Line Tying Research Articles

How does the magnetosphere go to sleep?

Energy and circulation in the Earth's magnetosphere and ionosphere are largely determined by conditions in the solar wind and interplanetary magnetic field. When the driving from the solar wind is turned off (to a minimum), we expect the activity to die down but exactly how this happens is not known. A recent study utilized global MHD simulations to addressed the questions of what constitutes the quietest state for the magnetosphere and how it is approached following a northward turning in the IMF that minimizes the driving. An exponential decay with a decay time of about 1 h was observed in several integrated parameters related to different aspects of magnetospheric activity, including the total field-aligned current into and out of the ionosphere. The same time rate of change for the cessation of activity has also been measured in total field aligned current estimates from the AMPERE project, adding observational support to this finding. The observational study also revealed both a seasonal and a day/night variation in the decay parameter, with faster decay observed in the winter than in the summer hemisphere and on the nightside than on the dayside. Decay time averages varied between 0.8 and 2.0 h for these scenarios. The results can be understood in terms of stronger/weaker line tying of the ionospheric foot points of magnetospheric field lines for higher/lower conductivity. Additional global modeling results with varying conductance scenarios for the ionosphere confirm this interpretation and provide a quantitative understanding of the effect.

Estimating the Rate of Cessation of Magnetospheric Activity in AMPERE Field‐Aligned Currents

AbstractThe decay of magnetospheric activity when driving is turned off (to a minimum) was measured in total field‐aligned current estimates from the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) project. Events of distinct northward turnings of the interplanetary magnetic field were identified, with prolonged periods of stable southward driving conditions followed by northward interplanetary magnetic field conditions. All but 4 of 43 identified events exhibit a well‐defined exponential decay in the total hemispheric field‐aligned current following the northward turning. A superposed epoch analysis yields a generic decay constant of 0.9, corresponding to an e‐folding time of 1.1 hr. A statistical analysis of the ensemble of events also reveals a seasonal variation in the decay parameter with faster decay observed in the winter than in the summer hemisphere. This result can be understood in terms of stronger/weaker line tying of the ionospheric foot points of magnetospheric field lines for higher/lower conductivity.

Helical kink instability in the confined solar eruption on 2002 May 27

AbstractThis paper presents an improved MHD modeling of the confined filament eruption in solar active region NOAA 9957 on 2002 May 27 by extending the parametric studies of the event in Török & Kliem (2005) and Hassanin & Kliem (2016). Here the initial flux rope equilibrium is chosen to possess a small apex height identical to the observed initial filament height, which implies a more realistic inclusion of the photospheric line tying. The model matches the observations as closely as in the preceding studies, with the closest agreement again being obtained for an initial average flux rope twist of about 4π. Thus, the model for strongly writhing confined solar eruptions, which assumes that a kink‐unstable flux rope in the stability domain of the torus instability exists at the onset of the eruption's main acceleration phase, is further substantiated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Propagation of Pi2 pulsations through the braking region in global MHD simulations

AbstractWe investigate the propagation of Pi2 period pulsations from their origin in the plasma sheet through the braking region, the region where the fast flows are slowed as they approach the inner edge of the plasma sheet. Our approach is to use both the University of California, Los Angeles (UCLA) and Lyon‐Fedder‐Mobarry (LFM) global magnetohydrodynamic (MHD) computer codes to simulate the Earth's magnetosphere during a substorm that occurred on 14 September 2004 when Pi2 pulsations were observed. We use two different MHD models in order to test the robustness of our conclusions about Pi2. The simulations are then compared with ground‐based and satellite data. We find that the propagation of the pulsations in the simulations, especially through the braking region, depends strongly on the ionospheric models used at the inner boundary of the MHD models. With respect to typical observed values, the modeled conductances are high in the UCLA model and low in the LFM model. The different conductances affect the flows, producing stronger line tying that slows the flow in the braking region more in the UCLA model than in the LFM model. Therefore, perturbations are able to propagate much more freely into the inner magnetosphere in the LFM results. However, in both models Pi2 period perturbations travel with the dipolarization front (DF) that forms at the earthward edge of the flow channel, but as the DF slows in the braking region, −8≤x≤−6 RE, the Pi2 period perturbations begin to travel ahead of it into the inner magnetosphere. This indicates that the flow channels generate compressional waves with periods that fall within the Pi2 range and that, as the flows themselves are stopped in the braking region, the compressional wave continues to propagate into the inner magnetosphere.

