Long-lived Modes Research Articles

Hybrid guiding-centre/full-orbit simulations in non-axisymmetric magnetic geometry exploiting general criterion for guiding-centre accuracy

To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel currents and the local shearing of field-lines. The criterion is derived for general three-dimensional magnetic equilibria including stellarator plasmas. Details are provided on how to implement it in cylindrical coordinates and in flux coordinates that rely on the geometric toroidal angle. A means of switching between guiding-centre and full-orbit equations at first order in Larmor radius with minimal discrepancy is shown. Techniques are applied to a MAST (mega amp spherical tokamak) helical core equilibrium in which the inner kinked flux-surfaces are tightly compressed against the outer axisymmetric mantle and where the parallel current peaks at the nearly rational surface. This is put in relation with the simpler situation B(x, y, z) = B0[sin(kx)ey + cos(kx)ez], for which full orbits and lowest order drifts are obtained analytically. In the kinked equilibrium, the full orbits of NBI fast ions are solved numerically and shown to follow helical drift surfaces. This result partially explains the off-axis redistribution of neutral beam injection fast particles in the presence of MAST long-lived modes (LLM).

Nonlinear hybrid simulation of internal kink with beam ion effects in DIII-D

In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the n = 1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the n = 1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mode saturation as well as energetic particle transport. The nonlinear MHD simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. With beam ion effects, the fishbone-like mode can also transit to a saturated kink mode with a small but finite mode frequency. These results are consistent with the experimental observation of saturated kink mode between sawtooth crashes.

Vibrational coherence transfer in an electronically decoupled molecular dyad.

The ring opening of a dithienylethene photoswitch incorporated in a bridged boron-dipyrromethene - dithienylethene molecular dyad was investigated with ultrafast spectroscopy. Coherent vibrations in the electronic ground state of the boron-dipyrromethene are triggered after selective photoexcitation of the closed dithienylethene indicating vibrational coupling although the two moieties are electronically isolated. A distribution of short-lived modes and a long-lived mode at 143 cm−1 are observed. Analysis of the theoretical frequency spectrum indicates two modes at 97 cm−1 and 147 cm−1 which strongly modulate the electronic transition energy. Both modes exhibit a characteristic displacement of the bridge suggesting that the mechanical momentum of the initial geometry change after photoexcitation of the dithienylethene is transduced to the boron-dipyrromethene. The relaxation to the dithienylethene electronic ground state is accompanied by significant heat dissipation into the surrounding medium. In the investigated dyad, the boron-dipyrromethene acts as probe for the ultrafast photophysical processes in the dithienylethene.

A classification scheme for fluvial–aeolian system interaction in desert-margin settings

Abstract This study examines 130 case examples from 60 desert regions to propose a generalised framework to account for the diverse types of interaction known to exist between active aeolian and fluvial depositional systems at modern dune-field margins. Results demonstrate the significance of aeolian and fluvial system type, orientation of aeolian versus fluvial landforms, distribution of open versus closed interdune corridors, and fluvial flow processes in controlling the distance and type of penetration of fluvial systems into aeolian dune fields. Ten distinct types of fluvial–aeolian interaction are recognised: fluvial incursions aligned parallel to trend of linear chains of aeolian dune forms; fluvial incursions oriented perpendicular trend of aeolian dunes; bifurcation of fluvial flow between isolated aeolian dune forms; through-going fluvial channel networks that cross entire aeolian dune fields; flooding of dune fields due to regionally elevated water-table levels associated with fluvial floods; fluvial incursions emanating from a single point source into dune fields; incursions emanating from multiple sheet sources; cessation of the encroachment of entire aeolian dune fields by fluvial systems; termination of fluvial channel networks in aeolian dune fields; long-lived versus short-lived modes of fluvial incursion. Quantitative relationships describing spatial rates of change of desert-margin landforms are presented. The physical boundaries between geomorphic systems are dynamic: assemblages of surface landforms may change gradationally or abruptly over short spatial and temporal scales. Generalised models for the classification of types of interaction have application to the interpretation of ancient preserved successions, especially those known only from the subsurface.

Energetic ion behaviour in MAST

Recent studies of fast ion transport resulting from a range of instabilities, including n = 1 internal kink modes (fishbones and long-lived modes), toroidal Alfvén eigenmodes and sawteeth have been carried out at MAST. Strong correlations were found between relative changes in magnetic edge coils signals, edge Dα signal a fast ion Dα system, a prototype collimated neutron flux monitor and a recently installed prototype charged fusion product detector array, indicating both redistribution and loss of fast ions. Preliminary interpretation of these observations with a suite of stability, modelling and interpretative codes is discussed.

