We apply Numerical Analysis of Fundamental Frequency

The frequency map analysis of a Hamiltonian system [1],[2],[3] recently introduced to accelerators physics in combination with turn-by-turn phase space measurements opens new experimental opportunities for studying non linear dynamic in storage rings. In this paper we report on the experimental program at SPEAR having the goal of measuring the frequency map of the machine. In this paper we discuss the accuracy of the instantaneous tune extraction from experimental data and demonstrate the possibility of the frequency map measurement. 1 TURN-BY-TURN PHASE SPACE MONITOR We have previously reported on experimental beam dynamics studies at SPEAR and hardware used for this purpose [4], [5]. We have upgraded the electronics following the BPM base-band processor in order to achieve higher resolution by adding 6 channels of custom built high speed low noise track and holds serving as a front end for 14-bit Pentekä ADCs in the VME mainframe. The resolution achieved in the single pass is 125 mm for current per bunch 3mA. We have modified the fast kicker triggering circuitry to initiate the data acquisition cycle at fixed phase with respect to AC to avoid the influence of the 60 Hz ripple in the magnetic field [6]. The control of the data acquisition has also been automated using LabViewä running on Pentiumä workstation for effective use of machine time dedicated to accelerators physics