Contents

• Introduction
• Type INTERNAL_STATE of PTC
  • Definition of a State
  • Eternal States
  • State Default
  • State Time
  • State Totalpath
  • State Nocavity
  • State Fringe
  • State Spin
  • States controlling Radiation
    • State Radiation
    • State Envelope
    • State Stochastic
  • State Modulation
  • States Affectiong Map Calculations
    • State Only_4d
    • State Delta
  
  
• Geometry Routines of PTC
  • Survey Routines
  • Over Fibres
  • Over Integration_node: FILL_SURVEY_DATA_IN_NODE_LAYOUT(R)
  
  
• PTC Tracking Routines
  • Layouts Types
  • Objects which can be tracked (Rays, spin, Taylor maps)
    • Real or Real_8 X(1:6)
    • Probe and Probe_8
    • TEMPORAL_PROBE
    • Tracking 6 Rays as X(1:6): without wrapping a probe
    • Tracking 6 Rays as X(1:6) wrapping a probe
    • Tracking Probe
    • Tracking THREE_D_INFO
    • Filling a ray in the NODE_LAYOUT
    • Tracking TEMPORAL_PROBE
  
  
• Exception Handling in Tracking and Apertures
  • The various ways to crash!
  • Two types of routines in PTC
  • Example of using exceptions: correctly and incorrectly
  • Physical and mathematical aperture
    • Element Aperture
    • Distributed Aperture
  
  
• Tracking with Radiation in PTC
  • Tracking with Classical Radiation
    • Finding the Energy loss: GET_LOSS(R,energy,deltap)
  • Tracking a Quantum Envelope and computing the equilibrium sizes
  • Tracking the beam sizes around
    • ``Correctly'': Routine extract_beam_sizes
    • ``Incorrectly'': using lattice functions and Chao emittances
    • ``Incorrectly'' fixing the problem using nonsymplectic lattice function
  • Tracking a with a stochastic kick: two ways
    • Kicking the energy at every node: flag compute_stoch_kick
    • Kicking the energy at every turn using the result of the normal form
  
  
• Slow RF Modulation
  • The types rf_phasor and rf_phasor_8
  • Effect on the magnet
  • Tracking with RF modulation
  • Normal Form with RF modulation
  
  
• Tracking Spin in PTC
  • Find Orbit with Spin
  • Invariant Spin field with Normal Form
    • Invariant Spin field with Normal Form
    • Spin field Lattice Funcions
    • Stroboscopic Average
  
  
• Beam Beam Kick
  • Beam-Beam Flags
  • Approximately locating the beam-beam kick: standard rubish
  • Exactly locating the beam-beam kick: locate_beam_beam(r,o,m,t,f)
  
  
• Small Example Programs
  • Subroutine Track_a_ray(RADIATION_FLAG,SPIN_FLAG)
  • Subroutine Track_a_ray_time(RADIATION_FLAG,SPIN_FLAG)
  • Subroutine Track_a_ray_orbit
  • Subroutine Track_a_ray_around_ring
  • Subroutines to test the apertures flags
  • Subroutine displaying Radiation in PTC
  • Subroutine Showing a Beam-Beam Kick
  • Subroutine Track_with_rf_modulation
  • Subroutine Track_a_ray_with_spin
  
  
• Review of normal form: Orbital and Spin
  • Very short revew of the Orbital Normal From
    • The Orbital Normal Form Itself
    • The Normal Form Itself
  • The case of spin
    • Spin Maps in FPP
    • Spin Maps Concatenation
    • Spin Normal Form
    • Factoring the Map $T$ and the invariant spin axis $\vec{n}$
  • Corollaries of normal form: phase advance and stroboscopic average
    • Phase Advance
    • ``Stroboscopic'' average
  
  
• Bibliography