We show that the representation theory for the toroidal extended affine Lie algebra is controlled by a VOA which is a tensor product of four VOAs: a sub-VOA V + Hyp of a hyperbolic lattice VOA, affine ˙ g and sl N VOAs and a Virasoro VOA. A tensor product of irre-ducible modules for these VOAs admits the structure of an irreducible module for the toroidal extended affine Lie algebra. We also sh...

The plasma response to resonant magnetic perturbation RMP and nonresonant perturbation fields is computed within a linear, full toroidal, single-fluid resistive magnetohydrodynamic framework. The response of resonant harmonics depends sensitively on the plasma resistivity and on the toroidal rotation. The response of nonresonant harmonics is not sensitive to most of the plasma parameters, excep...

A toroidal embedding is defined which does not assume the fan consists of rational cones. For a rational fan, the toroidal embedding is the usual toric variety. If the fan is not rational, the toroidal embedding is in general a quasicompact noetherian locally ringed space which is not a scheme. A divisor theory exists and a class group is defined. A second construction is also carried out which...

A generalized energy principle for finite-pressure, toroidal magnetohydrodynamic MHD equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces invariant tori , which act as barriers against leakage of magnetic flux, helicity, and pressure through chaotic field-line transport. It is ar...

a toroidalization of a dominant morphism $varphi: xto y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $x$ and $y$. we give a proof of toroidalization of locally toroidal morphisms of 3-folds.

Predictive transport simulations of tokamak discharges are continuously improving thanks to increasing computational resources available and to the efforts made in code development. As an example of the progress, a recent work [1] with the Elmfire code demonstrates the ability of global gyrokinetic full f electrostatic particle simulations, including both neoclassical and turbulence physics, to...