Quantifying the Effect of Non-Larmor Motion of Electrons on the Pressure Tensor

In space plasma, various effects of magnetic reconnection and turbulence cause the electron motion to significantly deviate from their Larmor orbits. Collectively these orbits affect the electron velocity distribution function and lead to the appearance of the "non-gyrotropic" elements in the pressure tensor. Quantification of this effect has important applications in space and laboratory plasma, one of which is tracing the electron diffusion region (EDR) of magnetic reconnection in space observations. Three different measures of agyrotropy of pressure tensor have previously been proposed, namely, $A\varnothing_e$, $D_{ng}$ and $Q$. The multitude of contradictory measures has caused confusion within the community. We revisit the problem by considering the basic properties an agyrotropy measure should have. We show that $A\varnothing_e$, $D_{ng}$ and $Q$ are all defined based on the sum of the principle minors (i.e. the rotation invariant $I_2$) of the pressure tensor. We discuss in detail the problems of $I_2$-based measures and explain why they may produce ambiguous and biased results. We introduce a new measure $AG$ constructed based on the determinant of the pressure tensor (i.e. the rotation invariant $I_3$) which does not suffer from the problems of $I_2$-based measures. We compare $AG$ with other measures in 2 and 3-dimension particle-in-cell magnetic reconnection simulations, and show that $AG$ can effectively trace the EDR of reconnection in both Harris and force-free current sheets. On the other hand, $A\varnothing_e$ does not show prominent peaks in the EDR and part of the separatrix in the force-free reconnection simulations, demonstrating that $A\varnothing_e$ does not measure all the non-gyrotropic effects in this case, and is not suitable for studying magnetic reconnection in more general situations other than Harris sheet reconnection.Comment: accepted by Phys. of Plasm

Spectral variation in the X-ray pulsar GX 1+4 during a low-flux episode

The X-ray pulsar GX 1+4 was observed with the RXTE satellite for a total of 51ks between 1996 July 19 - 21. During this period the flux decreased smoothly from an initial mean level of ~ 6 X 10^36 erg/s to a minimum of ~ 4 X 10^35 erg/s (2-60 keV, assuming a source distance of 10 kpc) before partially recovering towards the initial level at the end of the observation. BATSE pulse timing measurements indicate that a torque reversal took place approximately 10 d after this observation. Both the mean pulse profile and the photon spectrum varied significantly. The observed variation in the source may provide important clues as to the mechanism of torque reversals. The single best-fitting spectral model was based on a component originating from thermal photons with kT ~ 1 keV Comptonised by a plasma of temperature kT \~ 7 keV. Both the flux modulation with phase during the brightest interval and the evolution of the mean spectra over the course of the observation are consistent with variations in this model component; with, in addition, a doubling of the column density nH contributing to the mean spectral change. A strong flare of duration 50 s was observed during the interval of minimum flux, with the peak flux ~ 20 times the mean level. Although beaming effects are likely to mask the true variation in Mdot thought to give rise to the flare, the timing of a modest increase in flux prior to the flare is consistent with dual episodes of accretion resulting from successive orbits of a locally dense patch of matter in the accretion disc.Comment: 8 pages, 3 figures, submitted to MNRA

Who pays the taxes?

The European Union is legally entitled to the revenue from (1) agricultural and sugar levies, (2) customs duties, (3) a 1 percent rate on each Member States' value added tax base, and (4) a resource on the basis of GNP. Currently, the Union is actively involved in the search for a fifth own revenue source. Therefore, the European Commission (DG XIX) has invited the authors to trace 'who pays the taxes'. As requested, our report gives a general account of methods to investigate impacts of taxation. More specifically, we have estimated the incidence of national tax systems (Germany, the Netherlands, Spain and the United Kingdom), and the incidence of present own resources and prospective new (tax) resources of the European Union. Up till now, such information was not (readily) available.tax incidence in the European Union, prospective new EU tax resources

The distribution of effective tax burdens in four EU countries

National policymakers are increasingly aware that their tax policy options are constrained by international tax competition. Important features of national tax systems - notably the tax mix, tax rates and rules which define the tax base - will influence decisions of firms and individuals regarding the location and (re)structuring of economic activities. The aim of the present paper is twofold: Firstly, we detail the tax mix of four member states of the European Union (Germany, The Netherlands, Spain and United Kingdom). Secondly, the paper aims to trace the distribution of the tax burden over rich and poor households in these four countries. Although tax mix and tax rates differ considerably among the four countries included in the study, the distribution of tax burdens proves to be amazingly similar.Distribution of tax burden, European Union; tax mix of Germany, the Netherlands, Spain and United Kingdom

Who pays the taxes?

The European Union is legally entitled to the revenue from (1) agricultural and sugar levies, (2) customs duties, (3) a 1 percent rate on each Member States' value added tax base, and (4) a resource on the basis of GNP. Currently, the Union is actively involved in the search for a fifth own revenue source. Therefore, the European Commission (DG XIX) has invited the authors to trace 'who pays the taxes'. As requested, our report gives a general account of methods to investigate impacts of taxation. More specifically, we have estimated the incidence of national tax systems (Germany, the Netherlands, Spain and the United Kingdom), and the incidence of present own resources and prospective new (tax) resources of the European Union. Up till now, such information was not (readily) available.tax incidence in the European Union, prospective new EU tax resources