Growth Time Of Instability Research Articles

Statistical fluctuations of radiation in quasi-Cherenkov generators

In a nonstationary (self-modulation) regime, terahertz quasi-Cherenkov generators can operate at MHz–GHz repetition rates and megawatt power levels. Shot noise, intrinsic to electron beams, is the cause of statistical fluctuations of radiation in the generators. The shot-noise related spread of instability growth time imposes appreciable limitations on the possibility of coherent summation of electromagnetic oscillations from several quasi-Cherenkov generators operating in a nonstationary mode.

KELVIN–HELMHOLTZ INSTABILITY IN SOLAR CHROMOSPHERIC JETS: THEORY AND OBSERVATION

ABSTRACT Using data obtained by the high-resolution CRisp Imaging SpectroPolarimeter instrument on the Swedish 1 m Solar Telescope, we investigate the dynamics and stability of quiet-Sun chromospheric jets observed at the disk center. Small-scale features, such as rapid redshifted and blueshifted excursions, appearing as high-speed jets in the wings of the Hα line, are characterized by short lifetimes and rapid fading without any descending behavior. To study the theoretical aspects of their stability without considering their formation mechanism, we model chromospheric jets as twisted magnetic flux tubes moving along their axis, and use the ideal linear incompressible magnetohydrodynamic approximation to derive the governing dispersion equation. Analytical solutions of the dispersion equation indicate that this type of jet is unstable to Kelvin–Helmholtz instability (KHI), with a very short (few seconds) instability growth time at high upflow speeds. The generated vortices and unresolved turbulent flows associated with the KHI could be observed as a broadening of chromospheric spectral lines. Analysis of the Hα line profiles shows that the detected structures have enhanced line widths with respect to the background. We also investigate the stability of a larger-scale Hα jet that was ejected along the line of sight. Vortex-like features, rapidly developing around the jet’s boundary, are considered as evidence of the KHI. The analysis of the energy equation in the partially ionized plasma shows that ion–neutral collisions may lead to fast heating of the KH vortices over timescales comparable to the lifetime of chromospheric jets.

The impulsive phase of magnetar giant flares: assessing linear tearing as the trigger mechanism

Giant $\gamma$-ray flares comprise the most extreme radiation events observed from magnetars. Developing on (sub)millisecond timescales and generating vast amounts of energy within a fraction of a second, the initial phase of these extraordinary bursts present a significant challenge for candidate trigger mechanisms. Here we assess and critically analyse the linear growth of the relativistic tearing instability in a globally twisted magnetosphere as the trigger mechanism for giant $\gamma$-ray flares. Our main constraints are given by the observed emission timescales, the energy output of the giant flare spike, and inferred dipolar magnetic field strengths. We find that the minimum growth time of the linear mode is comparable to the $e$-folding rise time, i.e. $\sim10^{-1}$ ms. With this result we constrain basic geometric parameters of the current sheet. We also discuss the validity of the presumption that the $e$-folding emission timescale may be equated with the growth time of an MHD instability.

Self-organized criticality revisited: non-local transport by turbulent amplification

We revise the applications of self-organized criticality (SOC) as a paradigmatic model for tokamak plasma turbulence. The work, presented here, is built around the idea that some systems do not develop a pure critical state associable with SOC, since their dynamical evolution involves as a competing key factor an inverse cascade of the energy in reciprocal space. Then relaxation of slowly increasing stresses will give rise to intermittent bursts of transport in real space and outstanding transport events beyond the range of applicability of the ‘conventional’ SOC. Also, we are concerned with the causes and origins of non-local transport in magnetized plasma, and show that this type of transport occurs naturally in self-consistent strong turbulence via a complexity coupling to the inverse cascade. We expect these coupling phenomena to occur in the parameter range of strong nonlinearity and time scale separation when the Rhines time in the system is small compared with the instability growth time.

Observation of Rayleigh-Taylor-instability evolution in a plasma with magnetic and viscous effects.

