Non-linear resonance

Rautian S. G., Smirnov G. I., Shalagin A. M. Non-linear Resonance in Spectra of Atoms and Molecules. (Nauka, Novosibirsk) (1979) [in Russian]. 

AUieit, R. Kleinadam, S. Vedel, F. Vedel, M. Werth, G. Higher Order Non-Linear Resonances in a Paul Trap. Int. J. Mass Spectrom. Ion Proc. 1996, 154, 155-169. 

A tapping mode (also called intermittent contact mode) it is a non linear resonance mode. In this case, the oscillation amplitude is larger and the mean position of the tip is closer to the surface. The tip almost touches the surface at each oscillation. In this mode, friction can be avoided as well as the sample deformation and wear. Adhesion is also avoided thanks to the extremely short time of contact . The height of the sample is generally controlled so that the oscillation amplitude remains constant. The phase shift of the oscillation is then characteristic of the system dissipation, which is very useful for characterizing viscoelastic materials. 

The population of vibrationally excited states at the Treanor minimum E = Exr) is large in this regime, and the non-linear resonant W exchange dominates and provides a plateau at > i Tr even though < 5yy. At low levels E < E-y ), the linear non-resonant W exchange dominates over the non-linear one. It does not change the vibrational distribution function, however, because both non-resonant and resonant components of the W exchange result in the same Treanor distribution at < Ej. ... 

The major peculiarity of CO2 dissociation kinetics in supersorric plasma flow is related to a very low translational temperature (about 100 K) and, hence, a very high degree of VT non-equilibrium T /To > 30). The population of highly excited vibrational levels of the CO2 asymmetric mode can be essentially affected by non-linear resonant W exchange (strong excitation case, see Chapter 3 for details, see Fridman Kennedy, 2004). The critical vibrational temperature corresponding to equal rates of dissociation and VT relaxation (see Section 5.3.5), can be estimated in this case as (Asisov etal., 1983 compare with (5-46)) ... 

The term non-linear resonance describes the resonant absorption of potential energy from higher-order trapping fields. Such absorption occurs when combinations of an ion s secular frequencies match harmonic sidebands of the RF drive frequency. Conditions for non-linear resonance exist in all QITs but the effect on ion motion is dependent upon the order, sign (+ or -) and strength of the superimposed non-linear fields. Due in large part to the work of Franzen and co-workers [87-92], the phenomenon of non-linear fields and their contribution to non-linear resonance effects in ion traps is now well understood. In addition to the quadrupolar resonance, there are a series of resonance conditions desaibed by Equations 9.11 and 9.12 where V is an integer 0 and n is the order of the multipole. The overall order of the resonance (AO is described by Equation 9.13. 

These single-ion trajectories illustrate several aspects of the modified hyperbo-loidal angle geometry. The observation of non-linear resonance lines in the power... 

The pseudohalogen concept has been extended to include non-linear resonance-stabilised... 

M Ganz, W Kiefer, M Leuchs, A Matemy, J Strempel, P Vogt. Linear and non-linear resonance Raman scattering from simple systems. Vibrat Spectrosc 5 1-24, 1993. 

Wang, Y Franzen, J. J. The non-linear resonance QUISTOR Part 1. Potential distribution in hyperboloidal QUlSTORs. Int. J. Mass Spectrom Ion Proc. 1992, 112, 167-178. 

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