Nearly all designs of accelerators for heavy ion fusion rely on a velocity (energy) ramp to compress the beam longitudinally from its length in the accelerator to the length required at the target. The size of the velocity ramp is constrained by the longitudinal emittance of the beam. For example, if the longitudinal emittance is 0.05 eV (center dot) s and we wish to produce a pulse having a width of (+-)2.5 ns at the target, we must supply an energy tilt such that the energy spread at the target is at least (+-)0.05 eV (center dot) s/2.5 ns = (+-)2 x 10(sup 7) eV. The minimal value of energy spread occurs when the beam has propagated to the point where there is no correlation between the time and energy variables of the beam particles. (In the simple approximation where the boundary of the longitudinal phase space containing the particles is an ellipse, the ellipse is erect at this point, i.e., not tilted with respect to the axes.) In any case, the energy spread can affect focusing. If, for example, the beam kinetic energy is of the order of 5 GeV, a tilt of (+-)2 x 10(Sup 7) eV corresponds to a fractional energy spread of 0.004 and it may be possible to focus the beam to the required spot size without using an achromatic optical system. Nevertheless, an optical system that allows larger longitudinal emittance should lead to a less expensive accelerator since the tolerances on acceleration waveforms could be relaxed.
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