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* News 04/04/20 * The archive is using a new backend database. This has thrown up a few SQL errors in the last few days. If you have any issues please email adavey@nso.edu with either the number of eprint you are trying to edit or a link to your preprint.

Diagnostics of plasma ionisation using torsional Alfvén waves  

Istvan Ballai   Submitted: 2020-02-20 02:39

Using the recently observed torsional Alfvén waves in solar prominences, we determine the ionisation state of the plasma by taking into account that Alfvén waves propagate in a partially ionised prominence plasma. We derive the evolutionary equation of waves and compare the analytical solutions to observations to determine the number density of neutrals.Using a single fluid plasma approximation, where the wave damping is provided by the Cowling resistivity, we study the temporal evolution of waves. By comparing the solution of equations with observational data (period, amplitude, propagation speed), we determined the value of the Cowling resistivity that led us to draw a conclusion on the amount of neutrals in the partially ionised plasma, a quantity that cannot be measured directly or indirectly.Our results show that damped torsional Alfvén waves are an ideal diagnostic tool for the ionisation state of the plasma. Using a simple model, we find that at the observational temperature of torsional Alfvén waves, the number of neutrals, is of the order of 5 x 1010 cm-3.

Authors: Istvan Ballai
Projects:

Publication Status: in press
Last Modified: 2020-02-24 14:13
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Magnetic Rayleigh-Taylor Instability at a Contact Discontinuity With Oblique Magnetic Field  

Istvan Ballai   Submitted: 2019-12-03 04:03

In the present work we investigate the nature of the magnetic Rayleigh-Taylor instability at a density interface permeated by an oblique, homogeneous magnetic field in an incompressible limit. Using the system of linearised ideal incompressible magnetohydrodynamics (MHD) equations we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by solving numerically the dispersion relation. The critical wavenumber at which waves become unstable, present for a parallel magnetic field, disappears, due to the inclination of the magnetic field and instead waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When applying our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angle; from 0.5 degrees up to 30 degrees. These results highlight the diagnostic possibility of our study.

Authors: E. Vickers, I. Ballai, R. Erdelyi
Projects: None

Publication Status: accepted
Last Modified: 2019-12-04 11:30
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Linear waves in a non-equilibrium ionisation partially ionised plasma  

Istvan Ballai   Submitted: 2019-05-24 13:48

We aim to investigate the properties of linear Alfvén and slow magnetoacoustic waves in a partially ionised plasma in ionisation non-equilibrium. The propagation characteristics of these 5 waves are studied within the framework of a two-fluid plasma in terms of the collisional strength between heavy particles for different degrees of ionisation. In the ionisation non-equilibrium state the rates of ionisation and recombinations are not equal. For analytical progress we assume a background that is ionisation equilibrium, the non-equilibrium is driven by perturbations in the system, therefore, non-equilibrium effects are related to the perturbed state of the plasma. Using simple analytical methods, we show that ionisation non-equilibrium can provide an additional coupling between ions and neutrals (implicitly a secondary damping mechanism in the collisionless limit) and this process is able to keep the neutrals in the system even in the collisionless limit. Due to the coupling between different species waves become dispersive.

The present study improves our understanding of the complexity of dynamical processes partially ionised plasma in the lower solar atmosphere and solar prominences. Our results clearly show that the problem of partial ionisation and non-equilibrium ionisation introduce new aspects of plasma dynamics with consequences on the evolution waves and their dissipation.

