arXiv subjects

Andrew Hillier

Publications and source records attributed to Andrew Hillier.

At least 37 records · Page 2Linked to original sources

arXiv2021

Coalescence Instability in Chromospheric Partially Ionised Plasmas

Fast magnetic reconnection plays a fundamental role in driving explosive dynamics and heating in the solar chromosphere. The reconnection time scale of traditional models is shortened at the onset of the coalescence instability, which forms a turbulent reconnecting current sheet through plasmoid interaction. In this work we aim to investigate the role of partial ionisation on the development of fast reconnection through the study of the coalescence instability of plasmoids. Unlike the processes occurring in fully ionised coronal plasmas, relatively little is known about how fast reconnection develops in partially ionised plasmas of the chromosphere. We present 2.5D numerical simulations of coalescing plasmoids in a single fluid magnetohydrodynamic (MHD) model, and a two-fluid model of a partially ionised plasma (PIP). We find that in the PIP model, which has the same total density as the MHD model but an initial plasma density two orders of magnitude smaller, plasmoid coalescence is faster than the MHD case, following the faster thinning of the current sheet and secondary plasmoid dynamics. Secondary plasmoids form in the PIP model where the effective Lundquist number $S = 7.8 \cdot 10^3$, but are absent from the MHD case where $S = 9.7 \cdot 10^3$: these are responsible for a more violent reconnection. Secondary plasmoids also form in linearly stable conditions as a consequence of the non-linear dynamics of the neutrals in the inflow. In the light of these results we can affirm that two-fluid effects play a major role on the processes occurring in the solar chromosphere.

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arXiv2020

Estimating the energy dissipation {from Kelvin-Helmholtz instability induced} turbulence in oscillating coronal loops}

Kelvin-Helmholtz {instability induced} turbulence is one promising mechanism by which loops in the solar corona can be heated by MHD waves. In this paper we present an analytical model of the dissipation rate of {Kelvin-Helmholtz instability induced} turbulence $\varepsilon_{\rm D}$, finding it scales as the wave amplitude ($d$) to the third power ($\varepsilon_{\rm D}\propto d^3$). Based on the concept of steady-state turbulence, we expect the turbulence heating throughout the volume of {the} loop to match the total energy injected through its footpoints. In situations where this holds, the wave amplitude has to vary as the cube-root of the injected energy. Comparing the analytic results with those of simulations shows that our analytic formulation captures the key aspects of the turbulent dissipation from the numerical work. Applying this model to the observed characteristics of decayless kink waves we predict that the amplitudes of these observed waves is insufficient to turbulently heat the solar corona.

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arXiv2020

Mode conversion of two-fluid shocks in a partially-ionised, isothermal, stratified atmosphere

The plasma of the lower solar atmosphere consists of mostly neutral particles, whereas the upper solar atmosphere is mostly ionised particles and electrons. A shock that propagates upwards in the solar atmosphere therefore undergoes a transition where the dominant fluid is either neutral or ionised. An upwards propagating shock also passes a point where the sound and Alfvén speed are equal. At this point the energy of the acoustic shock can separated into fast and slow components. How the energy is distributed between the two modes depends on the angle of magnetic field. The separation of neutral and ionised species in a gravitationally stratified atmosphere is investigated. The role of two-fluid effects on the structure of the shocks post-mode-conversion and the frictional heating is quantified for different levels of collisional coupling. Two-fluid numerical simulations are performed using the (P\underline{I}P) code of a wave steepening into a shock in an isothermal, partially-ionised atmosphere. The collisional coefficient is varied to investigate the regimes where the plasma and neutral species are weakly, strongly and finitely coupled. The propagation speeds of the compressional waves hosted by neutral and ionised species vary, therefore velocity drift between the two species is produced as the plasma attempts to propagate faster than the neutrals. This is most extreme for a fast-mode shock. We find that the collisional coefficient drastically changes the features present in the system, specifically the mode conversion height, type of shocks present, and the finite shock widths created by the two-fluid effects. In the finitely-coupled regime fast-mode shock widths can exceed the pressure scale height leading to a new potential observable of two-fluid effects in the lower solar atmosphere.

