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On the basis of an analysis of the ITER L-mode energy confinement database, two new scaling expressions for tokamak L-mode energy confinement are proposed, namely a power law scaling and an offset-linear scaling. The analysis indicates that the present multiplicity of scaling expressions for the energy confinement time TE in tokamaks (Goldston, Kaye, Odajima-Shimomura, Rebut-Lallia, etc.) is due both to the lack of variation of a key parameter combination in the database, fs = 0.32 R a^.75 k^ 5 ~ A a^.25 k^.5, and to variations in the dependence of rE on the physical parameters among the different tokamaks in the database. By combining multiples of fs and another factor, fq = 1.56 a^2 kB/R Ip = qeng/3.2, which partially reflects the tokamak to tokamak variation of the dependence of TE on q and therefore implicitly the dependence of TE on Ip and n,., the two proposed confinement scaling expressions can be transformed to forms very close to most of the common scaling expressions. To reduce the multiplicity of the scalings for energy confinement, the database must be improved by adding new data with significant variations in fs, and the physical reasons for the tokamak to tokamak variation of some of the dependences of the energy confinement time on tokamak parameters must be clarified