Larmor formula

A qualitative criterion to assess the extent of radiation damping may be derived[55] from the Larmor formula that estimates the energy radiated in terms of an electronic acceleration of magnitude a, for a period of time T,... 

In a SR source the electron moves at a speed close to c so that for a radius of curvature, q, the relativistic generalisation of the Larmor formula is... 

When an electron is accelerated, it produces electromagnetic radiation. The power radiated by an accelerated charge, P, whose speed is significantly less than the speed of light, is described in classical electrodynamics by the Larmor formula. In a synchrotron, the electrons are moving at a speed close to the speed of light (relativistic electrons). The power radiated by relativistic electrons is given by... 

Additional evidence on electron-cloud radii is given by diamagnetic susceptibility and by refractive index. For the well-known Larmor-Langevin theory of diamagnetism (11—13) gives for the molecular diamagnetic susceptibility —Xm the formula... 

Larmor s formula), the energy radiated per unit angular frequency per encounter with a given vo and b. The classical line shape is then given by... 

The precessional motion of the magnetic moment around Bq occurs with angular frequency wq, called the Larmorfrequency, whose units are radians per second (rad s ). As Bq increases, so does the angular frequency that is, coq cx Bq, as is demonstrated in Appendix 1. The constant of proportionality between o>o and Bq is the gyromagnetic ratio 7, so that wq = Bq. The natural precession frequency can be expressed as linear frequency in Planck s relationship AE = Hvq or angular frequency in Planck s relationship AE = h(x)Q (coq = 2 rrvo). In this way, the energy difference between the spin states is related to the Larmor frequency by the formula... 

The first thing to do is to verify that these formulae give us the expected result when we impose the condition that the separation of the Larmor frequencies is large compared to the coupling. In this limit it is clear that... 

Figure 2.14 shows a series of spectra computed using the above formulae in which the Larmor frequency of spin 1 is held constant while the Larmor frequency of spin 2 is progressively moved towards that of spin 1. This makes the spectrum more and more strongly coupled. The spectrum at the bottom is almost weakly coupled the peaks are just about all the same intensity and where we expect them to be. 

If an isolated nucleus is considered, the Larmor precession formula may be written in terms of [Pg.190]

In the non-relativistic case the radiated power, Q, is given by the Larmor (1897) formula... 

Although the phase of the field cj) is not important when a single pulse is applied, we keep it in this formula because it becomes relevant when we consider double pulses. As the state (c) is excited, the effect of any static magnetic field will be to rotate it into the third state ( ) at the Larmor frequency A. This has been ignored in deriving Equation 15.19, under the assumption that the rf excitation will be performed quickly in comparison with the Larmor precession. Taken together. Equations 15.17, 15.18, and 15.19 provide us with all the tools we need to investigate the evolution of this three-level system under any sequence of short rf pulses. 

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