We present time-resolved observations of Rayleigh-Taylor-instability (RTI) evolution at the interface between an unmagnetized plasma jet colliding with a stagnated, magnetized plasma. The observed instability growth time (∼10 μs) is consistent with the estimated linear RTI growth rate calculated using experimentally inferred values of density (∼10(14) cm(-3)) and deceleration (∼10(9) m/s(2)). The observed mode wavelength (≳1 cm) nearly doubles within a linear growth time. Theoretical estimates of magnetic and viscous stabilization and idealized magnetohydrodynamic simulations including a physical viscosity model both suggest that the observed instability evolution is subject to magnetic and/or viscous effects.

STABILITY OF ROTATING MAGNETIZED JETS IN THE SOLAR ATMOSPHERE. I. KELVIN–HELMHOLTZ INSTABILITY

Observations show various jets in the solar atmosphere with significant rotational motions, which may undergo instabilities leading to heat ambient plasma. We study the Kelvin-Helmholtz (KH) instability of twisted and rotating jets caused by the velocity jumps near the jet surface. We derive a dispersion equation with appropriate boundary condition for total pressure (including centrifugal force of tube rotation), which governs the dynamics of incompressible jets. Then, we obtain analytical instability criteria of Kelvin-Helmholtz instability in various cases, which were verified by numerical solutions to the dispersion equation. We find that twisted and rotating jets are unstable to KH instability when the kinetic energy of rotation is more than the magnetic energy of the twist. Our analysis shows that the azimuthal magnetic field of 1-5 G can stabilize observed rotations in spicule/macrospicules and X-ray/EUV jets. On the other hand, non-twisted jets are always unstable to KH instability. In this case, the instability growth time is several seconds for spicule/macrospicules and few minutes (or less) for EUV/X-ray jets. We also find that standing kink and torsional Alfven waves are always unstable near the antinodes due to the jump of azimuthal velocity at the surface, while the propagating waves are generally stable. KH vortices may lead to enhanced turbulence development and heating of surrounding plasma, therefore rotating jets may provide energy for chromospheric and coronal heating.

Observation of polar cap patches and calculation of gradient drift instability growth times: A Swarm case study

AbstractThe Swarm mission represents a strong new tool to survey polar cap patches and plasma structuring inside the polar cap. In the early commissioning phase, the three Swarm satellites were operated in a pearls‐on‐a‐string configuration making noon‐midnight transpolar passes. This provides an unparalleled opportunity to examine the potential role of the gradient drift instability (GDI) process on polar cap patches by systematically calculating GDI growth times during their transit across the pole from day to night. Steep kilometer‐scale gradients appeared in this study as initial structures that persisted during the approximate 90 min it took a patch to cross the polar cap. The GDI growth times were calculated for a selection of the steep density gradients on both the dayside and the nightside. The values ranged from 23 s to 147 s, which is consistent with recent rocket measurements in the cusp auroral region and provides a template for future studies. Growth times of the order of 1 min found both on the dayside and on the nightside support the existing view that the GDI may play a dominant role in the generation of radio wave scintillation irregularities as the patches transit the polar cap from day to night.

The intimate relation between the low T/W instability and the corotation point

We study the low T/W instability associated with the f-mode of differentially rotating stars. Our stellar models are described by a polytropic equation of state and the rotation profile is given by the standard j-constant law. The properties of the relevant oscillation modes, including the instability growth time, are determined from time evolutions of the linearised dynamical equations in Newtonian gravity. In order to analyse the instability we monitor also the canonical energy and angular momentum. Our results demonstrate that the l=m=2 f-mode becomes unstable as soon as a co-rotation point develops inside the star (i.e. whenever there is a point where the mode's pattern speed matches the bulk angular velocity). Considering various degrees of differential rotation, we show that the instability grows faster deep inside the co-rotation region and deduce an empirical relation that correlates the mode frequency and the star's parameters, which captures the main features of the l=m=2 f-mode growth time. This function is proportional to the product of the kinetic to gravitational energy ratio and the gradient of the star's spin, strengthening further the relationship between the co-rotation point and the low T/W instability. We briefly consider also the l=m=2 r-mode and demonstrate that it never moves far inside the co-rotation region even for significant differential rotation.

