Tail Instability Research Articles

On the role of tail in stability and energetic cost of bird flapping flight

Migratory birds travel over impressively long distances. Consequently, they have to adopt flight regimes being both efficient—in order to spare their metabolic resources—and robust to perturbations. This paper investigates the relationship between both aspects, i.e., energetic performance and stability, in flapping flight of migratory birds. Relying on a poly-articulated wing morphing model and a tail-like surface, several families of steady flight regime have been identified and analysed. These families differ by their wing kinematics and tail opening. A systematic parametric search analysis has been carried out, in order to evaluate power consumption and cost of transport. A framework tailored for assessing limit cycles, namely Floquet theory, is used to numerically study flight stability. Our results show that under certain conditions, an inherent passive stability of steady and level flight can be achieved. In particular, we find that progressively opening the tail leads to passively stable flight regimes. Within these passively stable regimes, the tail can produce either upward or downward lift. However, these configurations entail an increase of cost of transport at high velocities penalizing fast forward flight regimes. Our model-based predictions suggest that long range flights require a furled tail configuration, as confirmed by field observations, and consequently need to rely on alternative mechanisms to stabilize the flight.

Linear analysis of bump on tail instability with non-Maxwellian distribution function

The growth rate of bump on tail instability propagating in unmagnetized plasma has been derived. The dispersion relation has been characterized for (r, q) distribution function with spectral indices r and q which ultimately contributes towards tails and shoulder of distribution function. The growth rate of the bump on tail instability has been estimated numerically for different ratios of temperature and number density using solar wind data and also by varying values of indices r and q . The higher value of q play the role towards decreasing the growth rate where the instability has the higher value when the number density of the superthermal electrons in the bump is higher and the temperature is low. The maximum growth rate increases with the increase in number density of electrons and decreases with the increasing temperature in the bump.

Bump-on-tail instability across coupling and interaction-range regimes

The authors study the bump-on tail instability using molecular dynamics to explore the roles of collisionality, correlations and the effective interparticle force law across wide ranges of plasma temperatures, densities and charge states, and show that, even with a small number of point particles, the results are robust.

Drift frequency of kilometric radio burst type III with solar wind speed and density

Solar radio burst is a signature of solar flare generated by plasma emission mechanism. Radio burst is a diagnostic tool to study electron beam evolution and plasma background properties in corona and interplanetary medium. Sudden release magnetic energy up to 1032 ergs due to magnetic connection accelerates electron located at accelerated site to propagate near relativistic. This fast group of electron propagating through plasma background induced high level of Langmuir wave due to bump in tail instability. Non linear wave-wave causing radio burst near the local plasma frequency. In this paper, frequency drift of radio burst is calculated only from 1 MHz to 400 kHz and the data is obtained from Coordinated Data Analysis Web (CDAweb). The data is analysed by identifying time during maximum intensity of burst at the particular frequency range. Only 45 burst observed in September 2017 is considered in this paper. Meanwhile the data of solar wind speed and density is collected from Advanced Composition Explorer (ACE) satellite. Drift frequency of burst then compared to average of solar wind and density. From the analysis, drift frequency of burst decreasing against solar wind speed and solar wind density. But both relationship shows very weak correlation between drift frequency and solar wind properties.

Bunch length scaling due to broadband impedance as a parameter for transverse feedback application

This paper investigates the possibility for suppression of the head–tail instability in an electron storage ring using a bunch-by-bunch transverse feedback system. General conditions are found whereby the Gaussian bunch profile may be modeled by a two-particle system which interacts with the vacuum chamber broadband impedance. We choose the kick factor received by a Gaussian bunch with the rms bunch length σt, from a broadband impedance with the resonance frequency ωr and quality factor Qr, as the relevant parameter and explain why the kick factor depends on ωrσt∕Qr. Finally, we demonstrate that a Gaussian bunch can be modeled by a two-particle system when the parameter ωrσt∕Qr is sufficiently small.

On the relationship between residual zonal flows and bump-on tail saturated instabilities.

A connection is established between two classical problems: the non linear saturation of a bump-on tail instability in collisionless regime, and the decay of a zonal flow towards a finite amplitude residual. Reasons for this connection are given and commented.

Landau damping and the head–tail instability of the coupled synchro-betatron coherent oscillations

Within the hollow-bunch approximation we study variations in the stability conditions of the coupled synchro-betatron coherent oscillations due to common effects of the lattice chromaticity and of the Landau damping of such oscillations. We assume that the Landau damping of coherent oscillations is provided by octupole fields of the ring lattice. We also assume that the wakefields of the bunch decay substantially during the revolution period of particles along the closed orbit. For this reason, the memory of the bunch wakefields is ignored in this paper.