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arXiv2019

Coronal cooling as a result of mixing by the nonlinear Kelvin--Helmholtz instability

Recent observations show cool, oscillating prominence threads fading when observed in cool spectral lines and appearing in warm spectral lines. A proposed mechanism to explain this evolution is that the threads were heated by turbulence driven by the Kelvin--Helmholtz instability that developed as a result of wave-driven shear flows on the surface of the thread. As the Kelvin--Helmholtz instability is an instability that works to mix the fluids, in the solar corona it can be expected to work by mixing the cool prominence material with that of the hot corona to form a warm boundary layer. In this paper we develop a simple phenomenological model of nonlinear Kelvin--Helmholtz mixing, using it to determine the characteristic density and temperature of the mixing layer, which for the case under study with constant pressure across the two fluids are $ρ_{\rm mixed}=\sqrt{ρ_1ρ_2}$ and $T_{\rm mixed}=\sqrt{T_1T_2}$. One result from the model is that it provides an accurate, as determined by comparison with simulation results, determination of the kinetic energy in the mean velocity field. A consequence of this is that the magnitude of turbulence, and with it the energy that can be dissipated on fast time-scales, as driven by this instability can be determined. For the prominence-corona system, the mean temperature rise possible from turbulent heating is estimated to be less than 1\% of the characteristic temperature (which is found to be $10^5$\,K). These results highlight that mixing, and not heating, are likely to be the cause of the observed transition between cool to warm material in Okamoto et. al (2015). One consequence of this result is that the mixing creates a region with higher radiative loss rates on average than either of the original fluids, meaning that this instability could contribute a net loss of thermal energy from the corona, i.e. coronal cooling.

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arXiv2019

Ion-neutral decoupling in the nonlinear Kelvin--Helmholtz instability: Case of field-aligned flow

The nonlinear magnetic Kelvin-Helmholtz instability (KHi), and the turbulence it creates, appears in many astrophysical systems. This includes those systems where the local plasma conditions are such that the plasma is not fully ionised, for example in the lower solar atmosphere and molecular clouds. In a partially ionised system, the fluids couple via collisions which occur at characteristic frequencies, therefore neutral and plasma species become decoupled for sufficiently high-frequency dynamics. Here we present high-resolution 2D two-fluid simulations of the nonlinear KHi for a system that traverses the dynamic scales between decoupled fluids and coupled dynamics. We discover some interesting phenomena, including the presence of a density coupling that is independent of the velocity coupling. Using these simulations we analyse the heating rate, and two regimes appear. The first is a regime where the neutral flow is decoupled from the magnetic field that is characterised with a constant heating rate, then at larger scales the strong coupling approximation holds and the heating rate. At large scales with the KHi layer width to the $-2$ power. There is an energy cascade in the simulation, but the nature of the frictional heating means the heating rate is determined by the largest scale of the turbulent motions, a fact that has consequences for understanding turbulent dissipation in multi-fluid systems.

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arXiv2019

Intermediate shock substructures within a slow-mode shock occurring in partially ionised plasma

Slow-mode shocks are important in understanding fast magnetic reconnection, jet formation and heating in the solar atmosphere, and other astrophysical systems. The atmospheric conditions in the solar chromosphere allow both ionised and neutral particles to exist and interact. Under such conditions, fine substructures exist within slow-mode shocks due to the decoupling and recoupling of the plasma and neutral species. We study numerically the fine substructure within slow-mode shocks in a partially ionised plasma, in particular, analysing the formation of an intermediate transition within the slow-mode shock. High-resolution 1D numerical simulations are performed using the (P\underline{I}P) code using a two-fluid approach. We discover that long-lived intermediate (Alfven) shocks can form within the slow-mode shock, where there is a shock transition from above to below the Alfven speed and a reversal of the magnetic field across the shock front. The collisional coupling provides frictional heating to the neutral fluid, resulting in a Sedov-Taylor-like expansion with overshoots in the neutral velocity and neutral density. The increase in density results in a decrease of the Alfven speed and with this the plasma inflow is accelerated to above the Alfven speed within the finite width of the shock leading to the intermediate transition. This process occurs for a wide range of physical parameters and an intermediate shock is present for all investigated values of plasma-$β$, neutral fraction, and magnetic angle. As time advances the magnitude of the magnetic field reversal decreases since the neutral pressure cannot balance the Lorentz force. The intermediate shock is long-lived enough to be considered a physical structure, independent of the initial conditions.

