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 (R m < 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

Sausage oscillations of coronal loops

Aims. Analytical theory predicts the existence of trapped global (or fundamental) sausage fast magnetoacoustic modes in thick and dense coronal loops only, with the periods estimated as the ratio of double the loop length and the Alfvén speed outside the loop. We extend this study to the leaking regime, considering global sausage modes of long loops with small density contrasts. Methods. Anti-symmetric fast magnetoacoustic perturbations (sausage, or m = 0 modes) of a low β plasma slab with the symmetric Epstein profile of plasma density are modelled numerically. Results. It was found that long loops with sufficiently small density contrast can support global sausage leaky modes of detectable quality. The periods of the leaky modes are found to be approximately determined by the loop length and the external Alfvén speed. If the loop length can be estimated from imaging observations, the observed period of this mode provides us with the information about the Alfvén speed outside the loop. For typical flaring coronal loops, the estimated periods of the global sausage modes are about 5−60 s

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

Stabilisation of BGK modes by relativistic effects

Context. We examine plasma thermalisation processes in the foreshock region of astrophysical shocks within a fully kinetic and self-consistent treatment. We concentrate on proton beam driven electrostatic processes, which are thought to play a key role in the beam relaxation and the particle acceleration. Our results have implications for the effectiveness of electron surfing acceleration and the creation of the required energetic seed population for first order Fermi acceleration at the shock front. Aims. We investigate the acceleration of electrons via their interaction with electrostatic waves, driven by the relativistic Buneman instability, in a system dominated by counter-propagating proton beams. Methods. We adopt a kinetic Vlasov-Poisson description of the plasma on a fixed Eulerian grid and observe the growth and saturation of electrostatic waves for a range of proton beam velocities, from 0.15c to 0.9c. Results. We can report a reduced stability of the electrostatic wave (ESW) with increasing non-relativistic beam velocities and an improved wave stability for increasing relativistic beam velocities, both in accordance with previous findings. At the highest beam speeds, we find the system to be stable again for a period of ≈160 plasma periods. Furthermore, the high phase space resolution of the Eulerian Vlasov approach reveals processes that could not be seen previously with PIC simulations. We observe a, to our knowledge, previously unreported secondary electron acceleration mechanism at low beam speeds. We believe that it is the result of parametric couplings to produce high phase velocity ESW’s which then trap electrons, accelerating them to higher energies. This allows electrons in our simulation study to achieve the injection energy required for Fermi acceleration, for beam speeds as low as 0.15c in unmagnetised plasma

Nonlinear wave propagation and reconnection at magnetic X-points in the Hall MHD regime

The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that non-MHD effects should be considered in studies of magnetic energy release in this environment. This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic X-points and the nature of the resulting reconnection. A Lagrangian remap shock-capturing code (Lare2d) is used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth in resistive Hall MHD. A magnetic null-point finding algorithm is also used to locate and track the evolution of the multiple null-points that are formed in the system. Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wave-null interaction. In particular, the initial fast-wave pulse now consists of whistler and ion-cyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null, (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced.Comment: 13 pages, 10 figure

Radiative hydrodynamic modeling of the Bastille-Day flare (14 July, 2000). I, Numerical simulations

A 1D loop radiative hydrodynamic model that incorporates the effects of gravitational stratification, heat conduction, radiative losses, external heat input, presence of helium, and Braginskii viscosity is used to simulate elementary flare loops. The physical parameters for the input are taken from observations of the Bastille-Day flare of 2000 July 14. The present analysis shows that: a) the obtained maximum values of the electron density can be considerably higher (4.2 × 10 11 cm −3 or more) in the case of footpoint heating than in the case of apex heating (2.5 × 10 11 cm −3); b) the average cooling time after the flare peak takes less time in the case of footpoint heating than in the case of apex heating; c) the peak apex temperatures are significantly lower (by about 10 MK) for the case of footpoint heating than for apex heating (for the same average loop temperature of about 30 MK). This characteristic would allow to discriminate between different heating positioning; d) in both cases (of apex and footpoint heating), the maximum obtained apex temperature T max is practically independent of the heating duration σ t , but scales directly with the heating rate E H0 ; e) the maximum obtained densities at the loop apex, n max e, increase with the heating rate E H0 and heating duration σ t for both footpoint and apex heating. In Paper II we will use the outputs of these hydrodynamic simulations, which cover a wide range of the parameter space of heating rates and durations, as an input for forward-fitting of the multi-loop arcade of the Bastille-day flare

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

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 (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 Alfvén waves over a wide spectrum through this partially ionised region is investigated. Estimates of the efficiency of this region in the damping of Alfvén waves are made and compared for both approaches. We find that Alfvén waves with frequencies above 0.6 Hz are completely damped and frequencies below 0.01 Hz unaffected

Suppression of energetic electron transport in flares by double layers

During flares and coronal mass ejections, energetic electrons from coronal sources typically have very long lifetimes compared to the transit times across the systems, suggesting confinement in the source region. Particle-in-cell simulations are carried out to explore the mechanisms of energetic electron transport from the corona to the chromosphere and possible confinement. We set up an initial system of pre-accelerated hot electrons in contact with ambient cold electrons along the local magnetic field, and let it evolve over time. Suppression of transport by a nonlinear, highly localized electrostatic electric field (in the form of a double layer) is observed after a short phase of free-streaming by hot electrons. The double layer (DL) emerges at the contact of the two electron populations. It is driven by an ion-electron streaming instability due to the drift of the back-streaming return current electrons interacting with the ions. The DL grows over time and supports a significant drop in temperature and hence reduces heat flux between the two regions that is sustained for the duration of the simulation. This study shows transport suppression begins when the energetic electrons start to propagate away from a coronal acceleration site. It also implies confinement of energetic electrons with kinetic energies less than the electrostatic energy of the DL for the DL lifetime, which is much longer than the electron transit time through the source region