Tracking and Assessment of Technical Skills Acquisition Among Urology Residents for Open, Laparoscopic, and Robotic Skills Over 4 Years: Is There a Trend?

Tracking the progression of technical skill acquisition during urology residency training is an essential yet challenging task that has been mostly based on anecdotal and subjective performance assessment. We evaluated five surgical tasks used at our institution to assess skill acquisition among residents over 4 consecutive years in an effort to determine appropriate skill testing for resident proficiency relative to level of training for future performance testing. Urology residents were tested yearly throughout the course of their residency with five surgical tasks in an open, laparoscopic, and robotic format. The five tasks were: (1) rings on a peg, (2) thread the rings, (3) cut the line, (4) hexagonal suturing, and (5) suture and knot tying. Evaluation was performed by a trained instructor to assess quantity and quality of the skill task performance. The highest scores were obtained on all open tasks regardless of training level. Residents performed second best on robotic and lowest on the laparoscopic skill tasks. The score difference among surgery platforms was statistically significant P<0.0005 across all tasks. It was Tasks 2 and 5, however, that showed a statistically significant difference in overall quantity×quality score between different postgraduate year (PGY) residents (P=0.03 and P=0.02). In addition, the quantity score for Task 5 also showed a statistically significant difference among PGY residents (P=0.04). There was no statistically significant difference in time to perform tasks among PG years. The high-level Tasks 2 and 5 were the most useful in differentiating different levels of skill task competency among urology residents and appear to be most useful in assessing the degree of improvement among residents during training. These tasks have subsequently been worked into our institution's testing curriculum.

An interchange instability in an open system and the line-tying effect on it

An interchange instability is the most dangerous instability to an open system such as GAMMA10 (Inutake et al 1985 Phys. Rev. Lett. 55 939). A line tying is a powerful tool for stabilizing an interchange instability because the magnetic field lines terminate at the conducting ends in an open system. This paper studies the mechanism of the appearance of line tying in an interchange instability by a particle simulation (taking into account the electron inertia along a magnetic field line precisely) and the line-tying effect on the interchange instability in GAMMA10 by a reduced MHD simulation. We have newly found the nonlinear (quasi-linear) stability criterion to an interchange instability with conducting ends. The limiters of Movable Limiter Outside the anchor mirror cell (MLO) installed in GAMMA10 are found to have a stabilization effect on the interchange instability, which is consistent with the experimental results.

DEMONSTRATIONS THAT THE SOLAR WIND IS NOT ACCELERATED BY WAVES OR TURBULENCE

The present work uses observations and theoretical considerations to provide both qualitative and quantitative arguments that hydromagnetic waves, whether turbulent or not, cannot produce the acceleration of the fast solar wind and the related heating of the open solar corona. Waves do exist, and can play a role in the differential heating and acceleration of minor ions, but their amplitudes are not sufficient to power the wind, as demonstrated by extrapolation of magnetic spectra from Helios and Ulysses observations. Dissipation mechanisms invoked to circumvent this conclusion cannot be effective for a variety of reasons. In particular, turbulence does not play a strong role in the corona as shown both by observations of coronal striations and other features, and by theoretical considerations of line tying to a nonturbulent photosphere, nonlocality of interactions, and the nature of the kinetic dissipation. We consider possible ways out of the arguments presented, and suggest that in the absence of wave or turbulent heating and acceleration, the chromosphere and transition region become the natural source, if yet unproven, of open coronal energization through the production of nonthermal particle distributions.

