TY - JOUR A1 - Fuhrmann, Marcel A1 - Seehafer, Norbert A1 - Valori, Gherardo A1 - Wiegelmann, Thomas T1 - A comparison of preprocessing methods for solar force-free magnetic field extrapolation Y1 - 2011 UR - http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/full_html/ 2011/02/aa15453-10/aa15453-10.html SN - 0004-6361 ER - TY - JOUR A1 - Fuhrmann, Marcel A1 - Seehafer, Norbert A1 - Valori, Gherardo A1 - Wiegelmann, T. T1 - A comparison of preprocessing methods for solar force-free magnetic field extrapolation JF - Astronomy and astrophysics : an international weekly journal N2 - Context. Extrapolations of solar photospheric vector magnetograms into three-dimensional magnetic fields in the chromosphere and corona are usually done under the assumption that the fields are force-free. This condition is violated in the photosphere itself and a thin layer in the lower atmosphere above. The field calculations can be improved by preprocessing the photospheric magnetograms. The intention here is to remove a non-force-free component from the data. Aims. We compare two preprocessing methods presently in use, namely the methods of Wiegelmann et al. (2006, Sol. Phys., 233, 215) and Fuhrmann et al. (2007, A&A, 476, 349). Methods. The two preprocessing methods were applied to a vector magnetogram of the recently observed active region NOAA AR 10 953. We examine the changes in the magnetogram effected by the two preprocessing algorithms. Furthermore, the original magnetogram and the two preprocessed magnetograms were each used as input data for nonlinear force-free field extrapolations by means of two different methods, and we analyze the resulting fields. Results. Both preprocessing methods managed to significantly decrease the magnetic forces and magnetic torques that act through the magnetogram area and that can cause incompatibilities with the assumption of force-freeness in the solution domain. The force and torque decrease is stronger for the Fuhrmann et al. method. Both methods also reduced the amount of small-scale irregularities in the observed photospheric field, which can sharply worsen the quality of the solutions. For the chosen parameter set, the Wiegelmann et al. method led to greater changes in strong-field areas, leaving weak-field areas mostly unchanged, and thus providing an approximation of the magnetic field vector in the chromosphere, while the Fuhrmann et al. method weakly changed the whole magnetogram, thereby better preserving patterns present in the original magnetogram. Both preprocessing methods raised the magnetic energy content of the extrapolated fields to values above the minimum energy, corresponding to the potential field. Also, the fields calculated from the preprocessed magnetograms fulfill the solenoidal condition better than those calculated without preprocessing. KW - Sun: magnetic topology KW - Sun: atmosphere KW - magnetohydrodynamics (MHD) Y1 - 2011 U6 - https://doi.org/10.1051/0004-6361/201015453 SN - 0004-6361 VL - 526 PB - EDP Sciences CY - Les Ulis ER - TY - JOUR A1 - Hassanin, Alshaimaa A1 - Kliem, Bernhard A1 - Seehafer, Norbert A1 - Török, Tibor T1 - A model of homologous confined and ejective eruptions involving kink instability and flux cancellation JF - The astrophysical journal : an international review of spectroscopy and astronomical physics N2 - In this study, we model a sequence of a confined and a full eruption, employing the relaxed end state of the confined eruption of a kink-unstable flux rope as the initial condition for the ejective one. The full eruption, a model of a coronal mass ejection, develops as a result of converging motions imposed at the photospheric boundary, which drive flux cancellation. In this process, parts of the positive and negative external flux converge toward the polarity inversion line, reconnect, and cancel each other. Flux of the same amount as the canceled flux transfers to a flux rope, increasing the free magnetic energy of the coronal field. With sustained flux cancellation and the associated progressive weakening of the magnetic tension of the overlying flux, we find that a flux reduction of approximate to 11% initiates the torus instability of the flux rope, which leads to a full eruption. These results demonstrate that a homologous full eruption, following a confined one, can be driven by flux cancellation. Y1 - 2022 U6 - https://doi.org/10.3847/2041-8213/ac64a9 SN - 2041-8205 SN - 2041-8213 VL - 929 IS - 2 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Seehafer, Norbert A1 - Zienicke, Egbert A1 - Feudel, Fred T1 - Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch Y1 - 1996 ER - TY - JOUR A1 - Seehafer, Norbert T1 - Alpha effect in the solar atmosphere Y1 - 1994 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Schumacher, Jörg T1 - Bifurcation analysis of an electrically driven fluid layer N2 - The equilibrium states of electrically conducting fluids or plasmas have been a subject of intense study for a long time, motivated in particular by the interest in controlled thermonuclear fusion, as well as that in space and astrophysical phenomena such as plasma loops in the solar corona. If high temperatures prohibit solid walls, a conducting fluid can be held together by the action of an electric current passing through it with the pressure gradients being balanced by the Lorentz force. The resultant configuration is known as a pinch. In this paper we report on studies of the pinch in the geometry of a plane sheet. Y1 - 2000 ER - TY - JOUR A1 - Schumacher, Jörg A1 - Seehafer, Norbert T1 - Bifurcation analysis of the plane sheet pinch N2 - A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three- dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three- dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state. Y1 - 2000 UR - http://publish.aps.org/abstract/PRE/v61/p2695 ER - TY - JOUR A1 - Feudel, Fred A1 - Rüdiger, Sten A1 - Seehafer, Norbert T1 - Bifurcation phenomena and dynamo effect in electrically conducting fluids N2 - Electrically conducting fluids in motion can act as self-excited dynamos. The magnetic fields of celestial bodies like the Earth and the Sun