Author name code: botha ADS astronomy entries on 2022-09-14 author:"Botha, Gert J.J." ------------------------------------------------------------------------ Title: The Independence of Oscillatory Reconnection Periodicity from the Initial Pulse Authors: Karampelas, Konstantinos; McLaughlin, James A.; Botha, Gert J. J.; Régnier, Stéphane Bibcode: 2022ApJ...933..142K Altcode: 2022arXiv220701980K Oscillatory reconnection can manifest through the interaction between the ubiquitous MHD waves and omnipresent null points in the solar atmosphere and is characterized by an inherent periodicity. In the current study, we focus on the relationship between the period of oscillatory reconnection and the strength of the wave pulse initially perturbing the null point, in a hot coronal plasma. We use the PLUTO code to solve the fully compressive, resistive MHD equations for a 2D magnetic X-point. Using wave pulses with a wide range of amplitudes, we perform a parameter study to obtain values for the period, considering the presence and absence of anisotropic thermal conduction separately. In both cases, we find that the resulting period is independent of the strength of the initial perturbation. The addition of anisotropic thermal conduction only leads to an increase in the mean value for the period, in agreement with our previous study. We also consider a different type of initial driver and we obtain an oscillation period matching the independent trend previously mentioned. Thus, we report for the first time on the independence between the type and strength of the initializing wave pulse and the resulting period of oscillatory reconnection in a hot coronal plasma. This makes oscillatory reconnection a promising mechanism to be used within the context of coronal seismology. Title: Oscillatory Reconnection of a 2D X-point in a hot coronal plasma Authors: Karampelas, Konstantinos; Botha, Gert J. J.; Regnier, Stephane; Mclaughlin, James A. Bibcode: 2022cosp...44.2559K Altcode: Oscillatory reconnection (a relaxation mechanism with periodic changes in connectivity) has been proposed as a potential physical mechanism underpinning several periodic phenomena in the solar atmosphere including, but not limited to, quasi-periodic pulsations (QPPs) and flows. In the past, this mechanism had been extensively studied numerically for 2D and 3D simulations of null points in cold plasma. In our latest studies, we have expanded our understanding of oscillatory reconnection, by considering for the first time hot, coronal plasma. We will be presenting our latest results, from numerically solving the fully-compressive, resistive MHD equations for a 2D magnetic X-point under coronal conditions using the PLUTO code. We report on the resulting oscillatory reconnection including its periodicity and decay rate, by tracking the evolution of the current density profile at the null point. We also consider, for the first time, the effect of adding anisotropic thermal conduction to the mechanism, and how it simplifies the spectrum of the oscillation profile and increases its decay rate, while still allowing the mechanism to manifest. Finally, we reveal how the equilibrium magnetic field strength, density distribution and the amplitude of the initial perturbation relate to the decay rate, and period of oscillatory reconnection, opening the tantalising possibility of utilizing oscillatory reconnection as a seismological tool. Title: Using Oscillatory Reconnection of a 2D X-point as a tool for coronal seismology. Authors: Karampelas, Konstantinos; Botha, Gert J. J.; Regnier, Stephane; Mclaughlin, James A. Bibcode: 2022cosp...44.2487K Altcode: The mechanism of oscillatory reconnection of a null point has been one of the proposed mechanisms behind phenomena like quasi-periodic pulsations (QPPs). The manifestation of this mechanism through the interaction of the ubiquitous waves with null points in the solar atmosphere opens the possibility of utilizing oscillatory reconnection as a tool for coronal seismology. In the past, the first steps had been taken, by connecting the length of the initial current sheet with the period of oscillatory reconnection, and by identifying a linear regime where the period is affected by resistivity. Our recent numerical studies have expanded upon these findings, by considering plasma at coronal conditions, with the addition of anisotropic thermal conduction. We have performed a series of parameter studies with the use of the PLUTO code, which reveal a relation between the equilibrium magnetic field strength and density distribution with the period and decay rate of oscillatory reconnection. In addition, we see an independence of the oscillation period from the type and strength of the external wave pulse, which perturbs the null from its initial equilibrium state. This allows us to formulate an empirical formula connecting these four quantities, opening the way in using oscillatory reconnection for coronal seismology. Title: Oscillatory Reconnection of a 2D X-point in a Hot Coronal Plasma Authors: Karampelas, Konstantinos; McLaughlin, James A.; Botha, Gert J. J.; Régnier, Stéphane Bibcode: 2022ApJ...925..195K Altcode: 2021arXiv211205712K Oscillatory reconnection (a relaxation mechanism with periodic changes in connectivity) has been proposed as a potential physical mechanism underpinning several periodic phenomena in the solar atmosphere, including, but not limited to, quasi-periodic pulsations (QPPs). Despite its importance, however, the mechanism has never been studied within a hot, coronal plasma. We investigate oscillatory reconnection in a one million Kelvin plasma by solving the fully-compressive, resistive MHD equations for a 2D magnetic X-point under coronal conditions using the PLUTO code. We report on the resulting oscillatory reconnection including its periodicity and decay rate. We observe a more complicated oscillating profile for the current density compared to that found for a cold plasma, due to mode-conversion at the equipartition layer. We also consider, for the