T. D. Arber

Contemporary particle-in-cell approach to laser-plasma modelling

Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions. Early electromagnetic codes used the Yee staggered grid for field variables combined with a leapfrog EM-field update and the Boris algorithm for particle pushing. The general properties of such schemes are well documented. Modern PIC codes tend to add to these high-order shape functions for particles, Poisson preserving field updates, collisions, ionisation, a hybrid scheme for solid density and high-field QED effects. In addition to these physics packages, the increase in computing power now allows simulations with real mass ratios, full 3D dynamics and multi-speckle interaction. This paper presents a review of the core algorithms used in current laser-plasma specific PIC codes. Also reported are estimates of self-heating rates, convergence of collisional routines and test of ionisation models which are not readily available elsewhere. Having reviewed the status of PIC algorithms we present a summary of recent applications of such codes in laser-plasma physics, concentrating on SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects.

Nature of the heating mechanism for the diffuse solar corona

The temperature of the Suns outer atmosphere (the corona) exceeds that of the solar surface by about two orders of magnitude, but the nature of the coronal heating mechanisms has long been a mystery. The corona is a magnetically dominated environment, consisting of a variety of plasma structures including X-ray bright points, coronal holes and coronal loops. The latter are closed magnetic structures that occur over a range of scales and are anchored at each end in the solar surface. Large-scale regions of diffuse emission are made up of many long coronal loops. Here we present X-ray observations of the diffuse corona from which we deduce its likely heating mechanism. We find that the observed variation in temperature along a loop is highly sensitive to the spatial distribution of the heating. From a comparison of the observations and models we conclude that uniform heating gives the best fit to the loop temperature distribution, enabling us to eliminate previously suggested mechanisms of low-lying heating near the footpoints of a loop. Our findings favour turbulent breaking and reconnection of magnetic field lines as the heating mechanism of the diffuse solar corona.

A Method to Determine the Heating Mechanisms of the Solar Corona

One of the paradigms about coronal heating has been the belief that the mean or summit temperature of a coronal loop is completely insensitive to the nature of the heating mechanisms. However, we point out that the temperature profile along a coronal loop is highly sensitive to the form of the heating. For example, when a steady state heating is balanced by thermal conduction, a uniform heating function makes the heat flux a linear function of distance along the loop, while T7/2 increases quadratically from the coronal footpoints; when the heating is concentrated near the coronal base, the heat flux is small and the T7/2 profile is flat above the base; when the heat is focused near the summit of a loop, the heat flux is constant and T7/2 is a linear function of distance below the summit. It is therefore important to determine how the heat deposition from particular heating mechanisms varies spatially within coronal structures such as loops or arcades and to compare it to high-quality measurements of the temperature profiles. We propose a new two-part approach to try and solve the coronal heating problem, namely, first of all to use observed temperature profiles to deduce the form of the heating, and second to use that heating form to deduce the likely heating mechanism. In particular, we apply this philosophy to a preliminary analysis of Yohkoh observations of the large-scale solar corona. This gives strong evidence against heating concentrated near the loop base for such loops and suggests that heating uniformly distributed along the loop is slightly more likely than heating concentrated at the summit. The implication is that large-scale loops are heated in situ throughout their length, rather than being a steady response to low-lying heating near their feet or at their summits. Unless waves can be shown to produce a heating close enough to uniform, the evidence is therefore at present for these large loops more in favor of turbulent reconnection at many small randomly distributed current sheets, which is likely to be able to do so. In addition, we suggest that the decline in coronal intensity by a factor of 100 from solar maximum to solar minimum is a natural consequence of the observed ratio of magnetic field strength in active regions and the quiet Sun; the altitude of the maximum temperature in coronal holes may represent the dissipation height of Alfven waves by turbulent phase mixing; and the difference in maximum temperature in closed and open regimes may be understood in terms of the roles of the conductive flux there.

Acoustic oscillations in solar and stellar flaring loops

Evolution of a coronal loop in response to an impulsive energy release is numerically modelled. It is shown that the loop density evolution curves exhibit quasi-periodic perturbations with the periods given approximately by the ratio of the loop length to the average sound speed, associated with the second standing harmonics of an acoustic wave. The density perturbations have a maximum near the loop apex. The corresponding field-aligned flows have a node near the apex. We suggest that the quasi-periodic pulsations with periods in the range 10-300 s, frequently observed in flaring coronal loops in the radio, visible light and X-ray bands, may be produced by the second standing harmonic of the acoustic mode.

