An in-board ohmic solenoid, along with the shielding needed for its insulation, can dramatically increase the size and, hence, the cost of the future fusion power plant. In addition, an elimination of in-board ohmic solenoid greatly reduces the coil stresses and simplifies the coil design. In this thesis, two complementary solenoid-free plasma start-up approaches were examined: the one utilizes only the outer poloidal field (PF) coils to create a relatively high quality field null region while retaining significant poloidal flux and the another takes advantage of the poloidal flux stored in the conducting centerpost to create a start-up condition similar to that of the conventional ohmic solenoid method.
For the first start-up scheme, dynamic modeling utilizing only outer PF coils were performed for the Next Step Spherical Torus (NSST) and the National Spherical Torus Experiment (NSTX) based on the static calculation results. Time-dependent calculations using the two-dimensional axisymmetric dynamic code and the plasma evolution code enabled to find the appropriate waveform of PF coils that satisfied various start-up conditions such as formation and sustainment of field null, a significant amount of magnetic flux for further plasma current ramp-up, force balance condition, sufficient size of the $E_tㆍB_t/B_{\perp} = 0.1kV/m$ contour for successful breakdown where $E_t$ is the toroidal electric field, $B_t$ is the toroidal magnetic field, and $B_{\perp}$ is the stray field perpendicular to the toroidal field. With the obtained PF coil current waveforms, it is shown that multipole quality field null can be sustained for several milli-seconds with a reasonably large size inside the vacuum vessel. The available induction fluxes at the expected starting time of the breakdown period are about 3.56Wb for the NSST and 0.15Wb for the NSTX, respectively. These flux values are expected to be sufficient to raise the plasma current up to a few mega-amperes and a few hundred kilo-amperes based on the experience from the conventional in-board ohmic solenoid start-up on the NSTX. The size of the $E_tㆍB_t/B_{\perp} = 0.1kV/m$ contour in which successful breakdown occurred in the presence of strong pre-ionization on DIII-D is as large as 60cm (NSST) and 25cm (NSTX), which also sustains for several milli-seconds. Analyses for the force balance and the field index suggest that the produced plasma can be stable for radial as well as vertical perturbations during the initial start-up phase. For the NSST case, the temporal change of coil resistance was taken into account in the calculation because of the self-heating effect due to massive coil currents and the use of liquid nitrogen ($LN_2$) cooled copper coils.
The second plasma start-up scheme using a conducting centerpost can be used either independently or in conjunction with the PF coil-only start-up scheme. It also showed promising results on the NSST geometry in which an in-board ohmic solenoid was replaced by a conducting copper cylinder. In the proposed scheme, a successful breakdown and plasma initiation can be possible by utilizing the high loop voltage generated by the large flux change from vacuum vessel eddy currents and the significant poloidal flux (several Wb) provided by the conducting centerpost that is inductively charged by utilizing outer PF coils. Most of all, this start-up method has a favorable aspect which is a similarity of the resulting magnetic field structure to that of a typical in-board ohmic solenoid, i.e. efficient flux providing without field leakage. Thus, it can easily generate a null field structure required during the plasma initiation. Therefore, it is found that the proposed start-up method is indeed possible to come up with a promising configuration, which produces a quality multipole field null and sufficient loop voltage needed for plasma initiation and significant poloidal flux for subsequent current ramp-up.