MHD instability fluctuation measurement on the HL-2A tokamak by using the HCN laser interferometer

The multichannel HCN laser interferometer has been routinely used to measure the electron density (n e ) on the HL-2A tokamak for several years. In order to explore its capability for qualitatively evaluating the Magnetohydrodynamic (MHD) fluctuation in plasmas from the probing signal, we implemented two important modifications on the hardware of channel #3 (r = −10.5 cm): (1) application of the high-response Schottky diode waveguide detector, and (2) utilization of a preamplifier with a broad pass-band of up to 500 kHz so as not to filter the fluctuation component mixed with the intermediate frequency (IF). Many MHD fluctuation phenomena, such as tearing modes (TMs), fishbones, long lived modes (LLMs), have been successfully detected by using the modified channel #3 in the HL-2A experimental campaign, and the results were quite coincident with those derived from the magnetic probe and the soft X-ray systems. We propose to apply this novel approach to more channels of the HCN laser interferometer.

Magnons and continua in a magnetized and dimerized spin-12chain

We examine the magnetic field dependent excitations of the dimerized spin-1/2 chain, copper nitrate, with antiferromagnetic intra-dimer exchange $J_1=0.44$ meV and exchange alternation $\alpha=J_2/J_1=0.24$. Magnetic excitations in three distinct regimes of magnetization are probed through inelastic neutron scattering at low temperatures. At low and high fields there are three and two long-lived magnon-like modes, respectively. The number of modes and the anti-phase relationship between the wave-vector dependent energy and intensity of magnon scattering reflect the distinct ground states: A singlet ground state at low fields $\mu_0H < \mu_0H_{c1} = 2.8$~T and an $S_z=1/2$ product state at high fields $\mu_0H > \mu_0H_{c2} = 4.2$~T. In the intermediate field regime, a continuum of scattering for $\hbar\omega\approx J_1$ is indicative of a strongly correlated gapless quantum state without coherent magnons.

Light rings as observational evidence for event horizons: Long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects

Ultracompact objects are self-gravitating systems with a light ring. It was recently suggested that fluctuations in the background of these objects are extremely long-lived and might turn unstable at the nonlinear level, if the object is not endowed with a horizon. If correct, this result has important consequences: objects with a light ring are black holes. In other words, the nonlinear instability of ultracompact stars would provide a strong argument in favor of the "black hole hypothesis," once electromagnetic or gravitational-wave observations confirm the existence of light rings. Here we explore in some depth the mode structure of ultracompact stars, in particular constant-density stars and gravastars. We show that the existence of very long-lived modes -- localized near a second, stable null geodesic -- is a generic feature of gravitational perturbations of such configurations. Already at the linear level, such modes become unstable if the object rotates sufficiently fast to develop an ergoregion. Finally, we conjecture that the long-lived modes become unstable under fragmentation via a Dyson-Chandrasekhar-Fermi mechanism at the nonlinear level. Depending on the structure of the star, it is also possible that nonlinearities lead to the formation of small black holes close to the stable light ring. Our results suggest that the mere observation of a light ring is a strong evidence for the existence of black holes.

Long-lived Higgs mode in a two-dimensional confined Fermi system

The Higgs mode corresponds to the collective motion of particles due to the vibrations of an invisible field. It plays a fundamental role in our understanding of both low- and high-energy physics, giving elementary particles their mass and leading to collective modes in condensed-matter and nuclear systems. The Higgs mode has been observed in a limited number of table-top systems, where it however is characterized by a short lifetime due to decay into a continuum of modes. A major goal which has remained elusive so far is, therefore, to realize a long-lived Higgs mode in a controllable system. Here, we show how an undamped Higgs mode can be observed unambiguously in a Fermi gas in a two-dimensional trap, close to a quantum phase transition between a normal and a superfluid phase. We develop a first-principles theory of the pairing and the associated collective modes, which is quantitatively reliable when the pairing energy is much smaller than the trap level spacing, yet simple enough to allow the derivation of analytical results. The theory includes the trapping potential exactly, which is demonstrated to stabilize the Higgs mode by making its decay channels discrete. It is shown to be realistic to realize the proposed system using atoms in microtraps. The unrivaled flexibility of atomic gases combined with the quantitatively accurate theory opens the door to a systematic study of the Higgs mode, including the role of confinement and finite-size effects.

