Cycloidal frequency

Ions generated by an electron beam from a heated filament are passed into a cubic cell where they are held by an electric trapping potential and a constant magnetic field. Each ion assumes a cycloidal orbit at its own characteristic frequency, which depends on mJz the cell is maintained under high vacuum. Originally, these frequencies were scanned by varying the electric field until each cycloidal frequency was, in turn, in resonance with an applied constant radiofrequency. At resonance, the motion of the ions of the same frequency is coherent and a signal can be detected. 

The newer instruments (Figure 2.4c) utilize a radiofrequency pulse in place of the scan. The pulse brings all of the cycloidal frequencies into resonance simultaneously to yield a signal as an interferogram (a time-domain spectrum). This is converted by Fourier Transform to a frequency-domain spectrum, which then yields the conventional m/z spectrum. Pulsed Fourier transform spectrometry applied to nuclear magnetic resonance spectrometry is explained in Chapters 4 and 5. 

In the double coiled helical beam gyrotron, the cycloidal frequency / of the double coiled trajectory is... 

This cycloidal frequency must be made equal to the operating microwave frequency. 

Figure 1 shows a schematic view of a typical ICR spectrometer. The operation of most current ICR spectrometers may be generally described as follows. Ions are produced by an electron beam in an ion source just as in any mass spectrometer. (In Fig. 1, the source region is denoted by A.) A uniform magnetic field B is oriented along the z axis and a dc electric field Fj is present in the y direction. An ion in crossed dc electric and magnetic fields (Section 2.5) will drift in the x direction following a cycloidal trajectory with a characteristic frequence of revolution co -... 

The above results for the motion of the tip of a spiral wave induced by the periodic modulation of the properties of an excitable medium were derived, in a slightly different form, in 1986 in [22] and later extensively discussed in [13, 26, 28, 29]. They show that the tip perforjns a cycloidal motion that represents a superposition of a rotation around a circle of radius Ro and of a circular motion with radius i i (hence the momentary rotation centre of the spiral wave moves along a circle of this radius). The type of the cycloid depends on the relationship between the two frequencies. If ujo > u>t, the centre of the spiral wave moves in the direction which is opposite to the direction of its rotation (i.e. clockwise if the spiral wave rotates in the counterclockwise direction, see Figure 5). When wq > wi, these two rotation directions coincide. 

---