Symmetry Constraints on the Dynamics of Magnetically Confined Plasma

In respect of their symmetry properties, toroidal magnetically confined plasmas have much in common with the Taylor-Couette flow. A symmetry-based analysis (equivalent bifurction theory) has proved very powerful in the analysis of the latter problem. This Letter discusses the applicability of the method to nuclear fusion experiments such as tokamaks and pinches. The likely behavior of the simplest models of rotationally symmetric tokamaks is described, and found to be potentially consistent with observation.

Figure 1

Time series plots of solutions to the system of Eq. (10) coupled to Eq. (11). Parameters $\mu =1$, $2\sigma =-1$, $\alpha =1$, $\beta =0.001$, initial values $r=0.01$ and $z=0$.