Scatter Plot from Scientific Research

(<Omega>, sigma_Omega) diagram. For each shot, we compute the turn-by-turn evolution of Omega along the storage period, and the corresponding mean value <Omega> and standard deviation sigma_Omega. The black solid line represents Omega_{fl}^{drt}. The blue area shows the selected shots close to the excited fixed line. Recall that Omega=phi_x+2phi_y with phi x and phi y the phase advances of the horizontal and vertical planes. Omega_{fl}^{drt} is the resonance phase advance of the resonance we have excited. The dashed lines show what is expected when Omega is not bounded and evolves randomly. In this case, the average of Omega is 0.5, and its standard deviation sigma_Omega =1/sqrt(12), (in units of 2 pi). The random error (precision) of <Omega> is sigma_(Omega) < 6 x 10^-4 and, hence, is within the marker size.

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