Effects of an external toroidal field on the rotating field driven current in a Rotamak for fusion plasma confinement

The mechanism which creates toroidal currents in Tokamaks to magnetically confine hot fusion plasmas is cyclic and subjects the components to large periodic stresses. An alternative method of driving the toroidal current steadily using a rotating magnetic field (RMF) is being explored in a device called the Rotamak. In its spherical tokamak configuration, the Rotamak also employs a steady 'vertical' field to create a compact torus field-reversed configuration (FRC), and a toroidal field to create helical magnetic field lines of high safety factor for plasma confinement and prolonged collision time between ions to increase their chances of fusing with each other. This research analytically explores whether the presence of a toroidal field in a Rotamak has any effect on the Rotamak operation, especially the current drive efficiency since this is the Rotamak’s distinct advantage. The Rotamak plasma was modelled as a fluid made of mobile electrons and immobile ions. The electron fluid motion is governed by Maxwell's Equations and the Generalized Ohm's Law. The analysis also uses vector spherical harmonics and perturbation theory to minimise the complexity arising from the use of partial differential equations, thus, simplifying the analysis in the limits of partial and full penetration of the RMF separately. The additional toroidal field in this study was approximated as a sum of a few harmonics which is physically adequate to replicate the underlying mechanisms in terms of vector spherical harmonics (VSH). A set of numerical codes was written to facilitate the operations and visualization involving VSH. This includes generating the VSH, finding the interactions between VSHs, visualising the VSH in 3D and most importantly, solving 2nd order ordinary differential equations involving VSH. The results from the solver code verified previous studies of the Rotamak in the FRC, thus, confirming the reliability of the code. Through the perturbation analysis in the partial penetration limit, this research has shown that the current reversal near the central axis of the Rotamak occurs due to successive interaction between the zeroth order screening current and the toroidal field which flips the screening current in the opposite direction before it interacts with the penetrated RMF. The analysis also showed that the presence of a toroidal field improves the current drive in the outer regions of the plasma in partial penetration configurations and more importantly, the current drive efficiency shown in this work resembles the experiments conducted in the past. However, the analysis predicted that there should be toroidal current asymmetry between the top and bottom hemispheres in the presence of a toroidal field, which has never been observed in experiments. In the full penetration limit, the analysis provided a thorough description of the electron motion influenced by the deeply penetrating fields. The analysis predicted that the presence of a vertical or toroidal field in the full penetration limit reduces the current drive efficiency and the environment in this limit is not suitable for the operation of the Rotamak as a fusion plasma confinement device. Thus, this work provides a method to estimate the upper limit of a parameter that should be used to optimize a Rotamak operation, keeping other variables constant.