Thomas Neukirch

The structure of three‐dimensional magnetic neutral points

The local configurations of three‐dimensional magnetic neutral points are investigated by a linear analysis about the null. It is found that the number of free parameters determining the arrangement of field lines is four. The configurations are first classified as either potential or non‐potential. Then the non‐potential cases are subdivided into three cases depending on whether the component of current parallel to the spine is less than, equal to or greater than a threshold current; therefore there are three types of linear non‐potential null configurations (a radial null, a critical spiral and a spiral). The effect of the four free parameters on the system is examined and it is found that only one parameter categorizes the potential configurations, whilst two parameters are required if current is parallel to the spine. However, all four parameters are needed if there is current both parallel and perpendicular to the spine axis. The magnitude of the current parallel to the spine determines whether the n...

Magnetic Pinching of Hyperbolic Flux Tubes. I. Basic Estimations

The concept of hyperbolic flux tubes (HFTs) is a generalization of the concept of separator field lines for coronal magnetic fields with a trivial magnetic topology. An effective mechanism of a current layer formation in HFTs is proposed. This mechanism is called magnetic pinching, and it is caused by large-scale shearing motions applied to the photospheric feet of HFTs in a way as if trying to twist the HFT. It is shown that in the middle of an HFT such motions produce a hyperbolic flow that causes an exponentially fast growth of the current density in a thin force-free current layer. The magnetic energy associated with the current layer that is built up over a few hours is sufficient for a large flare. Other implications of HFT pinching for solar flares are discussed as well.

Including stereoscopic information in the reconstruction of coronal magnetic fields

We present a method to include stereoscopic information about the three-dimensional structure of flux tubes into the reconstruction of the coronal magnetic field. Due to the low plasma beta in the corona we can assume a force-free magnetic field, with the current density parallel to the magnetic field lines. Here we use linear force-free fields for simplicity. The method uses the line-of-sight magnetic field on the photosphere as observational input. The value of α is determined iteratively by comparing the reconstructed magnetic field with the observed structures. The final configuration is the optimal linear force-free solution constrained by both the photospheric magnetogram and the observed plasma structures. As an example we apply our method to SOHO MDI/EIT data of an active region. In the future it is planned to apply the method to analyse data from the SECCHI instrument aboard the STEREO mission.

One-dimensional Vlasov-Maxwell equilibrium for the force-free Harris sheet.

In this Letter, the first nonlinear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudoparticle in a two-dimensional conservative potential. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet.

PARTICLE MOTION IN COLLAPSING MAGNETIC TRAPS IN SOLAR FLARES. I. KINEMATIC THEORY OF COLLAPSING MAGNETIC TRAPS

We present a model of collapsing magnetic traps in magnetic field configurations associated with solar flares. The model is based on a kinematic description of the magnetic field obeying the ideal Ohms law. The dynamic evolution of the models is given in terms of a time-dependent transformation from Eulerian to Lagrangian coordinates. The transformation can be used to determine the corresponding flow field, the magnetic field, and the electric field from given initial conditions. The theory is formulated for translationally invariant situations, but a fully three-dimensional version is also given. The effect of various transformations and initial conditions is discussed with a view to calculating charged particle orbits in the given electromagnetic fields.

Energy Release And Transfer In Solar Flares: Simulations Of Three-Dimensional Reconnection

Using three-dimensional magnetohydrodynamic simulations we investigate energy release and transfer in a three-dimensional extension of the standard two-ribbon flare picture. In this scenario, reconnection is initiated in a thin current sheet (suggested to form below a departing coronal mass ejection) above a bipolar magnetic field. Two cases are contrasted: an initially force-free current sheet (low beta) and a finite-pressure current sheet (high beta), where beta represents the ratio between gas (plasma) and magnetic pressure. The energy conversion process from reconnection consists of incoming Poynting flux turned into up- and downgoing Poynting flux, enthalpy flux, and bulk kinetic energy flux. In the low-beta case, the outgoing Poynting flux is the dominant contribution, whereas the outgoing enthalpy flux dominates in the high-beta case. The bulk kinetic energy flux is only a minor contribution in the downward direction. The dominance of the downgoing Poynting flux in the low-beta case is consistent with an alternative to the thick target electron beam model for solar flare energy transport, suggested recently by Fletcher & Hudson, whereas the enthalpy flux may act as an alternative transport mechanism. For plausible characteristic parameters of the reconnecting field configuration, we obtain energy release timescales and energy output rates that compare favorably with those inferred from observations for the impulsive phase of flares. Significant enthalpy flux and heating are found even in the initially force-free case with very small background beta, resulting mostly from adiabatic compression rather than Ohmic dissipation. The energy conversion mechanism is most easily understood as a two-step process (although the two steps may occur essentially simultaneously): the first step is the acceleration of the plasma by Lorentz forces in layers akin to the slow shocks in the Petschek reconnection model, involving the conversion of magnetic energy to bulk kinetic energy. However, due to pressure gradient forces that oppose the Lorentz forces in approximate, or partial force balance, the accelerated plasma becomes slowed down and compressed, whereby the bulk kinetic energy is converted to heat, either locally deposited or transported away by enthalpy flux and deposited later. This mechanism is most relevant in the downflow region, which is more strongly governed by force balance; it is less important in the outflow above the reconnection site, where more energy remains in the form of fast bulk flow.