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arXiv2019

Dynamic evolution of current sheets, ideal tearing, plasmoid formation and generalized fractal reconnection scaling relations

Magnetic reconnection may be the fundamental process allowing energy stored in magnetic fields to be released abruptly, solar flares and coronal mass ejection (CME) being archetypal natural plasma examples. Magnetic reconnection is much too slow a process to be efficient on the large scales, but accelerates once small enough scales are formed in the system. For this reason, the fractal reconnection scenario was introduced (Shibata and Tanuma 2001) to explain explosive events in the solar atmosphere: it was based on the recursive triggering and collapse via tearing instability of a current sheet originally thinned during the rise of a filament in the solar corona. Here we compare the different fractal reconnection scenarios that have been proposed, and derive generalized scaling relations for the recursive triggering of fast, `ideal' - i.e. Lundquist number independent - tearing in collapsing current sheet configurations with arbitrary current profile shapes. An important result is that the Sweet-Parker scaling with Lundquist number, if interpreted as the aspect ratio of the singular layer in an ideally unstable sheet, is universal and does not depend on the details of the current profile in the sheet. Such a scaling however must not be interpreted in terms of stationary reconnection, rather it defines a step in the accelerating sequence of events of the ideal tearing mediated fractal cascade. We calculate scalings for the expected number of plasmoids for such generic profiles and realistic Lundquist numbers.

physics.plasm-ph↗

arXiv2018

On Kelvin-Helmholtz and parametric instabilities driven by coronal waves

The Kelvin-Helmholtz instability has been proposed as a mechanism to extract energy from magnetohydrodynamic (MHD) kink waves in flux tubes, and to drive dissipation of this wave energy through turbulence. It is therefore a potentially important process in heating the solar corona. However, it is unclear how the instability is influenced by the oscillatory shear flow associated with an MHD wave. We investigate the linear stability of a discontinuous oscillatory shear flow in the presence of a horizontal magnetic field within a Cartesian framework that captures the essential features of MHD oscillations in flux tubes. We derive a Mathieu equation for the Lagrangian displacement of the interface and analyse its properties, identifying two different instabilities: a Kelvin-Helmholtz instability and a parametric instability involving resonance between the oscillatory shear flow and two surface Alfvén waves. The latter occurs when the system is Kelvin-Helmholtz stable, thus favouring modes that vary along the flux tube, and as a consequence provides an important and additional mechanism to extract energy. When applied to flows with the characteristic properties of kink waves in the solar corona, both instabilities can grow, with the parametric instability capable of generating smaller scale disturbances along the magnetic field than possible via the Kelvin-Helmholtz instability. The characteristic time-scale for these instabilities is $\sim 100$ s, for wavelengths of $200$ km. The parametric instability is more likely to occur for smaller density contrasts and larger velocity shears, making its development more likely on coronal loops than on prominence threads.

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arXiv2018

Observations of the Kelvin-Helmholtz instability driven by dynamic motions in a solar prominence

Prominences are incredibly dynamic across the whole range of their observable spatial scales, with observations revealing gravity-driven fluid instabilities, waves, and turbulence. With all these complex motions, it would be expected that instabilities driven by shear in the internal fluid motions would develop. However, evidence of these have been lacking. Here we present the discovery in a prominence, using observations from the Interface Region Imaging Spectrograph (IRIS), of a shear flow instability, the Kelvin-Helmholtz sinusoidal-mode of a fluid channel, driven by flows in the prominence body. This finding presents a new mechanism through which we can create turbulent motions from the flows observed in quiescent prominences. The observation of this instability in a prominence highlights their great value as a laboratory for understanding the complex interplay between magnetic fields and fluid flows that play a crucial role in a vast range of astrophysical systems.