Tokamak operation with safety factor q95 < 2 via control of MHD stability.

Magnetic feedback control of the resistive-wall mode has enabled the DIII-D tokamak to access stable operation at safety factor q(95) = 1.9 in divertor plasmas for 150 instability growth times. Magnetohydrodynamic stability sets a hard, disruptive limit on the minimum edge safety factor achievable in a tokamak, or on the maximum plasma current at a given toroidal magnetic field. In tokamaks with a divertor, the limit occurs at q(95) = 2, as confirmed in DIII-D. Since the energy confinement time scales linearly with current, this also bounds the performance of a fusion reactor. DIII-D has overcome this limit, opening a whole new high-current regime not accessible before. This result brings significant possible benefits in terms of fusion performance, but it also extends resistive-wall mode physics and its control to conditions never explored before. In present experiments, the q(95) < 2 operation is eventually halted by voltage limits reached in the feedback power supplies, not by intrinsic physics issues. Improvements to power supplies and to control algorithms have the potential to further extend this regime.

PLASMA EFFECTS ON EXTRAGALACTIC ULTRA-HIGH-ENERGY COSMIC RAY HADRON BEAMS IN COSMIC VOIDS

The linear instability of an ultrarelativistic hadron beam (? b 106) in the unmagnetized intergalactic medium (IGM) is investigated with respect to the excitation of collective electrostatic and aperiodic electromagnetic fluctuations. This analysis is important for the propagation of extragalactic ultrarelativistic cosmic rays (E > 1015?eV) from?their distant sources to Earth. We calculate minimum instability growth times that are orders of magnitude shorter than the cosmic ray propagation time in the IGM. Due to nonlinear effects, especially the modulation instability, the cosmic ray beam stabilizes and can propagate with nearly no energy loss through the IGM.

Aspects of the non-zonal transition

The non-zonal transition, a process which can bring about very large heat fluxes in gyrokinetic simulations, occurs once a certain threshold plasma β is reached. This threshold is parameterized via a simulation database, yielding an expression estimating at what β a given system may approach the transition. Furthermore, the diffusive outward transport of a heat blob in a temperature profile marginally stable with respect to the non-zonal transition is discussed: the resulting transport timescale combines the underlying turbulent transport timescale and the linear instability growth time, thus demonstrating that the non-zonal transition provides a mechanism for very fast heat dissipation.

OBLIQUE ALFVÉN INSTABILITIES DRIVEN BY COMPENSATED CURRENTS

Compensated-current systems created by energetic ion beams are widespread in space and astrophysical plasmas. The well-known examples are foreshock regions in the solar wind and around supernova remnants. We found a new oblique Alfv\'enic instability driven by compensated currents flowing along the background magnetic field. Because of the vastly different electron and ion gyroradii, oblique Alfv\'enic perturbations react differently on the currents carried by the hot ion beams and the return electron currents. Ultimately, this difference leads to a non-resonant aperiodic instability at perpendicular wavelengths close to the beam ion gyroradius. The instability growth rate increases with increasing beam current and temperature. In the solar wind upstream of Earth's bow shock the instability growth time can drop below 10 proton cyclotron periods. Our results suggest that this instability can contribute to the turbulence and ion acceleration in space and astrophysical foreshocks.

