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...

For a better understanding of the role of control parameters in nonlinear dynamical systems, we examined numerically the effect of the oscillatory control parameter D = C0 cos(ω1t) on the Lorenz model for a dynamo, where C0 and ω1 are the driving amplitude and frequency, respectively. Despite the absence of the mean value of D, finite amplitude solutions are found for sufficiently large C0 and small ω1. Overall, smaller C0 and higher ω1 are less efficient in generating finite amplitude solutions, the bifurcation occurring at a larger value of C0 and a smaller value of ω1. Furthermore, we find a linear relationship between C0 and ω1 for the transition between finite amplitude and damping solutions.

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The article is an extension of the brief study by [Sarah Douglas et al., Phys. Plasmas 20, 114504 (2013)], where in the study 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. Using a function,for the transition of input heating power for tokamak plasmas i.e. the addition of the perturbation, ) / tanh( T t A , 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 ) / tanh( T t A perturbation. It is seen that the input heating power Q that consists of constant part q 0 in addition to a function ) / tanh( T t A provides the L-H transition for relatively small A and much wider range values of 1/T as compare to [Sarah Douglas et al., Phys. Plasmas 20, 114504 (2013)].