## Reversed Field Pinch Historical Review (3)

Centro di Studi sui Gas Ionizzati was assigned the project ETA-BETA I (1974 - 78) (fig.2), for the study of the "Stabilized Pinch" configuration. It obtained priority support by EURATOM, so 45 % of the investment cost was provided by the European Community.

At the same time in Culham Laboratory, near Oxford (G.B.), the experiment HBTX-1 for research on the same plasma configuration was built.

Woltjer, an astrophysicist at the University of Chicago, in 1958 enunciated and proved a theorem on "Force-free" magnetic field, i.e. a field configuration where the Lorentz force vanishes. The field satisfies the equation:**rot B = k B,**

where k is a scalar constant.

The same field minimizes the energy with respect to the single invariant:

where the integral is taken over the whole volume of the system and the vector potential A is given by**rot A = B**

Woltjer stated that, because the B fields satisfy the variational principle, "....the force free fields with constant k represent the lowest state of magnetic energy which a closed system may attain.

This has two important consequences. It proves ... the stability of force free fields with constant k ...It also shows that in a system in which the magnetic forces are dominant and in which there is a mechanism to dissipate the fluid motions the force free fields with constant k are the natural end configurations".

Thus Woltjer stated the possibility of the presence and the stability of force-free magnetic fields with non-constant k and suggested possible mechanisms to dissipate the particle velocities. He concluded: "This condition will probably be fulfilled in most astrophysical situations." [Woltjer I., (1958), Proc. Natl. Acad. Sci. U.S.A., 44,489]