Oscillating electric field, acceleration

X-rays have both electric field and magnetic field components associated with them. Classically, the oscillating electric field can accelerate electrons, and these electrons, in turn, can emit new x-rays usually of the same energy (elastic scattering), but in arbitrary directions in space. Since the dimension of an atones electron cloud is approximately the same as an x-ray wavelength, interference occurs. Diffraction is an interference phenomenon that produces scattered x-ray intensity maxima and minima dependent upon the arrangement of the scatterers (1.2). 

In the actual cyclotron, the particles are caused to go in their circles by a large magnet, and the up and downhill is provided by an oscillating electric field—a radio frequency voltage that reverses in step with the circulation of the particles. The particles go around hundreds of times and therefore acquire hundreds of times as much energy as that which corresponds to the maximum accelerating voltage in the... 

Figure 2. (a) Schematic representation of electrostatic acceleration, (b) Schematic representation of acceleration by an oscillating electric field. Arrow lengths indicate the strength and direction of the acceleration that electrons undergo at different points in the RF phase. 

Whenever an electrical charge is accelerated, it radiates energy. If the oscillating electric field of a light beam acts on a charge, the charge oscillates, is accelerated, and... 

The single quadrupole is one of the earliest mass analyzers to become widely available. A quadrupole separates ions according to their m/z ratio as a function of their trajectory through an oscillating electric field. With a transmission quadrupole mass analyzer, direct-current (DC) and radiofrequency (RF) voltages are applied to four parallel rods (Fig. 6.7a). As ions are accelerated through... 

The theory of coherent scattering by a classical free electron was developed by J, J, Thompson in 1898. The electron is considered to be a classical free particle of charge - e and of mass m accelerated by the oscillating electric field of the... 

If an oscillating electric field E t) is introduced in the xy plane such that its frequency co f is equal to for a given ion, the ion will absorb energy from the field and will be accelerated by it (see below). From Eq. (4) it can be inferred that the radius of the ion s trajectory will become larger as the ion is accelerated, and as shown in Fig. 3a, the ion will follow a spiral trajectory as long as it remains in the crossed magnetic and rf electric fields. 

For X-rays, the interaction between radiation and matter is primarily via interaction between the electrons and the oscillatory electric field of the electromagnetic beam. E = EoCOs(a>t). An electron will, in the X-ray beam, be accelerated by the oscillating electric field an accelerated charged particle, on the other hand, will... 

Ion trap A type of mass filter. It has a closed space, in which an oscillating electric field is generated to direct the flow of ions made up by charged fragments, formed Ifom an analyte and accelerated into the field. Only those ions with mass/charge ratios that do not suit the electric potentials of the oscillating field are thrown out of the cell to become recorded. 

FIGURE 5 Separation of mass fragments with quadrupole instrument. Ions (M, Mj, M are accelerated out of the ion source into the space between four parallel rods with an oscillating electric field. At a certain ac and dc potential, ions with a specific m/z (M ) value will become stable and oscillate in a fixed path through the quadrupole to reach the detector to be recorded, whereas the unstable ones (M j, M, ...) will stick to the rods. 

Let us consider an X-ray beam propagating along the x-axis and encountering an electron at the experimental origin, O. If this electron has a velocity small compared with the velocity of light, c, it will be accelerated by interaction with the oscillating electric field of the X-ray beam and will become a source of radiation at the same frequency as the X-rays. This effectively gives rise to... 

The time-averaged potential profile is shown in Figure 4b. As ions cannot follow the oscillations in the applied electric field, it is this profile that ions experience. The bulk plasma is characterized by a constant potential, Vpi. In both sheaths (regions between plasma bulk and the electrodes), the ions experience a potential difference and are accelerated towards the electrodes. This leads to energetic ion bombardment of the electrodes. Electrons are expelled from the sheaths, so all ionization and dissociation processes must occur in the plasma bulk. Plasma light, resulting from emission from excited molecules, is emitted only from the plasma bulk the sheaths are dark. 

In this section we discuss the interaction between an electric field and a charge that is free to move with the field. Such a charge experiences a force that accelerates it with the field. If the field is oscillating, the acceleration of the charge will also oscillate. One of the basic results of classical electromagnetics is that the acceleration of a charge leads to the emission of radiation. 

FIG. 5.4 Coordinates and acceleration relevant to the interaction of an electric field with a charge (a) the coordinates of an electric field E relative to an oscillating charge located at the origin (b) projection of the acceleration in the plane perpendicular to the line of sight. 

---