Authors: Istvan Ballai
Projects: None

Publication Status: Frontiers in Astronomy, Submitted
Last Modified: 2019-05-24 13:48
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Dispersive shock waves in partially ionised plasmas  

Istvan Ballai   Submitted: 2018-10-18 23:12

Compressional waves propagating in the partially ionised solar lower atmospheric plasmas can easily steepen into nonlinear waves, including shocks. Here we investigate the effect of weak dispersion generated by Hall currents perpendicular to the ambient magnetic field on the characteristics of shock waves. Our study will also focus on the interplay between weak dispersion and partial ionisation of the plasma. Using a multiple scale technique we derive the governing equation in the form of a Korteweg-de Vries-Burgers equation. The effect of weak dispersion on shock waves is obtained using a perturbation technique. The secular behaviour of second order terms is addressed with the help of a renormalisation technique. Our results show that dispersion modifies the characteristics of shock waves and this change is dependent also on the ionisation degree of the plasma. Dispersion can create short lived oscillations in the shocked plasma. The shock fronts become wider with the increase in the number of neutrals in the plasma.

Authors: I. Ballai, E. Forgacs-Dajka, A. Marcu
Projects: None

Publication Status: Accepted
Last Modified: 2018-10-24 10:43
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Dissipative instability in a partially ionised prominence slab  

Istvan Ballai   Submitted: 2017-03-23 05:45

We investigate the nature of dissipative instability appearing in a prominence planar thread filled with partially ionised plasma in the incompressible limit. The importance of partial ionisation is investigated in terms of the ionisation factor and wavelength of waves propagating in the slab. To highlight the role of partial ionisation, we have constructed models describing various situations we can meet in solar prominence fine structure. Matching the solutions for the transversal component of the velocity and total pressure at the interfaces between the prominence slab and surrounding plasmas, we derived a dispersion relation whose imaginary part describes the evolution of the instability. Results are obtained in the limit of weak dissipation. We have investigated the appearance of instabilities in prominence dark plumes using single and two-fluid approximations. We show that dissipative instabilities appear for flow speeds that are less than the Kelvin-Helmholtz instability threshold. The onset of instability is determined by the equilibrium flow strength, the ionisation factor of the plasma, the wavelength of waves and the ion-neutral collisional rate. For a given wavelength and for ionisation degrees closer to a neutral gas, the propagating waves become unstable for a narrow band of flow speeds, meaning that neutrals have a stabilising effect. Our results show that the partially ionised plasma describing prominence dark plumes becomes unstable only in a two-fluid (charged particles-neutrals) model, that is for periods that are smaller than the ion-neutral collision time. The present study improves our understanding of stability of solar prominences and the role of partial ionisation in destabilising the plasma. We show the necessity of two-fluid approximation when discussing the nature of instabilities: waves in a single fluid approximation show a great deal of stability.

Authors: I. Ballai, B. Pinter, R. Oliver and M. Alexandrou
Projects: None

Publication Status: A&A (in press)
Last Modified: 2017-03-23 14:51
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Dissipative instability in partially ionised prominence plasmas  

Istvan Ballai   Submitted: 2015-03-26 16:10

We investigate the nature of dissipative instability at the boundary (seen here as tangential discontinuity) between the viscous corona and the partially ionised prominence plasma in the incompressible limit. The importance of the partial ionisation is investigated in terms of the ionisation fraction. Matching the solutions for the transversal component of the velocity and total pressure at the interface between the prominence and coronal plasmas, we derive a dispersion relation whose imaginary part describes the evolution of the instability. Results are obtained in the limit of weak dissipation. Using simple analytical methods, we show that dissipative instabilities appear for flow speeds that are lower than the Kelvin-Helmholtz instability threshold. While viscosity tends to destabilise the plasma, the effect of partial ionisation (through the Cowling resistivity) will act towards stabilising the interface. For ionisation degrees closer to a neutral gas the interface will be unstable for larger values of equilibrium flow. The same principle is assumed when studying the appearance of instability at the interface between prominences and dark plumes. The unstable mode appearing in this case has a very small growth rate and dissipative instability cannot explain the appearance of flows in plumes. The present study improves our understanding of the complexity of dynamical processes at the interface of solar prominences and solar corona, and the role partial ionisation can have on the stability of the plasma. Our results clearly show that the problem of partial ionisation introduces new aspects of plasma stability with consequences on the evolution of solar prominences.

