Experimental evidence of low-dimensional chaotic convection dynamics in a toroidal magnetized plasma

In a toroidal plasma confined by a purely toroidal magnetic field with a weak vertical field superimposed a system of convection cells are generated spontaneously, interacting with a background electron density gradient. The dynamics of this interaction is low-dimensional, chaotic, and consistent with solutions of the Lorenz equations in the diffusionless limit.

Figure 1

(Color online) Power density spectra of plasma potential fluctuations in radial positions $x=8,10,12,14,16\text{cm}$ in the equatorial plane $\left(y=8\text{cm}\right)$ are shown in red (gray).

Figure 2

(Color online) (a) Conditionally averaged electron density structures. Similar structures in plasma potential and animation of the time evolution of these structures [12] show that they are field aligned convection cells propagating with the vertical plasma flow in the negative $y$ direction. (b) Conditional average low-pass filtered density fluctuations. Animation of these low-frequency fluctuations show that they are standing oscillations of the plasma density profile [12].

Figure 3

(Color online) (a) Upper dashed trace is the signal for the profile gradient variable $z$ in the diffusionless Lorenz equations for $R=3.3$. The lower rapidly fluctuating red (gray) trace is the electron density fluctuation signal at $x=12\text{cm}$, along with the black signal filtered by a moving average. (b) Spectral power density for diffusionless Lorenz signal (dashed) and for low-pass filtered electron density signal (black).

Figure 4

Recurrence plots. (a) Low-pass filtered electron density fluctuations. (b) Diffusionless Lorenz equations.

Figure 5

(Color online) Computation of growth rate $\overline{\lambda }\left(t\right)$ from diffusionless Lorenz model signal (dashed) and low-pass filtered electron density signal in light blue (dark gray). The limit of large $t$ yields the Lyapunov exponent $\lambda$.