Effects of line tying on resistive tearing instability in slab geometry

The effects of line tying on resistive tearing instability in slab geometry are studied within the framework of reduced magnetohydrodynamics [B. B. Kadomtsev and O. P. Pogutse, Sov. Phys. JETP 38, 283 (1974); H. R. Strauss, Phys. Fluids 19, 134 (1976)]. It is found that line tying has a stabilizing effect. The tearing mode is stabilized when the system length L is shorter than a critical length Lc, which is independent of the resistivity η. When L is not too much longer than Lc, the growth rate γ is proportional to η. When L is sufficiently long, the tearing mode scaling γ∼η3/5 is recovered. The transition from γ∼η to γ∼η3/5 occurs at a transition length Lt∼η−2/5.

Magnetospheric convection during prolonged intervals with southward interplanetary magnetic field

We have used a global magnetohydrodynamic simulation to investigate magnetospheric convection during a prolonged interval with modest southward driving. The interval simulated occurred on 13 and 14 February 2001 during a period when the interplanetary magnetic field (IMF) remained weakly southward for over 12 hours. Early in the simulation a near‐Earth neutral line located between 20 RE and 40 RE in the tail drove flows earthward and then around the near‐Earth obstacle to return magnetic flux to the dayside. The earthward flow led to increased ionospheric conductance and developed a modest earthward pressure gradient in the inner plasma sheet. Ionospheric line tying slowed the earthward flow. The pressure gradient caused the inner tail to become interchange unstable and lead to the tailward flow. When the tailward moving flux tube reached the near‐Earth neutral line additional reconnection occurred between the tailward moving flux tube and IMF field lines created by lobe reconnection thereby returning flux to the nightside tail lobes. Late in the event the new lobe field lines reconnected at the duskside magnetopause creating additional rapid tailward motion. The tailward flow led to a reduction in both the ionospheric conductance and near‐Earth tail pressure gradient and earthward flow was again established. This sequence repeated at least three times during the interval simulated.

Ideal magnetohydrodynamic interchanges in low density plasmas

The ideal magnetohydrodynamic equations are usually derived under the assumption VA⪡c, where VA is the Alfvén speed and c is the speed of light. This system of equations is extended to low density plasmas wherein VA can be comparable to or greater than c. This involves relaxation of the usual charge quasineutrality assumption and the inclusion of electromagnetic momentum on par with plasma momentum. The extended system is applied to interchange instabilities in “line-tied” slab geometry as well as to centrifugally confined plasmas. It is found that interchange growth rates are reduced by a factor of 1+VA2∕c2, corresponding to a larger effective mass resulting from the extra electromagnetic momentum. Line tying is unaffected.

Circulation and dynamics in the jovian magnetosphere

Io continually adds mass to the Io torus and this density builds up until centrifugal force is sufficient to overcome the line tying of the jovian ionosphere. The magnetic flux is carried outward with this slow radial convection. Under the assumption that 1 ton per second is added to the torus at Io and that the Voyager observed densities and average ion mass are pertinent for the Pioneer and Galileo epochs, a consistent flow pattern arises. The outward flow near Io is a few meters per second. Near Europa the velocity, based on the observations of a Europa plume, rises to about 400 m/s. Beyond 24 R J in the magnetodisk it is possible to again estimate the velocity. It is about 20 km/s at 25 R J and about 50 km/sec at 40 R J consistent with the Voyager LECP measurements. This outflow of magnetic flux is replenished by reconnection of magnetic flux in the near tail and the subsequent inward convection of empty flux tubes into the inner magnetosphere. These flux tubes are seen in the middle magnetosphere and the Io torus. Their scarcity as judged by the fact that they constitute only about 0.4% of the observing time indicates that they are moving inward at a much higher rate than the mass-loaded magnetospheric plasma moves outward. In the neighborhood of the magnetodisk the outflow appears not to be steady as the magnetic flux crossing the current sheet varies greatly from orbit to orbit. This unsteadiness may lead the occasional auroral storms seen in the ionosphere at the feet of these field lines.