first time, the effect of adding anisotropic thermal conduction to the oscillatory reconnection mechanism, and we find this simplifies the spectrum of the oscillation profile and increases the decay rate. Crucially, the addition of thermal conduction does not prevent the oscillatory reconnection mechanism from manifesting. Finally, we reveal a relationship between the equilibrium magnetic field strength, decay rate, and period of oscillatory reconnection, which opens the tantalising possibility of utilizing oscillatory reconnection as a seismological tool. Title: Observing solar wind turbulence in the corona with ground-based radio telescopes Authors: Toit Strauss, Du; Botha, Gert; Chibueze, James; Kontar, Eduard; Engelbrecht, Eugene; Lotz, Stefan; Wicks, Robert; Krupar, Vratislav; Bale, Stuart; Maharaj, Shimul; Jeffrey, Natasha; Nel, Amore; Steyn, Ruhann; van den Berg, Jabus Bibcode: 2021EGUGA..2314180T Altcode: When point-like galactic and extragalactic radio sources are observed through the solar corona by ground-based radio telescopes, plasma density fluctuations in the turbulent solar wind scatter these photons, leading to an observed broadening and/or elongation of such sources. By observing this broadening for several sources, over several days, we can get information about e.g. the wavenumber and radial dependence of solar wind density fluctuations at very small scales (~30m - 8km) inside the Alfven radius, thereby capturing details of the turbulence dissipation range. Here, we present very initial results of such a study with the MeerKAT radio telescope in South Africa (being, of course, a precursor to the much larger Square Kilometer Array, SKA), discuss the preliminary results, and compare these with theoretical estimates and previous observations. Title: A chromospheric resonance cavity in a sunspot mapped with seismology Authors: Jess, David B.; Snow, Ben; Houston, Scott J.; Botha, Gert J. J.; Fleck, Bernhard; Krishna Prasad, S.; Asensio Ramos, Andrés; Morton, Richard J.; Keys, Peter H.; Jafarzadeh, Shahin; Stangalini, Marco; Grant, Samuel D. T.; Christian, Damian J. Bibcode: 2020NatAs...4..220J Altcode: 2019NatAs...4..220J; 2019NatAs.tmp..502J Sunspots are intense collections of magnetic fields that pierce through the Sun's photosphere, with their signatures extending upwards into the outermost extremities of the solar corona1. Cutting-edge observations and simulations are providing insights into the underlying wave generation2, configuration3,4 and damping5 mechanisms found in sunspot atmospheres. However, the in situ amplification of magnetohydrodynamic waves6, rising from a few hundreds of metres per second in the photosphere to several kilometres per second in the chromosphere7, has, until now, proved difficult to explain. Theory predicts that the enhanced umbral wave power found at chromospheric heights may come from the existence of an acoustic resonator8-10, which is created due to the substantial temperature gradients experienced at photospheric and transition region heights11. Here, we provide strong observational evidence of a resonance cavity existing above a highly magnetic sunspot. Through a combination of spectropolarimetric inversions and comparisons with high-resolution numerical simulations, we provide a new seismological approach to mapping the geometry of the inherent temperature stratifications across the diameter of the underlying sunspot, with the upper boundaries of the chromosphere ranging between 1,300 ± 200 km and 2,300 ± 250 km. Our findings will allow the three-dimensional structure of solar active regions to be conclusively determined from relatively commonplace two-dimensional Fourier power spectra. The techniques presented are also readily suitable for investigating temperature-dependent resonance effects in other areas of astrophysics, including the examination of Earth-ionosphere wave cavities12. Title: 3D WKB solution for fast magnetoacoustic wave behaviour within a separatrix dome containing a coronal null point Authors: McLaughlin, James A.; Thurgood, Jonathan O.; Botha, Gert J. J.; Wiggs, Joshua A. Bibcode: 2019MNRAS.484.1390M Altcode: 2019MNRAS.tmp..133M The propagation of the fast magnetoacoustic wave is studied within a magnetic topology containing a 3D coronal null point whose fan field lines form a dome. The topology is constructed from a magnetic dipole embedded within a global uniform field. This study aims to improve the understanding of how magnetohydrodynamics (MHD) waves propagate through inhomogeneous media, specifically in a medium containing an isolated 3D magnetic null point. We consider the linearized MHD equations for an inhomogeneous, ideal, cold plasma. The equations are solved utilizing the WKB approximation and Charpit's Method. We find that for a planar fast wave generated below the null point, the resultant propagation is strongly dependent upon initial location and that there are two main behaviours: the majority of the wave escapes the null (experiencing different severities of refraction depending upon the interplay with the equilibrium Alfvén-speed profile) or, alternatively, part of the wave is captured by the coronal null point (for elements generated within a specific critical radius about the spine and on the z = 0 plane). We also generalize the magnetic topology and find that the height of the null determines the amount of wave that is captured. We conclude that for a wavefront generated below the null point, nulls at a greater height can trap proportionally less of the corresponding wave energy. Title: Predictions of DKIST/DL-NIRSP Observations for an Off-limb Kink-unstable Coronal Loop Authors: Snow, B.; Botha, G. J. J.; Scullion, E.; McLaughlin, J. A.; Young, P. R.; Jaeggli, S. A. Bibcode: 2018ApJ...863..172S Altcode: 2018arXiv180704972S Synthetic intensity maps are generated from a 3D kink-unstable flux rope simulation using several DKIST/DL-NIRSP spectral lines to make a prediction of the observational signatures of energy transport and release. The reconstructed large