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arXiv2017

Quiescent prominence dynamics observed with the Hinode Solar Optical Telescope . II. Prominence Bubble Boundary Layer Characteristics and the Onset of a Coupled Kelvin-Helmholtz Rayleigh-Taylor Instability

We analyze solar quiescent prominence bubble characteristics and instability dynamics using Hinode/Solar Optical Telescope (SOT) data. We measure bubble expansion rate, prominence downflows, and the profile of the boundary layer brightness and thickness as a function of time. The largest bubble analyzed rises into the prominence with a speed of about 1.3 km/s until it is destabilized by a localized shear flow on the boundary. Boundary layer thickness grows gradually as prominence downflows deposit plasma onto the bubble with characteristic speeds of 20 - 35 km/s. Lateral downflows initiate from the thickened boundary layer with characteristic speeds of 25 - 50 km/s, "draining" the layer of plasma. Strong shear flow across one bubble boundary leads to an apparent coupled Kelvin-Helmholtz Rayleigh-Taylor (KH-RT) instability. We measure shear flow speeds above the bubble of 10 km/s and infer interior bubble flow speeds on the order of 100 km/s. Comparing the measured growth rate of the instability to analytic expressions, we infer a magnetic flux density across the bubble boundary of ~10^{-3} T (10 gauss) at an angle of ~70 degrees to the prominence plane. The results are consistent with the hypothesis that prominence bubbles are caused by magnetic flux that emerges below a prominence, setting up the conditions for RT, or combined KH-RT, instability flows that transport flux, helicity, and hot plasma upward into the overlying coronal magnetic flux rope.

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arXiv2017

The Non-Linear Growth of the Magnetic Rayleigh-Taylor Instability

This work examines the effect of the embedded magnetic field strength on the non-linear development of the magnetic Rayleigh-Taylor Instability (RTI) (with a field-aligned interface) in an ideal gas close to the incompressible limit in three dimensions. Numerical experiments are conducted in a domain sufficiently large so as to allow the predicted critical modes to develop in a physically realistic manner. The ratio between gravity, which drives the instability in this case (as well as in several of the corresponding observations), and magnetic field strength is taken up to a ratio which accurately reflects that of observed astrophysical plasma, in order to allow comparison between the results of the simulations and the observational data which served as inspiration for this work. This study finds reduced non-linear growth of the rising bubbles of the RTI for stronger magnetic fields, and that this is directly due to the change in magnetic field strength, rather than the indirect effect of altering characteristic length scales with respect to domain size. By examining the growth of the falling spikes, the growth rate appears to be enhanced for the strongest magnetic field strengths, suggesting that rather than affecting the development of the system as a whole, increased magnetic field strengths in fact introduce an asymmetry to the system. Further investigation of this effect also revealed that the greater this asymmetry, the less efficiently the gravitational energy is released. By better understanding the under-studied regime of such a major phenomenon in astrophysics, deeper explanations for observations may be sought, and this work illustrates that the strength of magnetic fields in astrophysical plasmas influences observed RTI in subtle and complex ways.

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arXiv2016

Investigating prominence turbulence with Hinode SOT Dopplergrams

Quiescent prominences host a diverse range of flows, including Rayleigh-Taylor instability driven upflows and impulsive downflows, and so it is no surprise that turbulent motions also exist. As prominences are believed to have a mean horizontal guide field, investigating any turbulence they host could shed light on the nature of MHD turbulence in a wide range of astrophysical systems. In this paper we have investigated the nature of the turbulent prominence motions using structure function analysis on the velocity increments estimated from H$α$ Dopplergrams constructed with observational data from Hinode SOT. The pdf of the velocity increments shows that as we look at increasingly small spatial separations the distribution displays greater departure from a reference Gaussian distribution, hinting at intermittency in the velocity field. Analysis of the even order structure functions for both the horizontal and vertical separations showed the existence of two distinct regions displaying different exponents of the power law with the break in the power law at approximately 2000km. We hypothesise this to be a result of internal turbulence excited in the prominence by the dynamic flows of the system found at this spatial scale. We found that the scaling exponents of the p-th order structure functions for these two regions generally followed the p/2 (smaller scales) and p/4 (larger scales) laws that are the same as those predicted for weak MHD turbulence and Kraichnan-Iroshnikov turbulence respectively. However, the existence of the p/4 scaling at larger scales than the p/2 scaling is inconsistent with the increasing nonlinearity expected in MHD turbulence. Estimating the heating from the turbulent energy dissipation showed that this turbulent heating would be very inefficient, but that the mass diffusion through turbulence driven reconnection was of the order of $10^{10}$cm$^2$/s.

