinate system, and the governing equations, after orthogonal mapping is applied, are solved numerically by an iterative finite-difference method. Many computer runs were made with various duct cross-sections ranging from a circle to a square, to learn the transition of bifurcation structure with this change in cross-section and to reconcile the differences between them. In addition, a simpler technique is proposed to generate symmetric four-cell solutions in a circular pipe and a means is put forward to stabilize four-vortex structures in a complete cross-section.

Kao, Hsiao C.↗

NASA NTRS1993

Bifurcating optical pattern recognition in photorefractive crystals

A new concept and experimental demonstration of a bifurcating optical pattern recognizer that uses a nonlinear gain saturation memory medium such as a high-gain photorefractive crystal are presented. A barium titanate crystal is used as a typical example of the nonlinear medium for the demonstration of the bifurcating optical pattern recognizer.

Liu, Hua-Kuang↗

NASA NTRS1996

Local and Global Bifurcations of Flow Fields During Physical Vapor Transport: Application to a Microgravity Experiment

The local bifurcation of the flow field, during physical vapor transport for a parametric range of experimental interest, shows that its dynamical state ranges from steady to aperiodic. Comparison of computationally predicted velocity profiles with laser doppler velocimetry measurements shows reasonable agreement in both magnitude and planform. Correlation of experimentally measured crystal quality with the predicted dynamical state of the flow field shows a degradation of quality with an increase in Rayleigh number. The global bifurcation of the flow field corresponding to low crystal quality indicates the presence of a traveling wave for Ra = 1.09 x 10(exp 5). For this Rayleigh number threshold a chaotic transport state occurs. However, a microgravity environment for this case effectively stabilizes the flow to diffusive-advective and provides the setting to grow crystals with optimal quality.

Duval, W. M. B.↗