field-of-view intensity mosaics and single tile sit-and-stare high-cadence image sequences show detailed, fine-scale structure and exhibit signatures of wave propagation, redistribution of heat, flows, and fine-scale bursts. These fine-scale bursts are present in the synthetic Doppler velocity maps and can be interpreted as evidence for small-scale magnetic reconnection at the loop boundary. The spectral lines reveal the different thermodynamic structures of the loop, with the hotter lines showing the loop interior and braiding and the cooler lines showing the radial edges of the loop. The synthetic observations of DL-NIRSP are found to preserve the radial expansion, and hence the loop radius can be measured accurately. The electron number density can be estimated using the intensity ratio of the Fe XIII lines at 10747 and 10798 Å. The estimated density from this ratio is correct to within ±10% during the later phases of the evolution; however, it is less accurate initially when line-of-sight density inhomogeneities contribute to the Fe XIII intensity, resulting in an overprediction of the density by ≈30%. The identified signatures are all above a conservative estimate for instrument noise and therefore will be detectable. In summary, we have used forward modeling to demonstrate that the coronal off-limb mode of DKIST/DL-NIRSP will be able to detect multiple independent signatures of a kink-unstable loop and observe small-scale transient features including loop braiding/twisting and small-scale reconnection events occurring at the radial edge of the loop. Title: Onset of 2D magnetic reconnection in the solar photosphere, chromosphere, and corona Authors: Snow, B.; Botha, G. J. J.; McLaughlin, J. A.; Hillier, A. Bibcode: 2018A&A...609A.100S Altcode: 2017arXiv171100683S
Aims: We aim to investigate the onset of 2D time-dependent magnetic reconnection that is triggered using an external (non-local) velocity driver located away from, and perpendicular to, an equilibrium Harris current sheet. Previous studies have typically utilised an internal trigger to initiate reconnection, for example initial conditions centred on the current sheet. Here, an external driver allows for a more naturalistic trigger as well as the study of the earlier stages of the reconnection start-up process.
Methods: Numerical simulations solving the compressible, resistive magnetohydrodynamic (MHD) equations were performed to investigate the reconnection onset within different atmospheric layers of the Sun, namely the corona, chromosphere and photosphere.
Results: A reconnecting state is reached for all atmospheric heights considered, with the dominant physics being highly dependent on atmospheric conditions. The coronal case achieves a sharp rise in electric field (indicative of reconnection) for a range of velocity drivers. For the chromosphere, we find a larger velocity amplitude is required to trigger reconnection (compared to the corona). For the photospheric environment, the electric field is highly dependent on the inflow speed; a sharp increase in electric field is obtained only as the velocity entering the reconnection region approaches the Alfvén speed. Additionally, the role of ambipolar diffusion is investigated for the chromospheric case and we find that the ambipolar diffusion alters the structure of the current density in the inflow region.
Conclusions: The rate at which flux enters the reconnection region is controlled by the inflow velocity. This determines all aspects of the reconnection start-up process, that is, the early onset of reconnection is dominated by the advection term in Ohm's law in all atmospheric layers. A lower plasma-β enhances reconnection and creates a large change in the electric field. A high plasma-β hinders the reconnection, yielding a sharp rise in the electric field only when the velocity flowing into the reconnection region approaches the local Alfvén speed. Title: Observational Signatures of a Kink-unstable Coronal Flux Rope Using Hinode/EIS Authors: Snow, B.; Botha, G. J. J.; Régnier, S.; Morton, R. J.; Verwichte, E.; Young, P. R. Bibcode: 2017ApJ...842...16S Altcode: 2017arXiv170505114S The signatures of energy release and energy transport for a kink-unstable coronal flux rope are investigated via forward modeling. Synthetic intensity and Doppler maps are generated from a 3D numerical simulation. The CHIANTI database is used to compute intensities for three Hinode/EIS emission lines that cover the thermal range of the loop. The intensities and Doppler velocities at simulation-resolution are spatially degraded to the Hinode/EIS pixel size (1″), convolved using a Gaussian point-spread function (3″), and exposed for a characteristic time of 50 s. The synthetic images generated for rasters (moving slit) and sit-and-stare (stationary slit) are analyzed to find the signatures of the twisted flux and the associated instability. We find that there are several qualities of a kink-unstable coronal flux rope that can be detected observationally using Hinode/EIS, namely the growth of the loop radius, the increase in intensity toward the radial edge of the loop, and the Doppler velocity following an internal twisted magnetic field line. However, EIS cannot resolve the small, transient features present in the simulation, such as sites of small-scale reconnection (e.g., nanoflares). Title: 3D WKB solution for fast magnetoacoustic wave behaviour around an X-line Authors: McLaughlin, J. A.; Botha, G. J. J.; Régnier, S.; Spoors, D. L. Bibcode: 2016A&A...591A.103M Altcode: 2016arXiv160702379M Context. We study the propagation of a fast magnetoacoustic wave in a 3D magnetic field created from two magnetic dipoles. The magnetic topology contains an X-line.
Aims: We aim to contribute to the overall understanding of MHD wave propagation within inhomogeneous media, specifically around X-lines.
Methods: We investigate the linearised, 3D MHD equations under the assumptions of ideal and cold plasma. We utilise the WKB approximation and Charpit's method during our investigation.