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arXiv2016

The formation and evolution of reconnection-driven slow-mode shocks in a partially ionised plasma

The role of slow-mode MHD shocks in magnetic reconnection is one of great importance for energy conversion and transport, but in many astrophysical plasmas the plasma is not fully ionised. In this paper, we investigate, using numerical simulations, the role of collisional coupling between a proton-electron charge-neutral fluid and a neutral hydrogen fluid for the 1D Riemann problem initiated in a constant pressure and density background state by a discontinuity in the magnetic field. This system, in the MHD limit, is characterised by two waves: a fast-mode rarefaction wave that drives a flow towards a slow-mode MHD shock. The system evolves through four stage: initiation, weak coupling, intermediate coupling and a quasi steady state. The initial stages are characterised by an over-pressured neutral region that expands with characteristics of a blast wave. In the later stages, the system tends towards a self-similar solution where the main drift velocity is concentrated in the thin region of the shock front. Due to the nature of the system, the neutral fluid is overpressured by the shock when compared to a purely hydrodynamic shock which results in the neutral fluid expanding to form the shock precursor. The thickness of the shockfront once it has formed proportional to the ionisation fraction to the power -1.2, which is a smaller exponent than would be naively expected from simple scaling arguments. One interesting result is that the shock front is a continuous transition of the physical variables for sub-sonic velocity upstream of the shock front (a c-shock) to a sharp jump in the physical variables followed by a relaxation to the downstream values for supersonic upstream velocity (a j-shock). The frictional heating that results from the velocity drift across the shock front can amount to approximately two per cent of the reference magnetic energy.

astro-ph.SR↗

arXiv2016

On the nature of the magnetic Rayleigh-Taylor instability in Astrophysical Plasma: The case of uniform magnetic field strength

The magnetic Rayleigh-Taylor instability has been shown to play a key role in many astrophysical systems. The equation for the growth rate of this instability in the incompressible limit, and the most-unstable mode that can be derived from it, are often used to estimate the strength of the magnetic field that is associated with the observed dynamics. However, there are some issues with the interpretations given. Here we show that the class of most unstable modes $k_u$ for a given $θ$, the class of modes often used to estimate the strength of the magnetic field from observations, for the system leads to the instability growing as $σ^2=1/2 A g k_u$, a growth rate which is independent of the strength of the magnetic field and which highlights that small scales are preferred by the system, but not does not give the fastest growing mode for that given $k$. We also highlight that outside of the interchange ($\mathbf{k}\cdot\mathbf{B}=0$) and undular ($\mathbf{k}$ parallel to $\mathbf{B}$) modes, all the other modes have a perturbation pair of the same wavenumber and growth rate that when excited in the linear regime can result in an interference pattern that gives field aligned filamentary structure often seen in 3D simulations. The analysis was extended to a sheared magnetic field, where it was found that it was possible to extend the results for a non-sheared field to this case. We suggest that without magnetic shear it is too simplistic to be used to infer magnetic field strengths in astrophysical systems.

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arXiv2016

Nonlinear Instability and Intermittent Nature of Magnetic Reconnection in Solar Chromosphere

The recent observations of Singh et al. (2012) have shown multiple plasma ejections and the intermittent nature of magnetic reconnection in the solar chromosphere, highlighting the need for fast reconnection to occur in highly collisional plasma. However, the physical process through which fast magnetic reconnection occurs in partially ionized plasma, like the solar chromosphere, is still poorly understood. It has been shown that for sufficiently high magnetic Reynolds numbers, Sweet-Parker current sheets can become unstable leading to tearing mode instability and plasmoid formation, but when dealing with a partially ionized plasma the strength of coupling between the ions and neutrals plays a fundamental role in determining the dynamics of the system. We propose that as the reconnecting current sheet thins and the tearing instability develops, plasmoid formation passes through strongly, intermediately, and weakly coupled (or decoupled) regimes, with the time scale for the tearing mode instability depending on the frictional coupling between ions and neutrals. We present calculations for the relevant time scales for fractal tearing in all three regimes. We show that as a result of the tearing mode instability and the subsequent non-linear instability due to the plasmoid-dominated reconnection, the Sweet-Parker current sheet tends to have a fractal-like structure, and when the chromospheric magnetic field is sufficiently strong the tearing instability can reach down to kinetic scales, which are hypothesized to be necessary for fast reconnection.

