Plasmas: frequency

Going back to the Equation 24.44 for velocity of the electrons, note that as wt 1, the electron velocity starts to fall with increasing frequency because the electrons are not sufficiently mobile to keep up with the changing field. Note also that if we write a-o/so = we T/m o/ the group nPfmso has the dimensions of s, hence we define this as the square of the plasma frequency, or 

The real and imaginary parts of the complex dielectric constant can be written in terms of the plasma frequency  

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Above approximately 80 km, the prominent bulge in electron concentration is called the ionosphere. In this region ions are created from UV photoionization of the major constituents—O, NO, N2 and O2. The ionosphere has a profound effect on radio conmumications since electrons reflect radio waves with the same frequency as the plasma frequency, f = 8.98 x where 11 is the electron density in [147]. The... 

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)... 

Maximum power transfer to electrons for a given internal field occurs when = u). The plasma frequency, CO, is the frequency at which e = 0 ... 

The primary characteristic frequency of an ordinary gas is the rate of coUision f = V/X = ttVnD, where V is the mean particle velocity, and V = [SkT for particles of mass m. Among the special frequencies associated with plasmas, the most notable is the plasma frequency ... 

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

Transverse electromagnetic waves propagate in plasmas if their frequency is greater than the plasma frequency. For a given angular frequency, CO, there is a critical density, above which waves do not penetrate a plasma. The propagation of electromagnetic waves in plasmas has many uses, especially as a probe of plasma conditions. 

We now want to study the consequences of such a model with respect to the optical properties of a composite medium. For such a purpose, we will consider the phenomenological Lorentz-Drude model, based on the classical dispersion theory, in order to describe qualitatively the various components [20]. Therefore, a Drude term defined by the plasma frequency and scattering rate, will describe the optical response of the bulk metal or will define the intrinsic metallic properties (i.e., Zm((a) in Eq.(6)) of the small particles, while a harmonic Lorentz oscillator, defined by the resonance frequency, the damping and the mode strength parameters, will describe the insulating host (i.e., /((0) in Eq.(6)). 

Fig. 7. Model calculations for the reflectivity (a) and the optical conductivity (b) for a simple (bulk) Drude metal and an effective medium of small metallic spherical particles in a dielectric host within the MG approach. The (bulk) Drude and the metallic particles are defined by the same parameters set the plasma frequency = 2 eV, the scattering rate hr = 0.2 eV. A filling factor/ = 0.5 and a dielectric host-medium represented by a Lorentz harmonic oscillator with mode strength fttOy, 1 = 10 eV, damping ftF] = I eV and resonance frequency h(H = 15 eV were considered for the calculations.

The function g describes the collective motions of the electrons kc is the cut-off vector for the plasma oscillations and is the plasma frequency (see Pines 1955, particularly p. 391) see also Section III.C. 

Photochemical dissociation, 202 Photolyses, 200 Pine s wave function, 306 Plasma frequency, 306 Plasma model, 207, 304, 306, 318, 319, 323... 

The energy position Cp of peak p in the lED of an ion with mass m is seen to be dependent on the plasma potential Vpi, the RE period T, and the ion plasma frequency cd, = yje n j m(o). Equation (48) can be used to determine the (net) charge carrier density in the sheath and the time-averaged potential Vpi from measured lEDs. The mean position Xp follows from combining Eq. (47) and Eq. (48) ... 

The maximum in the lED at 11 eV is the first charge exchange maximum of H2. The energy of this maximum is always somewhat lower than the energy of the fourth charge exchange maximum in the SiH lED. This is due to the almost four times higher plasma frequency of the ion (m/e = 2 amu/e) than that of the SiHj ion (m/e = 30 amu/c). 

The Hj saddle structure is broader than the saddle structures of the other ions, due to the larger ion plasma frequency of. The ions with an energy larger than 25 eV are part of the high-energy side of the main saddle structure. 

Treating the free electrons in a metal as a collection of zero-frequency oscillators gives rise51 to a complex frequency-dependent dielectric constant of 1 - a>2/(co2 - ia>/r), with (op = (47me2/m)l/2 the plasma frequency and r a collision time. For metals like Ag and Au, and with frequencies (o corresponding to visible or ultraviolet light, this simplifies to give a real part... 

Indeed, most of the applications of laser-plasmas rely on the efficient production of energetic electrons driven by the interaction of ultraintense laser pulses with plasmas created from solids or gases. In fact, in these interaction conditions, laser energy is efficiently transferred to electrons generating a population of so-called fast or hot electrons. The process of fast electron generation often takes place near the critical density (the density at which the laser frequency iv0 equals the local plasma frequency wpe) surface [8, 9]... 

Picosecond pedestal, 143 Pin-hole camera, 128 Plasma channels, 112, 147, 148 Plasma defocusing, 84, 91 Plasma frequency, 166 Plasma index of refraction, 147 Plasma mirror (PM) technique, 194 Plasma wakefield acceleration, 172 Plasma wavelength, 166 Plasma-induced effects, 83 Polarization, 97 Polarization control, 87 Ponderomotive force, 170 Population inversions, 19 Post-irradiation spectroscopy, 156 Pre-pulse, 143 Propagation, 81 Protein, 102 Pump depletion, 151... 

Thus, the Drude model predicts that ideal metals are 100 % reflectors for frequencies up to cop and highly transparent for higher frequencies. This result is in rather good agreement with the experimental spectra observed for several metals. In fact, the plasma frequency cop defines the region of transparency of a metal. It is important to realize that, according to Equation (4.20), this frequency only depends on the density of the conduction electrons N, which is equal to the density of the metal atoms multiplied by their valency. This allows us to determine the region of transparency of a metal provided that N is known, as in the next example. 

EXAMPLE 4.2 Sodium is a metal with a density of conduction electrons N = 2.65 X 10 cm f Determine (a) its plasma frequency, (b) the wavelength region of transparency, and (c) the optical density at very low frequencies for a Na sample of 1 mm thickness. 

In the previous example, we have calculated the plasma frequency for metallic Na from the free electron density N. In Table 4.1, the measnred cutoff wavelengths, Xp, for different alkali metals are listed together with their free electron densities. The relatively good agreement between the experimental values of Xp and those calculated from Equation (4.20), within the ideal metal model, should be noted. It can also be observed that the N values range from abont 10 to about 10 cm leading to... 

Figure 4.16 The reflectivity spectra of sUver and copper. The photon energy corresponding to the plasma frequency is indicated in each case (reproduced with permission from Ehrenreich and Philipp, 1962).

Figure E4.3 shows the room temperature absorption spectra of an insulator (LiNbOs), a semiconductor (Si), and a metal (Cu). (a) Determine the spectrum associated with each one of these materials, (b) From these spectra, estimate the energy-gap values of Si and LiNbOj and the plasma frequency of Cu. (c) What can be said about the transparency in the visible range for each of these materials ... 

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