MHD mode conversion in a stratified atmosphere

Mode conversion in the region where the sound and Alfven speeds are equal is a complex process, which has been studied both analytically and numerically, and has been seen in observations. In order to further the understanding of this process we set up a simple, one-dimensional model, and examine wave propagation through this system using a combination of analytical and numerical techniques. Simulations are carried out in a gravitationally stratified atmosphere with a uniform, vertical magnetic field for both isothermal and non-isothermal cases. For the non-isothermal case a temperature profile is chosen to mimic the steep temperature gradient encountered at the transition region. In all simulations, a slow wave is driven on the upper boundary, thus propagating down from low-beta to high-beta plasma across the mode-conversion region. In addition, a detailed analytical study is carried out where we predict the amplitude and phase of the transmitted and converted components of the incident wave as it passes through the mode-conversion region. A comparison of these analytical predictions with the numerical results shows good agreement, giving us confidence in both techniques. This knowledge may be used to help determine wave types observed and give insight into which modes may be involved in coronal heating.Comment: 7 pages, 5 figure

MHD mode conversion of fast and slow magnetoacoustic waves in the solar corona

There are three main wave types present in the Sun’s atmosphere: Alfvén waves and fast and slow magnetoacoustic waves. Alfvén waves are purely magnetic and would not exist if it was not for the Sun’s magnetic field. The fast and slow magnetoacoustic waves are so named due to their relative phase speeds. As the magnetic field tends to zero, the slow wave goes to zero as the fast wave becomes the sound wave. When a resonance occurs energy may be transferred between the different modes, causing one to increase in amplitude whilst the other decreases. This is known as mode conversion. Mode conversion of fast and slow magnetoacoustic waves takes place when the characteristic wave speeds, the sound and Alfvén speeds, are equal. This occurs in regions where the ratio of the gas pressure to the magnetic pressure, known as the plasma β, is approximately unity. In this thesis we investigate the conversion of fast and slow magnetoacoustic waves as they propagate from low- to high-β plasma. This investigation uses a combination of analytical and numerical techniques to gain a full understanding of the process. The MacCormack finite-difference method is used to model a wave as it undergoes mode conversion. Complementing this analytical techniques are employed to find the wave behaviour at, and distant from, the mode-conversion region. These methods are described in Chapter 2. The simple, one-dimensional model of an isothermal atmosphere permeated by a uniform magnetic field is studied in Chapter 3. Gravitational acceleration is included to ensure that mode conversion takes place. Driving a slow magnetoacoustic wave on the upper boundary conversion takes place as the wave passes from low- to high-β plasma. This is expanded upon in Chapter 4 where the effects of a non-isothermal temperature profile are examined. A tanh profile is selected to mimic the steep temperature gradient found in the transition region. In Chapter 5 the complexity is increased by allowing for a two-dimensional model. For this purpose we choose a radially-expanding magnetic field which is representative of a coronal hole. In this instance the slow magnetoacoustic wave is driven upwards from the surface, again travelling from low to high β. Finally, in Chapter 6 we investigate mode conversion near a two-dimensional, magnetic null point. At the null the plasma β becomes infinitely large and a wave propagating towards the null point will experience mode conversion. The methods used allow conversion of fast and slow waves to be described in the various model atmospheres. The amount of transmission and conversion are calculated and matched across the mode-conversion layer giving a full description of the wave behaviour

MHD mode conversion of fast and slow magnetoacoustic waves in the solar corona

There are three main wave types present in the Sun’s atmosphere: Alfvén waves and fast and slow magnetoacoustic waves. Alfvén waves are purely magnetic and would not exist if it was not for the Sun’s magnetic field. The fast and slow magnetoacoustic waves are so named due to their relative phase speeds. As the magnetic field tends to zero, the slow wave goes to zero as the fast wave becomes the sound wave. When a resonance occurs energy may be transferred between the different modes, causing one to increase in amplitude whilst the other decreases. This is known as mode conversion. Mode conversion of fast and slow magnetoacoustic waves takes place when the characteristic wave speeds, the sound and Alfvén speeds, are equal. This occurs in regions where the ratio of the gas pressure to the magnetic pressure, known as the plasma β, is approximately unity. In this thesis we investigate the conversion of fast and slow magnetoacoustic waves as they propagate from low- to high-β plasma. This investigation uses a combination of analytical and numerical techniques to gain a full understanding of the process. The MacCormack finite-difference method is used to model a wave as it undergoes mode conversion. Complementing this analytical techniques are employed to find the wave behaviour at, and distant from, the mode-conversion region. These methods are described in Chapter 2. The simple, one-dimensional model of an isothermal atmosphere permeated by a uniform magnetic field is studied in Chapter 3. Gravitational acceleration is included to ensure that mode conversion takes place. Driving a slow magnetoacoustic wave on the upper boundary conversion takes place as the wave passes from low- to high-β plasma. This is expanded upon in Chapter 4 where the effects of a non-isothermal temperature profile are examined. A tanh profile is selected to mimic the steep temperature gradient found in the transition region. In Chapter 5 the complexity is increased by allowing for a two-dimensional model. For this purpose we choose a radially-expanding magnetic field which is representative of a coronal hole. In this instance the slow magnetoacoustic wave is driven upwards from the surface, again travelling from low to high β. Finally, in Chapter 6 we investigate mode conversion near a two-dimensional, magnetic null point. At the null the plasma β becomes infinitely large and a wave propagating towards the null point will experience mode conversion. The methods used allow conversion of fast and slow waves to be described in the various model atmospheres. The amount of transmission and conversion are calculated and matched across the mode-conversion layer giving a full description of the wave behaviour.EThOS - Electronic Theses Online ServiceCarnegie Trust for the Universities of ScotlandGBUnited Kingdo

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