Authors: I. Ballai, R. OIiver, M. Alexandrou
Projects: None

Publication Status: in press, Astron. & Astrophys.
Last Modified: 2015-03-27 14:07
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Nonlinear effects in resonant layers in solart and space plasmas  

Istvan Ballai   Submitted: 2010-11-26 07:01

The present paper reviews recent advances in the theory of nonlinear driven magnetohydrodynamic (MHD) waves in slow and Alfvén resonant layers. Simple estimations show that in the vicinity of resonant positions the amplitude of variables can grow over the threshold where linear descriptions are valid. Using the method of matched asymptotic expansions, governing equations of dynamics inside the dissipative layer and jump conditions across the dissipative layers are derived. These relations are essential when studying the efficiency of resonant absorption. Nonlinearity in dissipative layers can generate new effects, such as mean flows, which can have serious implications on the stability and efficiency of the resonance.

Authors: Istvan Ballai, Michael Ruderman
Projects: None

Publication Status: accepted
Last Modified: 2010-11-27 03:00
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Mean shear flows generated by nonlinear resonant Alfvén waves  

Istvan Ballai   Submitted: 2009-07-15 09:52

In the context of resonant absorption, nonlinearity has two different manifestations. The first is the reduction in amplitude of perturbations around the resonant point (wave energy absorption). The second is the generation of mean shear flows outside the dissipative layer surrounding the resonant point. Ruderman et al. [Phys. Plasmas, 4, 75 (1997)] studied both these effects at the slow resonance in isotropic plasmas. Clack et al. [Astron. Astrophys., 494, 317 (2009)] investigated nonlinearity at the Alfvén resonance, however, they did not include the generation of mean shear flow. In this present paper, we investigate the mean shear flow, analytically, and study its properties. We find that the flow generated is parallel to the magnetic surfaces and has a characteristic velocity proportional to epsilon1/2, where epsilon is the dimensionless amplitude of perturbations far away from the resonance. This is, qualitatively, similar to the flow generated at the slow resonance. The jumps in the derivatives of the parallel and perpendicular components of mean shear flow across the dissipative layer are derived. We estimate the generated mean shear flow to be of the order of 10 km s-1 in both the solar upper chromosphere and solar corona, however, this value strongly depends on the choice of boundary conditions. It is proposed that the generated mean shear flow can produce a Kelvin-Helmholtz instability at the dissipative layer which can create turbulent motions. This instability would be an additional effect, as a Kelvin-Helmholtz instability may already exist due to the velocity field of the resonant Alfvén waves. This flow can also be superimposed onto existing large scale motions in the solar upper atmosphere.

Authors: Christopher Clack, Istvan Ballai
Projects: None

Publication Status: accepted
Last Modified: 2009-07-15 10:25
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Nonlinear resonant absorption of fast magnetoacoustic waves in strongly anisotropic and dispersive plasmas  

Istvan Ballai   Submitted: 2009-03-05 04:02

The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly anisotropic and dispersive plasmas, developed for slow resonance by Clack and Ballai [Phys. Plasmas 15(8), 2310 (2008)] and Alfvén resonance by Clack et al. [A&A 494, 317 (2009)], is used to study the weakly nonlinear interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar plasma. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localized slow or Alfvén dissipative layer and are partly reflected, dissipated and transmitted by this region. The nonlinearity parameter defined by Clack and Ballai (2008) is assumed to be small and a regular perturbation method is used to obtain analytical solutions in the slow dissipative layer. The effect of dispersion in the slow dissipative layer is to further decrease the coefficient of energy absorption, compared to its standard weakly nonlinear counterpart, and the generation of higher harmonics in the outgoing wave in addition to the fundamental one. The absorption of external drivers at the Alfvén resonance is described within the linear MHD with great accuracy.

