Multi-timescale Solar Cycles and the Possible Implications

Based on analysis of the annual averaged relative sunspot number (ASN) during 1700 -- 2009, 3 kinds of solar cycles are confirmed: the well-known 11-yr cycle (Schwabe cycle), 103-yr secular cycle (numbered as G1, G2, G3, and G4, respectively since 1700); and 51.5-yr Cycle. From similarities, an extrapolation of forthcoming solar cycles is made, and found that the solar cycle 24 will be a relative long and weak Schwabe cycle, which may reach to its apex around 2012-2014 in the vale between G3 and G4. Additionally, most Schwabe cycles are asymmetric with rapidly rising-phases and slowly decay-phases. The comparisons between ASN and the annual flare numbers with different GOES classes (C-class, M-class, X-class, and super-flare, here super-flare is defined as $\geq$ X10.0) and the annal averaged radio flux at frequency of 2.84 GHz indicate that solar flares have a tendency: the more powerful of the flare, the later it takes place after the onset of the Schwabe cycle, and most powerful flares take place in the decay phase of Schwabe cycle. Some discussions on the origin of solar cycles are presented.Comment: 8 pages, 4 figure

On the role of strain rate and vorticity in plasmas

It is shown that the magnetic field's local evolution in plasmas is directly affected by an interplay between the deformation (strain rate) and the self-rotation (vorticity) of the elementary plasma fluid volumes. At regions of strong strain rate, the fast local convergence or divergence of the flow causes exponential increase or decrease of the field's components, respectively. At regions of strong vorticity, faster directional than magnitude variations of the field occur, explaining the field alignment of the field minimum-variance direction and the random wandering of the field's tip on a sphere, both observed in the solar wind plasma, even in the absence of Alfven waves. We further investigate the coupling between the maximum strain-rate direction and the local magnetic field, that was previously deduced from magnetic field measurements in the outer heliosphere. Cases of long-lasting, non-Parkerian, radial heliospheric magnetic field are also shown to be periods of field-aligned strain rate. A statistical proof for this alignment is given, assuming that the small-scale field fluctuations are weakly stationary and time reversible. We further propose a generalization of the Stokesian fluid stress-strain relation to the case of one-fluid, collisionless MHD plasmas, including the effects of turbulent viscosity and magnetically induced shearing motion. For a negligible or isotropic or 'field-aligned' thermal pressure tensor, the proposed 'Stokesian plasma' relation implies the field alignment of the solar wind plasma strain-rate direction and leads to anisotropic stress-strain balance equations, related to those of 'firehose' plasma instability. The field alignment of a principal strain-rate direction leads to simplifications in the magnetic-induction equation, especially in the case of force-free fields. For the simplified case of homogeneous, isotropic and incompressible plasma turbulence, the proposed stress-strain-rate relation implies that the velocity and magnetic field inertial range spectra should be identical, further reducing to the Kolmogorov-like k-5/3 law for scale-invariant eddy cascade at constant energy-dissipation rate

Detection of nonlinear dynamics in solar wind and a comet using phase-correlation measures

Nonlinear dynamics in the solar wind and cometary plasma over small time scales are identified using sensitive entropy measures of the weak wave organization in the magnetic field polarized components. All possible linear Gaussian stochastic models are rejected at a high confidence level in all cases. The association of the detected correlations with a forward CIR shock is demonstrated using a large set of very high-resolution Pioneer-10 field measurements. © 1995 Kluwer Academic Publishers

Mean free paths of energetic charged particles parallel and antiparallel to the interplanetary magnetic field

A new method to calculate the mean free paths of energetic particles propagating parallel and anti-parallel to the interplanetary magnetic field, based on quasi-linear theory and the complex spectral polarization analysis of the field, is developed and presented. Applications of the method using HEOS 2 (1 AU), Pioneer 10 (5 AU), Pioneer 11 (20 AU), ICE (Giacobini-Zinner's comet) data have been made, showing that: (a) The mean free paths parallel and anti-parallel to the field can be completely different in various regions of the interplanetary medium and different time periods. (b) Particles are preferentially scattered in one direction. (c) The parallel and anti-parallel mean free paths become equal at certain energy. Comparisons with the results from another computational method are made. © 1994 Kluwer Academic Publishers

Calculating the plasma deformation tensor and kinetic vorticity from magnetic field time series: Applications to the solar wind

It is shown that the magnetic induction equation reduces to an autoregressive model equation. Assuming weakly ergodic field variations in steady mean plasma flow, this model permits the estimation of the mean flow deformation tensor, velocity divergence and kinetic vorticity from magnetic field time series. Applications, made to hourly-averaged, in-ecliptic interplanetary magnetic field (IMF) measurements from Ulysses spacecraft, showed that the direction of maximum deformation rate was, for most of the time, aligned to the mean field, while the vorticity tended to become perpendicular to the mean radial direction at large heliodistances. © 1996 Kluwer Academic Publishers

On experimental evidence of chaotic dynamics over short time scales in solar wind and cometary data using nonlinear prediction techniques

