Space-time focusing of charged particles in radio-frequency linear electric fields

Abstract

The fundamental properties of oscillations of charged particles in high frequency (HF) fields char acterized by two and three dimensional quadratic distributions of potentials have received quite pro found study and have been extensively used in dynamic mass analyzers of the quadrupole type [1]. These properties include the independence of charged particle motion in all coordinates and a stable or an unstable character of oscillations versus the par ticle charge to mass ratio m/e. Quadrupole analyzers involving static fields are also used as electron-ion optical systems for spatial focusing and energy analysis of charged particles [2]. However, the potential of selective properties of quadrupole fields is not exhausted by the possibilities for the stable versus unstable discrimination between particles. An analysis of solutions of second order differential equations (Mathieu's equations) reveals that the spectral com position of ion oscillations in linear HF electric fields is a function of the ratio m/e, but it is independent of the initial parameters of particle motion [3]. The space-time focusing and the time of flight mass sep aration of nonmonoenergetic ions can be accom plished by using these properties, which follow from the similarity of the trajectories of motion in quadru pole high frequency fields characterized by identical coordinate to velocity ratio.The possibility of the time of flight mass separa tion of ions in static linear electric fields via measuring the period of oscillations was considered in [3]. How ever, this method was not implemented in practice because of ion scattering in the transverse direction. In order to confine ions in the space of drift in all coordi nates, it was proposed in [4] to supplement a static lin ear field with a high frequency component. Although this does not change the fundamental regularities of ion motion in a static field along the drift axis, the oscillations in question cease to be strictly periodic, the quasiperiod being dependent on the initial coordi nates and velocities of charged particles. Calculations and experiments showed a bounded potential of the method of the time of flight mass separation of ions in mixed fields because of a complex aperiodic character of oscillations of charged particles in the traditional modes of operation of quadrupole mass analyzers [4]. Subsequent investigations revealed that an efficient time of flight mass separation of ions in two dimen sional linear radio frequency fields is possible under the condition that the oscillations of charged particles in both coordinates are close to monochromatic oscil lations and have equal or integral multiple secular fre quencies. These requirements are satisfied if ions move in linear HF electric fields without a constant compo nent at parameter values in the range of q < 0.1 [5]. We will now consider the focusing properties of such fields from the point of view of implementing in them the time of flight mass separation of nonmonoenergetic charged particles.In dynamic mass spectrometry, ...

Development of the analytical method of the general mathieu equation solution

“…The paper [16] is devoted to estimation of the potential energy of an ion in the quadrupole field for a = 0 and small values of q. With the same values of the parameters, in [17] the time-offlight mass-separation of ions in two-dimensional radio-frequency fields is considered.…”

“…-on motion stability and resonance phenomena in quadrupole traps and filters used in mass spectrometers [10,[12][13][14][15][16][17][18][19][20][21][22][23].…”