Emergence of a Flux Tube through a Partially Ionized Solar Atmosphere

For a magnetic flux tube, or indeed any flux, to emerge into the solar corona from the convection zone it must pass through the partially ionized layers of the lower atmosphere: the photosphere and the chromosphere. In such regions, the ion-neutral collisions lead to an increased resistivity for currents flowing across magnetic field lines. This Cowling resistivity can exceed the Spitzer resistivity by orders of magnitude and, in 2.5-dimensional (2.5D) simulations, has been shown to be sufficient to remove all cross field current from emerging flux. Here we extend this modeling into three dimensions (3D). Once again it is found that the Cowling resistivity removes perpendicular current. However, the presence of 3D structure prevents the simple comparison possible in 2.5D simulations. With a fully ionized atmosphere, the flux emergence leads to an unphysically low temperature region in the overlying corona, lifting of chromospheric material, and the subsequent onset of the Rayleigh-Taylor instability. Including neutrals removes the low-temperature region, lifts less chromospheric matter, and shows no signs of the Rayleigh-Taylor instability. Simulations of flux emergence therefore should include such a neutral layer in order to obtain the correct perpendicular current, remove the Rayleigh-Taylor instability, and get the correct temperature profile. In situations when the temperature is not important, i.e., when no simulated spectral emission is required, a simple model for the neutral layer is demonstrated to adequately reproduce the results of fully consistent simulations.

The emergence of magnetic flux through a partially ionised solar atmosphere

We present results from 2.5D numerical simulations of the emergence of magnetic flux from the upper convection zone through the photosphere and chromosphere into the corona. Certain regions of the solar atmosphere are at sufficiently low temperatures to be only partially ionised, in particular the lower chromosphere. This leads to Cowling resistivities orders of magnitude larger than the Coulomb values, and thus to anisotropic dissipation in Ohm’s law. This also leads to localised low magnetic Reynolds numbers (Rm < 1). We find that the rates of emergence of magnetic field are greatly increased by the partially ionised regions of the model atmosphere, and the resultant magnetic field is more diffuse. More importantly, the only currents associated with the magnetic field to emerge into the corona are aligned with the field, and thus the newly formed coronal field is force-free.

Modelling gamma-ray photon emission and pair production in high-intensity laser-matter interactions

In high-intensity (>10^2^1 Wcm^-^2) laser-matter interactions gamma-ray photon emission by the electrons can strongly affect the electron@?s dynamics and copious numbers of electron-positron pairs can be produced by the emitted photons. We show how these processes can be included in simulations by coupling a Monte Carlo algorithm describing the emission to a particle-in-cell code. The Monte Carlo algorithm includes quantum corrections to the photon emission, which we show must be included if the pair production rate is to be correctly determined. The accuracy, convergence and energy conservation properties of the Monte Carlo algorithm are analysed in simple test problems.

Collisional dissipation of Alfvén waves in a partially ionised solar chromosphere

Certain regions of the solar atmosphere are at sufficiently low temperatures to be only partially ionised. The lower chromosphere contains neutral atoms, the existence of which greatly increases the efficiency of the damping of waves due to collisional friction momentum transfer. More specifically the Cowling conductivity can be up to 12 orders of magnitude smaller than the Spitzer value, so that the main damping mechanism in this region is due to the collisions between neutrals and positive ions. Using values for the gas density and temperature as functions of height taken from the VAL C model of the quiet Sun, an estimate is made for the dependance of the Cowling conductivity on height and strength of magnetic field. Using both analytic and numerical approaches the passage of Alfven waves over a wide spectrum through this partially ionised region is investigated. Estimates of the efficiency of this region in the damping of Alfven waves are made and compared for both approaches. We find that Alfven waves with frequencies above 0.6Hz are completely damped and frequencies below 0.01 Hz unaffected.Certain regions of the solar atmosphere are at sufficiently low temperatures to be only partially ionised. The lower chromosphere contains neutral atoms, the existence of which greatly increases the efficiency of the damping of waves due to collisional friction momentum transfer. More specifically the Cowling conductivity can be up to 12 orders of magnitude smaller than the Spitzer value, so that the main damping mechanism in this region is due to the collisions between neutrals and positive ions (Khodachenko et al. 2004, A&A, 422, 1073). Using values for the gas density and temperature as functions of height taken from the VAL C model of the quiet Sun (Vernazza et al. 1981, ApJS, 45, 635), an estimate is made for the dependance of the Cowling conductivity on height and strength of magnetic field. Using both analytic and numerical approaches the passage of Alfven waves over a wide spectrum through this partially ionised region is investigated. Estimates of the efficiency of this region in the damping of Alfven waves are made and compared for both approaches. We find that Alfven waves with frequencies above 0.6 Hz are completely damped and frequencies below 0.01 Hz unaffected.

Chromospheric resonances above sunspot umbrae

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.

Flare-generated acoustic oscillations in solar and stellar coronal loops

Long period longitudinal oscillations of a flaring coronal loop are studied numerically. In the recent work of Nakariakov et al. (2004) it has been shown that the time dependence of density and velocity in a flaring loop contain pronounced quasi-harmonic oscillations associated with the 2nd harmonic of a standing slow magnetoacoustic wave. In this work we investigate the physical nature of these oscillations in greater detail, namely, their spectrum (using the periodogram technique) and how heat positioning affects mode excitation. We found that excitation of such oscillations is practically independent of the location of the heat deposition in the loop. Because of the change of the background temperature and density, the phase shift between the density and velocity perturbations is not exactly a quarter of the period; it varies along the loop and is time dependent, especially in the case of one footpoint (asymmetric) heating.