A New Twist on the Magnetic Equilibrium of a Toroidal Plasma

The reversed field pinch’s helical state reveals nonlinear physics of plasma self-organization.

Image courtesy of University of Wisconsin-Madison
The 3D helical structure in the core of the plasma is revealed in the measurements of (a) magnetic field and (b) plasma density, shown projected on a cross-section plane of the plasma torus.

The Science

A new behavior in the reversed field pinch of the Madison Symmetric Torus Experiment whereby the plasma spontaneously attains a 3D helical equilibrium leads to improved understanding and performance of magnetically confined fusion plasmas, in particular the reversed field pinch magnetic configuration.

The Impact

The helical equilibrium observed in the reversed field pinch is the result of the plasma’s self-organization to a low-energy state that has a surprising 3D character. The reduced turbulence associated with this state holds promise to improve the quality of energy confinement, a key to obtaining burning plasmas.


3D physics plays a critical role in nominally axisymmetric toroidal magnetic fusion devices such as the tokamak and the reversed field pinch. It takes great effort to make such a device perfectly axisymmetric so that the toroidal coordinate is ignorable, making the plasma effectively 2D. The stellarator configuration is a counter example where a 3D helical magnetic field is produced on purpose using twisted magnets surrounding the plasma. Making a 3D field with high quality plasma confinement characteristics is yet more challenging. In the reversed field pinch, a new behavior has been discovered recently whereby the plasma spontaneously attains a 3D helical equilibrium. The core of the plasma is helical, much like the plasma in a stellarator, but the boundary remains nominally axisymmetric. One aspect of this helical state is that magnetic turbulence is reduced, presumably an impact of the large helical structure on other possible helical motion of the plasma. The confinement quality of these plasmas is therefore improved, leading to enhanced understanding and performance of the reversed field pinch magnetic configuration. This work was performed as a collaboration between groups at the University of Wisconsin-Madison, UCLA, and a team of scientists from Padua, Italy where another reversed field pinch experiment called RFX-Mod is located.


Dr. David Brower

Dr. John Sarff
University of Wisconsin-Madison


DOE Office of Science, Office of Fusion Energy Sciences


W.F. Bergerson et al. “Bifurcation to 3D helical magnetic equilibrium in an axisymmetric toroidal device.” 2011. Phys. Rev. Lett. 107: 255001

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Program: FES

Performer: University

Additional: Collaborations , International Collaboration