Generalization and consolidation of scaling laws of potential formation and associated effects are investigated in the GAMMA 10 tandem mirror. The scaling covers over representative tandem-mirror operational modes, characterized in terms of (i) a high-potential mode having kV-order plasma-confining potentials, and (ii) a hot-ion mode yielding fusion neutrons with 10-20 keV bulk-ion temperatures. A novel proposal of extended consolidation and generalization of the two major theories of (i) Cohen's strong electron cyclotron heating (ECH) theory for the formation physics of plasma confining potentials, and (ii) the generalized Pastukhov theory for the effectiveness of the produced potentials on plasma confinement has been made through the use of the energy-balance equation. This proposal is then followed by the verification on the basis of experimental data from the above two representative modes in GAMMA 10. The importance of the validity of this proposed consolidation is highlighted by a possibility of extended capability inherent in Pastukhov's prediction of requiring ion-confining potential (ɸc) of 30 kV for a fusion Q value of unity through an application of Cohen's potential formation method. In addition to the above potential physics scaling, an externally controllable parameter scaling including ECH powers for potential formation is investigated: The construction of the ɸc formation scaling with both plug and barrier ECH is carried out. Data on ɸc. [kV] (or equivalently ɸh with np/nc from the strong ECH theory) as a function of externally controllable plug and barrier ECH powers, (PPECH [kW] and PBECH [kW], respectively), and nc [1018 m−3] are summarized as follows:

ɸc= 1.0×10−4(1+5.0×10−3 ×PBECH1.04±0.02) PPECH1.73±0.02 × [c (np/nc)2/3-1]exp [-(0.33±0.05) nc]. Here, c=9-11 and 7-9 for the hot-ion and high-potential modes, respectively. The present paper covers the following updated results: (i) A verification of our novel proposal for potential formation and effects is carried out so as to consolidate two major (Pastukhov's and Cohen's) theories by the use of the “third mode” with the central ECH. The validity of the theory provides a future scenario for combining present representative modes so as to upgrade to hot-ion plasmas with high potentials. (ii) A novel efficient scaling of ɸc formation with both plug and barrier ECH is summarized. The combination of the physics scaling of (i) with the externally controllable practical power scaling of (ii) provides a scalable way for the future tandem-mirror researches.