@article{oai:repo.qst.go.jp:00086086,
 author = {Akihiko, Mizuno and Kai, Masuda and Akihiko, Mizuno and Kai, Masuda},
 journal = {Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment},
 month = {Jun},
 note = {An rms emittance, which is often used in linear accelerators, is not an invariant value, since it is different from the constant value of Liouville's theorem. Therefore, it can be reduced, and the authors have already reported the mechanisms of the emittance reduction phenomenon (Mizuno et al., 2015). This phenomenon is completely different from the emittance compensation scheme, not only the projected emittance but also the slice rms emittance itself can be reduced. In this previous paper, the authors also showed several examples of the calculation of the emittance reduction in a continuous beam and in a pulsed beam. However, those discussions are qualitative making research on this phenomenon difficult. In this paper, the authors introduce two new physical quantities for treating the emittance reduction phenomenon quantitatively. One is named "mean emittance", whose concept is an extension of that of the rms emittance. It can express value of the emittance as well as the configuration of the phase space, which is directly related to the increase and decrease in emittance. The other is named "mean force nonlinearity". It represents the extent of the nonlinearity of the transverse force that acts on the beam, and it can also express the configuration of the r-fr, which is also closely related to the variation in emittance. Using these two quantities, the increase and decrease in emittance can be simply described quantitatively. Several examples of calculation for the ideal DC-accelerated continuous beam and the practical pulsed beam are demonstrated in this paper, and comprehensible discussions of the variation in emittance in these examples are presented using the two new expressions.},
 pages = {166733-1--166733-7},
 title = {Quantitative expressions for reduction in rms emittance},
 volume = {1033},
 year = {2022}
}