October 2005 44 1066-033X/05/$20.00©2005IEEE IEEE Control Systems Magazine By Alessandro Beghi and Angelo Cenedese From gaps to snakes F E A T U R E F E A T U R E T he efficient and safe operation of large fusion devices relies on accu- rate knowledge of the position and shape of the plasma column inside the vacuum chamber. There are several reasons for optimizing plas- ma shape and position, namely, to maintain adequate clearance from the chamber wall to avoid high densities of power and particle deposi- tion, to be sufficiently close to the wall to ensure adequate passive stabilization, to achieve efficient radio frequency (RF) heating by maximizing antenna coupling (see “Tutorial 9”), and finally, to reduce magnetohydrodynamic (MHD) activity (see “Tutorial 2” in [1]). Unfortunately, plasma shape is not a directly measurable quantity and thus can only be evaluated using diagnostic data, such as the magnetic measurements of flux and field. Current trends in existing fusion plants, as well as operating sce- narios envisioned for future tokamaks, present the control engineer with the chal- lenge of regulating highly unstable, strongly shaped plasmas with precision and reliability. Therefore, whether to improve fusion performance or to protect the machine components, the problem of reconstructing the plasma boundary is criti- cal for both diagnostic and control purposes. In this respect, shape estimation assumes a key role in fulfilling the requirements for real-time applications. Overview of Methods for Shape Estimation The Equilibrium Problem Today, the tokamak is the most common machine for fusion research, used to mag- netically confine a gas in the plasma state inside a doughnut-shaped (a torus) metallic