arXiv subjects

J. A. McLaughlin

Publications and source records attributed to J. A. McLaughlin.

33 records · Page 2Linked to original sources

arXiv2013

Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force

Context : In the linear, β=0 MHD regime, the transient properties of MHD waves in the vicinity of 2D null points are well known. The waves are decoupled and accumulate at predictable parts of the magnetic topology: fast waves accumulate at the null point; whereas Alfvén waves cannot cross the separatricies. However, in nonlinear MHD mode conversion can occur at regions of inhomogeneous Alfvén speed, suggesting that the decoupled nature of waves may not extend to the nonlinear regime. Aims: We investigate the behaviour of low-amplitude Alfvén waves about a 2D magnetic null point in nonlinear, β= 0 MHD. Methods: We numerically simulate the introduction of low-amplitude Alfvén waves into the vicinity of a magnetic null point using the nonlinear LARE2D code. Results: Unlike in the linear regime, we find that the Alfvén wave sustains cospatial daughter disturbances, manifest in the transverse and longitudinal fluid velocity, owing to the action of nonlinear magnetic pressure gradients (viz. the ponderomotive force). These disturbances are dependent on the Alfvén wave and do not interact with the medium to excite magnetoacoustic waves, although the transverse daughter becomes focused at the null point. Additionally, an independently propagating fast magnetoacoustic wave is generated during the early stages, which transports some of the initial Alfvén wave energy towards the null point. Subsequently, despite undergoing dispersion and phase-mixing due to gradients in the Alfvén-speed profile (Grad c_A \neq 0) there is no further nonlinear generation of fast waves. Conclusions: We find that Alfvén waves at 2D cold null points behave largely as in the linear regime, however they sustain transverse and longitudinal disturbances - effects absent in the linear regime - due to nonlinear magnetic pressure gradients.

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arXiv2013

On ponderomotive effects induced by Alfven waves in inhomogeneous 2.5D MHD plasmas

Where spatial gradients in the amplitude of an Alfven wave are non-zero, a nonlinear magnetic-pressure gradient acts upon the medium (the ponderomotive force). We investigate the nature of such a force in inhomogeneous 2.5D MHD plasmas by analysing source terms in the nonlinear wave equations for the general case of inhomogeneous B and ρ, and consider supporting nonlinear numerical simulations. Our equations indicate there are two distinct classes of ponderomotive effect induced by Alfven waves in general 2.5D MHD, each with both a longitudinal and transverse manifestation; i) Geometric Effects: Gradients in the pulse geometry relative to the background magnetic field cause the wave to sustain cospatial disturbances, the longitudinal and transverse daughter disturbances - where we report on the transverse disturbance for the first time. ii) Grad (c_A) Effects: Where a pulse propagates through an inhomogeneous region (where the non-zero gradients in the Alfven-speed profile are non-zero), the nonlinear magnetic-pressure gradient acts to accelerate the plasma. Transverse gradients (phase mixing regions) excite independently propagating fast magnetoacoustic waves (generalising the result of Nakariakov et al. 1997, Solar Physics, 175, 93) and longitudinal gradients perturb along the field (thus creating static disturbances in β = 0, and slow waves in β \= 0). We additionally demonstrate that mode conversion due the nonlinear Lorentz force is a one-way process, and does not act as a mechanism to nonlinearly generate Alfven waves due to propagating magnetoacoustic waves. We conclude that these ponderomotive effects are induced by an Alfven wave propagating in any MHD medium, and have the potential to have significant consequences on the dynamics of energy transport and aspects of dissipation provided the system is sufficiently nonlinear and inhomogeneous.

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arXiv2012

On the Periodicity of Oscillatory Reconnection

Oscillatory reconnection is a time-dependent magnetic reconnection mechanism that naturally produces periodic outputs from aperiodic drivers. This paper aims to quantify and measure the periodic nature of oscillatory reconnection for the first time. We solve the compressible, resistive, nonlinear MHD equations using 2.5D numerical simulations. We identify two distinct periodic regimes: the impulsive and stationary phases. In the impulsive phase, we find the greater the amplitude of the initial velocity driver, the longer the resultant current sheet and the earlier its formation. In the stationary phase, we find that the oscillations are exponentially decaying and for driving amplitudes 6.3 - 126.2 km/s, we measure stationary-phase periods in the range 56.3 - 78.9 s, i.e. these are high frequency (0.01 - 0.02 Hz) oscillations. In both phases, we find that the greater the amplitude of the initial velocity driver, the shorter the resultant period, but note that different physical processes and periods are associated with both phases. We conclude that the oscillatory reconnection mechanism behaves akin to a damped harmonic oscillator.

