By Avenhaus R., Canty M.J.
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Higher order terms are proportional . to (p__)n with n > l, which is of the order l0 -3 or less in comparison with the dominant terms discussed m Sec. 3. Some important higher order resonances arises from synchrotron motion, betatron coupling, and sextupoles will be discussed in this appendix. Al. Spin Depolarization due to Linear Betatron Coupling Linear coupling in synchrotrons arises from skew quadrupoles, solenoids, vertical closed orbit in sextupoles and feed down from higher order multipoles.
2_rZ2Ehlrll hlr]l (c3) ^ The action integral• is 7r__-z¢ pO in the phase space coordinates of (¢, pa__. ). has its action. A bunch Is made of particles with different actions. The mammum action of the bunch is called the phase space area. Sometimes, the rms action -4r,n, of the bunch is used to define the phase space area. The 95%of the beam with Gaussian distribution is then said to be within the phase space area of 2, = 6Arms. Bunch with different distribution functions, the factor 6 can be different.
6 meters when 2 Tesla magnets and a 15 cm spacing between magnets are used. The corresponding 5% snake for m = 2 will be about 50 cm longer. 58 cre. (E13)), the actual transverse closed orbit displacement can be smaller. ake, which minimizes orbit displacements and the total length of a snake. Such an optimization needed for small accelerators, where the length of straight section is small. D. 578B_-_-l[m-:], Bp d_ b = /3± the spinor equation (El8) + (1+ equation of motion is given by /SH (El9) of motion is given by i ds - _n(_rl cosks + e3sinks)_ Transforming -a
Compliance quantified by Avenhaus R., Canty M.J.