An approximate single fluid 3-dimensional magnetohydrodynamic equilibrium model with toroidal flow

An approximate model for a single fluid three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium with pure isothermal toroidal flow with imposed nested magnetic flux surfaces is proposed. It recovers the rigorous toroidal rotation equilibrium description in the axisymmetric limit. The approximation is valid under conditions of nearly rigid or vanishing toroidal rotation in regions with significant 3D deformation of the equilibrium flux surfaces. Bifurcated helical core equilibrium simulations of long-lived modes in the MAST device demonstrate that the magnetic structure is only weakly affected by the flow but that the 3D pressure distortion is important. The pressure is displaced away from the major axis and therefore is not as noticeably helically deformed as the toroidal magnetic flux under the subsonic flow conditions measured in the experiment. The model invoked fails to predict any significant screening by toroidal plasma rotation of resonant magnetic perturbations in MAST free boundary computations.

NBI fast ion confinement in the helical core of MAST hybrid-like plasmas

Energetic ions are found to be transported strongly from the core of MAST hybrid-like plasmas during long-lived mode (LLM) magnetohydrodynamic activity. The resulting impact on the neutral beam ion deposition and concurrent current drive is modelled using the guiding-centre approximation in the internal kinked magnetic topology. General coordinate guiding-centre equations are extended for this purpose. It is found that the kinked core spirals around the position of strongest ionization, which remains geometrically centred, so that a large fraction of the population is deposited in the high shear external region where the plasma is almost axisymmetric. Those particles ionized in the low shear region exhibit exotic drift motion due to the strongly non-axisymmetric equilibrium, periodically passing near the magnetic axis and then reflected by the boundary of the kinked equilibrium, which in this respect acts as a confining pinch. Broad agreement is found against experimental measurement of fast ion particle confinement degradation as the MAST LLM amplitude varies.

Resonant excitation of black holes by massive bosonic fields and giant ringings

We consider the massive scalar field, the Proca field and the Fierz-Pauli field in the Schwarzschild spacetime and we focus more particularly on their long-lived quasinormal modes. We show numerically that the associated excitation factors have a strong resonant behavior and we confirm this result analytically from semiclassical considerations based on the properties of the unstable circular geodesics on which a massive particle can orbit the black hole. The conspiracy of (i) the long-lived behavior of the quasinormal modes and (ii) the resonant behavior of their excitation factors induces intrinsic giant ringings, i.e., ringings of a huge amplitude. Such ringings, which are moreover slowly decaying, are directly constructed from the retarded Green function. If we describe the source of the black hole perturbation by an initial value problem with Gaussian initial data, i.e., if we consider the excitation of the black hole from an extrinsic point of view, we can show that these extraordinary ringings are still present. This suggests that physically realistic sources of perturbations should generate giant and slowly decaying ringings and that their existence could be used to constrain ultralight bosonic field theory interacting with black holes.

Multi-region relaxed magnetohydrodynamics with flow

We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite, our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as "snakes" and long-lived modes.

The single-channel regime of transport through random media.

The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi-1D systems, the single dominant transmission eigenchannel is formed by an individual Anderson-localized mode or by a ‘necklace state’. In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

Holographic Path to the Turbulent Side of Gravity

We study the dynamics of a 2+1 dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the "gravity/fluid correspondence", to 3+1 dimensional asymptotically anti-de Sitter (AAdS) black brane solutions to the Einstein equation. We examine stability properties of shear flows, which correspond to hydrodynamic quasinormal modes of the black brane. We find that, for sufficiently high Reynolds number, the solution undergoes an inverse turbulent cascade to long wavelength modes. We then map this fluid solution, via the gravity/fluid duality, into a bulk metric. This suggests a new and interesting feature of the behavior of perturbed AAdS black holes and black branes, which is not readily captured by a standard quasinormal mode analysis. Namely, for sufficiently large perturbed black objects (with long-lived quasinormal modes), nonlinear effects transfer energy from short to long wavelength modes via a turbulent cascade within the metric perturbation. As long wavelength modes have slower decay, this lengthens the overall lifetime of the perturbation. We also discuss various implications of this behavior, including expectations for higher dimensions, and the possibility of predicting turbulence in more general gravitational scenarios.

