Experimental Evidence of a Zonal Magnetic Field in a Toroidal Plasma

A zonal magnetic field is found in a toroidal plasma. The magnetic field has a symmetric bandlike structure, which is uniform in the toroidal and poloidal directions and varies radially with a finite wavelength of mesoscale, which is analogous to zonal flows. A time-dependent bicoherence analysis reveals that the magnetic field should be generated by the background plasma turbulence. The discovery is classified as a new kind of phenomenon of structured magnetic field generation, giving insight into phenomena such as dipole field generation in rotational planets.

Figure 1

Magnetic field fluctuation spectrum and existence of the mean field. (a) Power spectrum (poloidal component) and coherence between the magnetic field at two toroidal locations. The fluctuation less than $\sim 1\mathrm{kHz}$ shows a quite high coherence, which means generation of a global magnetic field of azimuthal symmetry. The spectrum is calculated for the stationary period of $\sim 50\mathrm{ms}$ for the discharge duration of $\sim 100\mathrm{ms}$ with a frequency resolution of 0.24 kHz and a Nyquist frequency of 250 kHz. (b) The waveforms of zonal fields at the same radial but different toroidal locations. The positive sign means the direction of vacuum field direction. (c) The other waveforms of zonal fields at the different positions in both the toroidal and radial directions. The difference in radial direction is 1 cm.

Figure 2

Radial structure of the zonal field. (a) Correlation function of space and time, $C(\Delta r,\Delta t)$, around the radial position of $r=12\mathrm{cm}$. (b) Correlation functions with three different time delays;$\Delta t=0$, 1, and 2 ms. These correlation diagrams show radial structure of zonal field, which has a quasisinusoidal radial structure with a characteristic radial wavelength ($\sim 1\mathrm{cm}$) in mesoscale. On the other hand, the temporal correlation indicates that the memory of the mesoscale structure fades away with oscillation in $\sim 2\mathrm{ms}$.

Figure 3

Coupling of zonal field and turbulence. Bicoherence analysis using Gabour’s wavelet to show the existence of a linkage between zonal field and turbulence. Here the analysis adopts the conditional average to take into account the dependence of the coupling on the zonal field phase. Bicoherence diagrams of (a) phase A, (b) phase C, and (c) phase E. The insets are expanded views of a frequency range of $50<f_1<60\mathrm{kHz}$ and $-60<f_2<-50\mathrm{kHz}$. (d) Total bicoherences in the frequency range below 2 kHz for all five phases. The dashed line shows an estimator giving a rough criterion of convergence. (e) The total bicoherence as a function of the averaged amplitude of the zonal field for the five phases.