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Fig. 2. 8-GeV hybrid lattice dynamie aperture with only random conventional errors. The solid linę represents the ideał dynamie aperture; the open sąuares represent the dynamie aperture with the random conventional errors.

Fig. 4. 8-GeV hybrid lattice dynamie aperture with a -1% constant momentum error, systematic multipole error fields, and random conventional errors. The solid linę represents the ideał dynamie aperture; the open and filled sąuares represent respectively the dynamie aperture with only random conventional errors and three kinds of errors.

Fig. 3. 8-GeV hybrid lattice dynamie aperture with only systematic multipole error fields. The solid linę represents the ideał dynamie aperture; the filled sąuares represent the dynamie aperture with expected error fields. The open sąuares and triangles represent respectively the dynamie aperture with error fields five and ten times stronger than an expected one.

sequently generate nonlinear effects greatly morę than the systematic multipole error fields. This phenomenon can be explained as follows. The linear field errors break the periodicity of linear functions. This symmetry breaks of the linear functions much enhance the resonance driving terms by the sex-tupole magnets, which are almost cancelled out with perfect symmetries of linear functions under an ideał condition.

References

1)    J. Ohnishi and S. Motonaga: llth Int. Conf. on Magnet Technology, Tsukuba, Japan, p. 194 (1989).

2)    A. Wrulich: DESY Rep., 84-026 (1984).

3)    H. Tanaka, R. Nagaoka, K. Tsumaki, K. Yoshida, and M. Mara: R1KEN Accel. Próg. Rep., 22. 231 (1988).

4)    H. Tanaka, R. Nagaoka, K. Yoshida, K. Tsumaki, and M. Hara: ibid., p. 235.