By Kurt O. Friedrichs
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Extra resources for Spectral theory of operators in Hilbert space
Bohr and J. Lindhard, Dan. Mat. Fys. Medd. 28, no. 7 (1954). D. Betz and Ch. Schmelzer, UNILAC 1-67 (1967). D. Betz, G. Hortig, E. Leischner, Ch. Schmelzer, B. Stadler, and J. Weihrauch, Phys. Lett. 22 No. 5 (1966)643 11 W. Joho, “High Intensity Problems in Cyclotrons”, 9th Int. Conference on Cyclotrons, p337, Caen, France 1981. M. Gordon, “The longitudinal space charge effect and energy resolution”, 5th Intl. , pages 305-317, Butterworths, London, 1971. M. Gordon and V. Taivassalo, “The z4 code and the focusing bar fields used in the extraction calculations for superconducting cyclotrons”, Nucl.
Below are summary elements of the overall accelerator system. 30 MeV/u Pre-Accelerator Approximately 250 MV of linac sections will provide a system suitable for producing 30 MeV/u heavy ions. The light ion variable energy criteria is met since this system will also produce protons energies of ≈145 MeV and 4He energies of ≈90 MeV/u (360 MeV total). Three stripper locations will be required to strip all ions to a Q/A ≈ 1/3 though each beam will be stripped only once. The longitudinal dynamics are well matched to the Separated Sector Cyclotron requirements.
These values are only ≈10% of the energy gain per turn, and therefore, would result in a relatively insignificant effect. 73 mA. Since this is about one half the operating current for the achieved high-efficiency 1 MW extraction, it would suggest that these estimates are pessimistic. Further, even in the absence of this pessimism, the calculations would imply that the Separated Sector Cyclotron operating parameters will not present performance limitations due to space charge effects. 7 Horizontal-Vertical Coupling The coupling of the horizontal and vertical motions can potentially decrease the turn separation at extraction by increasing the turn width through non-linear coupling.