Global Simulation of the GAM Oscillation and Damping in a Drift Kinetic Model

Collisionless damping of the geodesic acoustic mode (GAM) is investigated by a drift kinetic simulation. The main subject of the study is to analyze how the magnetic configuration and the finite-orbit-width(FOW) effect of the ion drift motion affect the collisionless damping of GAM. We utilize the neoclassical transport code ”FORTEC-3D”, which solves the drift kinetic equation based on the delta-f method, to study these issues. In recent analytical study on GAM and zonal flow it is found that the FOW effect and the helical components of magnetic field spectrum change the damping rate of the GAM oscillation. We inspect the change of the damping rate in our simulation. First, the dependence of the damping rate on the FOW effect is investigated. We find that the collisionless damping becomes faster as typical banana width becomes wider. On the other hand, the damping rate in helical magnetic configuration is mainly determined by the effect of helical ripples. It is found that the sideband components, which appear as the axis moves inward, make the GAM damping faster. This result suggests the possibility of controlling both the neoclassical transport level and the GAM oscillation, or zonal flow, in helical plasma. The collisional effect on the GAM damping is also investigated in banana and plateau regimes

On the geometry of Siegel-Jacobi domains

We study the holomorphic unitary representations of the Jacobi group based on Siegel-Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces based on the Siegel-Jacobi disk are obtained. The scalar holomorphic discrete series of the Jacobi group for the Siegel-Jacobi disk is constructed and polynomial orthonormal bases of the representation spaces are given.Comment: 15 pages, Latex, AMS fonts, paper presented at the the International Conference "Differential Geometry and Dynamical Systems", August 25-28, 2010, University Politehnica of Bucharest, Romani

Hodge structures associated to SU(p,1)

Let A be an abelian variety over C such that the semisimple part of the Hodge group of A is a product of copies of SU(p,1) for some p>1. We show that any effective Tate twist of a Hodge structure occurring in the cohomology of A is isomorphic to a Hodge structure in the cohomology of some abelian variety

New reductions of integrable matrix PDEs: Sp(m)Sp(m)-invariant systems

We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semi-discretizations of the obtained systems and present new soliton solutions to both continuous and semi-discrete systems. As a by-product, a new integrable semi-discretization of the Manakov model (self-focusing vector NLS equation) is obtained.Comment: 33 pages; (v4) to appear in JMP; This paper states clearly that the elementary function solutions of (a vector/matrix generalization of) the derivative NLS equation can be expressed as the partial $x$-derivatives of elementary functions. Explicit soliton solutions are given in the author's talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida