Zagier introduced toroidal automorphic forms to study the zeros of zeta functions: an automorphic form on GL2 is toroidal if all its right translates integrate to zero over all nonsplit tori in GL2, and an Eisenstein series is toroidal if its weight is a zero of the zeta function of the corresponding field. We compute the space of such forms for the global function fields of class number one an...

This paper treats the dipolar interactions of a two-dimensional system of discs upon which a triangle of spins is mounted. We obtain the leading term of the multipole expansion of the interaction energy of discs on which is mounted a regular n-gon of spins. A definition of the toroidal magnetic moment Ti of the ith plaquette is proposed such that the magnetostatic interaction between plaquettes...

I.._._& .".^^I --.----.--.: ~ . . ~ ~ . ~ ~ . . ~ ~ I l . l ~ ~ . ~ ~ ~ ~ I ~ ~ ~ ~ I _ L ~ ~ -,.~-~ ..: fiML..CI. lllr rrrru".aiglLso* plupcrocr "I m s LUrVlUa, SDlenOl" W l l " an allsmarlng sYrrsI11 are discussed. The multipole expansion for the electromagnetic field of the toroidal solenoid is obtained and explicit expressions for the toroidal form factors and moments are given. Concrete re...

MHD properties of low-aspect-ratio (low-A) reversed field pinch (RFP) plasmas have been studied in RELAX machine with aspect ratio of 2. The MHD behavior appeared in edge magnetic field fluctuations shows strong dependence on toroidal field reversal. In standard or deep-reversal plasmas, the edge magnetic fluctuation has broad toroidal mode spectrum, while it is narrowed by reducing the toroida...

A connection between creation of toroidal moments and breaking of the relativistic crystalline group associated to a given crystal, is presented in this paper. Indeed, if magnetoelectric effects exist, the interaction between electrons and elementary magnetic cells appears in such a way that the resulting local polarization and magnetization break the local relativistic crystalline symmetry. Th...

Associated Legendre functions of half-odd degree and arguments larger than one, also known as toroidal harmonics, appear in the solution of Dirichlet problems with toroidal symmetry. It is shown how the use of series expansions, continued fractions and uniform asymptotic expansions, together with the application of recurrence relations over degrees and orders, permits the evaluation of the whol...

A method for analyzing the structural behavior of toroidal magnet systems subjected to Lorentz fomes both in and out of the winding planes, and thermal loads is considered in this paper. The toroidal coil assembly is treated as a finite thickness, orthotropic, rotationally symmetric shell of revolution acted upon by symmetrical and antisymmetrical loads. The equations based on Reissner's shell ...

The original description of alpha particle driven instabilities in the Tokamak Fusion Test Reactor in terms of toroidal Alfvén eigenmodes (TAEs) remained inconsistent with three fundamental characteristics of the observations: (i) the variation of the mode frequency with toroidal mode number, (ii) the chirping of the mode frequency for a given toroidal mode number, and (iii) the antiballooning ...

Mercier‘s localized perturbed criterion of stability near an arbitrary modulated curvature magnetic axis of a non-circular toroidal plasma cross section is investigated. In this magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. The influence of the non-circular cross section of the magnetic surface and that of the modulation of the magnetic axis on the d...

ABSTRACT During the last decade it has become evident that the magnetorotational instability is at the heart of the enhanced angular momentum transport in weakly magnetized accretion disks around neutron stars and black holes. In this paper, we investigate the local linear stability of differentially rotating, magnetized flows and the evolution of the magnetorotational instability beyond the we...