Minimum electron beam size of a triple bend lattice

It is well known that the electron beam emittance can be lowered by keeping positive dispersion in the insertion straight section of an otherwise double bend achromat lattice. But the fact that the beam size at the straight section is not simply determined by the emittance any more has made the scheme suspicious. There was even a claim that the minimum electron beam size in the straight section remains unchanged regardless of the dispersion. It is shown in this article that the electron beam size can really be decreased by the positive dispersion of the straight section. It is also shown that the minimum of σ 2 / β of the dispersive straight section is 0.64 of that of the minimum double bend achromat lattice.