Zonal flow sawteeth and the time period between edge-localized transport bursts in tokamaks

Abstract

The time period between particle and energy transport bursts in simulations of tokamak edge turbulence is determined by the magnitude of the diamagnetic drift parameter αd≡ω*∕γ0, where the diamagnetic drift frequency ω*=ρscs∕L0Ln and the characteristic ballooning mode growth rate γ0=cs∕(RLn∕2)1∕2. Here, R is the major radius of the torus, Ln is the density gradient scale length, ρs is the ion gyroradius, and cs is the ion acoustic speed. The scale length L0 is given by L0=2πqR(νeiρs∕2ωeR)1∕2(2R∕Ln)1∕4, where q is the safety factor, νei is the electron-ion collision frequency, and ωe is the electron cyclotron frequency. When the diamagnetic drift frequency becomes larger than the ballooning mode growth rate (αd>1), then the transport in the tokamak edge is characterized by regularly recurring bursts of particles and energy with a single well-defined frequency. As αd increases above unity, the time period between the bursts becomes much longer. The temporal dependence of the energy in the zonal flow generated nonlinearly has the appearance of sawteeth.