Explosive instabilities and detonation in magnetohydrodynamics

Many plasma systems exhibit large-scale explosive events. Solar flares, magnetic substorms and tokamak disruptions are examples of large-scale explosive events. Since the rate at which the stability boundary is crossed is usually slow, systems rarely achieve a large linear growth rate. Thus explosive events almost always require nonlinear destabilization to achieve the fast time-scales that are observed. A new mechanism for explosive behavior is demonstrated in a nonlinear MHD model of the line tied Rayleigh-Taylor instability. In this mechanism the system crosses the instability threshold in a small region of space. The nonlinearity is destabilizing and broadening causing the linear instability to develop fingers and broaden into the linearly stable region. A front forms separating the disturbed and undisturbed regions. Because the nonlinearity is destabilizing the linearly stable region is, in fact, meta stable. The energy in the fingers is large enough to destabilize the meta-stable region — a process we call detonation. In the simple system analyzed a finite time singularity occurs where the displacement becomes singular like ( t 0 − t) −2.1. the energy like ( t 0 − t) −6.4 and the destabilized region width like ( t 0 − t) −0.4. The analysis of this problem is simplified by expanding around the marginal stability point. The behavior of the displacement along the field line is determined at low order. At higher order the behavior across the field is determined to be the solution of a two-dimensional nonlinear equation. The coefficients in this equation depend on field line averages of the behavior along the field. The same nonlinear equation can be shown to govern the nonlinear behavior near marginal stability of small perpendicular wavelength instabilities in more complicated geometries where line tying or ballooning are present. Thus, the mechanism can be considered generic. Analytic and numerical results will be shown. The relevance of this mechanism to solar flares, magnetic substorms and tokamak disruptions will be discussed briefly.

Reply to Comments by E. N. Parker

There are three important points on which a recent paper by E. N. Parker implies disagreement with a previous paper by this author where none actually exists: (1) The way dynamics should be treated in magnetohydrodynamics (MHD), (2) the speed of energy propagation in a plasma, and (3) the conditions under which line tying is valid. Points on which there is disagreement between Parker and this author are as follows. (1) The significance of the vector magnetogram data for flare models: Parker suggests that these data cannot be used to deduce currents because they do not resolve the presumably fibril state of the magnetic field, and I disagree strongly with this view. (2) Whether or not the current viewpoint is useful in understanding the physics of solar flares: I maintain that the currents need to be considered when deciding on appropriate boundary conditions at the edges and ends of portions of MHD models for flux tubes. (3) The location of the dynamo that supplies the magnetic energy stored in the corona and released in a flare: Parker argues for a dynamo region at a depth of 5 × 103 km, and I argue that such a dynamo is inconsistent with the vector magnetogram data.

Effect of limiter end loss in finite Larmor radius theory

We have examined the effect of incomplete line tying on the MHD flute mode with FLR (finite Larmor radius) effects. We show that the combination of line tying and FLR effects can slow down MHD instability, but cannot produce complete stabilization.

Sub-Alfvénic plasma expansion

A large ion Larmor radius plasma undergoes a particularly robust form of Rayleigh–Taylor instability when sub-Alfvénically expanding into a magnetic field. Results from an experimental study of this instability are reported and compared with theory, notably a magnetohydrodynamic (MHD) treatment that includes the Hall term, a generalized kinetic lower-hybrid drift theory, and with computer simulations. Many theoretical predictions are confirmed while several features remain unexplained. New and unusual features appear in the development of this instability. In the linear stage there is an onset criterion insensitive to the magnetic field, initial density clumping (versus interchange), linear growth rate much higher than in the ‘‘classic’’ MHD regime, and dominant instability wavelength of order of the plasma density scale length. In the nonlinear limit free-streaming flutes, apparent splitting (bifurcation) of flutes, curling of flutes in the electron cyclotron sense, and a highly asymmetric expansion are found. Also examined is the effect on the instability of the following: an ambient background plasma (that adds collisionality and raises the expansion speed/Alfvén speed ratio), magnetic-field line tying, and expansion asymmetries (that promotes plasma cross-field jetting).

