Then we have extended the FBC concept using the virial theorem which is the relation between magnetic field energy and working stress in coils and their supporting structure. According to the theorem, high-field coils should have the same averaged principal stresses in all directions, whereas conventional FBC reduces stress in the toroidal direction only. In Ref. 3, we derived the poloidal rotation number of helical coils which satisfy the uniform stress condition, and named the coil as virial-limit coil (VLC). According to Ref. 3, VLC with a circular cross section of aspect ratio A=2 reduces the maximum stress to 60% compared with that of TF coils.
In order to prove the advantage of the VLC concept, we manufactured a small VLC pulsed tokamak "Todoroki-II'' with a major radius of 0.3 m, a minor radius of 0.08 m, toroidal magnetic field strengths of BT < 1.5 T and plasma currents of IP < 40 kA.
Since error fields in the vacuum vessel of Todoroki-II by VLCs in Todoroki-II were much reduced by their modulated winding pitch, plasma breakdown became easier than that in Todoroki-I while pre-ionization was still required. In the initial phase of experiments without external vertical field, a plasma pulse length of 0.4 ms and a maximum plasma current of 5 kA were achieved by two-step VLC excitations. External vertical field increased both the plasma pulse length and current to 1 ms and 11 kA, respectively, while they were restricted because of no vertical field control. Using a Cauchy-condition surface (CCS) method , the shape and displacement of plasma boundary was reconstructed, and the validity of CCS under large eddy currents was verified.
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