Strong indications of chaotic dynamics underlying in the interplanetary and cometary magnetic field fluctuations over short time scales are identified using HEOS-2 spacecraft (at 1 AU), Pioneer 10 (at 4.8 AU), Pioneer 11 (at 20 AU) and ICE (Giacobini-Zinner cometary environment) high-resolution measurements. Other non-chaotic candidate processes, such as linear deterministic models, fractal Brownian motion, and linear gaussian stochastic models are rejected at a high confidence level using nonlinear prediction methods. Experimental proofs of phase correlations are obtained. Assuming chaotic dynamics, estimations of the Kolmogorov-Sinai entropy are provided. © 1994 Kluwer Academic Publishers

Magnetized vortex tubes in the solar wind plasma

We make new applications of our previously proposed method for estimating the strain-rate tensor and vorticity vector in plasmas (concerning the local deformation and self rotation of the plasma fluid elements, respectively) solely from magnetic field time series. Here we use solar wind measurements of Ulysses spacecraft made in the outer heliosphere, on and off the ecliptic plane, during the period 1990-1998. The application results imply that the solar wind plasma is, to a good approximation, weakly incompressible, being nearly incompressible on the local magnetic field-normal plane, while expanding at maximum strain rate in the magnetic field direction. This property is theoretically expected, at least for low and intermediate beta plasmas, and supports previous arguments for two-dimensional MHD turbulence in the solar wind. In the magnetic induction equation the vorticity term is favoured, being at least an order of magnitude larger than the strain-rate term, thus explaining the magnetic field alignment of the minimum magnetic field variance and the random wandering of the magnetic field's vector tip on a sphere, both being well known, general features of the heliospheric magnetic field fluctuations. Further, the solar wind is found dominated by magnetized vortex sheet structures (MVS), on the tangential plane of which lie the, (not generally aligned) average vectors of magnetic field, vorticity and plasma velocity in the solar-corotating frame of reference. These coplanarity properties are shown to be consistent with a theoretically predicted force-free state, minimizing the total energy while conserving a generalized helicity function. The theory additionally implies that the (not directly measured by Ulysses) electric current density also lies on the MVS tangential plane, hence the MVS also constitute current sheets. The MVS spatial orientation implies that the MVS are wrapped in the form of magnetized vortex tubes with axes aligned to the average magnetic field. The vector couplings, characterizing the MVS, are found to weaken with increasing heliodistance and near the heliospheric current sheet

Review of magneto-vorticity induction in Hall-MHD plasmas

The ideal induction of vector fields in fluids and plasmas is presented as invariance under local convection, 'freezing' into flowlines and transfer of potential. Related consequences are discussed, namely the conservation of local flux and total helicity and the force-free relaxation state. In the framework of single-fluid Hall-MHD plasma flow model, the magnetic field and vorticity (which are formally analogous and generally anti-correlated, but each not ideally inducted, i.e. perfectly 'frozen-into' the flow) are shown to combine in a unified magneto-vorticity field, which is ideally inducted in perfectly-conducting, however even forced, non-isentropic and viscous plasmas. Relaxation plasma states of conserved or extreme helicity magnetor-vorticity fields are derived and shown to be generalized force-free states, similar to those previously derived in the framework of Hall-MHD and the multi-component plasma model. The magneto-vorticity induction in visco-resistive plasmas is also discussed. Application of the magneto-vorticity field concept in the study of type I superconductors and the spontaneous generation of magnetic fields are reviewed. The Cowling 'anti-dynamo' theorem for axisymmetric flows is extended in Hall-MHD and for arbitrary flows and is shown that, in principle, the resistive (ohmic) dissipation of the magnetic field can be balanced by non-isentropic heating and/or helical forcing effects

Towards a fluid description of directional particle flux observations

We propose that, whenever directional flux measurements of a population of particles (e.g. solar energetic particles, cosmic rays, solar wind plasma) of well-defined energy resolution are available, new macroscopic fluid-like quantities (namely the energy dependent analog of density, mean velocity, anisotropic pressure, temperature and heat flux) can be rigorously estimated, thus describing the sub-flux referring to that energy range in fluid terms. Exact, closed relations for these quantities as functions of lower order spherical harmonics coefficients are analytically derived, offering a new interpretation of the anisotropy flux components in fluid terms. Among them, the, most commonly used, first order anisotropy vector is shown that can be interpreted as the direction of the population's mean velocity and, for strongly isotropic distributions, the direction of heat flux. Indicative applications are presented, using energetic particle flux measurements of Ulysses spacecraft. © 2004 Elsevier B.V. All rights reserved

A nonlinear rlc solar cycle model

A simplified, monoparametric model, based on the Van der Pol nonlinear RLC electric oscillator, is found capable of describing the shape and related morphological properties (such as the Waldmeier effect) of the sunspot cycles. The model can also exhibit long periods of sunspot inactivity of the Maunder Minimum type. According to the model, the significant rise-to-fall time asymmetry of the most recent cycles suggests that it is unlikely that another cycle suppression will occur in the forthcoming decades. The complete sunspot record and the system's attractor are successfully emulated, given the sunspot number at cycle maxima. © 1996 Kluwer Academic Publishers