@article{HassaninKliemSeehaferetal.2022, author = {Hassanin, Alshaimaa and Kliem, Bernhard and Seehafer, Norbert and T{\"o}r{\"o}k, Tibor}, title = {A model of homologous confined and ejective eruptions involving kink instability and flux cancellation}, series = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, volume = {929}, journal = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {2041-8205}, doi = {10.3847/2041-8213/ac64a9}, pages = {7}, year = {2022}, abstract = {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.}, language = {en} } @article{KliemSeehafer2022, author = {Kliem, Bernhard and Seehafer, Norbert}, title = {Helicity shedding by flux rope ejection}, series = {Astronomy and astrophysics : an international weekly journal}, volume = {659}, journal = {Astronomy and astrophysics : an international weekly journal}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0004-6361}, doi = {10.1051/0004-6361/202142422}, pages = {9}, year = {2022}, abstract = {We quantitatively address the conjecture that magnetic helicity must be shed from the Sun by eruptions launching coronal mass ejections in order to limit its accumulation in each hemisphere. By varying the ratio of guide and strapping field and the flux rope twist in a parametric simulation study of flux rope ejection from approximately marginally stable force-free equilibria, different ratios of self- and mutual helicity are set and the onset of the torus or helical kink instability is obtained. The helicity shed is found to vary over a broad range from a minor to a major part of the initial helicity, with self helicity being largely or completely shed and mutual helicity, which makes up the larger part of the initial helicity, being shed only partly. Torus-unstable configurations with subcritical twist and without a guide field shed up to about two-thirds of the initial helicity, while a highly twisted, kink-unstable configuration sheds only about one-quarter. The parametric study also yields stable force-free flux rope equilibria up to a total flux-normalized helicity of 0.25, with a ratio of self- to total helicity of 0.32 and a ratio of flux rope to external poloidal flux of 0.94. These results numerically demonstrate the conjecture of helicity shedding by coronal mass ejections and provide a first account of its parametric dependence. Both self- and mutual helicity are shed significantly; this reduces the total initial helicity by a fraction of ∼0.4--0.65 for typical source region parameters.}, language = {en} } @article{HassaninKliemSeehafer2016, author = {Hassanin, Alshaimaa and Kliem, Bernhard and Seehafer, Norbert}, title = {Helical kink instability in the confined solar eruption on 2002 May 27}, series = {Astronomische Nachrichten = Astronomical notes}, volume = {337}, journal = {Astronomische Nachrichten = Astronomical notes}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {0004-6337}, doi = {10.1002/asna.201612446}, pages = {1082 -- 1089}, year = {2016}, language = {en} } @article{FeudelTuckermanGellertetal.2015, author = {Feudel, Fred and Tuckerman, L. S. and Gellert, M. and Seehafer, Norbert}, title = {Bifurcations of rotating waves in rotating spherical shell convection}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {92}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {5}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.92.053015}, pages = {7}, year = {2015}, abstract = {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.}, language = {en} } @article{FuhrmannSeehaferValorietal.2011, author = {Fuhrmann, Marcel and Seehafer, Norbert and Valori, Gherardo and Wiegelmann, T.}, title = {A comparison of preprocessing methods for solar force-free magnetic field extrapolation}, series = {Astronomy and astrophysics : an international weekly journal}, volume = {526}, journal = {Astronomy and astrophysics : an international weekly journal}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0004-6361}, doi = {10.1051/0004-6361/201015453}, pages = {12}, year = {2011}, abstract = {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.}, language = {en} } @article{FeudelSeehaferTuckermanetal.2013, author = {Feudel, Fred and Seehafer, Norbert and Tuckerman, Laurette S. and Gellert, Marcus}, title = {Multistability in rotating spherical shell convection}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {87}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.87.023021}, pages = {8}, year = {2013}, abstract = {The multiplicity of stable convection patterns in a rotating spherical fluid shell heated from the inner boundary and driven by a central gravity field is presented. These solution branches that arise as rotating waves (RWs) are traced for varying Rayleigh number while their symmetry, stability, and bifurcations are studied. At increased Rayleigh numbers all the RWs undergo transitions to modulated rotating waves (MRWs) which are classified by their spatiotemporal symmetry. The generation of a third frequency for some of the MRWs is accompanied by a further loss of symmetry. Eventually a variety of MRWs, three-frequency solutions, and chaotic saddles and attractors control the dynamics for higher Rayleigh numbers.