| Paper | Title | Page |
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| MOPEC041 | Calculation of Second Order Moments for an Ion Beam in a Degrader | 549 |
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In order to decrease the energy of an ion accelerated in a cyclotron on value of some MeV/eau it is possible to run an ion beam through a thin metal foil (degrader). One can calculate the final ion energy, angular and energy stragglings, which the beam attains in the degrader, for example, by means of code LISE++. The formulae for calculation of the beam second order moments after degrader were obtained. The formulae for calculation of final beam momentum spread, new values of rms beam emittances, Twiss parameters and the dispersion functions were also obtained. The new ion beam parameters allow one to calculate the beam transportation along the beam line after degrader. |
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| THPE013 | Invariants of Linear Equations of Motion | 4539 |
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Courant-Snyder invariant and Root Mean Square (RMS) beam emittance are well-known invariants of linear equation of motion. They are connected with the second order moments of a beam distribution function. Other invariants of linear equations of motion generated by second and higher order moments are presented in this report. |