are generated by such dynamos. Their theory aims at modeling and understanding both the kinematic and dynamic aspects of the underlying processes. Kinematic dynamo models, in which for a prescribed flow the linear induction equation is solved and growth rates of the magnetic field are calculated, have been studied for many decades. But in order to get consistent models and to take into account the back-reaction of the magnetic field on the fluid motion, the full nonlinear system of the magnetohydrodynamic (MHD) equations has to be studied. It is generally accepted that these equations, i.e. the Navier-Stokes equation (NSE) and the induction equation, provide a theoretical basis for the explanation of the dynamo effect. The general idea is that mechanical energy pumped into the fluid by heating or other mechanisms is transferred to the magnetic field by nonlinear interactions. For two special helical flows which are known to be effective kinematic dynamos and which can be produced by appropriate external mechanical forcing, we review the nonlinear dynamo properties found in the framework of the full MHD equations. Specifically, we deal with the ABC flow (named after Arnold, Beltrami and Childress) and the Roberts flow (after G.~O. Roberts). The appearance of generic dynamo effects is demonstrated. Applying special numerical bifurcation-analysis techniques to high-dimensional approximations in Fourier space and varying the Reynolds number (or the strength of the forcing) as the relevant control parameter, qualitative changes in the dynamics are investigated. We follow the bifurcation sequences until chaotic states are reached. The transitions from the primary flows with vanishing magnetic field to dynamo-active states are described in particular detail. In these processes the stagnation points of the flows and their heteroclinic connections play a promoting role for the magnetic field generation. By the example of the Roberts flow we demonstrate how the break up of the heteroclinic lines after the primary bifurcation leads to a complicated intersection of stable and unstable manifolds forming a chaotic web which is in turn correlated with the spatial appearance of the dynamo. Y1 - 2001 ER - TY - JOUR A1 - Feudel, Fred A1 - Seehafer, Norbert A1 - Schmidtmann, Olaf T1 - Bifurcation phenomena of the magnetofluid equations N2 - We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier representations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (increasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non- magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by further, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory. Y1 - 1996 UR - http://www.mathematicsweb.org/mathematicsweb/show/Index.htt?Issn=03784754 ER - TY - JOUR A1 - Demircan, Ayhan A1 - Seehafer, Norbert T1 - Bifurcation to oscillations and chaos in rotating convection Y1 - 1999 ER - TY - JOUR A1 - Scheel, S. A1 - Seehafer, Norbert T1 - Bifurcation to oscillations in three-dimensional Rayleigh-Bénard convection Y1 - 1997 ER - TY - JOUR A1 - Braun, Robert A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Bifurcations and chaos in an array of forced vortices Y1 - 1997 ER - TY - JOUR A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Bifurcations and pattern formation in two-dimensional Navier-Stokes fluid Y1 - 1995 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Feudel, Fred A1 - Galanti, B. T1 - Bifurcations in a magnetofluid with helical forcing Y1 - 1998 SN - 1-563-47284-8 ER - TY - JOUR A1 - Zienicke, Egbert A1 - Seehafer, Norbert A1 - Feudel, Fred T1 - Bifurcations in two-dimensional Rayleigh-Bénard convection Y1 - 1998 ER - TY - JOUR A1 - Feudel, Fred A1 - Tuckerman, L. S. A1 - Gellert, Marcus A1 - Seehafer, Norbert T1 - Bifurcations of rotating waves in rotating spherical shell convection JF - Physical Review E N2 - The dynamics and bifurcations of convective waves in rotating and buoyancy-driven spherical Rayleigh-Benard convection are investigated numerically. The solution branches that arise as rotating waves (RWs) are traced by means of path-following methods, by varying the Rayleigh number as a control parameter for different rotation rates. The dependence of the azimuthal drift frequency of the RWs on the Ekman and Rayleigh numbers is determined and discussed. The influence of the rotation rate on the generation and stability of secondary branches is demonstrated. Multistability is typical in the parameter range considered. KW - nonsymmetric linear-systems KW - thermal-convection KW - fluid shells KW - hopf-bifurcation KW - onset KW - magnetoconvection KW - number KW - flow Y1 - 2015 U6 - https://doi.org/10.1103/PhysRevE.92.053015 SN - 1539-3755 SN - 1550-2376 VL - 92 IS - 5 PB - American Physical Society CY - Woodbury ER - TY - JOUR A1 - Feudel, Fred A1 - Tuckerman, L. S. A1 - Gellert, M. A1 - Seehafer, Norbert T1 - Bifurcations of rotating waves in rotating spherical shell convection JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - The dynamics and bifurcations of convective waves in rotating and buoyancy-driven spherical Rayleigh-Benard convection are investigated numerically. The solution branches that arise as rotating waves (RWs) are traced by means of path-following methods, by varying the Rayleigh number as a control parameter for different rotation rates. The dependence of the azimuthal drift frequency of the RWs on the Ekman and Rayleigh numbers is determined and discussed. The influence of the rotation rate on the generation and stability of secondary branches is demonstrated. Multistability is typical in the parameter range considered. Y1 - 2015 U6 - https://doi.org/10.1103/PhysRevE.92.053015 SN - 1539-3755 SN - 1550-2376 VL - 92 IS - 5 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Seehafer, Norbert T1 - Current helicity and the turbulent electromotive force Y1 - 1994 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Demircan, Ayhan T1 - Dynamo action in cellular convection Y1 - 2003 ER - TY - JOUR A1 - Rüdiger, Sten A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Dynamo bifurcations in an array of driven convectionlike rolls Y1 - 1998 ER -