The primary goal of the program was to discuss the current understanding and new approaches to solving the problem of the origin of solar and stellar magnetic field, which is one of the central problems of physics and astrophysics, and a key to understanding the cosmic magnetism, in general. There are two main difficulties in studying this problem: 1) magnetic fields are generated by turbulent dynamos in convection zones below the visible surface, not accessible by direct observations; 2) solar and stellar magnetic activity is a multi-scale phenomenon, involving physical processes on very small scales, probably, below the current observational limit, and at the same time showing remarkable large-scale spatial and temporal organizations over a whole star. The prime target of our investigation is the Sun, which serves as the Rosetta Stone in this field and holds the key to unlocking the secrets of magnetic field generation in the Universe. The most detailed observational data and theoretical models have been obtained for the Sun, but also a very significant progress has been in observations and theories of magnetism on other stars.

The program was focused on the recent observational results from Solar Dynamics Observatory and large ground-based telescopes, Swedish Solar Telescope and New Solar Telescope, as well as on the results of turbulence theory and numerical simulations. The program brought together observers and theorists and provided a forum for broad discussions of the physical processes in the Sun and stars and related fundamental problems of theoretical physics, such as MHD turbulence, magnetic self-organization in plasma, radiative and turbulent energy transport, multi-scale dynamics, magnetic helicity and topological interpretation.

The main achievements of the program are in establishing links between the dynamo theory, numerical simulations and observational results, developing collaborations, approaches and ideas, and getting new science results. The Nordita program stimulated further development of the dynamo theory, numerical simulations and observational programs.

The overall duration was 4 weeks. The program activity covered the following topics: Numerical simulations and mean-field theory, Recent results of numerical dynamo simulations, Effects of magnetic helicity and cross-helicity, Models of turbulent diffusivity and magnetic pumping, Progress in mean-field dynamo models.

As a rule, the morning hours were devoted to presentations and discussions, while the afternoons were left free for work, although most of us gathered for coffee each afternoon, during which some of the latest developments from participants were discussed.

The total number of program participants was 45
including 4 women, and 20 Nordic participant
(Denmark 1, Finland 3, Sweden 16, of which 12 from Stockholm).
A significant portion of the participants came from the US (5),
Russia (4), Brazil (2), as well as Germany (6), Israel (2),
and the UK (2).
Of the 33 people from outside Stockholm,
24 stayed for 3 weeks or longer.
The program marked a highlight in the ERC-supported
Astrophysical
Dynamo Project at Nordita,
with two of the post-docs
(Piyali Chatterjee
and
Gustavo Guerrero,
right)
just departing.

Solar dynamo
models and effects of magnetic helicity and cross-helicity (A. Brandenburg, A. Bonanno, V.
Pipin, D. Sokoloff, K. Kuzanyan, N. Yokoi, S. Candelaresi, D.
Mitra, M. Reshetnyak, G. Guerrero)

An important quadratic invariant of MHD is cross helicity.
Theory now predicts that at the solar surface is should be a
negative multiple of the mean radial field. Results from new
near-surface shear layer dynamos were presented, showing the
importance of magnetic helicity. In this connection, new aspects
of the Yoshizawa effect were also considered.

Flow-turbulence interaction in magnetic reconnection was
investigated. Breakage of symmetry associated with mean-field
configurations will lead to pseudoscalar generation in turbulence.
Cross helicity (velocity--magnetic-field correlation) is a
topological invariant of the magnetohydrodynamic equations.
Cross-helicity effects in the momentum and magnetic-induction
equations were analyzed. On the basis of this analysis, modulation
of magnetic-reconnection rate due to the turbulent cross-helicity
was estimated for the first time. Such work is expected to pave
the way for understanding the turbulence effects in magnetic
reconnection. Possibility and validity of the cross-helicity
effect in magnetic reconnection were discussed with several
researchers participating in this program. In relation to the
cross-helicity dynamo, spatiotemporal distributions of the
turbulent cross helicity were numerically investigated in the
local and global convection domains in collaboration with some
participants. In the context of solar activity cycle,
incorporation of the cross-helicity effects into dynamical-system
equations were examined.

Kinetic helicity is a topological invariant of the hydrodynamic
equations. According to the turbulence theory of inhomogeneous
hydrodynamic turbulence, inhomogeneity of turbulent helicity
coupled with the rotational motion has been expected to play an
important role in the large-scale vorticity generation. Such
effects should be examined in numerical simulations. Validation of
such effect using the pencil-code calculation has been preparing
in collaboration with NORDITA researchers.