Vlasov on GPU (VOG project)

This work concerns the numerical simulation of the Vlasov-Poisson equation using semi-Lagrangian methods on Graphics Processing Units (GPU). To accomplish this goal, modifications to traditional methods had to be implemented. First and foremost, a reformulation of semi-Lagrangian methods is performed, which enables us to rewrite the governing equations as a circulant matrix operating on the vector of unknowns. This product calculation can be performed efficiently using FFT routines. Nowadays GPU is no more limited to single precision; however, single precision may still be preferred with respect to performance and available memory. So, in order to be able to deal with single precision, a δf type method is adopted which only needs refinement in specialized areas of phase space but not throughout. Thus, a GPU Vlasov-Poisson solver can indeed perform high precision simulations (since it uses very high order of reconstruction and a large number of grid points in phase space). We show results for more academic test cases and also for physically relevant phenomena such as the bump on tail instability and the simulation of Kinetic Electrostatic Electron Nonlinear (KEEN) waves.

Nature of axial tail instability and bubble‐blob formation in near‐Earth plasma sheet

ABSTRACTPrevious global magnetohydrodynamic (MHD) simulations of substorm events have identified the dynamic presence of an axial tail instability that is uniform in the dawn‐dusk direction in the near‐Earth plasma sheet. The axial tail instability is found to be a major cause of the initial growing MHD force imbalance on closed field lines prior to the subsequent magnetic reconnection and substorm expansion onset processes. In this work, energy principle analysis indicates that a two‐dimensional thin current sheet configuration in the magnetotail is typically stable to the axial mode within the framework of ideal MHD model. However, linear resistive MHD calculations find axial tail instabilities on closed field lines in the generalized Harris sheet configurations. The properties of these instabilities are similar to the axial tail modes observed in the global MHD simulations. The axial tail mode is unstable in regimes of low Lundquist number and regions with small normal component of magnetic field. Such resistive axial tail instability would by many researchers be considered as tearing instability in a two‐dimensional tail configuration. Unlike the conventional tearing mode of Harris sheet, the linear axial tail instability does not involve any reconnection process. Instead, the nature of the mode is dominantly a slippage process among neighboring flux tubes as facilitated by resistive dissipation. A natural consequence of the axial tail instability is shown to be the formation of bubble‐blob pairs in the pressure and entropy profiles in the near‐Earth plasma sheet.

Analysis of beam plasma instability effects on incoherent scatter spectra

Abstract. Naturally Enhanced Ion Acoustic Lines (NEIALs) detected with Incoherent Scatter Radars (ISRs) can be produced by a Langmuir decay mechanism, triggered by a bump on tail instability. A recent model of the beam-plasma instability suggests that weak-warm beams, such those associated with NEIAL events, might produce Langmuir harmonics which could be detected by a properly configured ISR. The analysis performed in this work shows that such a beam-driven wave may be simultaneously detected with NEIALs within the baseband signal of a single ISR. The analysis shows that simultaneous detection of NEIALs and the first Langmuir harmonic is more likely than simultaneous detection of NEIALs and enhanced plasma line. This detection not only would help to discriminate between current NEIAL models, but could also aid in the parameter estimation of soft precipitating electrons.

Mechanisms for suppressing the transverse mode coupling instability in a circular accelerator

The chromatic and nonlinear suppression of the transverse mode coupling instability in a circular accelerator is analyzed. Analytical estimates are compared with the results of experiments and numerical simulations. The transverse mode coupling (or fast head—tail) instability is a significant factor that limits the beam intensity in circular accelerators. This instability arises when the bunch current exceeds a threshold value determined by the broadband impedance of the vacuum chamber. Feedback systems are traditionally used to suppress the instability. The experience of working with such systems shows that their efficiency depends strongly on the operating parameters of the amplifier, particularly on the chromaticity and nonlinearity of the magnetic lattice. Thus, both chromatic and nonlinear effects should be taken into account to better understand the physical processes and to increase the feedback efficiency.

Resolving the tail instability in weighted log-rank statistics for clustered survival data

In this note, we consider weighted log-rank statistics applied to clustered survival data with variable cluster sizes and arbitrary treatment assignments within clusters. Specifically, we verify that the contribution over the time interval for which the risk set proportion is arbitrarily small (the so-called “tail instability”) is asymptotically negligible. These results were claimed but not proven by Gangnon and Kosorok [2004. Sample-size formula for clustered survival data using weighted log-rank statistics. Biometrika 91, 263–275.] who developed sample size formulas in this context. The main difficulty is that standard martingale methods cannot be used on account of the dependencies within clusters, and new methods are required.

