Numerical study on neoclassical tearing mode stabilization via minimum seeking method for the island width growth rate

Abstract

We report that the control of the ‘island width growth rate’, which is defined as dW/dt, is more efficient than that of the ‘island width’ for neoclassical tearing mode stabilization using the minimum seeking method. A concept of the minimum island width growth rate seeking method is newly proposed for the real-time feedback control of the neoclassical tearing mode by using electron cyclotron current drive. To evaluate the performance of the proposed concept, predictive feedback control simulations with an integrated numerical system are performed based on two types of minimum seeking controllers; the first is a finite difference method based controller and the second is a sinusoidal perturbation based controller. The results are compared with the minimum ‘island width’ seeking method. It is revealed that the proposed control concept is less limited in minimum seeking, and more robust and efficient in reducing the misalignment in shorter time scales.

Comment on ‘Numerical study on neoclassical tearing mode stabilization via minimum seeking method for the island width growth rate’

“…However, the comparison is made using a numerical simulation which in this case is entirely free of noise. A comment is made in the last sentence of [1], indicating that future studies will consider the effect of noisy measurements on the results presented here. It is our view that publishing results without considering noise is at best premature, and at worst misleading, since a wealth of experimental evidence such as the measurements shown in figure 1 and reported in e.g.…”

“…The discussion in paper [1] is centred around the optimal method to localise a neoclassical tearing mode (NTM). Specifically, the authors compare two methods using the response of the NTM to a nearby Electron Cyclotron (EC) beam, since the closer the centre of the EC beam is to the centre of the NTM, the stronger the stabilising effect will be.…”

“…The noise can be mitigated to some extent by applying a low-pass filter. However, this inevitably results in a phase shift, while avoiding phase shifts was one of the reasons given in [1] for favouring the island width growth rate ( ) w t t d d over the island width w(t). Furthermore, the authors in [1] assume 'that the control time interval is small enough so that the island width growth rate and the island width space do not vary significantly'.…”

“…However, this inevitably results in a phase shift, while avoiding phase shifts was one of the reasons given in [1] for favouring the island width growth rate ( ) w t t d d over the island width w(t). Furthermore, the authors in [1] assume 'that the control time interval is small enough so that the island width growth rate and the island width space do not vary significantly'. Discussions in [8,10] conclude that the control interval should be on the order of 100 ms in order to minimise adverse effects from the noise.…”

Reply to ‘Comment on “Numerical study on neoclassical tearing mode stabilization via minimum seeking method for the island width growth rate”’

“…The 'Comment on "Numerical study on neoclassical tearing mode stabilization via minimum seeking method for the island width growth rate"' pointed out that the results of [1] can be misleading from a practical point of view due to the following reasons:…”