The solitary structure solution of the radial electric field E-r in th
e tokamak plasmas is obtained. It is shown to be stable under an exter
nal power supply, like a biased electrode at the edge. The radial grad
ient is governed by the ion viscosity and the nonlinearlity of the per
pendicular conductivity. The radial structure of E-r and reduction of
turbulent transport, which belong to key issues of the high confinemen
t mode (H-Mode) [F. Wagner et al., Phys. Rev. Lett. 49, 1408 (1982)],
are self-consistently determined. A bifurcation from a radially-unifor
m one to a solitary one occurs at a certain applied voltage, and a hys
teresis is associated. (C) 1998 American Institute of Physics. [S1070-
664X(98)01312-3].