Due to the limited statistics some of the mean-field quantities
considered in dynamo theory can fluctuate. These fluctuations can
produce new features in the dynamo systems. On an example of the
Parker's dynamo in the spherical shell we demonstrate how the
small fluctuations (about 5 percents) of the mean level of the
alpha-effect can cause significant equatorial asymmetry of the
oscillatory magnetic field, as well as propagation of the dynamo
wave through the equatorial plane.

Spherical convective rotating shells demonstrate existence of
kinematic helicity even in the incompressible case. However, due
to some theoretical background as well as to 3D simulations,
spatial distribution of the kinetic helicity for incompressible
and compressible systems can be quite different.

Solar dynamo with a positive alpha effect in the overshoot layer
and a deep meridional flow was investigated. In this model the
alpha effect is produced by a magnetic instability at the
tachocline. The parity selection mechanism was investigated.

Turbulence
models in dynamo theory (I. Rogachevskii, N. Kleeorin, K.-H. Raedler, N.
Mansour, M. Rheinhardt, A. Brandenburg, Y. Snellman)

The tau approach and other closure hypotheses were discussed at
length in a discussion session dedicated to this topic. Numerical
evidence for its validity is was presented, but a lack of overlap
with the second order correlation approximation was noted.

New work in connection with Reynolds stress modeling has been
discussed and simulations have been presented to quantify the
effect of the return to isotropy as a function of Reynolds number.

New work on two-dimensional turbulence has been performed using
graphics card computations and the saturation behavior of the
inversely cascading energy has been modeled with a 3-scale model.

Turbulent transport in stratified and/or rotating turbulence has
been investigated. The test-field method is used where transport
coefficients are determined by solving a set of equations with
properly chosen mean magnetic fields or mean scalars. The method
is adapted to mean fields which may depend on all thee space
coordinates. Anisotropy of turbulent diffusion is found to be
moderate in spite of rapid rotation or strong density
stratification. Contributions to the mean electromotive force
determined by the symmetric part of the gradient tensor of the
magnetic field turn out to be important. In stratified rotating
turbulence, the alpha effect is strongly anisotropic, suppressed
along the rotation axis on large length scales, but strongly
enhanced at intermediate length scales.

New ideas about the bottleneck effect in turbulence were
developed. This work emerged from one of the extended coffee
sessions. The closure in the one dimensional incompressible
Boussinesq case was investigated, and tried to modify it to better
match the numerical results from pencil-code. It would seem that
the results from the Pencil-code are much more affected by the
presence of vertical boundaries than the closure results. To shed
light on this problem a variety of different closure approaches
was investigated, none of which produced results similar to those
from pencil-code without some serious side effects. A lot of new
ideas and different approaches were discussed, and will most
probably lead to important breakthroughs in this field in the near
future.

Spontaneous Symmetry Breaking of the chiral symmetry in Tayler
Instability was investigated. The basic idea is to test the
recently proposed scenario for the SSB in MHD in the case of an
instability produced in stably stratified medium. In addition, to
study the Tayler Instability the pencil-code set-up was
implemented for the study of the possible helical modes that can
arise due to the instability. The aim is to see whether or not the
instability can give birth to a breaking of a non-helical state,
so causing the appearance of helicity. Several questions regarding
this phenomena are still unanswered, like the difference between
the linear and non-linear stages of the growth phase as well as
the role that such a breaking can have in generating a dynamo.

Magnetic
self-organization in turbulent plasma (I. Kitiashvili, N. Mansour, I.
Rogachevskii, N. Kleeorin, K. Kemel, A. Brandenburg)

The origin of magnetic flux concentrations in active regions and
sunspots was discussed. New work in connection with the negative
effective magnetic pressure instability has been initiated. A
related issue concerns the location of the solar dynamo, and more
work has been done to examine the idea that the solar dynamo is a
distributed one, shaped by near-surface shear.

Large-scale vortex instability and its applications to the
starspots in rapidly rotating stars were discussed. The mechanisms
of production of vorticity in the solar conditions were
investigated.