Magnetic field dependent long-lived spin states in amino acids and dipeptides

Magnetic field dependence of long-lived spin states (LLSs) of the β-CH2 protons of aromatic amino acids was studied. LLSs are spin states, which are immune to dipolar relaxation, thus having lifetimes far exceeding the longitudinal relaxation times; the simplest example of an LLS is given by the singlet state of two coupled spins. LLSs were created by means of the photo-chemically induced dynamic nuclear polarization technique. The systems studied were amino acids, histidine and tyrosine, with different isotopomers. For labeled amino acids with the α-CH and aromatic protons substituted by deuterium at low fields the LLS lifetime, TLLS, for the β-CH2 protons was more than 40 times longer than the T1-relaxation time. Upon increasing the number of protons the ratio TLLS/T1 was reduced; however, even in the fully protonated amino acids it was about 10; that is, the long-lived mode was still preserved in the system. In addition, the effect of paramagnetic impurities on spin relaxation was studied; field dependencies of T1 and TLLS were measured. LLSs were also formed in tyrosine-containing dyads; a TLLS/T1 ratio of ∼7 was found, usable for extending the spin polarization lifetime in such systems.

Investigation of the long-lived saturated internal mode and its control on the HL-2A tokamak

HL-2A plasmas heated by neutral beam injection (NBI) regularly exhibit n = 1 long-lived saturated magnetohydrodynamic instabilities. A reduction in the electron density and plasma stored energy and an increase in fast ion losses are usually observed in the presence of such perturbations. The observed long-lived saturated internal mode (LLM) occurs when the safety factor profile has a weak shear in a broad range of the plasma centre with qmin around unity. It is found that the ideal interchange mode can become marginally stable due to the weak magnetic shear reaching a critical value. The LLM, due to its pressure-driven feature, is destabilized by the strong interaction with fast ions in the low-shear region during the NBI. Furthermore, for the first time it is clearly observed that the LLMs can be suppressed by electron cyclotron resonant heating (ECRH), or by supersonic molecular beam injection in HL-2A plasmas. Low-n sidebands observed during the LLM are also suppressed by increasing the ECRH power. The control of LLMs is due to the change in the magnetic shear or in the pressure profile induced by the local heating or fuelling.

Multi-mode parametric coupling in an electromechanical resonator

Parametric coupling between multiple vibration modes in an electromechanical resonator is demonstrated via a strain inducing piezoelectric pump which enables construction of a mechanical-vibration register. In particular, the coupling between the flexural and torsional vibration modes can exceed their intrinsic dissipation rates enabling operation deep into the strong-coupling regime. The dynamic nature of this parametric coupling also permits temporal manipulation of the mechanical-vibration register enabling both long-lived modes to be rapidly switched off and phonon populations to be coherently exchanged between modes.

Linear stability and nonlinear dynamics of the fishbone mode in spherical tokamaks

Extensive linear and nonlinear simulations have been carried out to investigate the energetic particle-driven fishbone instability in spherical tokamak plasmas with weakly reversed q profile and the qmin slightly above unity. The global kinetic-MHD hybrid code M3D-K is used. Numerical results show that a fishbone instability is excited by energetic beam ions preferentially at higher qmin values, consistent with the observed appearance of the fishbone before the “long-lived mode” in MAST and NSTX experiments. In contrast, at lower qmin values, the fishbone tends to be stable. In this case, the beam ion effects are strongly stabilizing for the non-resonant kink mode. Nonlinear simulations show that the fishbone saturates with strong downward frequency chirping as well as radial flattening of the beam ion distribution. An (m, n) = (2, 1) magnetic island is found to be driven nonlinearly by the fishbone instability, which could provide a trigger for the (2, 1) neoclassical tearing mode sometimes observed after the fishbone instability in NSTX.

Organic magnetoresistance under resonant ac drive

We study the spin dynamics of an electron-hole pair in a random hyperfine magnetic field and an external field, B0, under a resonant drive with frequency omega0 = gamma B0. The fact that the pair decays by recombination exclusively from a singlet configuration, S, in which the spins of the pair-partners are entangled, makes this dynamics highly nontivial. Namely, as the amplitude, B1, of the driving field grows, mixing all of the triplet components, the long-living modes do not disappear, but evolve from T+, T- into (T+ +/- sqrt(2) T0 + T-)/2. Upon further increase of B1, the lifetime of the S-mode is cut in half, while the T0-mode transforms into an antisymmetric combination (T- - T-)/sqrt(2) and acquires a long lifetime, in full analogy to the superradiant and subradiant modes in the Dicke effect. Peculiar spin dynamics translates into a peculiar dependence on B1. In particular, at small B1, the radiation-induced correction to the current is linear in B1.