Sign conventions for FEL studies

1. Sign conventions for FEL studies Initiated by A. Latina at CERN – Nov 28 2013

2. MAD-X: MAD-X’s phase-space 5th coordinate is: At a certain time t, the reference particle is at s0: tail head Particles ahead of the reference particle have s > s0 , therefore z > 0. Acceleration is: • In chicanes R56>0 and full compression is achieved with ΦRF= -π/2 • Compensation of Energy loss due to longitudinal wakes is achieved with ΦRF < 0 tail head

3. PLACET: PLACET uses: Ahead particles pass at s0 earlier than the reference particle, t < t0 , therefore have z < 0. head tail Acceleration is the same as in MAD-X (although z has a different meaning, which implies: ΦRF = -ΦRF,MAD): • In chicanes R56<0 and full compression is achieved with ΦRF= +π/2 • Compensation of Energy loss due to longitudinal wakes is achieved with ΦRF > 0 head tail

4. ELEGANT, RFCA: Like PLACET and PARMELA, ELEGANT uses: Ahead particles pass at s0 earlier than the reference particle, t < t0 , therefore have z < 0. head tail Acceleration is (which implies: ΦRF = 90o+ΦRF,MAD): • In chicanes R56<0 and full compression is achieved with ΦRF= 0o • Compensation of Energy loss due to longitudinal wakes is achieved with ΦRF < 90o head tail

5. Summary Table Some comments about this matter can be found in Andy Wolski’s notes at USPAS 2003, “A Short Introduction to Bunch Compressors for Linear Colliders” http://www.desy.de/~njwalker/uspas/coursemat/notes/unit_5_notes.pdf