The Dependence of Dynamo α\alpha-Effect on Reynolds Numbers, Magnetic Prandtl Number, and the Statistics of MHD Turbulence

We generalize the derivation of dynamo coefficient $\alpha$ of Field et al (1999) to include the following two aspects: first, the de-correlation times of velocity field and magnetic field are different; second, the magnetic Prandtl number can be arbitrary. We find that the contributions of velocity field and magnetic field to the $\alpha$ effect are not equal, but affected by their different statistical properties. In the limit of large kinetic Reynolds number and large magnetic Reynolds number, $\alpha$-coefficient may not be small if the de-correlation times of velocity field and magnetic field are shorter than the eddy turn-over time of the MHD turbulence. We also show that under certain circumstances, for example if the kinetic helicity and current helicity are comparable, $\alpha$ depends insensitively on magnetic Prandtl number, while if either the kinetic helicity or the current helicity is dominated by the other one, a different magnetic Prandtl number will significantly change the dynamo $\alpha$ effect.Comment: 44 pages, 4 figures, to appear in ApJ (vol. 552

Jupiter's magnetosphere

Magnetosphere, ionosphere, and thermal radiation of planet Jupite

Electrodynamic effects of Jupiter's satellite Io

Electrodynamic effects of Jupiters satellite I

Environmental Taxation in New Zealand: What Place Does it Have?

The 2001 Tax Review (McLeod et al, 2001) includes a timely discussion about the place of environmental taxation in New Zealand. The review’s discussion paper released on 20 June 2001 and the final report in October 2001 both devote a whole chapter to environmental taxation. This is not surprising given the current influence of the Greens in Parliament, the Kyoto Protocol and the enthusiasm of some analysts for using economic instruments to achieve environmental outcomes. In reviewing the academic case for environment taxation, it is appropriate to go back to the Pigouvian tradition, and its more recent interpretation by Coase, Tietenberg and others. At its simplest, an efficient Pigouvian tax and an effect regulation achieve the same outcome. The policy analyst is indifferent. However, given the range of real world circumstances, comparisons can be made between doing nothing, imposing a regulation, imposing a tax, implementing a tradeable permits system or some other policy instrument. Analysts are left to choose between instruments by comparing each instrument against a set of criteria. The Tax Review discussion paper took a cautious approach suggesting that eco-taxes are only appropriate when “damage of each unit of emissions is the same across the geographic area to which the tax applies; the volume of emission is measurable; and the marginal net damage of emissions is measurable”. At a regional level they are more optimistic, suggesting “eco-charges may be appropriate at a local level”. The review does see a real possibility for carbon taxes and notes there is no research available about the potential impact of methane taxes. The Tax Review discussion paper conclusions are driven by some critical assumptions. The authors place a tough standard as a requirement for any environmental tax. This requirement is not always or often met with regulations and other policy instruments. The authors are also concerned about taxes attenuating property rights at all levels of production. This is certainly an impact but it is an efficient impact. The authors suggest that double dividends result from the transfer of rents to the Crown and not productive efficiency. This assumption needs to be tested theoretically and empirically. The authors assume New Zealand should be slow to implement taxes as part of its response to the Kyoto protocol. This ignores the possibility that there may be gains from early adoption. Environmental taxation will continue to be an important political issue in this part of the world as evidenced by the current fuel tax enquiry in Australia. Despite its importance, the consideration of environmental taxation by the Tax Review Committee is unsatisfactory. Further analysis is required which considers the performance of environmental taxation against other instruments used to achieve government goals. This paper provides some history of the concept of environmental taxation as a framework for further research to address the issues raised by the Taxation Review 2001. This paper should form a basis for further work in New Zealand examining specific opportunities for environmental and resource-use taxation

Early Australian Optical and Radio Observations of Centaurus A

The discoveries of the radio source Centaurus A and its optical counterpart NGC 5128 were important landmarks in the history of Australian astronomy. NGC 5128 was first observed in August 1826 by James Dunlop during a survey of southern objects at the Parramatta Observatory, west of the settlement at Sydney Cove. The observatory had been founded a few years earlier by Thomas Brisbane, the new governor of the British colony of New South Wales. Just over 120 years later, John Bolton, Gordon Stanley and Bruce Slee discovered the radio source Centaurus A at the Dover Heights field station in Sydney, operated by CSIRO's Radiophysics Laboratory (the forerunner of the Australia Telescope National Facility). This paper will describe this early historical work and summarise further studies of Centaurus A by other Radiophysics groups up to 1960.Comment: 45 pages, 43 figure

The problem of small and large scale fields in the solar dynamo

Three closely related stumbling blocks of solar mean field dynamo theory are discussed: how dominant are the small scale fields, how is the alpha effect quenched, and whether magnetic and current helicity fluxes alleviate the quenching? It is shown that even at the largest currently available resolution there is no clear evidence of power law scaling of the magnetic and kinetic energy spectra in turbulence. However, using subgrid scale modeling, some indications of asymptotic equipartition can be found. The frequently used first order smoothing approach to calculate the alpha effect and other transport coefficients is contrasted with the superior minimal tau approximation. The possibility of catastrophic alpha quenching is discussed as a result of magnetic helicity conservation. Magnetic and current helicity fluxes are shown to alleviate catastrophic quenching in the presence of shear. Evidence for strong large scale dynamo action, even in the absence of helicity in the forcing, is presented.Comment: to appear in Astron. Nachr., in honour of the retirement of Michael Sti

Drift waves in the corona: heating and acceleration of ions at frequencies far below the gyro frequency

In the solar corona, several mechanisms of the drift wave instability can make the mode growing up to amplitudes at which particle acceleration and stochastic heating by the drift wave take place. The stochastic heating, well known from laboratory plasma physics where it has been confirmed in numerous experiments, has been completely ignored in past studies of coronal heating. However, in the present study and in our very recent works it has been shown that the inhomogeneous coronal plasma is, in fact, a perfect environment for fast growing drift waves. As a matter of fact, the large growth rates are typically of the same order as the plasma frequency. The consequent heating rates may exceed the required values for a sustained coronal heating by several orders of magnitude. Some aspects of these phenomena are investigated here. In particular the analysis of the particle dynamics within the growing wave is compared with the corresponding fluid analysis. While both of them predict the stochastic heating, the threshold for the heating obtained from the single particle analysis is higher. The explanation for this effect is given.Comment: To appear in MNRAS (2010

B polarization of the CMB from Faraday rotation

We study the effect of Faraday rotation due to a homogeneous magnetic field on the polarization of the cosmic microwave background (CMB). Scalar fluctuations give rise only to parity-even E-type polarization of the CMB. However in the presence of a magnetic field, a non-vanishing parity-odd B-type polarization component is produced through Faraday rotation. We derive the exact solution for the E and B modes generated by scalar perturbations including the Faraday rotation effect of a uniform magnetic field, and evaluate their cross-correlations with temperature anisotropies. We compute the angular autocorrelation function of the B-modes in the limit that the Faraday rotation is small. We find that primordial magnetic fields of present strength around $B_0=10^{-9}$G rotate E-modes into B-modes with amplitude comparable to those due to the weak gravitational lensing effect at frequencies around $\nu=30$ GHz. The strength of B-modes produced by Faraday rotation scales as $B_0/\nu^2$. We evaluate also the depolarizing effect of Faraday rotation upon the cross correlation between temperature anisotropy and E-type polarization.Comment: 11 pages, 4 figures. Minor changes to match the published versio