Reversed Field Pinch Historical Review (4)

In 1974, at the International Atomic Energy Agency Conference in Tokyo, J.B. Taylor indicated in the Reverse Field Pinch (RFP) a striking and very interesting plasma configuration.

Taylor reconsidered the experimental measurements of ZETA, observing that ".... after an initial violently unstable phase the plasma frequently relaxes into a 'quiescent' state in which it appears to be grossly stable.
Furthermore when the pinch ratio 'theta' exceeds some critical value this relaxation is accompanied by the generation of a reversed toroidal field in the outer regions of the plasma."

As a conclusion Taylor demonstrated that, if " ... the plasma is regarded as a conducting but viscous fluid enclosed in a rigid, perfectly conducting, toroidal vessel, .... the system is not in equilibrium and when released will therefore move (usually violently) and dissipate energy before coming to rest."

[J.B. Taylor, Plasma Physics and Contr. Nucl. Fus. React., (IAEA, Vienna, 1975)]. The predicted phenomena are possible if the magnetic field of the plasma satisfies the equation:

rot B = k B

The solutions of this differential equation are the Bessel functions:

Bz = B0 J0(kr)               BTh = B0 J1(kr)

where z, Theta, r are cylindrical coordinates of the plasma column, Bz and BTH are respectibely the toroidal and the poloidal fields.

The Taylor analysis came to the following conclusions:
- the presence of the Bessel Function J0 for the toroidal field allows the field reversal at the wall during the plasma quiescence;
- the theory states a strong connection between the Reverse Field Pinch (RFP) plasma and the astrophysical plasmas studied by Woltjer.

Taylor demonstrated theoretically that the quiescence states observed in ZETA were preferential states, named "relaxed states", i.e. natural asymptotic evolutions of the magnetically confined plasmas.
Taylor did not indicate the experimental method to obtain the relaxed states of the plasma. His theory only requires that the dynamical processes of the plasma relaxation must be described by the equations of resistive magnetohydrodynamics. The details of the dynamics are not present in his variational theory.

The following years were spent investigating and understanding the causes and the processes used by the plasmas for obtaining quiescence. The experiments showed that relatively high frequency and short spatial scales characterized the RFP plasma fluctuations. These fluctuations were reproduced in large scale computer simulations of RFP discharges and the simulations also exhibited plasma relaxation.
The advent of Taylor's theory led to the conclusion that fast programming did not offer the anticipated advantages in terms of optimising the configuration. Attention, therefore, switched again to form the field configuration slowly in metal walled systems. A new generation of machines appeared, utilizing metal bellows liners and slowly rising magnetic fields as in ZETA. The configuration was set up using self-reversal or an external aid for reversing the field at the wall.

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