Authors: C.T.M. Clack, I. Ballai
Projects:

Publication Status: Physics of Plasmas, accepted
Last Modified: 2010-06-16 11:19
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On the validity of nonlinear Alfvén resonance in space plasmas  

Istvan Ballai   Submitted: 2008-12-01 06:38

In the approximation of linear dissipative magnetohydrodynamics (MHD) it can be shown that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfvén (or slow) frequency of a magnetic surface. This near resonant behaviour is confined to a thin region, known as the dissipative layer, which embraces the resonant magnetic surface. Although driven MHD waves have small dimensionless amplitude far away from the resonant surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. Our aim is to study the nonlinear effects in Alfvén dissipative layer. In the present paper, the method of simplified matched asymptotic expansions developed for nonlinear slow resonant waves is used to describe nonlinear effects inside the Alfvén dissipative layer. The nonlinear corrections to resonant waves in the Alfvén dissipative layer are derived and it is proved that at the Alfvén resonance (with isotropic/anisotropic dissipation) wave dynamics can be described by the linear theory with great accuracy.

Authors: C.T.M. Clack, I. Ballai and M.S. Ruderman
Projects: None

Publication Status: Astron. & Astrophys. accepted
Last Modified: 2008-12-01 07:59
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Nonlinear theory of resonant slow waves in anisotropic and dispersive plasmas  

Istvan Ballai   Submitted: 2008-08-23 08:32

The solar corona is a typical example of a plasma with strongly anisotropic transport processes. The main dissipative mechanisms in the solar corona acting on slow magnetoacoustic waves are the anisotropic thermal conductivity and viscosity. Ballai et al. [Phys. Plasmas, 5, 252 (1998)] developed the nonlinear theory of driven slow resonant waves in such a regime. In the present paper the nonlinear behaviour of driven magnetohydrodynamic waves in the slow dissipative layer in plasmas with strongly anisotropic viscosity and thermal conductivity is expanded by considering dispersive effects due to Hall currents. The nonlinear governing equation describing the dynamics of nonlinear resonant slow waves is supplemented by a term which describes nonlinear dispersion and is of the same order of magnitude as nonlinearity and dissipation. The connection formulae are found to be similar to their non-dispersive counterparts.

Authors: Christopher Clack, Istvan Ballai
Projects: None

Publication Status: Physics of Plasmas, in press
Last Modified: 2008-08-23 09:20
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Forced oscillations of coronal loops driven by EIT waves  

Istvan Ballai   Submitted: 2008-07-08 09:46

We study the generation of transversal oscillations in coronal loops represented as a straight thin flux tube under the effect of an external driver modeling the global coronal EIT wave. We investigate how the generated oscillations depend on the nature of the driver, and the type of interaction between the two systems. We consider the oscillations of a magnetic straight cylinder with fixed-ends under the influence of an external driver modeling the force due to the global EIT wave. Given the uncertainties related to the nature of EIT waves, we first approximate the driver by an oscillatory force in time and later by a shock with a finite width. Results show that for a harmonic driver the dominant period in the generated oscillation belongs to the driver. Depending on the period of driver, compared to the natural periods of the loop, a mixture of standing modes harmonics can be initiated. In the case of a non-harmonic driver (modeling a shock wave), the generated oscillations in the loop are the natural periods only. The amplitude of oscillations is determined by the position of the driver along the tube. The full diagnosis of generated oscillations is achieved using simple numerical methods.

Authors: I. Ballai, M. Douglas, A. Marcu
Projects: None

Publication Status: A&A accepted
Last Modified: 2008-09-23 20:57
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Global coronal seismology  

Istvan Ballai   Submitted: 2007-03-20 11:59

Following the observation and analysis of large-scale coronal wave-like disturbances, we discuss the theoretical progress made in the field of global coronal seismology. Using simple mathematical techniques we determine average values for magnetic field together with a magnetic map of the quiet Sun. The interaction between global coronal waves and coronal loops allows us to study loop oscillations in a much wider context, i.e. we connect global and local coronal oscillations.