The effect of line tying on Parker's instability

view Abstract Citations (14) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Effect of Line Tying on Parker's Instability Zweibel, Ellen G. ; Bruhwiler, David L. Abstract We consider the effect of line tying on the magnetic Rayleigh-Taylor or Parker instability. We find that stabilization occurs if the field lines are sufficiently short that the Alfven travel time between the boundaries is less than 2 pi times the instability growth time in an unbounded medium. In a magnetically dominated system, the critical field line length scales linearly with magnetic field strength. This criterion may be revelant to the stabilization of solar prominences. Publication: The Astrophysical Journal Pub Date: November 1992 DOI: 10.1086/171927 Bibcode: 1992ApJ...399..318Z Keywords: Solar Magnetic Field; Solar Prominences; Taylor Instability; Field Strength; Potential Energy; Solar Atmosphere; Stabilization; Solar Physics; INSTABILITIES; PLASMAS; SUN: PROMINENCES full text sources ADS |

Dynamical evolution of twisted magnetic flux tubes. I - Equilibrium and linear stability

The three-dimensional dynamical evolution of twisted magnetic flux tubes is studied using a time-dependent magnetohydrodynamic (MHD) model. The flux tubes are intended to model solar coronal loops, and include the stabilizing effect of photospheric line tying. The model permits the complete evolution of flux tubes to be followed self-consistently, including the formation, equilibrium, linear instability, and nonlinear behavior. Starting from an initial uniform background magnetic field, a twisted flux tube is created by the application of slow, localized photospheric vortex flows. The flux tube evolves quasi-statically through sequences of equilibria with increasing twist, until it becomes linearly unstable to an ideal MHD kink mode. In this paper, the equilibrium properties and the linear stability behavior are discussed. The application of the method to the uniform-twist, Gold-Hoyle field confirms the previous stability threshold for kink instability and provides estimates of the resulting growth rate.

Stable operation of an effectively axisymmetric neutral beam driven tandem mirror

A quiescent plasma is sustained for 80 energy confinement times by only gas fuelling and neutral beam heating in an axisymmetric region of the Tandem Mirror Experiment Upgrade (TMX-U). This plasma should be unstable because of the bad magnetic curvature and the absence of ion cyclotron heating which previously provided ponderomotive stabilization to sustain plasmas in bad-curvature regions of other axisymmetric mirror experiments. The TMX-U data are consistent with stabilization by a symbiosis between two mechanisms – line tying, which reduces the growth rate, and finite Larmor radius edge stabilization, which can result in quiescent operation.

Tearing modes in solar coronal loops

It is shown that solar coronal-like magnetic loops, that is loops emerging from and reentering heavy plasma, are unstable to tearing modes. In particular, the previously made assumption of line tying to the heavy plasma, resulting in stabilization, is shown to be inapplicable because the growth rate is sub-Alfvenic in the entire loop, including the submerged part. In fact, it is shown that the tearing mode may grow faster than ordinarily surmised because the growth rate is determined by the average resistivity along an entire flux line rather than by the resistivity in the corona alone.

Line tying of interchange modes in a nearly collisionless mirror-trapped plasma

If the confining potential of electrostatically trapped electrons fluctuates, then the number of trapped electrons also fluctuates. The linear relationship between potential fluctuations and the number of trapped electrons is investigated, considering two loss mechanisms for a nearly collisionless plasma: (1) small-angle collisions (diffusion), and (2) large-angle collisions. This nearly collisionless model predicts the line tying of interchange modes in a mirror-trapped plasma is orders of magnitude larger than previously thought for a fusion plasma, yet still not strong enough to completely line tie an axisymmetric mirror. Also, a nonlinearity in the response can occur at low amplitude.