Let Cq be the non-commutative Laurent polynomial ring associated with a (n+1)×(n+1) rational quantum matrix q. sld(Cq)⊕HC1(Cq) universal central extension of Lie subalgebra sld(Cq) gld(Cq). We take algebra τ=gld(Cq)⊕HC1(Cq). Der(Cq) all derivations and consider τ˜=τ⋊Der(Cq), called full toroidal coordinated by tori. In this paper we get classification irreducible integrable modules finite dimen...

the tenacity of a graph g, t(g), is dened by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we dene τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph's...

Abstract A non-linear Grad–Shafranov toroidal equilibrium reconstruction code (MSTFit) has been developed for the Madison Symmetric Torus. This is the first such code applied to the unique magnetohydrodynamic (MHD) equilibrium of the reversed field pinch. A new set of toroidal Green’s tables have been computed to impose the boundary condition of the close-fitting conducting shell. The non-linea...

Predictions of plasma parameters in the edge and scrape-off layer of tokamaks is difficult since most modern tokamaks have a divertor and the associated separatrix causes the usually employed field/flux-aligned coordinates to become singular on the separatrix/Xpoint. The presented field line map approach avoids such problems as it is based on a cylindrical grid: standard finite-difference metho...

Abstract. Error fields and resistive magnetohydrodynamic (MHD) modes are ubiquitous in real tokamaks. They break the toroidal symmetry in |B| in tokamaks. Here, B is the magnetic field. The broken toroidal symmetry leads to enhanced neoclassical toroidal plasma viscosity and consequently the rate of the toroidal flow damping. The neoclassical toroidal plasma viscosity also results in a steady s...

We investigate the Tits buildings of the paramodular groups with or without canonical level structure, respectively. These give important combinatorical information about the boundary of the toroidal compactification of the moduli spaces of non-principally polarised Abelian varieties. We give a full classification of the isotropic lines for all of these groups. Furthermore, for square-free, cop...

Three codes that solve the gyrokinetic equation in toroidal geometry are compared in the linear limit for the growth rates and real frequencies of the ion temperature gradient (ITG) mode and the trapped electron mode (TEM). The three codes are the gyrokinetic toroidal code (GTC) and GT3D, both of which are radially-global particle-in-cell initial-value codes, and FULL, which is a radially-local...

A new code is presented for solving linear eigenvalue problems from fluid models of the edge plasma of tokamaks. The 2DX code solves linearized fluid equations in a 2D cross-section of the plasma, with toroidal mode number resolving the third dimension. Geometry capabilities include both closed and open field lines, allowing solution of x-point problems as well as a variety of other toroidal an...

We highlight the necessity for evaluating and evolving the global axisymmetric radial electric field in a tokamak consistent with conservation of toroidal angular momentum for both € δf and full f gyrokinetic codes, where f is the full distribution function and € δf its departure from Maxwellian. We also consider the effects of a strong radial electric field in a subsonic pedestal in the banana...