Authors: Istvan Ballai
Projects:

Publication Status: Solar Physics (in press)
Last Modified: 2007-04-12 02:57
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Slow magnetohydrodynamic waves in stratified and viscous plasmas  

Istvan Ballai   Submitted: 2006-04-06 04:43

The propagation of slow magnetohydrodynamic waves in vertical thin flux tubes embedded in a vertically stratified plasma in the presence of viscosity is shown here to be governed by the Klein-Gordon-Burgers (KGB) equation which is solved in two limiting cases assuming an isothermal medium in hydrostatic equilibrium surrounded by a quiescent environment. The results presented here can be applied to, e.g. study the propagation of slow magnetohydrodynamic waves generated by the granular buffeting motion in thin magnetic photospheric tubes. When the variation in the reduced velocity occurs over typical lengths much larger than the gravitational scale height, the KGB equation can be reduced to a Klein-Gordon equation describing the propagation of an impulse followed by a wake oscillating with the frequency reduced by viscosity and the solution has no spatial or temporal decay. However, in the other limiting case, i.e. typical variations in the reduced velocity occur over characteristic lengths much smaller than the gravitational scale height, waves have a temporal and spatial decay.

Authors: Ballai, I., Erdelyi, R. and Hargreaves, J.
Projects: None

Publication Status: Physics of Plasmas (in press)
Last Modified: 2006-04-10 15:51
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On the nature of coronal EIT waves  

Istvan Ballai   Submitted: 2005-11-01 10:32

Large-scale eruption events in the solar atmosphere can generate global waves, i.e., waves that propagate over distances comparable to the solar radius. In the low solar corona, global waves observed by SOHO EIT, generated by coronal mass ejections or flares, are usually referred to as “EIT waves.” The nature of these global waves is the subject of strong debate, and opinions are divided between different interpretations (e.g., fast magnetohydrodynamic waves, shock waves, nonwave feature, etc.). In the present Letter, we studied TRACE EUV data to show that these global coronal disturbances are indeed waves with a well-defined period. Supposing that the EIT waves transfer all their energy to interacting loops, we also estimate the minimum energy threshold carried by EIT waves.

Authors: I. Ballai, R. Erdelyi and B. Pinter
Projects: TRACE

Publication Status: ApJL (in press)
Last Modified: 2005-11-01 10:32
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On dissipative effects in solar prominences  

Istvan Ballai   Submitted: 2003-12-03 04:01

The present paper aims to discuss the possible dissipative mechanisms acting in a coronal prominence. These mechanism are discussed within the context of spatial damping of linear compressional waves. The obtained results show that the dominant mechanism is thermal radiation provided the supposition of optically thin prominence is valid. Damping due to thermal conduction is a viable attenuation mechanism provided the wavelength of the waves is small.

Authors: Istvan Ballai
Projects: None

Publication Status: A&A, 410, L17, 2003
Last Modified: 2003-12-03 04:01
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Abstracts by Author
Diagnostics of plasma ionisation using torsional Alfven waves
Magnetic Rayleigh-Taylor Instability at a Contact Discontinuity With Oblique Magnetic Field
Linear waves in a non-equilibrium ionisation partially ionised plasma
Dispersive shock waves in partially ionised plasmas
Dissipative instability in a partially ionised prominence slab
Dissipative instability in partially ionised prominence plasmas
Nonlinear effects in resonant layers in solart and space plasmas
Mean shear flows generated by nonlinear resonant Alfven waves
Nonlinear resonant absorption of fast magnetoacoustic waves in strongly anisotropic and dispersive plasmas
On the validity of nonlinear Alfven resonance in space plasmas
Nonlinear theory of resonant slow waves in anisotropic and dispersive plasmas
Forced oscillations of coronal loops driven by EIT waves
Global coronal seismology
Slow magnetohydrodynamic waves in stratified and viscous plasmas
On the nature of coronal EIT waves
On dissipative effects in solar prominences

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