Transverse Beam Instability due to a Broad-band Impedance in Very Large Hadron–Collider Ring

The strong head–tail instability due to a broad-band impedance in the very large hadron–collider (VLHC) ring of 20 TeV is numerically investigated. It is shown that the beam size increases significantly when the impedance, Z|| /n, is 0.6 Ω, which is the estimated impedance budget in the design. The beam instability is shown to be cured by introducing tune spreads, such as RF quadrupole, chromaticity and amplitude-dependent tune shift. It is shown that any of these tune spreads limits the growth of the beam size to less than 3%. It is shown that threshold impedance for the instability is estimated to be about Z|| /n=0.3 Ω.

Improvement of the beam quality by chromaticity correction for wavelength shortening in the NIJI-IV FEL

Electron-beam qualities improved by chromaticity correction in the storage ring NIJI-IV were investigated at the beam energy of 309 MeV. Sextupole–quadrupole–sextupole (SQS) magnets, which were installed in all of the short-straight sections in NIJI-IV, perfectly corrected a horizontal and a vertical chromaticity. This improvement suppressed a head–tail instability, so that higher beam current (∼30 mA) and higher peak-electron density (∼6×10 16 m −3) were available for FEL experiments. The maximum FEL gain was estimated to be about 2.5% at a wavelength of 240 nm. The lasing of an FEL around 300 nm was achieved in March 1998, and the lasing of an FEL at around 240 nm was successfully observed in May 1998. The shortest wavelength of FELs with the NIJI-IV FEL system was 228 nm.

Lasing down to the deep UV in the NIJI-IV FEL

Lasing has been obtained at the wavelengths down to the deep UV on the NIJI-IV free electron laser (FEL) system. The shortest wavelength obtained was 228 nm and the laser peak power was estimated to be ∼200 and ∼40 mW at 300 and 240 nm, respectively. Suppression of the fast head–tail instability in the electron beam led to a drastic enhancement in the laser gain which enabled us to achieve such short-wavelength lasing even in a compact storage ring such as NIJI-IV. Low-loss cavity mirrors having Al 2 O 3/ SiO 2 dielectric layers are being prepared to obtain FEL operation at much shorter wavelengths.

Instability of the Lembège–Pellat equilibrium under ideal magnetohydrodynamics

The magnetotail-like equilibrium model of Lembège and Pellat [Phys. Fluids, 25, 1995 (1982)] has been used in a number of stability calculations over the past 13 years. Most of these computations examine collisionless tearing—a mode of tail instability first suggested by Coppi et al. [Phys. Rev. Lett. 16, 1207 (1966)]—or other kinetic modes and involve both analytical and computer analysis. In this Communication it is shown, analytically, that the equilibrium model of Lembège and Pellat is unstable according to ideal magnetohydrodynamics (MHD). More precisely, for the ideal MHD stability theory of Bernstein et al. [Proc. R. Soc. London Ser. A 244, 17 (1958)] it is proven that Λ=p′+Γp (v″/v′)<0.

What determines the latitudinal extent of the auroral acceleration region?

Characteristic scales associated with auroral precipitation are investigated on the basis of quasistatic magnetotail models, resistive MHD simulations of magnetotail dynamics, and a general relation between parallel electric fields and velocity shear. Since the inverted-V precipitation region of discrete auroras (on the dusk side) is associated with upward flowing, region 1, currents, we investigate the distribution of these currents first. The overall distribution of region 1 type field-aligned currents and their dynamic changes can be explained by characteristic scales in the magnetotail and their mapping to the ionosphere. The quiet time region 1 currents are associated with the decrease of tail flaring. Their overall extent in the north-south direction is closely related to the scale height of the cross-tail current. Dynamic region 1 currents are related to the velocity shear of earthward flow, which can be generated by a tail instability. In that case the peaks of the enhanced region 1 currents are found to map closer to midnight and to lower latitudes than the quiet region 1 currents, consistent with average observations [ Iijima and Potemra (1976a), J. geophys. Res. 81, 2165]. On the basis of a general relation between parallel electric fields and ‘slippage’ in the plasma transport [ Hesse and Schindler (1988), J. geophys. Res. 93, 5559; Schindler et al. (1991), Astrophys. J. 380, 293], we make estimates of the spatial extent of nonideal regions, where parallel electric fields may exist. For a plausible model of substorm reconfiguration, we find a latitudinal extent of about 7 km for a time scale of 1 min and a integrated parallel electric field of 5 kV. The length scale is proportional to the time scale. The sign of this parallel electric field is consistent with downward acceleration of electrons on the dusk side. The spatial extent of the parallel electric field region is independent of the microscopic generation mechanism if the time scale and the characteristic parallel potential difference (i.e. the integrated parallel electric field) are independent of this mechanism.