Results: It is found that the behaviour of the fast magnetoacoustic wave is entirely dictated by the local, inhomogeneous, equilibrium Alfvén speed profile. All parts of the wave experience refraction during propagation, where the magnitude of the refraction effect depends on the location of an individual wave element within the inhomogeneous magnetic field. The X-line, along which the Alfvén speed is identically zero, acts as a focus for the refraction effect. There are two main types of wave behaviour: part of the wave is either trapped by the X-line or escapes the system, and there exists a critical starting region around the X-line that divides these two types of behaviour. For the set-up investigated, it is found that 15.5% of the fast wave energy is trapped by the X-line.
Conclusions: We conclude that linear, β = 0 fast magnetoacoustic waves can accumulate along X-lines and thus these will be specific locations of fast wave energy deposition and thus preferential heating. The work here highlights the importance of understanding the magnetic topology of a system. We also demonstrate how the 3D WKB technique described in this paper can be applied to other magnetic configurations. Title: Chromospheric seismology above sunspot umbrae Authors: Snow, B.; Botha, G. J. J.; Régnier, S. Bibcode: 2015A&A...580A.107S Altcode: 2015arXiv150707371S Context. The acoustic resonator is an important model for explaining the three-minute oscillations in the chromosphere above sunspot umbrae. The steep temperature gradients at the photosphere and transition region provide the cavity for the acoustic resonator, which allows waves to be both partially transmitted and partially reflected.
Aims: In this paper, a new method of estimating the size and temperature profile of the chromospheric cavity above a sunspot umbra is developed.
Methods: The magnetic field above umbrae is modelled numerically in 1.5D with slow magnetoacoustic wave trains travelling along magnetic fieldlines. Resonances are driven by applying the random noise of three different colours - white, pink, and brown - as small velocity perturbations to the upper convection zone. Energy escapes the resonating cavity and generates wave trains moving into the corona. Line-of-sight integration is also performed to determine the observable spectra through SDO/AIA.
Results: The numerical results show that the gradient of the coronal spectra is directly correlated with the chromosperic temperature configuration. As the chromospheric cavity size increases, the spectral gradient becomes shallower. When line-of-sight integration is performed, the resulting spectra demonstrate a broadband of excited frequencies that is correlated with the chromospheric cavity size. The broadband of excited frequencies becomes narrower as the chromospheric cavity size increases.
Conclusions: These two results provide a potentially useful diagnostic for the chromospheric temperature profile by considering coronal velocity oscillations. Title: Simulation of the observed coronal kink instability and its implications for the SDO/AIA Authors: Srivastava, A. K.; Botha, G. J. J.; Arber, T. D.; Kayshap, P. Bibcode: 2013AdSpR..52...15S Altcode: 2013arXiv1301.2927S Srivastava et al. (2010) have observed a highly twisted coronal loop, which was anchored in AR10960 during the period 04:43 UT-04:52 UT on 4 June 2007. The loop length and radius are approximately 80 Mm and 4 Mm, with a twist of 11.5 π. These observations are used as initial conditions in a three dimensional nonlinear magnetohydrodynamic simulation with parallel thermal conduction included. The initial unstable equilibrium evolves into the kink instability, from which synthetic observables are generated for various high-temperature filters of SDO/AIA. These observables include temporal and spatial averaging to account for the resolution and exposure times of SDO/AIA images. Using the simulation results, we describe the implications of coronal kink instability as observables in SDO/AIA filters. Title: Formation of magnetic flux tubes in cylindrical wedge geometry Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E. Bibcode: 2012GApFD.106..701B Altcode: Three-dimensional (3D) MHD numerical simulations have not been able to demonstrate convincingly the spontaneous formation of large vertical flux tubes. Two-dimensional (2D) magnetoconvection in axisymmetric cylinders forms a central magnetic flux tube surrounded by annular convection rings. To study the robustness of this type of solution in three dimensions, the nonlinear resistive MHD equations are solved numerically in a 3D cylindrical wedge from an initially uniform vertical magnetic field. It is shown that the 2D result is retrieved for small domain radii. However, for larger radii the central axis loses its importance and in this case many convection cells form in the numerical domain. Magnetic flux is captured between cells where flow converges and the reduced amount of flux that congregates at the central axis is eroded by the surrounding convection. Title: Observation and Simulation of Coronal Kink Instability Authors: Srivastava, Abhishek K.; Botha, G. J. J.; Arber, T. D. Bibcode: 2012cosp...39.1881S Altcode: 2012cosp.meet.1881S No abstract at ADS Title: Observational Signatures of the Coronal Kink Instability with Thermal Conduction Authors: Botha, G. J. J.; Arber, T. D.; Srivastava, Abhishek K. Bibcode: 2012ApJ...745...53B Altcode: 2011arXiv1111.0456B It is known from numerical simulations that thermal conduction along magnetic field lines plays an important role in the evolution of the kink instability in coronal loops. This study presents the observational signatures of the kink instability in long coronal loops when parallel thermal conduction is included. The three-dimensional nonlinear magnetohydrodynamic equations are solved numerically to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The loop has length 80 Mm, width 8 Mm, and an initial maximum twist of Φ = 11.5π, where Φ is a function of the radius. The initial loop parameters are obtained from a highly twisted loop observed in the Transition Region and Coronal Explorer (TRACE) 171 Å wave band. Synthetic observables are generated from the data. These observables include spatial and temporal averaging to account for the resolution and exposure times of TRACE images. Parallel thermal conduction reduces the maximum local