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arXiv2012

Numerical Simulations of Magnetoacoustic-Gravity Waves in the Solar Atmosphere

We investigate the excitation of magnetoacoustic-gravity waves generated from localized pulses in the gas pressure as well as in vertical component of velocity. These pulses are initially launched at the top of the solar photosphere that is permeated by a weak magnetic field. We investigate three different configurations of the background magnetic field lines: horizontal, vertical and oblique to the gravitational force. We numerically model magnetoacoustic-gravity waves by implementing a realistic (VAL-C) model of solar temperature. We solve two-dimensional ideal magnetohydrodynamic equations numerically with the use of the FLASH code to simulate the dynamics of the lower solar atmosphere. The initial pulses result in shocks at higher altitudes. Our numerical simulations reveal that a small-amplitude initial pulse can produce magnetoacoustic-gravity waves, which are later reflected from the transition region due to the large temperature gradient. The atmospheric cavities in the lower solar atmosphere are found to be the ideal places that may act as a resonator for various oscillations, including their trapping and leakage into the higher atmosphere. Our numerical simulations successfully model the excitation of such wave modes, their reflection and trapping, as well as the associated plasma dynamics.

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arXiv2012

Linear and nonlinear MHD mode coupling of the fast magnetoacoustic wave about a 3D magnetic null point

Context: Coronal magnetic null points have been implicated as possible locations for localised heating events in 2D models. We investigate this possibility about fully 3D null points. Aims: We investigate the nature of the fast magnetoacoustic wave about a fully 3D magnetic null point, with a specific interest in its propagation, and we look for evidence of MHD mode coupling and/or conversion to the Alfvén mode. Methods: A special fieldline and flux-based coordinate system was constructed to permit the introduction of a pure fast magnetoacoustic wave in the vicinity of proper and improper 3D null points. We considered the ideal, β = 0, MHD equations, which are solved using the LARE3D numerical code. The constituent modes of the resulting wave were isolated and identified using the special coordinate system. Numerical results were supported by analytical work derived from perturbation theory and a linear implementation of the WKB method. Results: An initially pure fast wave is found to be permanently decoupled from the Alfvén mode both linearly and nonlinearly for both proper and improper 3D null points. The pure fast mode also generates and sustains a nonlinear disturbance aligned along the equilibrium magnetic field. The resulting pure fast magnetoacoustic pulse has transient behaviour, which is found to be governed by the (equilibrium) Alfvén-speed profile, and a refraction effect focuses all the wave energy towards the null point. Conclusions: Thus, the main results from previous 2D work do indeed carry over to the fully 3D magnetic null points and

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arXiv2012

Review article: MHD wave propagation near coronal null points of magnetic fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfven speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfven wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfven-speed profile. In a $β=0$ plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfven wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfven wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfven wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing.

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arXiv2012

Generation of quasi-periodic waves and flows in the solar atmosphere by oscillatory reconnection

We investigate the long-term evolution of an initially buoyant magnetic flux tube emerging into a gravitationally-stratified coronal hole environment and report on the resulting oscillations and outflows. We perform 2.5D nonlinear numerical simulations, generalizing the models of McLaughlin et al. (2009) and Murray et al. (2009). We find that the physical mechanism of oscillatory reconnection naturally generates quasi-periodic vertical outflows, with a transverse/swaying aspect. The vertical outflows consist of both a periodic aspect and evidence of a positively-directed flow. The speed of the vertical outflow (20-60 km/s) is comparable to those reported in the observational literature. We also perform a parametric study varying the magnetic strength of the buoyant flux tube and find a range of associated periodicities: 1.75-3.5 min. Thus, the mechanism of oscillatory reconnection may provide a physical explanation to some of the high-speed, quasi-periodic, transverse outflows/jets recently reported by a multitude of authors and instruments.

