|The nominally axisymmetric (2-D) magnetic configuration in the form of a tokamak has proven to be the best candidate for a future reactor, and yet it is susceptible to instabilities which lead to a complete loss of the confined plasma. Some of these instabilities are on account of the toroidal plasma current required to establish a magnetic cage to hold the plasma. On the other end of the spectrum is the non-axisymmetric (3-D) magnetic configuration of the stellarators in which the a robust magnetic cage is provided by the external coils, with no need for a plasma current. For the application as a fusion reactor, non-axisymmetric shaping of toroidal plasmas is expected to be incorporated in the design of future experiments (Spong 2015). Small amounts of non-axisymmetric magnetic fields have been used in improving the stability and control of the tokamak plasmas (Spong 2015). The effect of varying amounts of shaping effects in the hybrid configurations of current carrying stellarators, has been demonstrated to suppress unstable magnetohydrodynamic (MHD) modes (W VII-A Team 1980, Hirsch et al. 2008, Atkinson et al. 1976). This thesis presents an understanding of the 3-D structure of the MHD modes observed in the current carrying plasmas of the Compact Toroidal Hybrid (CTH) device. Also presented is the 3-D shaping effect of stellarator fields on the stability of current carrying plasmas.
CTH is a stellarator-tokamak hybrid device designed to investigate the stability of current-carrying plasmas. The magnetic configuration of CTH is non-axisymmetric like that of a stellarator, while on account of a toroidal plasma current, some of the equilibrium properties are similar to that of a tokamak. The flexible CTH magnetic configuration allows varying the amount of 3-D shaping by modifying the twist of the magnetic field lines, known as the rotational transform. In current carrying CTH plasmas when the rotational transform, $\iotabar$, assumes rational values, fluctuations in equilibrium magnetic field are measured by the arrays of magnetic probes, some of which were built in the course of the research work presented. These are believed to be associated with specific magnetic flux surfaces inside the plasma, known as rational surfaces. MHD modes that lie on the rational surfaces can drive the confined plasma unstable, especially if they are due to perturbations in the current parallel to the equilibrium magnetic field. Therefore, it is important to understand the structure of these MHD modes detected by the magnetic probes.
The structure of the current driven kink/tearing modes is flute-like, and in the cylindrical geometries their helicity is characterized by the poloidal mode number, $m$, and the toroidal mode number, $n$. The interpretation of the structure of these modes is complicated in the toroidal geometry, and even more so in a non-axisymmetric configuration like that of CTH. Information about the plasma equilibrium reconstructed by the V3FIT code (Hanson et al 2009) is used to model these observed MHD modes as helical current filaments within the equilibrium. It has been shown that these MHD modes are indeed a result of helical perturbations within the 3-D plasma equilibrium of CTH, that is their structure is flute-like, and they originate on rational flux surfaces with helicity given by $n/m$.
Studying the effect of increasing amounts of vacuum rotational transform, that is the rotational transform generated by the external magnet coils, on the stability of current-carrying discharges is an important research topic on CTH. A kink/tearing mode instability constrains the amount of plasma current that can be driven in a tokamak; with the edge safety factor constrained to values greater than two, $\edgeq>2$ (Wesson 2011). The edge safety factor value is inversely proportional to the plasma current. CTH discharges can operate without loss of confinement, even if $\edgeq<2$, if sufficient amounts of 3-D shaping is applied. It is observed that increasing the amount of 3-D shaping by 10\% is sufficient to successfully stabilize the CTH discharges operating in the low edge safety factor regime. Additionally, it is observed with the magnetic probes that the unstable modes implicated in the loss of confinement, have mode structures characterized by $m/n=3/2$, and $4/3$.