temperature by up to an order of magnitude. This means that different spectral lines are formed and different internal loop structures are visible with or without the inclusion of thermal conduction. However, the response functions sample a broad range of temperatures. The result is that the inclusion of parallel thermal conductivity does not have as large an impact on observational signatures as the order of magnitude reduction in the maximum temperature would suggest; the net effect is a blurring of internal features of the loop structure. Title: Coronal Kink Instability With Parallel Thermal Conduction Authors: Botha, Gert J. J.; Arber, Tony D.; Hood, Alan W.; Srivastava, A. K. Bibcode: 2012csem.conf....7B Altcode: Thermal conduction along magnetic field lines plays an important role in the evolution of the kink instability in coronal loops. In the nonlinear phase of the instability, local heating occurs due to reconnection, so that the plasma reaches high temperatures. To study the effect of parallel thermal conduction in this process, the 3D nonlinear magnetohydrodynamic (MHD) equations are solved for an initially unstable equilibrium. The initial state is a cylindrical loop with zero net current. Parallel thermal conduction reduces the local temperature, which leads to temperatures that are an order of magnitude lower than those obtained without thermal conduction. This process is important on the timescale of fast MHD phenomena; it reduces the kinetic energy released by an order of magnitude. The impact of this process on observational signatures is presented. Synthetic observables are generated that include spatial and temporal averaging to account for the resolution and exposure times of TRACE images. It was found that the inclusion of parallel thermal conductivity does not have as large an impact on observables as the order of magnitude reduction in the maximum temperature would suggest. The reason is that response functions sample a broad range of temperatures, so that the net effect of parallel thermal conduction is a blurring of internal features of the loop structure. Title: Nonlinear Three-dimensional Magnetoconvection around Magnetic Flux Tubes Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E. Bibcode: 2011ApJ...731..108B Altcode: Magnetic flux in the solar photosphere forms concentrations from small scales, such as flux elements, to large scales, such as sunspots. This paper presents a study of the decay process of large magnetic flux tubes, such as sunspots, on a supergranular scale. Three-dimensional nonlinear resistive magnetohydrodynamic numerical simulations are performed in a cylindrical domain, initialized with axisymmetric solutions that consist of a well-defined central flux tube and an annular convection cell surrounding it. As the nonlinear convection evolves, the annular cell breaks up into many cells in the azimuthal direction, allowing magnetic flux to slip between cells away from the central flux tube (turbulent erosion). This lowers magnetic pressure in the central tube, and convection grows inside the tube, possibly becoming strong enough to push the tube apart. A remnant of the central flux tube persists with nonsymmetric perturbations caused by the convection surrounding it. Secondary flux concentrations form between convection cells away from the central tube. Tube decay is dependent on the convection around the tube. Convection cells forming inside the tube as time-dependent outflows will remove magnetic flux. (This is most pronounced for small tubes.) Flux is added to the tube when flux caught in the surrounding convection is pushed toward it. The tube persists when convection inside the tube is sufficiently suppressed by the remaining magnetic field. All examples of persistent tubes have the same effective magnetic field strength, consistent with the observation that pores and sunspot umbrae all have roughly the same magnetic field strength. Title: Chromospheric Resonances above Sunspot Umbrae Authors: Botha, G. J. J.; Arber, T. D.; Nakariakov, V. M.; Zhugzhda, Y. D. Bibcode: 2011ApJ...728...84B Altcode: Three-minute oscillations are observed in the chromosphere above sunspot umbrae. One of the models used to explain these oscillations is that of a chromospheric acoustic resonator, where the cavity between the photosphere and transition region partially reflects slow magnetoacoustic waves to form resonances in the lower sunspot atmosphere. We present a phenomenological study that compares simulation results with observations. The ideal magnetohydrodynamic equations are used with a uniform vertical magnetic field and a temperature profile that models sunspot atmospheres above umbrae. The simulations are initialized with a single broadband pulse in the vertical velocity inside the convection zone underneath the photosphere. The frequencies in the spectrum of the broadband pulse that lie below the acoustic cutoff frequency are filtered out so that frequencies equal and above the acoustic cutoff frequency resonate inside the chromospheric cavity. The chromospheric cavity resonates with approximately three-minute oscillations and is a leaky resonator, so that these oscillations generate traveling waves that propagate upward into the corona. Thus, there is no requirement that a narrowband three-minute signal is present in the photosphere to explain the narrowband three-minute oscillations in the chromosphere and corona. The oscillations in the chromospheric cavity have larger relative amplitudes (normalized to the local sound speed) than those in the corona and reproduce the intensity fluctuations of observations. Different umbral temperature profiles lead to different peaks in the spectrum of the resonating chromospheric cavity, which can explain the frequency shift in sunspot oscillations over the solar cycle. Title: Thermal conduction effects on the kink instability in coronal loops Authors: Botha, G. J. J.; Arber, T. D.; Hood, A. W. Bibcode: 2011A&A...525A..96B Altcode: Context. Heating of the solar corona by nanoflares, which are small transient events in which stored magnetic energy is dissipated by magnetic reconnection, may occur as the result of the nonlinear phase of the kink instability (Hood et al. 2009). Because of the high temperatures reached through these reconnection events, thermal conduction cannot be ignored in the evolution of the kink instability.