The first numerical demonstration of the negative effective
magnetic pressure instability was obtained in direct numerical
simulations of stably-stratified, externally-forced, isothermal
hydromagnetic turbulence. By the action of this instability,
initially uniform horizontal magnetic field forms flux
concentrations whose scale is large compared to the turbulent
scale. It is shown that the magnetic energy of these large-scale
structures is only weakly dependent on the magnetic Reynolds
number. The results supports earlier mean-field calculations and
analytic work which identified this instability. Applications to
the formation of active regions in the Sun are discussed.

The magnetic self-organization effects were also investigated in
realistic simulations of solar magnetoconvections, including
spontaneous formation of magnetic structures and the filamentary
structure of sunspots. The sunspot penumbra is a transition zone
between the strong vertical magnetic field area (sunspot umbra)
and the quiet Sun. The penumbra has a fine filamentary structure
that is characterized by magnetic field lines inclined toward the
surface. Numerical simulations of solar convection in inclined
magnetic field regions have provided an explanation of the
filamentary structure and the Evershed outflow in the penumbra.
The radiative MHD simulations were used to investigate the
influence of the magnetic field inclination on the power spectrum
of vertical velocity oscillations. The results revealed a strong
shift of the resonance mode peaks to higher frequencies in the
case of a highly inclined magnetic field. The frequency shift for
the inclined field is significantly greater than that in
vertical-field regions of similar strength. This is consistent
with the behavior of fast MHD waves.

Observational
input and constraints for the dynamo problem and solar MHD (J. Stenflo, P. Goode, D. Sokoloff,
V. Pipin, K. Kuzanyan, A. Kosovichev, G. Scharmer)

The possibility to explain the statistical relations of the sunspot activity cycle, like the so-called Waldmeier relations, by means of the mean field dynamo model with the fluctuating alpha-effect was investigated. The dynamo model includes the long-term fluctuations of the alpha-effect and two types of the nonlinear feedback of the mean-field on the alpha-effect including the algebraic quenching and the dynamic quenching due to the magnetic helicity generation. We found that the models are able to reproduce qualitatively the inclination and dispersion across the Waldmeier relations with the 20% fluctuations of the alpha-effect. The models with the dynamic quenching are in a better agreement with observations than the models with the algebraic alpha-quenching. Statistical distributions of the modeled parameters, like the amplitude, period, the rise and decay rates of the sunspot cycles, are compared with observations for 2D- and 1D-models.

A tendency toward superdiffusion in solar surface turbulence has been mentioned and discussed in connection with expectations from local surface dynamos.

Differences between the actual meridional flow speed, as obtained from Doppler measurements, and that obtained from magnetic feature tracking has been discussed.

The recent global analysis of the 15 year synoptic data set of SOHO/MDI full disk magnetograms was presented and discussed in depth, since the results may have profound implications for our understanding of how the Sun's dynamo operates. The tilt angles of the 160,000 measured bipolar magnetic regions are found to increase with the sine of the latitude, which implies that emerging regions of all sizes, from large to small, contribute to a general N-S dipole moment that will lead to the reversal of the old global dipole field and the regeneration of the new one. Violations of Hale's polarity law are rather common, at a few percent level. Examples have been identified, which show medium-sized bipolar regions of opposite orientations side by side in the same latitude zone of a given magnetogram. These examples are manifestly incompatible with the old Babcock-Leighton type paradigm that sunspots originate from a coherent subsurface toroidal flux system, but they are consistent with turbulent dynamo theories, according to which fluctuations at all scales play a fundamental role.

New observational results of helioseismology and magnetic field measurements from the Solar Dynamics Observatory, as well as high-resolution observations from the Swedish Solar Telescope and Big Bear Solar Observatory were discussed in relation to the theoretical dynamo and MHD turbulence studies. New data assimilations of solar convection have been developed.

Numerical MHD simulations (F. Busse, R. Simitev, P. Käpylä, M. Mantere, A. Brandenburg, G. Guerrero, J. Warnecke, I. Kitiashvili, G. Di Bernardo)

Simulations of plasmoid ejections from convection in a spherical shell have been developed further.

The importance of fluctuating alpha effects have been discussed both in the geodynamo context, but also as a general mechanism to explain the phenomenon of what is known as shear dynamos.

