Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry

Gyrokinetic theory is based on an asymptotic expansion in the small parameter $\epsilon$, defined as the ratio of the gyroradius and the characteristic length of variation of the magnetic field. In this article, this ordering is strictly implemented to compute the electrostatic gyrokinetic phase-space Lagrangian in general magnetic geometry to order $\epsilon^2$. In particular, a new expression for the complete second-order gyrokinetic Hamiltonian is provided, showing that in a rigorous treatment of gyrokinetic theory magnetic geometry and turbulence cannot be dealt with independently. The new phase-space gyrokinetic Lagrangian gives a Vlasov equation accurate to order $\epsilon^2$ and a Poisson equation accurate to order $\epsilon$. The final expressions are explicit and can be implemented into any simulation without further computations.Comment: 55 pages. Version with typo in equation (135) corrected. The second term in the second line of (135) was missing the subindex that indicates that only the perpendicular component of the gradient enters this ter

Dual branes in topological sigma models over Lie groups. BF-theory and non-factorizable Lie bialgebras

We complete the study of the Poisson-Sigma model over Poisson-Lie groups. Firstly, we solve the models with targets $G$ and $G^*$ (the dual group of the Poisson-Lie group $G$) corresponding to a triangular $r$-matrix and show that the model over $G^*$ is always equivalent to BF-theory. Then, given an arbitrary $r$-matrix, we address the problem of finding D-branes preserving the duality between the models. We identify a broad class of dual branes which are subgroups of $G$ and $G^*$, but not necessarily Poisson-Lie subgroups. In particular, they are not coisotropic submanifolds in the general case and what is more, we show that by means of duality transformations one can go from coisotropic to non-coisotropic branes. This fact makes clear that non-coisotropic branes are natural boundary conditions for the Poisson-Sigma model.Comment: 24 pages; JHEP style; Final versio

El Mediterrani, l’Alguer i l’etnografia catalana noucentista: una recerca etnogràficolingüística a l’Alguer (1922)

D'ençà el restabliment de la Generalitat de Catalunya (980) en el marc de l'anomenat Estat de les Autonomies que fixa la Constitució Espanyola de 1978, el Mediterrani ha estat un referent, de primer ordre, en els discursos i en les argumentacions de bona part de la classe política catalana. Aquest interès no és nou ; com és ben conegut, ja en el segle XIX i, especialment, en les primeres dècades del seglel XX, les reflexions, comentaris, estudis i iniciatives foren moltes en aquests mateix sentit. Aquest breu treball vol presentar aquest aspecte i, sobretot, com aquesta preocupació va dur a l'Alguer a diversos estudiosos catalans a l'inici dels anys vint per tal de cercar dades etnogràfiques i lingüístiques, iniciativa que volia aconseguir confirmar els lligams amb la Mediterrània i ratificar la presència i herència històriques catalanes en diversos territoris, com l'Alguer.Peer reviewe

Dynamics of a 1-D model for the emergence of the plasma edge shear flow layer with momentum conserving Reynolds stress

A one-dimensional version of the second-order transition model based on the sheared flow amplification by Reynolds stress and turbulence supression by shearing is presented. The model discussed in this paper includes a form of the Reynolds stress which explicitly conserves momentum. A linear stability analysis of the critical point is performed. Then, it is shown that the dynamics of weakly unstable states is determined by a reduced equation for the shear flow. In the case in which the flow damping term is diffusive, the stationary solutions are those of the real Ginzburg-Landau equation.Comment: 21 pages, 8 figure

Less constrained omnigeneous stellarators

A stellarator is said to be omnigeneous if all particles have vanishing average radial drifts. In omnigeneous stellarators, particles are perfectly confined in the absence of turbulence and collisions, whereas in non-omnigeneous configurations, particle can drift large radial distances. One of the consequences of omnigeneity is that the unfavorable inverse scaling with collisionality of the stellarator neoclassical fluxes disappears. In the pioneering and influential article [Cary~J~R and Shasharina~S~G 1997 {\it Phys. Plasmas} {\bf 4} 3323], the conditions that the magnetic field of a stellarator must satisfy to be omnigeneous are derived. However, reference [Cary~J~R and Shasharina~S~G 1997 {\it Phys. Plasmas} {\bf 4} 3323] only considered omnigeneous stellarators in which all the minima of the magnetic field strength on a flux surface must have the same value. The same is assumed for the maxima. We show that omnigenenous magnetic fields can have local minima and maxima with different values. Thus, the parameter space in which omnigeneous stellarators are possible is larger than previously expected. The analysis presented in this article is only valid for orbits with vanishing radial width, and in principle it is not applicable to energetic particles. However, one would expect that improving neoclassical confinement would improve energetic particle confinement.Comment: 10 pages, 5 figure