An optimization principle for the computation of MHD equilibria in the solar corona

Context. We develop an optimization principle for computing stationary MHD equilibria. Aims. Our code for the self-consistent computation of the coronal magnetic fields and the coronal plasma uses non-force-free M HD equilibria. Previous versions of the code have been used to compute non-linear force-free coronal magnetic fields from photospheric measurements. The program uses photospheric vector magnetograms and coronal EUV images as input. We tested our reconstruction code with the help of a semi-analytic MHD-equilibrium. The quality of the reconstruction was judged by comparing the exact and reconstructed solution qualitatively by magnetic field-line plots and EUV-images and quantitativ ely by several different numerical criteria. Methods. Our code is able to reconstruct the semi-analytic test equil ibrium with high accuracy. The stationary MHD optimization code developed here has about the same accuracy as its predecessor, a non-linear force-free optimization code. The computing time for MHD- equilibria is, however, longer than for force-free magneti c fields. We also extended a well-known class of nonlinear for ce-free equilibria to the non-force-free regime for purposes of testing the code. Results. We demonstrate that the code works in principle using tests with analytical equilibria, but it still needs to be applied t o real data. Conclusions.

A detailed investigation of the properties of a Vlasov-Maxwell equilibrium for the force-free Harris sheet

A detailed discussion is presented of the Vlasov–Maxwell equilibrium for the force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)]. The derivation of the distribution function and a discussion of its general properties and their dependence on the distribution function parameters will be given. In particular, the distribution function can be single-peaked or multipeaked in two of the velocity components, with possible implications for stability. The dependence of the shape of the distribution function on the values of its parameters will be investigated and the relation to macroscopic quantities such as the current sheet thickness will be discussed.

A first step in reconstructing the solar corona self-consistently with a magnetohydrostatic model during solar activity minimum

Aims. We compute the distribution of the magnetic field and the plasma in the global corona with a self-consistent magnetohydrostatic (MHS) model. Methods. Because direct measurements of the solar coronal magnetic field and plasma are extremely difficult and inaccurate, we use a modeling approach based on observational quantities, e.g. the measured photospheric magnetic field, to reconstruct the structure of the global solar corona. We take an analytic magnetohydrostatic model to extrapolate the magnetic field in the corona from photospheric magnetic field measurement. In the model, the electric current density can be decomposed into two components: one component is aligned with the magnetic field lines, whereas the other component flows in spherical shells. The second component of the current produces finite Lorentz forces that are balanced by the pressure gradient and the gravity force. We derive the 3D distribution of the magnetic field and plasma self-consistently in one model. The boundary conditions are given by a synoptic magnetogram on the inner boundary and by a source surface model at the outer boundary. Results. The density in the model is higher in the equatorial plane than in the polar region. We compare the magnetic field distribution of our model with potential and force-free field models for the same boundary conditions and find that our model differs noticeably from both. We discuss how to apply the model and how to improve it.

On the quasistatic development of thin current sheets in magnetotail‐like magnetic fields

The mechanism for the formation of thin current sheets in magnetotail-like magnetic fields is investigated by numerical experiments using topology conserving equilibrium sequences. Motivated by the magnetotail magnetic field in the midnight meridian plane, a two-dimensional model field is computed including a line dipole-like (inner) part and a tail-like part. The plasma is modeled as a polytropic gas and the total amount of plasma in each flux tube is fixed during an equilibrium sequence. Topology conservation is ensured by the use of inverse coordinates. The resulting set of nonlinear partial integrodiiferential equations is solved numerically using a continuation method. Starting from a current-free field, stretching and compressing deformations are applied at the boundaries to mimic the analogue of a quasistatic substorm growth phase in our model. To investigate whether the process of thin current sheet formation is robust and to understand better the basic properties of that process, the boundary deformations are chosen such that there is no preferred location of compression of the field which would predetermine the site of thin current sheet formation. Current sheets are only found to form if a transition region between dipolar and tail-like field exists in the equilibrium, and the current density exhibits two different cross-tail length scales showing the importance of the transition region between the dipolar and the tail-like field. However, the thin current component is much smaller than in other models of thin current sheet formation in the magnetotail. This result can be attributed to the chosen type of boundary deformations. The results are consistent with the gradient-of-flux-volume mechanism which has been proposed as an explanation for the formation of thin current sheets in the Earths magnetotail.