Directional solidification: Transition from cells to dendrites

The evolution of cells and dendrites on a solidification front is analyzed numerically by a Green's-function method. We obtain a consistent picture of the pattern-forming processes in the whole experimentally accessible range of the phase-diagram cell spacing versus growth rate. We find a smooth transition from cells to free dendrites confirming suspected scaling relations. The selection of dendritic spacings appears to occur through a tail instability.

Regular and chaotic charged particle motion in magnetotaillike field reversals: 1. Basic theory of trapped motion

We give a systematic theoretical analysis of trapped nonadiabatic charged particle motion in two‐dimensional taillike magnetic field reversals. Particle dynamics is shown to be controlled by the curvature parameter κ, i.e., the ratio κ² = Rmin/ρmax between the minimum radius of curvature of the magnetic field and the maximum Larmor radius in it for a particle of given energy. κ≫1 corresponds to the usual adiabatic case with the magnetic moment μ as a first‐order invariant of motion. As κ decreases toward unity, the particle motion becomes stochastic due to deterministic chaos, caused by the overlapping of nonlinear resonances between the bounce‐ and the gyro‐motion. We determine the threshold of deterministic chaos and derive the related pitch angle diffusion coefficient which describes statistically the particle behavior in the limit κ → 1. Such behavior, which for κ ≅ 1 becomes strongly chaotic, applies, e.g., to thermal electrons in Earth's magnetotail and makes its collisionless tearing mode instability possible. We also show that in sharply curved field reversals, i.e., for κ<1, both a new kind of adiabaticity and a partially adiabatic but weakly chaotic type of motion appear. The latter is strongly effected by separatrix‐crossings in the phase space, which lead to a qualitatively different chaotic behavior compared with the case κ>1. Both types of trapped particle motion in sharply curved magnetic field reversals κ<1 are closely connected with fast oscillations perpendicular to the reversal plane. However, the trajectories are adiabatic only in the case that they permanently remain crossing the reversal plane. The adiabatic are of a ring type, i.e., they resemble rings in phase space and also in real physical space. For ring‐type orbits the action integral over the fast oscillations is an adiabatic invariant in the usual sense. On the other hand, the most common particle trajectories in a sharply curved field reversal with κ<1 are essentially of a cucumberlike quasi‐adiabatic type. For quasi‐adiabatic cucumberlike orbits the action integral over the fast oscillations is an adiabatic invariant only in a piecemeal way between successive traversals in the phase space of the fast motion of a separatrix between orbits which do and those, which do not cross the reversal plane. Due to the effect of separatrix traversals the slow motion shifts between different cucumber orbits with a conservation of the action integral on average but with its chaotic phase space diffusion even for very small perturbation parameters κ. The case κ<1 is applicable, e.g., to thermal ions and high‐energy electrons in Earth's magnetotail. Our findings lead to a systematic interpretation of particle observations in Earth's magnetotail and of numerous numerical calculations, carried out in the past. They also explain rather well, e.g., the pitch angle diffusion of plasma sheet particles, the isotropization of the plasma sheet electron distribution immediately before a substorm and provide with the transition to chaos a mechanism for the onset of a large‐scale tail instability and the explosion of isolated substorms. Further implications for magnetotail physics, such as acceleration processes and the influence of the particle escape from the field reversal will be discussed in a second related paper.

An experimental test of quasilinear theory

We give a brief summary of an experimental test of the quasilinear theory of the bump on tail instability. Recent theoretical work has suggested that the quasilinear description of the weak warm beam plasma instability is incomplete. It has been suggested that beam mediated mode coupling effects neglected in standard quasilinear theory play an important role, and that their average effect is a zeroth order increase in the growth rate. We have experimentally observed strong mode coupling effects when a weak warm beam interacts with waves on a slow wave structure. However, when we average the effects of the mode coupling we do not observe the predicted zeroth order increase in the growth rate. This intriguing result suggests the action of some statistical or dynamical conservation law whose origin has not yet been theoretically identified.