Transverse space-charge effects in heavy-ion storage rings for intertial-confinement fusion

Summary  The space-charge-induced crossing of half-integer and integer stop bands is examined for storage rings proposed to drive inertial-confinement fusion. Two different approaches are used: a classical resonance crossing picture and a diffusion model based on the addition of kicks due to field errorw with phase randomization due to rapidly changing tune shifts. Gradient and bending field tolerances to permit crossing of stop bands with acceptable emittance growth are established and compared to those observed in existing machines like the CERN-PS. Two different situations are to be distinguished in driver rings: the «stacking plus holding» period (of 5–50 ms) during which the rings are filled and the final bunching (during 10–50 μs) when the bunches are compressed from typically 100 to 10 ns length prior to extraction into the final transport system. Gradient tolerances to permit stop band crossing are found to be Δ(kl)/kl≤10−4 per quadrupole during stacking and ≤5·10−3 during final bunching; compared to a few 10−3 observed in the PS. Tolerances to survive resonances driven by bending field errors are Δ(Bl)/Bρ≤5·10−6 per element even in the final bunching period; an order of magnitude smaller than «typical» uncompensated values in the PS. Stop bands driven by gradient and bending field errors are affected by the «incoherent» and the «coherent» tuneshifts respectively. Hence for the driver rings one may contemplate working with a large incoherent tuneshift (ΔQ ic≤5) during final bunching but keeping the coherent detuning (during stacking and bunching) and the incoherent detuning during stacking small enough (ΔQ≤0.5) to avoid resonances in these conditions. The more conservative approach to avoid gradient error resonances even during final bunching leads to difficult constraints for other parameters. Experiments on the PS to test fast resonance crossing are also briefly discussed.