A comparison of Vlasov with drift kinetic and gyrokinetic theories

A kinetic consideration of an axisymmetric equilibrium with vanishing electric field near the magnetic axis shows that del f should not vanish on axis within the framework of Vlasov theory while it can either vanish or not in the framework of both a drift kinetic and a gyrokinetic theories (f is either the pertinent particle or the guiding center distribution function). This different behavior, relating to the reduction of phase space which leads to the loss of a Vlasov constant of motion, may result in the construction of different currents in the reduced phase space than the Vlasov ones. This conclusion is indicative of some limitation on the implications of reduced kinetic theories in particular as concerns the physics of energetic particles in the central region of magnetically confined plasmas.Comment: 9 page

Lyapunov stability of flowing MHD plasmas surrounded by resistive walls

A general stability condition for plasma-vacuum systems with resistive walls is derived by using the Frieman Rotenberg lagrangian stability formulation [Rev. Mod. Phys. 32, 898 (1960)]. It is shown that the Lyapunov stability limit for external modes does not depend upon the gyroscopic term but upon the sign of the perturbed potential energy only. In the absence of dissipation in the plasma such as viscosity, it is expected that the flow cannot stabilize the system.Comment: 9 page

Tokamak-like Vlasov equilibria

Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field can be reduced, up to a selection of ions and electrons distributions functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice of the distributions functions. In contrast to two-dimensional translationally symmetric equilibria whose electron distribution function consists of a displaced Maxwellian, the toroidal equilibria need deformed Maxwellians. In order to be able to carry through the calculations, this deformation is produced by means of either a Heaviside step function or an exponential function. The resulting Grad-Shafranov-like equations are established explicitly.Comment: 11 page

Vlasov versus reduced kinetic theories for helically symmetric equilibria

A new constant of motion for helically symmetric equilibria in the vicinity of the magnetic axis is obtained in the framework of Vlasov theory. In view of this constant of motion the Vlasov theory is compared with drift kinetic and gyrokinetic theories near axis. It turns out that as in the case of axisymmetric equilibria [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 18, 064507 (2011)] the Vlasov current density thereon can differ appreciably from the drift kinetic and gyrokinetic current densities. This indicates some limitation on the implications of reduced kinetic theories, in particular as concerns the physics of energetic particles in the central region of magnetically confined plasmas.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1104.042

The Size Distribution of Farms and International Productivity Differences

There is a 34-fold difference in average farm size (land per farm) between rich and poor countries and striking differences in their size distributions. Since labor productivity is much higher in large relative to small farms, we study the determinants of farm-size differences across countries and their impact on agricultural and aggregate productivity. We develop a quantitative model of agriculture and non-agriculture that features a non-degenerate size distribution of farms. We find that measured aggregate factors such as capital, land, and economy-wide productivity cannot account for more than 1/4 of the observed differences in farm size and productivity. We argue that, among the possible explanations, farm-level policies that misallocate resources from large to small farms have the most potential to account for the remaining differences. Such farm-size distortions are prevalent in poor countries. We quantify the effects of two specific policies in developing countries: (a) a land reform that imposes a ceiling on farm size and (b) a progressive land tax. We find that each individual policy generates a reduction of 3 to 7% in average size and productivity.aggregate productivity, agriculture, farm-size distortions, misallocation

Relative Stagnation alla Turca

Turkey is the only founding member of the OECD that has not converged to the US in terms of per-capita GDP since 1950: its real GDP per capita is stuck at 20% of that of the US. At a proximate level, we show that Turkey's relative stagnation over the past 50 years is due to: (1) the relative decline in its labor force participation, and (2) the relative stagnation of its TFP. We argue that the first fact is due to policies of high personal income taxation, and high social security contributions for both employees and employers. The second fact we argue is due to price support policies in agriculture, which distorted the allocation of resources in favor of agriculture, thereby delayed the process of the structural transformation. We develop a dynamic general equilibrium model with agricultural and non-agricultural sectors. The production of the non-agricultural good can take place in the market or the household sector. We show the extent to which these policies can account quantitatively for Turkey's relative stagnationRelative Stagnation, Labor Force Participation, Income Taxes