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This document explores the sign conventions used in Free Electron Laser (FEL) studies, initiated by a Latina at CERN on November 28, 2013. It elaborates on the phase-space representation in MAD-X, detailing how particles’ positions and timings relate to the reference particle. The variations in acceleration and energy compensation with RF phases in MAD-X, PLACET, and ELEGANT simulations are compared. A summary table is included for clarity, along with references to additional resources. This study is crucial for understanding particle dynamics in linear colliders.
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Sign conventions for FEL studies Initiated by A. Latina at CERN – Nov 28 2013
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
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
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
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