Aims: To study the effect of thermal conduction on the nonlinear evolution of the kink instability of a coronal loop. To assess the efficiency of loop heating and the role of thermal conduction, both during the kink instability and for the long time evolution of the loop.
Methods: Numerically solve the 3D nonlinear magnetohydrodynamic equations to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The initial state has zero net current. A comparison is made of the time evolution of the loop with thermal conduction and without thermal conduction.
Results: Thermal conduction along magnetic field lines reduces the local temperature. This leads to temperatures that are an order of magnitude lower than those obtained in the absence of thermal conductivity. Consequently, different spectral lines are activated with and without the inclusion of thermal conduction, which have consequences for observations of solar corona loops. The conduction process is also important on the timescale of the fast magnetohydrodynamic phenomena. It reduces the kinetic energy released by an order of magnitude.
Conclusions: Thermal conduction plays an essential role in the kink instability of coronal loops and cannot be ignored in the forward modelling of such loops. Title: Effect of Solar Chromospheric Neutrals on Equilibrium Field Structures Authors: Arber, T. D.; Botha, G. J. J.; Brady, C. S. Bibcode: 2009ApJ...705.1183A Altcode: Solar coronal equilibrium fields are often constructed by nonlinear force-free field (NLFFF) extrapolation from photospheric magnetograms. It is well known that the photospheric field is not force-free and the correct lower boundary for NLFFF construction ought to be the top of the chromosphere. To compensate for this, pre-filtering algorithms are often applied to the photospheric data to remove the non-force-free components. Such pre-filtering models, while physically constrained, do not address the mechanisms that may be responsible for the field becoming force-free. The chromospheric field can change through, for example, field expansion due to gravitational stratification, reconnection, or flux emergence. In this paper, we study and quantify the effect of the chromospheric neutrals on equilibrium field structures. It is shown that, depending on the degree to which the photospheric field is not force-free, the chromosphere will change the structure of the equilibrium field. This is quantified to give an estimate of the change in α profiles one might expect due to neutrals in the chromosphere. Simple scaling of the decay time of non-force-free components of the magnetic field due to chromospheric neutrals is also derived. This is used to quantify the rate at which, or equivalent at which height, the chromosphere is expected to become force-free. Title: Numerical simulations of rotating axisymmetric sunspots Authors: Botha, G. J. J.; Busse, F. H.; Hurlburt, N. E.; Rucklidge, A. M. Bibcode: 2008MNRAS.387.1445B Altcode: 2008MNRAS.tmp..702B; 2008arXiv0804.4429B A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain. Title: Numerical simulations of convection around magnetic features in the solar convection zone Authors: Botha, Gert; Rucklidge, Alastair; Hurlburt, Neal Bibcode: 2008cosp...37..354B Altcode: 2008cosp.meet..354B On the solar surface, magnetic flux elements collect in regions of converging flow and grow in field strength to become pores. In order to investigate convection around these magnetic flux tubes, we initialize a cylindrical simulation with an axisymmetric solution consisting of a flux tube surrounded by an inflowing collar flow. This is allowed to evolve using the 3D nonlinear magnetohydrodynamic equations for compressible resistive flow. The axisymmetric collar flow breaks into convection cells around the flux tube that are highly dynamic. Through vigorous convection they change the shape of the central magnetic flux tube, but do not succeed in destroying its integrity. We relate our calculation to recent helioseismic measurements of subsurface flows. Title: Nonaxisymmetric Instabilities of Convection around Magnetic Flux Tubes Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E. Bibcode: 2007ApJ...662L..27B Altcode: On the surface of the Sun, magnetic flux elements collect in regions of converging flow, grow in field strength, and become pores, which have been observed to exhibit nonaxisymmetric structure over a range of scales. Around a fully developed sunspot, as well as the fine scale of the penumbra, the moat sometimes shows a clearly observable spokelike structure at low azimuthal wavenumbers. We investigate the formation of azimuthal structure by computing the linear stability properties of fully nonlinear axisymmetric magnetoconvection, which takes the form of a central flux tube surrounded by a convecting field-free region. We find steady and oscillatory instabilities with a preferred azimuthal wavenumber. The unstable modes are concentrated in the convecting region close to the outer edge of the flux tube. The instability is driven by convection and is not a magnetic fluting instability. Title: Numerical simulations of sunspots Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E. Bibcode: 2007IAUS..239..507B Altcode: No abstract at ADS Title: Differential rotation and angular momentum Authors: Botha, G. J. J.; Evangelidis, E. A. Bibcode: 2007IAUS..239..451B Altcode: No abstract at ADS Title: Reply to comment on ``Relativistic Landau resonances'' Authors: Botha, G. J. J.; Evangelidis, E. A. Bibcode: 2007JGRA..112.5206B Altcode: 2007JGRA..11205206B No abstract at ADS Title: Numerical Simulations of Rotating Sunspots Authors: Botha, G. J. J.; Rucklidge, A. M.; Busse, F. H.; Hurlburt, N. E. Bibcode: 2006ESASP.617E..53B Altcode: 2006soho...17E..53B No abstract at ADS Title: Converging and diverging convection around axisymmetric magnetic flux tubes Authors: Botha, G. J. J.; Rucklidge, A. M.; Hurlburt, N. E. Bibcode: 2006MNRAS.369.1611B Altcode: 2006MNRAS.tmp..605B A numerical model of idealized sunspots and pores is presented, where