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JUAS 2011 Guided study and tutorial on RF Linear Accelerators A. Lombardi and JB. Lallement

JUAS 2011 Guided study and tutorial on RF Linear Accelerators A. Lombardi and JB. Lallement. Transit-time factor. The energy gain of a particle in a harmonically time-varying field is always less than the energy gain in a constant dc field

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JUAS 2011 Guided study and tutorial on RF Linear Accelerators A. Lombardi and JB. Lallement

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  1. JUAS 2011Guided study and tutorial onRF Linear AcceleratorsA. Lombardi and JB. Lallement

  2. Transit-time factor • The energy gain of a particle in a harmonically time-varying field is always less than the energy gain in a constant dc field • The transit-time factor T is the ratio of the energy gained in the time-varying RF field to that in a dc field • T is a measure of the reduction in the energy gain caused by the sinusoidal time variation of the field in the gap

  3. E(z) Ez Eg z -g/2 0 g/2 Square-wave electric field distribution TM010 mode in a pillbox cavity Pillbox cavity For a simple TM010 pillbox cavity of length g with a square profile of the electric field we find E0=Eg if L=g and the transit-time factor becomes

  4. Kilpatrick sparking criterion What is the maximum surface electric field that we can safely achieve in linac cavities? We can go up to the electric breakdown limit usually expressed in terms of Kilpatrick sparking criterion. • Electric field applied to a metal surface extracts large number of electrons enhanced by surface roughness and impurities • Kilpatrick (1957) has fitted existing data to a formula: f=1.64E2exp(-8.5/E)

  5. Kilpatrick sparking criterion Nowadays we can reach fields up to 2 Kilpatrick in CW operation thanks to cleaner vacuum and surface. We can define a bravery factor b=ES/EK

  6. Tuning plunger Drift tube Quadrupole lens Post coupler Cavity shell Alvarez Drift-Tube Linac (DTL) L=βλ=c/f

  7. Design of a DTL The fields, power, transit-time factors for the synchronous particle and the shunt impedance calculations are usually done using electromagnetic field-solver codes such as SUPERFISH. This procedure results in an optimum cell geometry in which the gap length, drift-tube shape and tank diameter are determined. Then the beam dynamics design is done.

  8. Design of a DTL

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