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arXiv2011

Determination of sub-resolution structure of jet by solar magnetoseismology

A thin dark thread is observed in a UV/EUV solar jet in the 171A, 193A and 211A and partially in 304A. The dark thread appears to originate in the chromosphere but its temperature does not appear to lie within the passbands of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We therefore implement solar magnetoseismology to estimate the plasma parameters of the dark thread. A propagating fast kink (transverse) wave is observed to travel along the dark thread. The wave is tracked over a range of ~7000km by placing multiple slits along the axis of the dark thread. The phase speed and amplitude of the wave are estimated and magnetoseismological theory is employed to determine the plasma parameters. We are able to estimate the plasma temperature, density gradient, magnetic field gradient and sub-resolution expansion of the dark thread. The dark thread is found to be cool, T~3x10^4$ with both strong density and magnetic field gradients. The expansion of the flux tube along its length is ~300-400km.

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arXiv2011

Phase Mixing of Nonlinear Visco-resistive Alfvén Waves

We investigate the behaviour of nonlinear, nonideal Alfvén wave propagation within an inhomogeneous magnetic environment. The governing MHD equations are solved in 1D and 2D using both analytical techniques and numerical simulations. We find clear evidence for the ponderomotive effect and visco-resistive heating. The ponderomotive effect generates a longitudinal component to the transverse Alfvén wave, with a frequency twice that of the driving frequency. Analytical work shows the addition of resistive heating. This leads to a substantial increase in the local temperature and thus gas pressure of the plasma, resulting in material being pushed along the magnetic field. In 2D, our system exhibits phase mixing and we observe an evolution in the location of the maximum heating, i.e. we find a drifting of the heating layer. Considering Alfvén wave propagation in 2D with an inhomogeneous density gradient, we find that the equilibrium density profile is significantly modified by both the flow of density due to visco-resistive heating and the nonlinear response to the localised heating through phase mixing.

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arXiv2009

Nonlinear Fast Magnetoacoustic Wave Propagation in the Neighbourhood of a 2D magnetic X-point: Oscillatory Reconnection

This paper extends the models of Craig & McClymont (1991) and McLaughlin & Hood (2004) to include finite $β$ and nonlinear effects. We investigate the nature of nonlinear fast magnetoacoustic waves about a 2D magnetic X-point. We solve the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Arber et al. 2001) and consider an initial condition in $ {\bf{v}}\times{\bf{B}} \cdot {\hat{\bf{z}}}$ (a natural variable of the system). We observe the formation of both fast and slow oblique magnetic shocks. The nonlinear wave deforms the X-point into a 'cusp-like' point which in turn collapses to a current sheet. The system then evolves through a series of horizontal and vertical current sheets, with associated changes in connectivity, i.e. the system exhibits oscillatory reconnection. Our final state is non-potential (but in force balance) due to asymmetric heating from the shocks. Larger amplitudes in our initial condition correspond to larger values of the final current density left in the system. The inclusion of nonlinear terms introduces several new features to the system that were absent from the linear regime.

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arXiv2007

MHD mode coupling in the neighbourhood of a 2D null point

At this time there does not exist a robust set of rules connecting low and high $β$ waves across the $β\approx 1$ layer. The work here contributes specifically to what happens when a low $β$ fast wave crosses the $β\approx 1$ layer and transforms into high $β$ fast and slow waves. The nature of fast and slow magnetoacoustic waves is investigated in a finite $β$ plasma in the neighbourhood of a two-dimensional null point. The linearised equations are solved in both polar and cartesian forms with a two-step Lax-Wendroff numerical scheme. Analytical work (e.g. small $β$ expansion and WKB approximation) also complement the work. It is found that when a finite gas pressure is included in magnetic equilibrium containing an X-type null point, a fast wave is attracted towards the null by a refraction effect and that a slow wave is generated as the wave crosses the $β\approx 1$ layer. Current accumulation occurs close to the null and along nearby separatrices. The fast wave can now \emph{pass through the origin} due to the non-zero sound speed, an effect not previously seen in related papers but clear seen for larger values of $β$. Some of the energy can now leave the region of the null point and there is again generation of a slow wave component (we find that the fraction of the incident wave converted to a slow wave is proportional to $β$). We conclude that there are two competing phenomena; the refraction effect (due to the variable Alfvén speed) and the contribution from the non-zero sound speed. These experiments illustrate the importance of the magnetic topology and of the location of the $β\approx 1$ layer in the system.

