A. A. Ruzmaikin

Rate of helicity production by solar rotation

In recent years, solar observers have discovered a striking pattern in the distribution of coronal magnetic structures: northern hemisphere structures tend to have negative magnetic helicity, while structures in the south tend to have positive magnetic helicity. This hemispheric dependence extends from photospheric observations to in situ measurements of magnetic clouds in the solar wind. Understanding the source of the hemispheric sign dependence, as well as its implications for solar and space physics has become known as the solar chirality problem. Rotation of open fields creates the Parker spiral which carries outward 1047 Mx2 of magnetic helicity (in each hemisphere) during a solar cycle. In addition, rough estimates suggest that each hemisphere sheds on the order 1045 Mx2 in coronal mass ejections each cycle. Both the α effect (arising from helical turbulence) and the Ω effect (arising from differential rotation) should contribute to the hemispheric chirality. We show that the Ω effect contribution can be captured in a surface integral, even though the helicity itself is stored deep in the convection zone. We then evaluate this surface integral using solar magnetogram data and differential rotation curves. Throughout the 22 year cycle studied (1976–1998) the helicity production in the interior by differential rotation had the correct sign compared to observations of coronal structures - negative in the north and positive in the south. The net helicity flow into each hemisphere over this cycle was approximately 4 × 1046 Mx2. For comparison, we estimate the α effect contribution; this may well be as high or higher than the differential rotation contribution. The subsurface helicity can be transported to the corona with buoyant rising flux tubes. Evidently only a small fraction of the subsurface helicity escapes to the surface to supply coronal mass ejections.

Kinematic dynamo problem in a linear velocity field

A magnetic field is shown to be asymptotically ( t → ∞) decaying in a flow of finite conductivity with v = Cr , where C = C ζ ( t ) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

Distributions of the interplanetary magnetic field revisited

The adequacy of the power spectrum to characterize the variations of a parameter depends on whether or not the parameter has a Gaussian distribution. We here perform very simple tests of Gaussianity on the distributions of the magnitudes of the interplanetary magnetic field, and on the distributions of the components; that is, we find the first four cumulants of the distributions (mean, variance, skewness, and kurtosis) and their solar cycle variations. We find, consistent with other recent analyses, that the traditional distributions of the 1-hour averaged magnitude are not distributed normally or lognormally as has often been assumed and the 1-hour averaged z component is found to have a nonzero kurtosis. Thus the power spectrum is insufficient to completely characterize these variations and polyspectra are needed. We have isolated variations in the 1/f frequency region of the spectrum and show that the distributions of the magnitudes have nonzero skewness and kurtosis, the magnitudes are not distributed lognormally, and the distributions of the components have nonzero kurtosis. Thus higher-order spectra are again needed for a full characterization.

Asymptotic solution of the α2-dynamo problem

Abstract The turbulent dynamo equation with non-uniform mean helicity is solved in an approximation, which is similar to the quasi-classical approximation of quantum mechanics. We evaluate the rate of growth of the magnetic field and obtain a condition for dynamo action. The generated magnetic field is concentrated in the vicinity of an extremum of mean helicity, but in general vanishes at the point of extremum itself. The field is asymptotically force-free. The results obtained here clarify the fact, known from numerical calculations, that the threshold values of the dynamo-number for excitation of dipole and quadrupole modes are very close to each other.

A dynamo theorem

Abstract It is shown that the frozen-in magnetic field in a given random homogeneous flow of an incompressible fluid which is renewed after a finite characteristic time grows exponentially. The rate-of-growth is positive in the limit of small magnetic diffusivity and continuous in v m . The increase of the rates-of-growth for successive field moments is revealed by the intermittent distribution of the magnetic field generated. The results are obtained by reducing the kinematic dynamo problem to the evaluation of the product of a large number of independent random operators.

A generalized two-disk dynamo model

Abstract A generalized two-disk dynamo model is considered that includes mechanical friction; this model is intended to simulate in its broad character the behavior of the geodynamo. Fixed points, limit cycles and chaotic attractors are located for different input parameters of the model. The chaotic regimes are of several kinds as are the “routes to chaos”. Several approximate models, helpful for studying the dynamo are discussed. A number of essential differences from the well-known Rikitake dynamo are demonstrated.

Maximally-efficient-generation approach in the dynamo theory

Abstract We propose a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number. The procedure reduces to matching the local asymptotic forms for the magnetic field generated near individual extrema of generation strength. The basis of the proposed method, named here the Maximally-Efficient-Generation Approach (MEGA), is the assertion that properties of global asymptotic solutions of the kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of the extrema. The general method is illustrated by the global asymptotic solution of the α2-dynamo problem in a slab. The nature of oscillatory solutions revealed earlier in numerical simulations and the reasons for the dominance of even magnetic modes in slab geometry are clarified. Applicability of the asymptotic solutions at moderate values of the asymptotic parameter is also discussed. We confirm this applicability u...

Properties of a nonlinear solar dynamo model

Abstract A simple nonlinear model is developed for the solar dynamo, in which the real convective spherical shell is approximated by a thin flat slab, and only the back-reaction of the field B on the helicity is taken into account by choosing the simple law α = α(1-ζB 2), where α and ζ are constants, to represent the decrease in generation coefficient ζ with increasing field strength. Analytic expressions are obtained for the amplitude of the field oscillation and its period, T, as functions of the deviation d - dCT of a dynamo number d from its critical value dcr for regeneration. A symmetry is found for the case of oscillations of small constant amplitude: B(t+½T)= -B(t). A Landau equation is obtained that describes the transition to such oscillations.

SEARCH FOR CLIMATE TRENDS IN SATELLITE DATA

Unambiguous determination of trends is the central theme of climate change studies. A promising way to validate and quantify a warming trend of few degrees on a time scale of a century, predicted by climate models, is the use of measurements provided by satellites. However, climate variables, such as temperature and concentration of water vapor in the Earths atmosphere, are noisy and subject to seasonal and interannual variabilities. The lifetime of any single satellite is relatively short (< 5–10 years) and producing long-term data records by using successive satellite introduces inter-calibration problems. Standard methods of trend determination, such as the least square fit of a linear trend, require sufficiently long time series and thus are not effective for the analysis of satellite data. Here, we applied the Empirical Mode Decomposition (EMD) and find it to be more efficient in the search for climate trends in the relatively short time series provided by satellites. We give examples of climate tim...

The spectrum of the interplanetary magnetic field near 1.3 AU

A time series of the interplanetary magnetic field measured near 1.3 AU by Phobos 2 is analyzed as a fractal. The fractal dimension of the curves corresponding to the components and to the strength of the magnetic field are found to be close to 5/3. The corresponding spatial spectra are interpreted in the framework of MHD turbulence.