Following the 19th IAEA Fusion Energy Conference (Lyon, 2002), (1) three-time progress in the formation of ion-confining potential heights ϕc including a record of 2.1 kV in comparison to those attained 1992–2002 is achieved for tandem-mirror plasmas in the hot-ion mode with ion temperatures of several kiloelectronvolts. (2) The advance in the potential formation gives the bases for finding the remarkable effects of radially produced shear of electric fields Er, or non-uniform sheared plasma rotation on the suppression of intermittent vortex-like turbulent fluctuations. (i) Such a shear effect is visually highlighted by x-ray tomography diagnostics; that is, spatially and temporally intermittent vortex-like fluctuated structures are clearly observed as two-dimensionally reconstructed visual structures for the first time in kiloelectronvolt order ion-cyclotron heated plasmas having a weak shear in GAMMA 10. (ii) However, during the application of plug electron-cyclotron heatings (ECH), the associated potential rise produces a stronger shear (dEr/dr = several 10 kV m−2) resulting in the disappearance of such intermittent turbulent vortices with plasma confinement improvement. X-ray observations also show elongation of a vortex structure from a circular into an ellipsoidal shape, as depicted in H-mode theories, with an outward shift. (3) For the physics interpretations and control of such potential and the associated shear formation, the validity of our proposed theory of the potential formation is extensionally tested under the conditions with auxiliary heating. The data described above fit well to the extended surfaces calculated from our proposed consolidated theory of the strong ECH theory (plateau formation) with Pastukhov's theory on energy confinement.