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One of the most important problems for space charge dominated beams in the low energy part of superconducting linacs is halo creation. Many authors show one of the key effects in halo creatiation is parametric resonance due to the mismatched betafunction oscillation (between core and particle). To estimate parametric resonance conditions the nonlinear tune shift for binomial distributed beam is described theoretically in this article. Simultaneously the beam dynamics simulation 3D PIC code was developed. The transverse oscillation frequencies are compared with parametric resonance criteria. As a result the recommendation for space charge shift is concluded to minimize halo creation.

The linear accelerator based on a superconducting structure with a high accelerating gradient accordingly has a strong rf defocusing factor. Usually, a quadrupole or solenoid focusing system is used in such accelerators. Both of these systems complicate the linear accelerator. The quadrupoles are located outside the cavity and a transition between the cold and the warm systems is required. Therefore an additional drift space between cryostats is needed, which can cause parametric resonance in the longitudinal plane in the energy range of 3-20 MeV. In the system with the solenoid the high magnetic field can affect the superconductivity. We consider the novel superconducting H resonator based on the TE211 mode with a slot and rf finger, providing the high-intensity beam focusing in the large range of low energy of 3-50 MeV. Above 50 MeV we suggest using the slot structure with the external quadrupoles.

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In case of superi-onducting injector in synchrotron due to high accelerating gradient the energy spread of beam after linac exceeds the longitudinal acceptance of ring. The problem becomes even more difficult, when we need to inject two beams with different chargel mass ratio. We consider the problem when H-andD-particles are injected and ratio of mass to charge differs by a factor of two. Both beams will he injected into ring at an approximately similar energy SO MeV. To fulfill the monochromatization requirement the momentum spread of H and D beams has to be decreased from &plp=_+(5+8).10" [I] to A p / p =~I . S~l O " , or in special case A p l p =k7.S.10d by the debuncher system optimized for both sorts of particle simultaneously. For this purpose the E and H debuncher types are considered. PHASE ADVANCE ADJUSTMENT.The first and obvious possibility is to adjust the advanced phase o -e i n the longitudinal plane of whole linear accelerator and rotate the phase portrait to get Lonl,"ll.l P h l Y Prnl.ll0, slim "I ii.lllmpl,i"drIIcmllln( hrn, .n.,W--'incllS:~on,, ns