= Solution
<Equilibrium> emittance obeys $\epsilon_x=C_q\gamma^2I_5/(J_xI_2)$, with $I_5=\oint H(s)|\rho|^{-3}ds$, $H=\gamma_x\eta^2+2\alpha_x\eta\eta'+\beta_x\eta'^2$. Thus reduce both bend angles and the dispersion invariant inside bends, rather than merely focusing to a small beam size elsewhere. The damping partition can also be adjusted within stability constraints.
A DBA uses two bends and quadrupoles to return dispersion and its slope to zero at the cell boundaries; this provides dispersion-free insertion straights, at some emittance cost. A multi-bend achromat distributes the total angle over more weak bends and carefully controls the interior dispersion. A non-achromatic theoretical-minimum-emittance cell permits nonzero boundary dispersion and chooses the <beta function> and dispersion near a bend's optimum; longitudinal-gradient or reverse bends offer further control of radiation <Integral>[integrals]. <Strong focusing> and dispersion suppression can increase natural chromaticity and sextupole demands, compromising dynamic aperture and <momentum> acceptance.
\Image[/past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2017-accelerator-cell-designs.png]
{title=Schematic double-bend, multi-bend and non-achromatic emittance-design strategies}
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