}, language = {en} } @article{MirandaRempelChianetal.2013, author = {Miranda, Rodrigo A. and Rempel, Erico L. and Chian, Abraham C.-L. and Seehafer, Norbert and Toledo, Benjamin A. and Munoz, Pablo R.}, title = {Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {23}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {3}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4811297}, pages = {13}, year = {2013}, abstract = {We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.}, language = {en} } @article{FeudelSeehaferTuckerman2013, author = {Feudel, Fred and Seehafer, Norbert and Tuckerman, Laurette S.}, title = {Multistability in rotating spherical shell convection}, issn = {1539-3755}, year = {2013}, language = {en} } @article{MirandaRempelChianetal.2013, author = {Miranda, Rodrigo A. and Rempel, Erico L. and Chian, Abraham C.-L. and Seehafer, Norbert and Toledo, Benjamin A.}, title = {Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations}, year = {2013}, language = {en} } @article{FuhrmannSeehaferValorietal.2011, author = {Fuhrmann, Marcel and Seehafer, Norbert and Valori, Gherardo and Wiegelmann, Thomas}, title = {A comparison of preprocessing methods for solar force-free magnetic field extrapolation}, issn = {0004-6361}, year = {2011}, language = {en} } @article{KliemRustSeehafer2010, author = {Kliem, Bernhard and Rust, S. and Seehafer, Norbert}, title = {Helicity transport in a simulated coronal mass ejection}, series = {Proceedings of the International Astronomical Union}, journal = {Proceedings of the International Astronomical Union}, publisher = {International Astronomical Union}, address = {Cambridge}, issn = {1743-9213}, doi = {10.1017/S1743921311006715}, pages = {125 -- 128}, year = {2010}, language = {en} } @article{FuhrmannSeehaferValori2007, author = {Fuhrmann, Marcel and Seehafer, Norbert and Valori, Gherardo}, title = {Preprocessing of solar vector magnetograms for force-free magnetic field extrapolation}, issn = {0004-6361}, doi = {10.1051/0004-6361:20078454}, year = {2007}, abstract = {Context. Reliable measurements of the solar magnetic field are restricted to the phoptosphere. As an alternative to measurements, the field in the higher layers of the atmosphere is calculated from the measured photospheric field, mostly under the assumption that it is force-free. However, the magnetic field in the photosphere is not force-free. Moreover, most methods for the extrapolation of the photospheric magnetic field into the higher layers prescribe the magnetic vector on the whole boundary of the considered volume, which overdetermines the force-free field. Finally, the extrapolation methods are very sensitive to small-scale noise in the magnetograph data, which, however, if sufficienly resolved numerically, should affect the solution only in a thin boundary layer close to the photosphere. Aims. A new method for the preprocessing of solar photospheric vector magnetograms has been developed that, by improving their compatibility with the condition of force- freeness and removing small-scale noise, makes them more suitable for extrapolations into three- dimensional nonlinear force-free magnetic fields in the chromosphere and corona. Methods. A functional of the photospheric field values is minimized whereby the total magnetic force and the total magnetic torque on the considered volume above the photosphere, as well as a quantity measuring the degree of small-scale noise in the photospheric boundary data, are simultaneously made small. For the minimization, the method of simulated annealing is used and the smoothing of noisy magnetograph data is attained by windowed median averaging. Results. The method was applied to a magnetogram derived from a known nonlinear force-free test field to which an artificial noise had been added. The algorithm recovered all main structures of the magnetogram and removed small- scale noise. The main test was to extrapolate from the noisy photospheric vector magnetogram before and after the preprocessing. The preprocessing was found to significantly improve the agreement of the extrapolated with the exact field.}, language = {en} } @article{DonnerFeudelSeehaferetal.2007, author = {Donner, Reik Volker and Feudel, Fred and Seehafer, Norbert and Sanjuan, Miguel Angel Fernandez}, title = {Hierarchical modeling of a forced Roberts Dynamo}, issn = {0218-1274}, doi = {10.1142/S021812740701941X}, year = {2007}, abstract = {We investigate the dynamo effect in a flow configuration introduced by G. O. Roberts in 1972. Based on a clear energetic hierarchy of Fourier components on the steady-state dynamo branch, an approximate model of interacting modes is constructed covering all essential features of the complete system but allowing simulations with a minimum amount of computation time. We use this model to study the excitation mechanism of the dynamo, the transition from stationary to time-dependent dynamo solutions and the characteristic properties of the latter ones.}, language = {en} } @phdthesis{SeehaferPipin2009, author = {Seehafer, Norbert and Pipin, Valerij V.