# Reversed-Field eXperiment

RFX in 2015

The Reversed-Field eXperiment (RFX) is the largest reversed field pinch device presently in operation, situated in Padua, Italy. It was constructed from 1985 to 1991, and is operated since 1992.[1]

The experiments carried out in the last two decades with two large RFP machines (MST in Madison, Wisconsin[2] and RFX in Padova[3]) provided new insight on the physical phenomena taking place in magnetically confined plasma dynamics.[4][5]

## Reversed Field Pinch (RFP)

The Reversed Field Pinch (RFP) is a nuclear fusion test machine in which an asymmetric toroidal vessel confines ionized particles by a poloidal field; this is produced by the plasma current that flows around the torus and a toroidal magnetic field which in turn is induced by currents flowing in both the plasma and external coils.

Schematically, the RFX-Mod machine is similar to a tokamak system. Both designs contain a toroidal vessel containing ionized particles under a strong confinement magnetic field coupled to a coaxial transformer whose secondary coil conducts the plasma toroidal current.

The configuration derives its name from the fact that the toroidal magnetic field in the outer region is reversed with respect to its direction on the axis. If the toroidal winding acts as a flux conserver, the field profile is generated by raising the plasma current to a convenient level. While the current is raised, the plasma generates an additional toroidal flux in the inner part of the column and the coil reacts in order to keep the total flux constant: in the outer region the toroidal field is thereby reduced and even reversed. The reversal can be enhanced and controlled by the external circuits. In a classical conductor the toroidal field in a steady state would reach, by diffusion, a uniform radial distribution. By contrast in an RFP the plasma relaxation processes maintain the configuration by a mechanism called dynamo effect (by analogy to theories of the earth magnetic field generation).

## Difference between RFX-Mod and Tokamak machines

The most significant difference between Tokamak and RFP magnetic field configurations is that in the first case the size of the toroidal field is much larger than the poloidal field, while in RFP these components are of the same order of magnitude; furthermore, the toroidal field reverses in the plasma outer region.

## Parameters identifying RFP configuration

The pinch parameter

${\displaystyle \Theta ={\frac {B_{\text{pol}}(a)}{\left\langle B_{\text{tor}}\right\rangle }}}$

and the reversal parameter

${\displaystyle F={\frac {B_{\text{tor}}(a)}{\left\langle B_{\text{tor}}\right\rangle }}}$

where ${\displaystyle B_{\text{pol}}(a)}$ and ${\displaystyle B_{\text{tor}}(a)}$ are the poloidal and toroidal field components at the wall and ${\displaystyle \left\langle B_{\text{tor}}\right\rangle }$ is the toroidal field averaged over the plasma cross-section.

Taylor's theory states that, if the magnetic helicity and the toroidal flux are conserved, a plasma, with ${\displaystyle \beta =0}$, spontaneously relaxes to a minimum energy force-free state described by the equation

${\displaystyle \nabla \times B=kB}$

where ${\displaystyle k}$ is uniform and ${\displaystyle ka=2\Theta }$. For cylindrical geometry, Bessel functions provide the solution of eq. (1) and for ${\displaystyle \Theta >1.2}$ the toroidal field reverses at the wall.

Experimentally, RFP plasmas have finite beta and the current density tends to vanish at the wall, i.e. ${\displaystyle k}$ is not uniform so that the experimental profile departs from the theoretical one. The obtained configurations is a result of the dynamical balance of the counteracting actions of resistive diffusion and relaxation processes.

The first process has the tendency to shrink the toroidal current distribution while the second induces destabilization by MHD modes. The resistive diffusion tends to restore to the previous state. As a consequence, an RFP configuration is continuously regenerated through magnetic fluctuations.