QA configurations with the rotational transform provided by the three-dimensional shaping in (a) 0:05, (b) 0.10, (c) 0.20, and (d) 0.30, shown in four cross sections with equally spaced toroidal angles over half period. Configuration (a) is passively stable to the vertical mode, (b) removes the need for current drive at , (c) remains in vacuum chamber if plasma pressure and current vanish instantaneously, and (d) is passively stable to the wall mode.
A modular coil set designed for the configuration shown in Fig. 1(a) with the current winding surface conformal to the boundary of the plasma and displaced outward by a distance equal to , where is the average minor radius of the plasma. The left frame shows the coils, six per field period, viewed from the top. The right frame shows the contours of current potential on the flattened winding surface in one field period with the abscissa being the toroidal angle, , and the ordinate the poloidal angle, . The toroidal angle starts at the crescent-shaped cross section and the poloidal angle starts at the outboard midplane.
Rotational transform for the plasma configuration shown in Fig. 1(d) as function of the normalized toroidal flux. The dotted line is the external transform supplied by the shaping. The solid line is the total transform including the internal contribution from the plasma-driven bootstrap current at .
Contours of flux surfaces for the configuration shown in Fig. 1(d) at from a PIES calculation showing the configuration has good surface quality despite the existence of rational values in the iota profile.
QA configurations with rotational transform provided by shaping in (a) 0.40, (b) 0.50, and (c) 0.60, shown in four cross sections equally spaced in toroidal angles over half period. The vacuum transform accounts for ≈70%, 80%, and 90% of the total transform at .
QA configurations with three periods, rotational transform from shaping ≈0.3 and are MHD stable to the external kink modes at . The aspect ratios are: (a) , (b) , (c) , (d) , and (e) .
Contours of flux surfaces for the configuration shown in Fig. 6(e) with at from a VMEC calculation. The Shafranov shift of the magnetic axis is about 32% of the half width at the crescent-shaped section.
Top view of modular coils constructed for configurations (b) with , (d) with , and (e) with of Fig. 6. Coil winding surfaces have been constructed such that the inboard midplane is displaced by , whereas the outboard midplane is displaced by , where is the plasma minor radius, with interpolation made for locations in between. In all cases, there are three types of coils for each half period for a total of 18 coils.
Left two frames: current carrying surface (dotted lines) relative to the plasma configuration shown in Fig. 1(d) in two cross sections. Right frame: the arrangement of the windowpane coils wound on the current carrying surface. Currents in the windowpane coils may be controlled to produce plasma configurations (a)–(d) of Fig. 1. The shading here indicates current levels for configuration (d) in linear scale, where darker shading corresponds to larger current.
Comparison of the last closed magnetic surface between the target plasma and the plasma reconstructed using the field and the window-pane coils whose currents are adjusted to minimize the normal field on the target boundary for the configuration with an external transform of ≈0.05 of Fig. 1(a). Left two frames: the right frame shows the comparison of the total rotational transform, target (solid) vs reconstructed (dotted) at .
Comparison of the last closed magnetic surface between the target plasma and the plasma reconstructed using the field and the windowpane coils whose currents are adjusted to minimize the normal field on the target boundary for the configuration with an external transform of ≈0.3 of Fig. 1(d). Left two frames: The right frame shows the comparison of the total rotational transform, target (solid) vs reconstructed (dotted) at .
The important Fourier coefficients for describing the boundary for the configurations shown in Fig. 1 are given with the normalization that . The coefficient is a measure of the plasma minor radius and the major radius.
Fourier coefficients that describe the boundary for the configurations shown in Fig. 5 are given. The normalization is .
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