}, title = {An advective solar-type dynamo without the alpha effect}, issn = {0004-6361}, doi = {10.1051/0004-6361/200912614}, year = {2009}, abstract = {Context: Most solar and stellar dynamo models use the alpha-Omega scenario where the magnetic field is generated by the interplay between differential rotation (the Omega effect) and a mean electromotive force due to helical turbulent convection flows (the alpha effect). There are, however, turbulent dynamo mechnisms that may complement the alpha effect or may be an alternative to it. Aims: We investigate models of solar-type dynamos where the alpha effect is completely replaced by two other turbulent dynamo mechanisms, namely the Omega x J effect and the shear- current effect, which both result from an inhomogeneity of the mean magnetic field. Methods: We studied axisymmetric mean-field dynamo models containing differential rotation, the Omega x J and shear-current effects, and a meridional circulation. The model calculations were carried out using the rotation profile of the Sun as obtained from helioseismic measurements and radial profiles of other quantities according to a standard model of the solar interior. Results: Without meridional flow, no satisfactory agreement of the models with the solar observations can be obtained. With a sufficiently strong meridional circulation included, however, the main properties of the large-scale solar magnetic field, namely, its oscillatory behavior, its latitudinal drift towards the equator within each half cycle, and its dipolar parity with respect to the equatorial plane, are correctly reproduced. Conclusions: We have thereby constructed the first mean-field models of solar-type dynamos that do not use the alpha effect.}, language = {en} } @article{PipinSeehafer2009, author = {Pipin, Valerij V. and Seehafer, Norbert}, title = {Stellar dynamos with Omega x J effect}, issn = {0004-6361}, doi = {10.1051/0004-6361:200810766}, year = {2009}, abstract = {Context. The standard dynamo model for the solar and stellar magnetic fields is based on the \$alphaOmega\$ mechanism, namely, an interplay between differential rotation (the \$Omega\$ effect) and a mean electromotive force generated by helical turbulent convection flows (the \$alpha\$ effect). There are, however, a number of problems with the \$alpha\$ effect and \$alphaOmega\$ dynamo models. Two of them are that, in the case of the Sun, the obtained cycle periods are too short and the magnetic activity is not sufficiently concentrated at low latitudes. Aims. We explore the role of turbulent induction effects that may appear in addition to the \$alpha\$ effect. The additional effects result from the combined action of rotation and an inhomogeneity of the large-scale magnetic field. The best known of them is the \$vec{Omega} imesvec{J}\$ effect. We also include anisotropic diffusion and a new dynamo term that is of third order in the rotation vector \$vec{Omega}\$. Methods. We studied axisymmetric mean-field dynamo models containing differential rotation, the \$alpha\$ effect, and the additional turbulent induction effects. The model calculations were carried out using the rotation profile of the Sun as obtained from helioseismic measurements and radial profiles of other quantities according to a standard model of the solar interior. In addition, we consider a dynamo model for a full sphere that is based solely on the joint induction effects of rotation and an inhomogeneity of the large-scale magnetic field, without differential rotation and the \$alpha\$ effect (a \$delta^{2}\$ dynamo model). This kind of dynamo model may be relevant for fully convective stars. Results. With respect to the solar dynamo, the inclusion of the additional turbulent induction effects increases the period of the dynamo and brings the large-scale toroidal field closer to the equator, thus improving the agreement of the models with the observations. For the \$delta^{2}\$ dynamo working in a full sphere, we find dynamo modes that are steady if the effect of anisotropic diffusion is not included. The inclusion of anisotropic diffusion yields a magnetic field oscillating with a period close to the turbulent magnetic diffusion time.}, language = {en} } @article{Seehafer1994, author = {Seehafer, Norbert}, title = {Relaxation to equilibrium and inverse energy cascades in solar active regions}, isbn = {1-563-47099-3}, issn = {0079-6050}, year = {1994}, language = {en} } @article{Seehafer1994, author = {Seehafer, Norbert}, title = {Alpha effect in the solar atmosphere}, year = {1994}, language = {en} } @article{Seehafer1994, author = {Seehafer, Norbert}, title = {Current helicity and the turbulent electromotive force}, year = {1994}, language = {en} } @article{FeudelSeehafer1995, author = {Feudel, Fred and Seehafer, Norbert}, title = {On the bifurcation phenomena in truncations of the 2D Navier-Stokes equations}, year = {1995}, language = {en} } @article{FeudelSeehaferSchmidtmann1995, author = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf}, title = {Fluid helicity and dynamo bifurcations}, year = {1995}, language = {en} }