Proposing new index for treating emittance reduction quantitatively

An rms emittance, which is often used in the linear accelerators, is not an invariant value, since it is different from the constant value of the Liouville's theorem. Therefore, it can be reduced and the author have already reported the mechanisms in this conference series. The author showed the electron injector design based on emittance reductions in that previous report, though the emittance reductions were not discussed quantitatively. In this report, the author propose a new index for treating emittance reductions quantitatively. The new index is defined by simple arithmetic mean in place of root-mean-square, and behavior of the new index along a beam axis is similar with that of the rms emittance. And it is defined as negative when a curve plotting on r-r′ plain is convex downward, and as positive when a curve is convex upward. In this conditions, the new index always reduces when forces whose shape is convex downward curve in the r-f_r plain act. Therefore, the emittance reduction mechanisms can be simply described, and the quantitative discussions on the emittance reductions become possible. In this report, the author discuss a definition of the new index, and some examples of behavior of the new index are presented. (author)