Simulation of intermittent beam ion loss in a Tokamak Fusion Test Reactor experiment

Y Todo,B N Breizman,H L Berk

doi:10.1063/1.1580122

Abstract

Recurrent bursts of toroidicity-induced Alfvén eigenmodes (TAE) are studied using a self-consistent simulation model. Bursts of beam ion losses observed in the neutral beam injection experiment at the Tokamak Fusion Test Reactor [K. L. Wong et al., Phys. Rev. Lett. 66, 1874 (1991)] are reproduced using experimental parameters. It is found that synchronized TAE bursts take place at regular time intervals of 2.9 ms, which is close to the experimental value of 2.2 ms. The stored beam energy saturates at about 40% of that of the classical slowing down distribution. The stored beam energy drop associated with each burst has a modulation depth of 10%, which is also close to the inferred experimental value of 7%. Surface of section plots demonstrate that both the resonance overlap of different eigenmodes and the disappearance of KAM surfaces in phase space due to overlap of higher-order islands created by a single eigenmode lead to particle loss. Only co-injected beam ions build up to a significant stored energy even though their distribution is flattened in the plasma center. However, they are not directly lost, as their orbits extend beyond the outer plasma edge when the core plasma leans on a high field side limiter. The saturation amplitude is δB/B∼2×10−2, which is larger than would appear to be compatible with experiment. Physical arguments are presented for why the stored energetic particle response observed in the simulation is still plausible.

Highlights

TAE spatial profile and where the linear eigenmodes were coupled to the beam ion dynamics
This simulation accelerated classical transport processes by using a shorter slowing-down time and a larger heating power than in experiment in order to perform the calculation in a reasonable computational time. This procedure leads to burst intervals that are shorter than experimental values by a factor of 1/4
Activity did not affect the stored beam energy the beam ion spatial profile was greatly flattened compared to the classical distribution

Summary

INTRODUCTION

TFTR experiment, which had balanced beam injection.2 The results of this simulation reproduce quite closely the following aspects of the experimental parameters; 共a兲 synchronized bursts of multiple TAEs taking place at regular time intervals close to the experimental value; 共b兲 a modulation depth in the stored energetic particles that is close to the one inferred in experiment; 共c兲 stored beam energy that is about one-third of the classical slowing-down distribution. In Eq 共4兲 we consider only the toroidal field gradient for ⵜB, which is consistent with the form for the grad-B and curvature drifts used in Eq. The simulation uses a perturbative approach where the TAE spatial profile is assumed fixed, while amplitudes and phases of the eigenmodes and the fast-ion nonlinear dynamics is followed self-consistently. The particle source 共beam ion injection兲 and sink 共beam ion loss兲 are essential ingredients for the establishment of the TAE bursts

Simulation results

Convergence with particle number

Particle loss mechanism

Effects of beam injection direction

Effects of the edge gradient on the stability

DISCUSSION AND SUMMARY