Confinement improvement by fluctuating input power

Abstract

An interesting effect of the fluctuating input power on plasma confinement is reported. Specifically, the addition of the sinusoidal perturbation, Asin(wt), to constant power q 0 is shown to promote the confinement, leading to the L-H transition at a lower value of q 0 , as compared to the case of constant q 0 without the sinusoidal perturbation. In general, higher amplitude (A) and lower frequency (w) are found to be more favorable for the L-H transition while an interesting linear relation between A and w leading to the L-H transition is established for different values of q 0 . V C 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4833655] Nuclear fusion has the potential to be the main future energy producer due to being environmentally friendly, safe to produce, and having a virtually unlimited fuel supply. The most successful fusion reactor, the tokamak, magnetically confines the plasma in a torus. However, at high temperatures, the plasma becomes turbulent and degrades confinement, which causes the high temperature and density to dissipate. Shear flows can help to reduce the turbulence by disrupting different sections of the eddies at different rates, in the direction orthogonal to the flow, causing the formation of transport barriers (see, for instance, Refs. 1-4 and references therein).Experimentally, it was first found 5 that as the input power increases, the confinement degrades until it reaches a certain value at which it suddenly begins to improve into a high confinement state-this bifurcation is known as the L-H transition. The bifurcation occurs when zonal flow causes a transport barrier (steep temperature gradient) to be produced at the edge of the plasma, improving plasma confinement. Zonal flow, excited by turbulence, is a poloidal flow with a small frequency and varies in the radial direction, thereby inhibiting radial transport. 1-6 Mean flows have smaller frequencies and move on a larger scale. Zonal flow is thought to take the lead in the suppression of turbulence before mean flow becomes large enough to influence it. Zonal and mean flows are amplified by different conditions, which permit them to take different roles in the transition. The study of the effect of zonal flows and its modelling has received a great attention in fusion research with on-going experimental tests (e.g., see Ref. 1 and references therein) to complement theoretical modelling.On theoretical front, the L-H transition has successfully been modelled by using zero-dimensional (0-D) models which describe the predator-prey relationship between turbulence E, zonal flow U, mean flow V, and the temperature gradient N for a given input power Q (e.g., Refs. 6-9). Assuming that a low turbulence value is solely responsible for the transition while the mean flow is driven only by ion pressure gradient, this model is able to demonstrate the L-H transition, including a midway mode, which is often called the transient oscillatory mode (T-mode). 3 Specifically, zonal flow reduces turbulence and increases mean flow, which also redu...

Study of improved confinement by a stepwise increase of the input heating power for tokamak plasmas

“…In this model [7], which is already adopted by [21], two predator (V and U) one prey model (E), the temperature gradient (which comes directly from the heat input) feeds the mean flow and dissipates as the turbulence and temperature gradient increase. Mean flow reduces turbulence and zonal flow while the zonal flow eats turbulence, creating the observed oscillatory behavior similar to [21]. The heat input generates turbulence, which generates zonal flows.…”

“…The heat input generates turbulence, which generates zonal flows. This complicated relationship is modeled [7,21] by the following Eqs. (1)Ð(4), where ϑ , ξ ,η , ρ and σ are constants:…”

“…This article is an extension of the also brief study Sarah Douglas [21], where in the study by Douglas [21] a sinusoidal perturbation of the heating power has been studied. In this paper a stepwise increase of the heating power and its influence on the L-H transition are studied.…”

“…The aim of this paper is to report on the interesting effect of a stepwise increase of the different heating powers on turbulence and confinement by extending [21]. …”

“…The bifurcation occurs when zonal flow causes a transport barrier (steep temperature gradient) [2][3][4][5][6], to be produced at the edge of the plasma, improving plasma confinement. Zero-dimensional models [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] [7], called MD model, which has one fewer variable for which oscillatory heating was studied in [21]. This distinctive phenomenology may offer a path to future experimental testing of the assumptions of zero-dimensional models, and perhaps distinguishing between them.…”