axisymmetric cylindrical domains are used with aspect ratios (radius versus depth) up to 4. The model contains a compressible plasma with density and temperature gradients simulating the upper layer of the Sun's convection zone. Non-linear magnetohydrodynamic equations are solved numerically and time-dependent solutions are obtained where the magnetic field is pushed to the centre of the domain by convection cells. This central magnetic flux bundle is maintained by an inner convection cell, situated next to it and with a flow such that there is an inflow at the top of the numerical domain towards the flux bundle. For aspect ratio 4, a large inner cell persists in time, but for lower aspect ratios it becomes highly time dependent. For aspect ratios 2 and 3 this inner convection cell is smaller, tends to be situated towards the top of the domain next to the flux bundle, and appears and disappears with time. When it is gone, the neighbouring cell (with an opposite sense of rotation, i.e. outflow at the top) pulls the magnetic field away from the central axis. As this happens a new inner cell forms with an inflow which pushes the magnetic field towards the centre. This suggests that to maintain their form, both pores and sunspots need a neighbouring convection cell with inflow at the top towards the magnetic flux bundle. This convection cell does not have to be at the top of the convection zone and could be underneath the penumbral structure around sunspots. For an aspect ratio of 1, there is not enough space in the numerical domain for magnetic flux and convection to separate. In this case the solution oscillates between two steady states: two dominant convection cells threaded by magnetic field and one dominant cell that pushes magnetic flux towards the central axis. Title: Relativistic Landau resonances Authors: Evangelidis, E. A.; Botha, G. J. J. Bibcode: 2005JGRA..110.2216E Altcode: 2005JGRA..11002216E The possible interactions between plasma waves and relativistic charged particles are considered. An electromagnetic perturbation in the plasma is formulated as an elliptically polarized wave, and the collisionless plasma is described by a distribution in phase space, which is realized in cylindrical coordinates. The linearized Vlasov equation is solved in the semi-relativistic limit, to obtain the distribution function in the rest frame of the observer. The perturbed currents supported by the ionized medium are then calculated, so that an expression can be written for the total amount of energy available for transfer through the Landau mechanism. It is found that only certain modes of the perturbed current are available for this energy transfer. The final expressions are presented in terms of Stokes parameters, and applied to the special cases of a thermal as well as a nonthermal plasma. The thermal plasma is described by a Maxwellian distribution, while two nonthermal distributions are considered: the kappa distribution and a generalized Weibull distribution. Title: Cylindrical linear force-free magnetic fields with toroidal flux surfaces Authors: Botha, G. J. J.; Evangelidis, E. A. Bibcode: 2004MNRAS.350..375B Altcode: A linear force-free field solution is presented in cylindrical coordinates, formulated in terms of trigonometric and Bessel functions. A numerical exploration has revealed that this solution describes magnetic field lines that meander in Cartesian space, as well as field lines that lie on toroidal flux surfaces. These tori are in (or close to) the plane perpendicular to the cylindrical axis. Nested tori, as well as tori with shells that have finite thickness, were found. The parameter space of the solution shows that the tori exist within a bounded range of values. Title: Cylindrical Solutions of Force Free Magnetic Fields Authors: Botha, G. J. J.; Evangelidis, E. A. Bibcode: 2004IAUS..219..743B Altcode: 2003IAUS..219E.148B A general method for the solution of force free magnetic fields in cylindrical coordinates is presented and a solution is formulated as a combination of trigonometric and Bessel functions. The numerical exploration has revealed the existence of trapped and untrapped orbits in the sense that they remain (or not) inside a specific part of space volume. Most interestingly orbits have been identified that wind on toroidal surfaces perpendicular to the z-axis. Title: Alfvén Wave-Charged Particle Interactions through Landau Damping Authors: Evangelidis, E. A.; Botha, G. J. J. Bibcode: 2004IAUS..219..748E Altcode: 2003IAUS..219E.147E The possibility of Landau damping of energetic particles in resonance with Alfven waves was first raised in the context of pulsar envelopes some decades ago. Today due to satellite observations there is a renewed interest in the topic as one of the possible mechanisms for transfer of energy in the solar atmosphere and solar wind. We therefore analyze the interaction of elliptically polarised Alfven waves with a semi-relativistic collisionless charged particle distribution by using the linearised Vlasov equation. Taking into consideration developments in the theory of Bessel functions we write the results in a concise form. The transfer of energy is thus expressed in terms of particle parameters as well as the Stokes parameter which is associated with the total energy of the wave. The frequency of the Alfven wave must be comparable with or larger than that of the cyclotron frequency in order to play an efficient role in the absorption or emission of the energy of the charged particle in agreement with the theorem of energy conservation. The role of the relative velocity of the particles against the Alfven velocity is elucidated in a natural way as a result of relativistic considerations. Title: A new family of solutions of the force-free field equation Authors: Evangelidis, E. A.; Botha, G. J. J. Bibcode: 2003SoPh..213...69E Altcode: A new family of solutions has been found for force-free magnetic fields and Beltrami flows, which admits a complete classification in terms of the eigenvalues of the problem. In