On the Behavior of the Generalized Alignment Index (GALI) Method for Regular Motion in Multidimensional Hamiltonian Systems

We investigate the behavior of the Generalized Alignment Index of order k (GALIk ) for regular orbits of multidimensional Hamiltonian systems. The GALIk is an efficient chaos indicator, which asymptotically attains positive values for regular motion when 2≤k ≤N, with N being the dimension (D) of the torus on which the motion occurs. By considering several regular orbits in the neighborhood of two typical simple, stable periodic orbits of the Fermi-Pasta-Ulam-Tsingou (FPUT) β model for various values of the system's degrees of freedom, we show that the asymptotic GALIk values decrease when the order k of the index increases and when the orbit's energy approaches the periodic orbit's destabilization energy where the stability island vanishes, while they increase when the considered regular orbit moves further away from the periodic one for a fixed energy. In addition, by performing extensive numerical simulations we show that the behavior of the index does not depend on the choice of the initial deviation vectors needed for its evaluation.

Quadrupole mass filter acceptance in stability island created by double-frequency quadrupole excitation

Increase in quadrupole mass filter resolution at separation in narrow band stability island (X-band) formed by biharmonic resonance excitation of ion oscillation is discussed. X-band and the normal working quadrupole mass filter modes are compared at theoretical resolution of 10,000 and different separation times. Transmission curves, acceptance ellipses parameters, and acceptance characteristics are obtained by numerical simulation. Transmission coefficients are approximately the same in both modes. Dependence of acceptance ellipses parameters on ion inlet phases has a complicated oscillating form in the X-band mode. Acceptance contours calculated for given transition levels have been compared. At low acceptance level, the combined acceptance in the X-band mode was found to be one order of magnitude higher than in the normal mode.