The generation of large scale magnetic field by strongly-driven chaotic convection in rotating spherical fluid shells under the assumption of the Boussinesq approximation has been studied. This configuration is the simplest self-consistent model of the spherical dynamo problem and it can be applied, with some adjustments of the values of the basic governing parameters, both to planetary dynamos and the Solar dynamo. The model was studied by direct numerical simulation of the coupled Navier-Stokes, magnetic induction and energy equations, with the inclusion of all nonlinear effects and without ad-hoc assumptions. In the case of thick-shell dynamos, which is appropriate to the Geodynamo, the possibility of the existence of two essentially different dynamo attractors at identical parameter values was studied. In the case of thin-shell dynamos, which is appropriate to the solar dynamo, a large number of numerical simulations was performed in an attempt to model the profile of differential rotation in the solar interior and the dynamics of large-scale magnetic structures and active regions in the Sun. In addition, the self-consistent dynamo model was used to compute maps of various quantities which are of particular interest, such as magnetic, kinetic and cross helicity, and discussed the results with other participants.

In the Pencil code a numerical setup was implemented for the study of the possible events of magnetic reconnection, with or without turbulence. This work aims, among others, to test numerically a model of fast magnetic reconnection in the presence of weak turbulence proposed by Lazarian & Vishniac. First, 2-D Sweet-Parker reconnection was investigated, the stage before turbulence injection. A full understanding of this process is required in order to perform further analysis of reconnection in the presence of turbulence. Numerical simulation setup in order to successfully reproduce the Sweet-Parker scaling of reconnection was investigated. In particular the behaviour at low values for resistivity and the role of the Guide Field was investigated.

Links between solar, astrophysical and geophysical dynamos

Links between solar, astrophysical and geophysical dynamos (R. Arlt, F. Busse, R. Simitev, M. Reshetnyak, E. de Gouveia Dal Pino, V. Duez, S. Sur, A. Bobrick, Xing Wei, M. Mantere, F. del Sordo)

The occurrence of an alpha effect in the absence of any
pseudo-scalars has been discussed in connection with spontaneous
symmetry breaking. New work on the Tayler instability has been
initiated and the possible relevance to magnetars has been
mentioned.

Turbulent fast reconnection and its role on the diffusive
transport of magnetic flux in astrophysical environments were
discussed. Potential applications of this transport to dynamo
problems is foreseen.

Outflow ejection by supernovae in galaxy disks was studied.
Numerical simulations of supernova triggered galactic outflow
formation were performed including realistic galactic disk/coronal
setups for the Milky Way and starburst galaxies, the possibility
of using these setups in magnetic helicity transport studies
related to galactic dynamos has been discussed. The role of
kinectic effects on turbulent dynamo models related to the IGM
using a Kinectic-MHD description was also discussed.

Progress on research on the generation of large scale magnetic
field by strongly-driven chaotic convection in rotating spherical
fluid shells under the assumption of the Boussinesq approximation
has been reported. In addition, self-consistent dynamo models have
been developed to compute maps of various quantities which are of
particular interest, such as magnetic, kinetic and cross helicity,
and discussed the results with other participants.

Thin shell dynamos were investigated with the goal of
understanding as many solar magnetic phenomena as is possible with
numerical simulations of a most simple physically consistent
convection driven dynamo model. With a given ratio of 0.65 between
inner and outer radii of the rotating spherical there are only 4
parameters of the coupled Navier-Stokes equations, heat equation,
and equation of magnetic induction that can be varied: Rayleigh
number R, rotation parameter tau, Prandtl number and magnetic
Prandtl number.

Although the geostrophic differential rotation found in the
simulations clearly differs from the solar differential rotation,
the oscillatory dynamo shares many features with the observed
solar magnetic cycle. The most important new result is the strong
non-axisymmetric (m=1) component of the oscillating magnetic
field, the energy of which far exceeds the energy of the
axisymmetric component. The latter is traditionally assumed to be
the dominant component of the solar magnetic field. The new result
is in good agreement with the phenomenon of active longitudes on
the sun.

In geodynamo, it's believed that Busse rolls generate the alpha
effect, namely the fluid helical motions in cyclonic and
anti-cyclonic convection rolls twist the toroidal field lines to
create the poloidal field lines. An alternative is the precession
which can generate inertial waves arising from the destabilization
of the internal shear layers (the so-called triad resonance) to
induce the alpha effect. The topography or ellipticity can help
the generation of these waves. However, with the spectral code,
it's impossible to calculate for the topography and large
ellipticity. Geodynamo calculations with the pencil code have been
discussed.