the absence of boundary values to determine them uniquely, the eigenvalues correspond to the entire set of real numbers, except for zero. The eigenvalues are degenerate in that each eigenvalue has many eigensolutions associated with it. For each eigensolution we have been able to identify sets of equilibrium or null points and lines. The linear mappings of these null points and lines are all unstable. Finally, we derive the first integral of energy associated with this family of solutions. Title: A new family of solutions of the force free field equation Authors: Evangelidis, E. A.; Botha, G. J. J. Bibcode: 2002ESASP.505..401E Altcode: 2002solm.conf..401E; 2002IAUCo.188..401E A new family of solutions has been found for force free magnetic fields and Beltrami flows, which admits a complete classification in terms of the eigenvalues of the problem. In the absence of boundary values to determine them uniquely, the eigenvalues correspond to the entire set of real numbers, except for zero. The eigenvalues are degenerate in that each eigenvalue has many eigensolutions associated with it. For each eigensolution we have been able to identify dense sets of equilibrium or null points and lines. We present a linear analysis of the magnetic field line configurations around these null points and lines, and derive the first integral of energy associated with this family of solutions. Title: Photoionized Plasma Calculations using Laboratory and Astrophysical Models Authors: Phillips, M. E.; Keenan, F. P.; Rose, S. J.; Botha, G. J. J.; Foord, M. E.; Heeter, R. F.; Ferland, G. J. Bibcode: 2001ASPC..247..123P Altcode: 2001scpp.conf..123P No abstract at ADS Title: A. Cylindrical Formulation of Force Free Magnetic Fields Authors: Evangelidis, E. A.; Botha, G. J. J. Bibcode: 2001IAUS..203..270E Altcode: It is shown that the behaviour of force free magnetic fields is governed by the existence of a first integral of energy. We give its explicit expression and we identify the parametric space where these fields are ergodic or non-ergodic. We further compare results based on toroidal geometries with results based on cylindrical geometries, to show the modification due to toroidal curvature. Title: A developed stage of Alfvén wave phase mixing Authors: Botha, G. J. J.; Arber, T. D.; Nakariakov, V. M.; Keenan, F. P. Bibcode: 2000A&A...363.1186B Altcode: Alfvén wave phase mixing is an extensively studied mechanism for dissipating wave energy in an inhomogeneous medium. It is common in the vast majority of phase mixing papers to assume that even though short scale lengths and steep gradients develop as a result of phase mixing, nonlinear wave coupling does not occur. However, weakly nonlinear studies have shown that phase mixing generates magnetoacoustic modes. Numerical results are presented which show the nonlinear generation of magnetosonic waves by Alfvén wave phase mixing. The efficiency of the effect is determined by the wave amplitude, the frequency of the Alfvén waves and the gradient in the background Alfvén speed. Weakly nonlinear theory has shown that the amplitude of the fast magnetosonic wave grows linearly in time. The simulations presented in this paper extend this result to later times and show saturation of the fast magnetosonic component at amplitudes much lower than that of the Alfvén wave. For the case where Alfvén waves are driven at the boundary, simulating photospheric footpoint motion, a clear modulation of the saturated amplitude is observed. All the results in this paper are for a low amplitude (<= 0.1), single frequency Alfvén wave and a uniform background magnetic field in a two dimensional domain. For this simplified geometry, and with a monochromatic driver, we concluded that the nonlinear generation of fast modes has little effect on classical phase mixing. Title: Extreme ultraviolet emission lines of Nixii in laboratory and solar spectra Authors: Keenan, F. P.; Botha, G. J. J.; Matthews, A.; Lawson, K. D.; Coffey, I. H. Bibcode: 2000MNRAS.318...37K Altcode: Wavelengths for emission lines arising from 3s23p5-3s3p6 and 3s23p5-3s23p43d transitions in Nixii have been measured in extreme ultraviolet spectra of the Joint European Torus (JET) tokamak. The 3s23p5 2P1/2- 3s23p4(3P)3d 2D3/2 line is found to lie at 152.90+/-0.02Å, a significant improvement over the previous experimental determination of 152.95+/-0.5Å. This new wavelength is in good agreement with a solar identification at 152.84+/-0.06Å, confirming the presence of this line in the solar spectrum. The Nixii feature at 152.15Å may be a result only of the 3s23p5 2P3/2- 3s23p4(3P)3d 2D5/2 transition, rather than a blend of this line with 3s23p5 2P3/2- 3s23p4(3P)3d 2P1/2, as previously suggested. Unidentified emission lines at 295.32 and 317.61Å in solar flare spectra from the Skylab mission are tentatively identified as the 3s23p5 2P3/2-3s3p6 2S1/2 and 3s23p5 2P1/2-3s3p6 2S1/2 transitions in Nixii, which have laboratory wavelengths of 295.33 and 317.50Å, respectively. Additional support for these identifications is provided by the line intensity ratio for the solar features, which shows good agreement between theory and observation. Title: The structure of force-free magnetic fields Authors: Evangelidis, E. A.; Vaughan, L. L.; Botha, G. J. J. Bibcode: 2000SoPh..193...17E Altcode: Incontrovertible evidence is presented that the force-free magnetic fields exhibit strong stochastic behavior. Arnold's solution is given with the associated first integral of energy. A subset of the solution is shown to be non-ergodic whereas the full solution is shown to be ergodic. The first integral of energy is applied to the study of these fields to prove that the equilibrium points of such magnetic configurations are saddle points. Finally, the potential function of the first integral of energy is shown to be a member of the Helmholtz family of solutions. Numerical results corroborate the theoretical conclusions and demonstrate the robustness of the energy integral, which remains constant for arbitrarily long computing times.