Resistive wall instability in rapid Cycling synchrotron of China spallation neutron source

China Spallation Neutron Source (CSNS) is a high intensity proton accelerator based facility, and its accelerator complex includes two main parts: an H- linac and a rapid cycling synchrotron (RCS). The RCS accumulates the 80MeV proton beam, and accelerates it to 1.6GeV, with a repetition rate of 25Hz. The 1.6GeV beam is fast extracted for striking the neutron target with average beam power of 100kW. The collective effect caused by the coupling impedance is one of the serious issues which limit the highest beam power. The impedance estimation of RCS components showed that the resistive wall impedance and its instability are serious. Based on the estimated impedance, the resistive wall instability growth time is theoretically calculated. In order to confirm the analytical results of resistive wall instability, a simplified resistive wall wake field model is used to track the bunch oscillation, and the growth time of resistive wall instability is obtained. In this model, the continuous resistive wall wake field is expressed as an equivalent wake field of one point in the ring, and the long bunch is sliced into many slices longitudinally. By tracking the dynamics of the slices, transverse growth time is obtained. The simulation results with constant energy agree well with the analytical results. The studies of energy ramping process show that if the damping effect of the chromaticity is not considered, the growth time of resistive wall instability is faster than the period of an RCS cycle, and the damping effect of chromaticity will play a key role in suppressing the instability.

Force-free pulsar magnetosphere: instability and generation of magnetohydrodynamic waves

Magnetohydrodynamic (MHD) instabilities can play an important role in the structure and dynamics of the pulsar magnetosphere. We consider the instabilitycaused by differential rotation that is suggested by many theoretical models. Stability is considered by means of a linear analysis within the frane of the force-free MHD. We argue that differentially rotating magnetospheres are unstable for any particular geometry of the magnetic field and rotation law. The characteristic growth time of instability is of the order of the rotation period. The instability can lead to fluctuations of the emission and enhancement of diffusion in the magnetosphere.

N-BODY SIMULATION OF PLANETESIMAL FORMATION THROUGH GRAVITATIONAL INSTABILITY OF A DUST LAYER IN LAMINAR GAS DISK

We investigate the formation process of planetesimals from the dust layer by the gravitational instability in the gas disk using local $N$-body simulations. The gas is modeled as a background laminar flow. We study the formation process of planetesimals and its dependence on the strength of the gas drag. Our simulation results show that the formation process is divided into three stages qualitatively: the formation of wake-like density structures, the creation of planetesimal seeds, and their collisional growth. The linear analysis of the dissipative gravitational instability shows that the dust layer is secularly unstable although Toomre's $Q$ value is larger than unity. However, in the initial stage, the growth time of the gravitational instability is longer than that of the dust sedimentation and the decrease in the velocity dispersion. Thus, the velocity dispersion decreases and the disk shrinks vertically. As the velocity dispersion becomes sufficiently small, the gravitational instability finally becomes dominant. Then wake-like density structures are formed by the gravitational instability. These structures fragment into planetesimal seeds. The seeds grow rapidly owing to mutual collisions.

Did tidal deformation power the core dynamo of Mars?

We first show that 7 out of the 20 giant impact basins of Mars recently reported by Frey [Frey, H., 2008. Geophys. Res. Lett. 35. L13203] trace a great circle on Mars. The other five basins trace another great circle and still the other three basins trace yet another great circle. The latter great circle is in good agreement with the pre-Tharsis equator of Mars that is estimated from modeling crustal magnetic anomalies [Arkani-Hamed, J., 2001. Geophys. Res. Lett. 28, 3409–3412] and diagonalizing the moment of inertia of Mars after removing the loading effects of Tharsis bulge [Sprenke, K.F., Baker, L.L., Williams, A.F., 2005. Icarus 174, 486–489]. It is shown in this paper that the three great circles were likely the equatorial plane of Mars at certain times and Mars experienced appreciable polar wander. The great circles also indicate that the asteroids that created the basins were satellites of Mars whose orbits decayed in time through spin–orbit coupling with tidally deforming Mars, and eventually impacted on the planet creating the giant basins at around 4 Ga. The orbital dynamics of four largest asteroids show that they could have orbited Mars for several hundred million years if they were retrograde satellites. Continual elliptical straining of otherwise circular fluid streamlines of the liquid core of Mars by tidal deformation could have exerted a strong strain that was large enough to overcome dissipation and excite the elliptical instability inside the core. We investigate the physical properties of the martian core that are required to allow the tidal deformation to power the core dynamo, i.e., the growth time of the elliptical instability to become shorter than the dissipation time. The tidal energy dissipation rate inside Mars caused by even only one of the 4 largest asteroids is found to be over two orders of magnitude greater than the magnetic energy dissipation rate in the core, indicating that if only one of the 4 largest asteroids were orbiting in retrograde sense, it would have likely powered the core dynamo of Mars for several hundred million years.

