Non Linear Beam Dynamics Studies at SPEAR Page: 3 of 3
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modulation of the transverse tunes at the synchrotron
frequency due to coherent synchrotron oscillations and
centroid amplitude modulations due to the decoherence-
recoherence effect, and due to non-zero energy spread
within the bunch . All these effects were indeed
observed using instantaneous tune measurements.
vertical amplitude (mm
0 250 500
500 750 10001250 1500 1750 200
Fig.4 Evolution of the instantaneous vertical tune V and
amplitude a as a function of turn number.
The instantaneous tune extraction technique can be
applied to experimental tracking data with reasonable
accuracy. Frequency map can be experimentally
determined using the existing turn-by-turn phase space
measurement techniques and NAFF instantaneous tune
The authors express their appreciation to D.Gough,
G.Johnson, D.Mostoffi, J.Yang. for their contribution in
the design and building of the electronics for the data
acquisition system. We greatefully acknowledge the input
into the program at earlier stages by P.Tran. We also
thank H.D.Nuhn, M.Lee, D.Robin, E.Todesco for useful
and inspiring discussions.
 H.Dumas, J.Laskar: 'Global Dynamics and Long-Time stamility
in Hamiltonian systems via numerical frequency analysis', Phys.
Rev. Lett. 70, 2975 (1993)
 J.Laskar, 'Frequency analysis for multi-dimensional syatems',
Physica D67 (1993) 257 - 281
 J.Laskar, D.Robin: 'Applications of frequency map analysis to the
ALS',Proc. of the International Workshop on Single-Particle
Effects in Large Hadron Colliders, Montreux, Switzerland (1995)
 P.Tran,C.Pellegrini, M.Cornacchia, M.Lee, W.Corbett: 'Non
linear beam dynamics experimental program at SPEAR' IEEE
PAC 1995 p. 3323
 P.Tran etal 'Measurement of the octupole induced tune shifts at
SPEAR' AIP Conf Proc. Vol. 315, 1994
 A.Terebilo, C.Pellegrini, M.Cornacchia, J.Corbett,
D.Martin:'Measurement of time variation of machine
parameters', these proceedings.
 S.Y.Lee:'Review of nonlinear beam dynamics experiments' AIP
Conf.Proc. (1992) 131 p.249-264.
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Terebilo, A.; Pellegrini, C.; /UCLA; Cornacchia, M.; Corbett, J.; Martin, D. et al. Non Linear Beam Dynamics Studies at SPEAR, article, September 12, 2011; United States. (digital.library.unt.edu/ark:/67531/metadc831829/m1/3/: accessed January 21, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.