astro-ph.SR↗

arXiv2014

Superflare occurrence and energies on G-, K- and M-type dwarfs

Kepler data from G-, K- and M-type stars are used to study conditions that lead to superflares with energies above $10^{34} {\rm erg}$. From the 117,661 stars included, 380 show superflares with a total of 1690 such events. We study whether parameters, like effective temperature or the rotation rate, have any effect on the superflare occurrence rate or energy. With increasing effective temperature we observe a decrease in the superflare rate, which is analogous to the previous findings of a decrease in dynamo activity with increasing effective temperature. For slowly rotating stars, we find a quadratic increase of the mean occurrence rate with the rotation rate up to a critical point, after which the rate decreases linearly. Motivated by standard dynamo theory, we study the behavior of the relative starspot coverage, approximated as the relative brightness variation. For faster rotating stars, an increased fraction of stars shows higher spot coverage, which leads to higher superflare rates. A turbulent dynamo is used to study the dependence of the Ohmic dissipation as a proxy of the flare energy on the differential rotation or shear rate. The resulting statistics of the dissipation energy as a function of dynamo number is similar to the observed flare statistics as a function of the inverse Rossby number and shows similarly strong fluctuations. This supports the idea that superflares might well be possible for solar-type G stars.

astro-ph.SR↗

arXiv2014

Investigating the Dynamics and Density Evolution of Returning Plasma Blobs from the 2011 June 7 Eruption

This work examines infalling matter following an enormous Coronal Mass Ejection (CME) on 2011 June 7. The material formed discrete concentrations, or blobs, in the corona and fell back to the surface, appearing as dark clouds against the bright corona. In this work we examined the density and dynamic evolution of these blobs in order to formally assess the intriguing morphology displayed throughout their descent. The blobs were studied in five wavelengths (94, 131, 171, 193 and 211 Å) using the Solar Dynamics Observatory Atmospheric Imaging Assembly (SDO/AIA), comparing background emission to attenuated emission as a function of wavelength to calculate column densities across the descent of four separate blobs. We found the material to have a column density of hydrogen of approximately 2 $\times$ 10$^{19}$ cm$^{-2}$, which is comparable with typical pre-eruption filament column densities. Repeated splitting of the returning material is seen in a manner consistent with the Rayleigh-Taylor instability. Furthermore, the observed distribution of density and its evolution are also a signature of this instability. By approximating the three-dimensional geometry (with data from STEREO-A), volumetric densities were found to be approximately 2 $\times$ 10$^{-14}$ g cm$^{-3}$, and this, along with observed dominant length-scales of the instability, was used to infer a magnetic field of the order 1 G associated with the descending blobs.

astro-ph.SR↗

arXiv2013

On the Support of Solar Prominence Material by the Dips of a Coronal Flux Tube

The dense prominence material is believed to be supported against gravity through the magnetic tension of dipped coronal magnetic field. For quiescent prominences, which exhibit many gravity-driven flows, hydrodynamic forces are likely to play an important role in the determination of both the large and small scale magnetic field distributions. In this study, we present the first steps toward creating three-dimensional magneto-hydrostatic prominence model where the prominence is formed in the dips of a coronal flux tube. Here 2.5D equilibria are created by adding mass to an initially force-free magnetic field, then performing a secondary magnetohydrodynamic relaxation. Two inverse polarity magnetic field configurations are studied in detail, a simple o-point configuration with a ratio of the horizontal field (B_x) to the axial field (B_y) of 1:2 and a more complex model that also has an x-point with a ratio of 1:11. The models show that support against gravity is either by total pressure or tension, with only tension support resembling observed quiescent prominences. The o-point of the coronal flux tube was pulled down by the prominence material, leading to compression of the magnetic field at the base of the prominence. Therefore tension support comes from the small curvature of the compressed magnetic field at the bottom and the larger curvature of the stretched magnetic field at the top of the prominence. It was found that this method does not guarantee convergence to a prominence-like equilibrium in the case where an x-point exists below the prominence flux tube. The results imply that a plasma beta of ~ 0.1 is necessary to support prominences through magnetic tension.

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