Counterstreaming magnetized plasmas with kappa distributions - I. Parallel wave propagation

Non-thermal particle distributions of kappa type are frequently encountered in collisionless plasmas from space. The electromagnetic emissions coming from space are believed to originate in the counterstreaming structures of plasmas, which are ubiquitous in many astrophysical systems. Here, we investigate the dispersion properties and the stability of a counterstreaming plasma system with temperature anisotropies modelled by a bi-kappa distribution function. The numerical evaluation of parallel modes shows growth rates lower than those obtained for Maxwellian plasmas, with a strong dependence on the spectral index of the particle distribution function. If all other parameters are known, measuring the instability growth time can provide a possible tool for the determination of the spectral index κ.

Comparison of shear banding in BMGs due to thermal-softening and free volume creation

This paper reports a comparative study of shear banding in BMGs resulting from thermal softening and free volume creation. Firstly, the effects of thermal softening and free volume creation on shear instability are discussed. It is known that thermal softening governs thermal shear banding, hence it is essentially energy related. However, compound free volume creation is the key factor to the other instability, though void-induced softening seems to be the counterpart of thermal softening. So, the driving force for shear instability owing to free volume creation is very different from the thermally assisted one. In particular, long wave perturbations are always unstable owing to compound free volume creation. Therefore, the shear instability resulting from coupled compound free volume creation and thermal softening may start more like that due to free volume creation. Also, the compound free volume creation implies a specific and intrinsic characteristic growth time of shear instability. Finally, the mature shear band width is governed by the corresponding diffusions (thermal or void diffusion) within the band. As a rough guide, the dimensionless numbers: Thermal softening related number B, Deborah number (denoting the relation of instability growth rate owing to compound free volume and loading time) and Lewis number (denoting the competition of different diffusions) show us their relative importance of thermal softening and free volume creation in shear banding. All these results are of particular significance in understanding the mechanism of shear banding in bulk metallic glasses (BMGs).

Possibility of the development of explosive instability in a two-stream gravitating medium

An expression for the energy of the density wave in a multicomponent gravitating medium is obtained that is similar to an appropriate expression in electrodynamics of continua. The possibility of birth of a wave triplet including both positive and negative wave energies in a nonequilibrium gravitating medium is demonstrated. It is shown that such a resonant interaction of waves leads to the development of explosive instability. An expression for the characteristic growth time of instability within a one-dimensional model is obtained by a method developed in plasma physics.

Nonthermal power dissipation and nonlinear wave dynamics in a plasma penetrated by a momentum-scattered relativistic electron stream

A previous analysis of the nonlinear dissipative equilibrium of a beam-penetrated plasma with nonthermal electron “tails” [D. V. Rose, J. Guillory, and J. H. Beall, Phys. Plasmas 9, 1000 (2002)] is extended to the case of a relativistic, momentum-angle-scattered electron beam (with or without accompanying ions) penetrating a fully ionized low-density nearly collisionless plasma, and to include the energy balance of the nonthermal plasma tail electron population on electron collisional timescales long compared with the primary instability growth time. Quasistationary nonlinear “dissipative equilibrium” states are quantified for various ranges of relativistic beam parameters and various tail-enhanced Landau damping rates for shorter-wavelength space-charge waves. Conditions for quasisteady wave populations are found, and for energy balance between beam energy input to and dynamic friction cooling of the nonthermal “tail electrons.” Finally, some potentially incorrect inferences based on a thermal interpretation of bremsstrahlung from such a plasma are quantified. All of these microphysical processes evolve on timescales inaccessible to conventional magnetohydrodynamic modeling of astrophysical jets, and may lead to energetics corrections to such fluid models.