Electrons plasma frequency

Any charge imbalance in a plasma (i.e. any local deviation from charge neutrality) results in a motion of tire electrons tliat, in turn, leads to oscillations of tire electrons witli tire electron plasma frequency C0p (Langmuir frequency)... 

If a S> 1, collective effects play an important role and the light scattering is no longer caused by individual electrons but by electron density fluctuations 280), Jn this case the spectrum shows a central line at Xq and two narrow lines located symmetrically about Xq, at a distance governed by the electron plasma frequency. The linewidth is smaller than in the case X < 1 and is determined rather by the thermal motion of the ions, not that of the electrons. The line shape depends on the ratio of electron to ion temperatures. Therefore, a measurement of the shape and width of this central line allows, under certain assumptions, a direct determination of the ion temperature. 

The charged particle collective behaviour (and thus the plasma) exists only if random collision processes do not smear out the coherence of the motion of the charged particles. This means in practice that the frequency of the electron-neutral collisions has to remain smaller than the electron plasma frequency. 

The electronic excitations caused by electron energy loss processes can be divided into two main classes collective electronic excitations and single electron excitation. The collective excitations may be regarded as plasma oscillations of a free or nearly free electron gas embedded in a homogeneously distributed positive charge. An extensive treatment of collective excitation losses is given by Lucas and Sunjic (1972). In a classical treatment the electron plasma frequency a>p is given by... 

The characteristic composite behavior of (t maM for medium consisting of spherical particles with volume fractions / of Drude conductor and 1 - / of insulator is shown in Figure 15.5. For a volume fraction / less than the percolation value (/ = 1/3 for spheres), (Tema (impurity band of localized plasmon-like excitations. As the system approaches the percolation threshold, the localized peak o-ema(w) shifts to lower frequency. Above the percolation threshold, a Drude peak corresponding to the carriers that have percolated through the composite structure occurs at low frequency. Only a fraction ( (3/— l)/2 [119]) of the full conduction electron plasma frequency appears in the Drude peak, depending on the proximity to the percolation threshold. The same percolating free electron behavior is observable in the dielectric response ema(w) for the system. 

TABLE 15.4 Free Electron Plasma Frequency fip and Scattering Time r vs. Temperature for Selected PAN-CSA Film Samples... 

The values obtained for fip are very small compared with the full conduction electron density (fipi 2 eV), suggesting that only a small fraction (Mfree/ cond) of the conduction electrons are delocalized macroscopically. This small fraction of delocalized carriers is consistent with the small number of percolation paths that occur close to the percolation threshold in composite systems. The fraction of the carriers that are delocalized can be estimated by comparing the plasma frequency of free electrons (fip) with the full conduction electron plasma frequency (fipi). 

Since the free electron plasma frequency ftp scales with the scattering time is estimated as t 10 s for samples A, C, and D (Table 15.4), assuming that only the free electrons participate in the low frequency transport. This estimate of the free electron scattering time is in good agreement with the... 

FIGURE 15.25 Temperature dependence of the free carrier dielectric response for metallic PAN-CSA sample A. (a) Far-IR e(o)) plotted against 1 as a function of temperature, (b) Comparison of the temperature dependence of the free electron plasma frequency fip and o-dc- (From Kohlman, R.S. and Epstein, A.J., Handbook of conducting polymers, 2nd ed., eds. Skotheim, T.A., Elsenbaumer, R.L., and Reynolds, J.R., Marcel Dekker, New York, 1988, chap. 3. Reprinted from Routledge/Taylor Francis Group, LLC. With permission.)... 

TABLE 15.6 Room Temperature Free Electron Plasma Frequency cOp and Scattering Time t for Selected PAN-CSA Samples Calculated from mw and ctmw Using the Drude Model... 

Fig. 3.21 Temperature dependence of the free carrier dielectric response for metallic PAN-CSA sample A. (a) Far-infrared eiw) plotted against l/oj- as a function of temperature. (b) Comparison of the temperature dependence of the free electron plasma frequency /ip and...

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