Field-mode amplitudes

We have developed a model to explain the time dependent change in sensitivity for ions during excitation and detection. The first step is to describe the image charge displacement amplitude, S(Ap, Az), as a function of cyclotron and z-mode amplitudes. The displacement amplitude was derived using an approximate description of the antenna fields in a cubic cell. The second step in developing the model is to derive a relationship to describe the cyclotron orbit as a function of time for an rf burst. An energy conservation... 

The observations that there is an "optimum" orbit size and that peaks split for orbits not too much larger than the optimum orbit suggest that the optimum orbit occurs because of special circumstances. One possible circumstance is a coincidence of frequencies for ions with low and high z-mode amplitudes so that if there are mass discriminating differences in the way the ions populate the trap or in the way ions are excited, then systematic mass measurement errors can be expected. Excitation of the cyclotron mode does produce a spread in cyclotron radii, and mass discriminating z-mode excitation is discussed elsewhere in this chapter. Thus, frequency variations that cause systematic mass errors are due in part to trap field inhomogeneities. These effects are evident at low ion populations and may be due in part to excitation induced ion cloud deformation which increases with ion number. 

For low ion populations, a first estimate of achievable ejection resolution might be obtained from the cyclotron frequency spread that occurs over the range of cyclotron orbit radii through which the ion must pass to be ejected. This is based on the notion that an ejection waveform that is just adequate to eject one ion must have a frequency spectral peak that is at least as wide as the above spread of frequencies. Such a waveform would then excite, at least to some extent, all ions with frequencies falling within the width of the peak, thus limiting the ejection resolution. For ions with low z-mode amplitudes, we can use Dunbar s (46) approximate expression for the average radial field strength,... 

Attenuated total reflection FTIR is a well-established technique for obtaining absorbance spectra of opaque samples. The mode of interaction is unique because the probing radiation is propagated in a high index-of-refraction internal reflection element (IRE). The radiation interacts with the material of interest, which is in close contact with the IRE, forming an interface across which a nonpropagating evanescent field penetrates the surface of the material of interest to a depth in the order of one wavelength of the radiation. The electric field at the interface penetrates the rarer medium in the form of an evanescent field whose amplitude decays exponentially with distance into the rarer medium. 

Phase contrast is a useful technique for specimens such as polymers that have little inherent contrast in the bright-field mode. In the technique, a phase change due to light diffraction by an object is converted to an amplitude change. This conversion is based on interference... 

The situation changes drastically if the field mode is allowed to interact with some detector placed inside the cavity. Following other findings [188,189] we demonstrate the effect in the framework of a simplified model, when a harmonic oscillator tuned to the frequency of the resonant mode is placed at the point of maximum of the amplitude mode function v /mn(x,y L ) in the 3D rectangular cavity. 

The central problem in understanding the chemical contribution to the overall enhancement reduces to the calculation of the polarizability of the adsorbate metal surface complex. The mixing of molecular states with metal states may bring about a large effective polarizability. The polarizability a depends on the normal mode amplitude of the molecular vibration Q. In the image field theory of SERS the effective polarizability aeff(Q) depends on the distance between the point molecule and the metal surface and on and e . In order to obtain Raman enhancement the distance between molecule and metal is in the range of 1.5 to 4 A. 

The time evolution of the probability amplitudes ae, t) and flg, (f) exhibits a characteristic periodic energy transfer between the two-level system and the electromagnetic field mode which is characterized by the n-photon Rabi frequency = /A + 4 g n. As the period of this energy exchange depends on the photon number the resulting time evolution exhibits interesting collapse and revival phenomena. 

If we specifically consider the mixing of two single-mode, amplitude-stabilized, first-order coherent waves, both of which are well collimated, parallel, plane polarized along a common unit vector, and normally incident onto a photosensitive material, we may write the positive portion of the electric field operator as the superposition of two scalar fields... 

Extensive laser-microwave investigations have also been performed in the spectrum of NH2. Hills and Curl, Jr. observed strong electric dipole microwave transitions between a previously unobserved rovibronic level and the J = 1/2 and J = 3/2 spin-rotational levels of ho, A ir(0,10,0), respectively. The NH2 molecules passed through a resonant half-wave microwave cavity with a 60-mW single-mode cw dye laser beam along the axis. The microwave field was amplitude modulated, and the laser-excited fiuorescence signal was detected with a phase sensitive amplifier. Microwave transitions in that part of the NH2 spectrum were used by Hills to assign numerous optical transitions. 

The deuterium line of the deuterated solvent is used for this purpose, and, as stated earlier, the intensity of this lock signal is also employed to monitor the shimming process. The deuterium lock prevents any change in the static field or radiofrequency by maintaining a constant ratio between the two. This is achieved via a lock feedback loop (Fig. 1.10), which keeps a constant frequency of the deuterium signal. The deuterium line has a dispersion-mode shape i.e., its amplitude is zero at resonance (at its center), but it is positive and negative on either side (Fig. 1.11). If the receiver reference phase is adjusted correcdy, then the signal will be exactly on resonance. If, however, the field drifts in either direction, the detector will... 

Figure 1.10 (a) The dispersion mode line should have zero amplitude at resonance, (b) The deuterium lock keeps a constant ratio between the static magnetic field and the radiofrequency. This is achieved by a lock feedback loop, which keeps the frequency of the deuterium signal of the solvent unchanged throughout the experiment. 

In Chapter 6 we presented an expression for the transition probability (or intensity, amplitude) of field-swept spectra from randomly oriented simple 5=1/2 systems (Equation 6.4), and we could perhaps tacitly assume (as is generally done in the bioEPR literature) that the expression also holds for effective S = 1/2 systems, such as for the high-spin subspectra defined by the rhombograms discussed in Chapter 5. But what about parallel-mode spectra And how do we compute intensities in complex situations like for systems in the B S B B intermediate-field regime Clearly, we need a more generic approach towards intensity calculations. 

The above picture points to the very interesting possibility of selectively inducing or enhancing the polymerisation process, at a temperature where this is unlikely, by resonantly driving with an intense laser beam in the infrared the vibrational modes and wc that are involved in the polymerisation. As a consequence of their anharmonicity (45) these modes, when driven near resonance by an electromagnetic field, beyond a certain critical value of the later, can reach amplitudes comparable to the critical ones required for the polymerisation to be initiated or proceed the anharmonicity in the presence of the intense laser beam acts as a defect and localizes the phonons creating thus a critical distorsion. 

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