Accelerator Physics Exercises

- hand in 31 October 2012

3.1 Slide 6 of lecture 6 implies two equations can be applied as the particle passes on each turn through the rf cavity:

E  V0 sin   sin s  2h    2 E E0   where

V0  peak gap voltage of the cavity 2 E0  m 0c  rest energy of the proton

These can be used to follow a trajectory in the longitudinal phase space

E, on each turn around the machine at 2 GeV.

(a) Write a simulation program which assumes an initial point of these coordinates

0, in the range 0     s calculates and applies the small changes

E, to the current coordinate E  E,   counting the turns around the machine.

Hand in a listing of the program with an example of the output.

(b) Change the initial phase to be a degree or so less than

 s and thus trace out the maximum bucket size. HINTS: Remember that the slip factor is positive (below transition) and that the order of applying the increments is to (1) use the last turns value of phase to calculate the energy increment, then (2) calculate the energy increment to be applied to the current turn before calculating the phase advance for the next turn (just imagine you were a particle!)

3.2 Compare the results with the tables below from page 36 of: http://doc.cern.ch/archive/electronic/other/preprints//CM-P/cm-p00047617.pdf 3.3 Modify the FODO2.MADX input file to describe the following sequence of elements and attempt to run it to find betax, betay, dispersion mux and muy (Ang is 2*pi/100):

Name Type Length Angle E1 E2 K1 GTMER SBEND 2.724721E-01 Ang/2 Ang/2 0 0.000000E+00 S1 DRIFT 1.078197E-01 0.000000E+00 0 0 0.000000E+00 GQFI QUADRUPOLE 1.600000E-01 0.000000E+00 0 0 2.720544E+01 S2 DRIFT 1.000031E-01 0.000000E+00 0 0 0.000000E+00 - GQF2 QUADRUPOLE 1.542959E-01 0.000000E+00 0 0 1.616559E+01 S3 DRIFT 7.005689E-02 0.000000E+00 0 0 0.000000E+00 S3 DRIFT 7.005689E-02 0.000000E+00 0 0 0.000000E+00 - GQF2 QUADRUPOLE 1.542959E-01 0.000000E+00 0 0 1.616559E+01 S2 DRIFT 1.000031E-01 0.000000E+00 0 0 0.000000E+00 GQFI QUADRUPOLE 1.600000E-01 0.000000E+00 0 0 2.720544E+01 S1 DRIFT 1.078197E-01 0.000000E+00 0 0 0.000000E+00 GTMEL SBEND 2.724721E-01 Ang/2 0 Ang/2 0.000000E+00