Preprints:

As a result of the program, several Nordita preprints have already appeared or are expected to appear:

- NORDITA-2011-060
*Mean-field transport in stratified and/or rotating turbulence*by A. Brandenburg, K.-H. Rädler, &K. Kemel - NORDITA-2011-072
*Detection of negative effective magnetic pressure instability in turbulence simulations*by A. Brandenburg, K. Kemel, N. Kleeorin, D. Mitra, & I. Rogachevskii - NORDITA-2011-077
*Effects of stratification in spherical shell convection*by P.J. Käpylä, M.J. Mantere, & A. Brandenburg - NORDITA-2011-078
*Verification of Reynolds stress parameterizations from simulations*by J.E. Snellman, A. Brandenburg, P.J. Käpylä, & M.J. Mantere - NORDITA-2011-079
*Dependence of the large-scale vortex instability on latitude, stratification and domain size*by M.J. Mantere, P.J. Käpylä, & T. Hackman - NORDITA-2011-087
*Modeling spatio-temporal nonlocality in mean-field dynamos*by M. Rheinhardt, & A. Brandenburg - NORDITA-2011-088
*The fluctuating α-effect and Waldmeier relations in the nonlinear dynamo models*by V.V. Pipin, & D.D. Sokoloff - NORDITA-2011-092
*Current helicity of active regions as a tracer of large-scale solar magnetic helicity*by H. Zhang, D. Moss, N. Kleeorin, K. Kuzanyan, I. Rogachevskii, D. Sokoloff, Y. Gao, & H. Xu - NORDITA-2011-108
*Spontaneous formation of flux concentrations in a stratified layer*by K. Kemel, A. Brandenburg, N. Kleeorin, D. Mitra, & I. Rogachevskii - NORDITA-2011-117
*Mean-field closure parameters for passive scalar turbulence*by J. E. Snellman, M. Rheinhardt, P. J. Käpylä, M. J. Mantere, & A. Brandenburg - NORDITA-2011-118
*Magnetic Flux Transport by turbulent reconnection in astrophysical flows*by Elisabete M. de Gouveia Dal Pino, Márcia R. M. Leão, Reinaldo Santos-Lima, Gustavo Guerrero, Grzegorz Kowal, & Alex Lazarian - NORDITA-2011-119
*Growth rate of small-scale dynamo at low magnetic Prandtl numbers*by N. Kleeorin, & I. Rogachevskii - NORDITA-2011-120
*Solar cycle properties described by simple convection-driven dynamos*by Radostin D. Simitev, & Friedrich H. Busse - NORDITA-2011-121
*Bipolar Magnetic Regions on the Sun: Global Analysis of the SOHO/MDI Data Set*by J. O. Stenflo, & A. G. Kosovichev - NORDITA-2011-122
*Vortex Tubes of Turbulent Solar Convection*by I.N. Kitiashvili, A.G. Kosovichev, N.N. Mansour, S.K. Lele & A.A. Wray - NORDITA-2012-6
*Dynamics of Magnetized Vortex Tubes in the Solar Chromosphere*by I.N. Kitiashvili, A.G. Kosovichev, N.N. Mansour, & A.A. Wray - NORDITA-2012-7
*Lagrangian chaos in an ABC--forced nonlinear dynamo*by E. L. Rempel, A. C.-L. Chian, & A. Brandenburg

*Thanks a lot for the fantastic program.**I think it was very good that we also had observers and "non-simulation people"*.*The organization was very good. I very much like the structure, with morning talks and after lunch just the coffee.**I am very grateful to the organizers of the program and to Nordita for creating excellent conditions for scientific work and cooperation.**In some parts of the program, the schedule became dense.**The portion of the participants who stay most period of the program was very high. As this result, as a whole, we could enjoy enough time to discuss and collaborate with these participants.**I enjoyed meeting and talking to many of the participants. The community of people on the meeting has been strong, lively and friendly.**It might be interesting, if the meeting had some list of open problems, which would be worked out by the participants during the program.**I found that you had got together a great group of people, and that the interactions were excellent. It is hard to improve on it. I think it would be great if this program could be repeated in a couple of years.**A lot of new ideas and different approaches were discussed, and will most probably lead to important breakthroughs in this field in the near future.**My comments on this Nordita program are enthusiastic! I have benefit a lot from this very scientifically intense and friendly atmosphere in during this month.*

During the meeting, Koen Kemel defended his licentiate thesis on "Mean-field theory in magneto-hydrodynamics and the generation of magnetic flux concentrations" with Sasha Kosovichev as opponent.