Betatron

This chapter introduces the betatron fixed orbit cyclic accelerator. It begins with a brief reminder of the historical context, and continues with the Widerøe condition and the principles of fixed orbit acceleration in a betatron. The latter is at the origin of the theory of the “betatron oscillations”—treated in Chaps.  3 and 8 . A realistic simulation of a betatron in zgoubi would require the simulation of an induction electric field: this is doable from existing dipole models such as DIPOLE[S], and can be seen as an interesting code development exercise. A simpler approach on the other hand only requires two optical elements: DIPOLE and CAVITE. Accounting for synchrotron radiation (SR) energy loss requires SRLOSS. Monte Carlo SR monitoring can use SRPRNT, which logs data in zgoubi.res. SRPRNT[PRINT] in addition logs data in zgoubi.SRPRNT.Out. Electron beam monitoring requires keywords introduced in the previous chapters, such FAISCEAU, FAISTORE. SR monitoring uses SRPRNT. INCLUDE allows simplifying the input data files. Graphs are part of data treatment and simulation outcomes, they are produced using zpop or gnuplot.