376 research outputs found
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
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
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
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