The cubic equation derived by B. Zotter has been popularly used for electron
storage rings to describe the scaling law of potential-well bunch lengthening.
This equation has also often been used to calculate the effective impedance
when the bunch lengthening is measured or simulated. This paper discusses the
validity of Zotter's equation and presents an alternative but self-consistent
equation for potential-well bunch lengthening. Its applications to predicting
bunch lengthening and extracting effective impedance from bunch length
measurements are also addressed.Comment: 6 pages, 4 figures, submitted to 20th Annual Meeting of Particle
Accelerator Society of Japan (PASJ2023). arXiv admin note: text overlap with
arXiv:2307.0128