An analysis of the fluctuations of the geomagnetic dipole

The time evolution of the strength of the Earth's virtual axial dipole moment (VADM) is analyzed by relating it to the Fokker-Planck equation, which describes a random walk with VADM-dependent drift and diffusion coefficients. We demonstrate first that our method is able to retrieve the correct shape of the drift and diffusion coefficients from a time series generated by a test model. Analysis of the Sint-2000 data shows that the geomagnetic dipole mode has a linear growth time of 13 to 33 kyr, and that the nonlinear quenching of the growth rate follows a quadratic function of the type [1-(x/x0)^2]. On theoretical grounds, the diffusive motion of the VADM is expected to be driven by multiplicative noise, and the corresponding diffusion coefficient to scale quadratically with dipole strength. However, analysis of the Sint-2000 VADM data reveals a diffusion which depends only very weakly on the dipole strength. This may indicate that the magnetic field quenches the amplitude of the turbulent velocity in the Earth's outer core.Comment: 11 pages, 6 figure

Fast plasma heating by anomalous and inertial resistivity effects

Fast plasma heating by anomalous and inertial resistivity effects is described. A small fraction of the plasma contains strong currents that run parallel to the magnetic field and are driven by an exponentiating electric field. The anomalous character of the current dissipation is caused by the excitation of electrostatic ion cyclotron and/or ion acoustic waves. The role of resistivity due to geometrical effects is considered. Through the use of a marginal stability analysis, equations for the average electron and ion temperatures are derived and numerically solved. The evolution of the plasma is described as a path in the drift velocity diagram, in which the drift velocity is plotted as a function of the electron to ion temperature ratio

Helical rotating turbulence. Part II. Intermittency, scale invariance and structures

We study the intermittency properties of the energy and helicity cascades in two 1536^3 direct numerical simulations of helical rotating turbulence. Symmetric and anti-symmetric velocity increments are examined, as well as probability density functions of the velocity field and of the helicity density. It is found that the direct cascade of energy to small scales is scale invariant and non-intermittent, whereas the direct cascade of helicity is highly intermittent. Furthermore, the study of structure functions of different orders allows us to identify a recovery of isotropy of strong events at very small scales in the flow. Finally, we observe the juxtaposition in space of strong laminar and persistent helical columns next to time-varying vortex tangles, the former being associated with the self-similarity of energy and the latter with the intermittency of helicity.Comment: 11 pages, 10 figure

Statistical dynamo theory: Mode excitation

We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B = sum_k a^k(t) b^k(r). We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients a^k(t) is governed by a stochastic differential equation from which we infer their averages , autocorrelation functions <a^k(t) a^{k*}(t+tau)>, and an equation for the cross correlations . The eigenfunctions of the dynamo equation (with eigenvalues lambda_k) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Im(lambda_k) and -1/(Re lambda_k), respectively. The relative r.m.s. excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for / in case the fundamental mode b^0 has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that / ~ 1/N where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or FOSA) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Re(lambda_k) < 0.Comment: 14 pages, 2 figures. Accepted for publication in Physical Review

A simple mechanism for the reversals of Earth's magnetic field

We show that a model, recently used to describe all the dynamical regimes of the magnetic field generated by the dynamo effect in the VKS experiment [1], also provides a simple explanation of the reversals of Earth's magnetic field, despite strong differences between both systems.Comment: update version, with new figure

Magnetic diffusivity tensor and dynamo effects in rotating and shearing turbulence

The turbulent magnetic diffusivity tensor is determined in the presence of rotation or shear. The question is addressed whether dynamo action from the shear-current effect can explain large-scale magnetic field generation found in simulations with shear. For this purpose a set of evolution equations for the response to imposed test fields is solved with turbulent and mean motions calculated from the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate turbulent transport coefficients. The diagonal components of the turbulent magnetic diffusivity tensor are found to be very close together, but their values increase slightly with increasing shear and decrease with increasing rotation rate. In the presence of shear, the sign of the two off-diagonal components of the turbulent magnetic diffusion tensor is the same and opposite to the sign of the shear. This implies that dynamo action from the shear--current effect is impossible, except perhaps for high magnetic Reynolds numbers. However, even though there is no alpha effect on the average, the components of the alpha tensor display Gaussian fluctuations around zero. These fluctuations are strong enough to drive an incoherent alpha--shear dynamo. The incoherent shear--current effect, on the other hand, is found to be subdominant.Comment: 12 pages, 13 figures, improved version, accepted by Ap

Mode analysis of numerical geodynamo models

It has been suggested in Hoyng (2009) that dynamo action can be analysed by expansion of the magnetic field into dynamo modes and statistical evaluation of the mode coefficients. We here validate this method by analysing a numerical geodynamo model and comparing the numerically derived mean mode coefficients with the theoretical predictions. The model belongs to the class of kinematically stable dynamos with a dominating axisymmetric, antisymmetric with respect to the equator and non-periodic fundamental dynamo mode. The analysis requires a number of steps: the computation of the so-called dynamo coefficients, the derivation of the temporally and azimuthally averaged dynamo eigenmodes and the decomposition of the magnetic field of the numerical geodynamo model into the eigenmodes. For the determination of the theoretical mode excitation levels the turbulent velocity field needs to be projected on the dynamo eigenmodes. We compare the theoretically and numerically derived mean mode coefficients and find reasonably good agreement for most of the modes. Some deviation might be attributable to the approximation involved in the theory. Since the dynamo eigenmodes are not self-adjoint a spectral interpretation of the eigenmodes is not possible

Energetic particles in solar flares. Chapter 4 in the proceedings of the 2nd Skylab Workshop on Solar Flares

The recent direct observational evidence for the acceleration of particles in solar flares, i.e. radio emission, bremsstrahlung X-ray emission, gamma-ray line and continuum emission, as well as direct observations of energetic electrons and ions, are discussed and intercorrelated. At least two distinct phases of acceleration of solar particles exist that can be distinguished in terms of temporal behavior, type and energy of particles accelerated and the acceleration mechanism. Bulk energization seems the likely acceleration mechanism for the first phase while Fermi mechanism is a viable candidate for the second one

Fast electron slowing-down and diffusion in a high temperature coronal X-ray source

Finite thermal velocity modifications to electron slowing-down rates may be important for the deduction of solar flare total electron energy. Here we treat both slowing-down and velocity diffusion of electrons in the corona at flare temperatures, for the case of a simple, spatially homogeneous source. Including velocity diffusion yields a consistent treatment of both "accelerated" and "thermal" electrons. It also emphasises that one may not invoke finite thermal velocity target effects on electron lifetimes without simultaneously treating the contribution to the observed X-ray spectrum from thermal electrons. We present model calculations of the X-ray spectra resulting from injection of a power-law energy distribution of electrons into a source with finite temperature. Reducing the power-law distribution low-energy cutoff to lower and lower energies only increases the relative magnitude of the thermal component of the spectrum, because the lowest energy electrons simply join the background thermal distribution. Acceptable fits to RHESSI flare data are obtained using this model. These also demonstrate, however, that observed spectra may in consequence be acceptably consistent with rather a wide range of injected electron parameters