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arXiv2007

3D MHD Coronal Oscillations About a Magnetic Null Point: Application of WKB Theory

This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit's Method and a Runge-Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, ${\bf{B}}=(x,εy -(ε+1)z)$. Under our cold plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfvén waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point, and that the effect of this refraction depends upon the Alfvén speed profile. The wave, and thus the wave energy, accumulates at the null point. We have found that current build up is exponential and the exponent is dependent upon $ε$. Thus, for the fast wave there is preferential heating at the null point. For the Alfvén wave, we find that the wave propagates along the fieldlines. For an Alfvén wave generated along the fan-plane, the wave accumulates along the spine. For an Alfvén wave generated across the spine, the value of $ε$ determines where the wave accumulation will occur: fan-plane ($ε=1$), along the $x-$axis ($0<ε<1$) or along the $y-$axis ($ε>1$). We have shown analytically that currents build up exponentially, leading to preferential heating in these areas. The work described here highlights the importance of understanding the magnetic topology of the coronal magnetic field for the location of wave heating.

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arXiv2007

MHD wave propagation in the neighbourhood of a two-dimensional null point

The nature of fast magnetoacoustic and Alfvén waves is investigated in a zero $β$ plasma. This gives an indication of wave propagation in the low $β$ solar corona. It is found that for a two-dimensional null point, the fast wave is attracted to that point and the front of the wave slows down as it approaches the null point, causing the current density to accumulate there and rise rapidly. Ohmic dissipation will extract the energy in the wave at this point. This illustrates that null points play an important role in the rapid dissipation of fast magnetoacoustic waves and suggests the location where wave heating will occur in the corona. The Alfvén wave behaves in a different manner in that the wave energy is dissipated along the separatrices. For Alfvén waves that are decoupled from fast waves, the value of the plasma $β$ is unimportant. However, the phenomenon of dissipating the majority of the wave energy at a specific place is a feature of both wave types.

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arXiv2007

MHD Wave Propagation in the Neighbourhood of Two Null Points

The nature of fast magnetoacoustic and Alfvén waves is investigated in a zero $β$ plasma in the neighbourhood of a pair of two-dimensional null points. This gives an indication of wave propagation in the low $β$ solar corona, for a more complicated magnetic configuration than that looked at by McLaughlin & Hood (2004). It is found that the fast wave is attracted to the null points and that the front of the wave slows down as it approaches the null point pair, with the wave splitting and part of the wave accumulating at one null and the rest at the other. Current density will then accumulate at these points and ohmic dissipation will then extract the energy in the wave at these points. This suggests locations where wave heating will occur in the corona. The Alfvén wave behaves in a different manner in that the wave accumulates along the separatrices. Hence, the current density will accumulate at this part of the topology and this is where wave heating will occur. However, the phenomenon of wave accumulation at a specific place is a feature of both wave types, and illustrates the importance of studying the topology of the corona when considering MHD wave propagation.

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arXiv2007

Magnetohydrodynamics wave propagation in the neighbourhood of two dipoles

This paper is the third in a series of investigations by the authors. The nature of fast magnetoacoustic and Alfvén waves is investigated in a 2D $β=0$ plasma in the neighbourhood of two dipoles. We use both numerical simulations (two-step Lax-Wendroff scheme) and analytical techniques (WKB approximation). It is found that the propagation of the linear fast wave is dictated by the Alfvén speed profile and that close to the null, the wave is attracted to the neutral point. However, it is also found that in this magnetic configuration some of the wave can escape the refraction effect; this had not been seen in previous investigations by the authors. The wave split occurs near the regions of very high Alfvén speed (found near the loci of the two dipoles). Also, for the set-up investigated it was found that 40% of the wave energy accumulates at the null. Ohmic dissipation will then extract the wave energy at this point. The Alfvén wave behaves in a different manner in that part of the wave accumulates along the separatrices and part escapes. Hence, the current density will accumulate at this part of the topology and this is where wave heating will occur. The phenomenon of wave accumulation at a specific place is a feature of both wave types, as is the result that a fraction of the wave can now escape the numerical box when propagating in this magnetic configuration.

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