Debye sphere

A = irnD ) where D is the atomic or molecular particle size. The number of electrons within a Debye sphere, A/, around an ion is then... 

Also shown in Figure 1 are the Debye screening length and Debye sphere size. For gaseous plasmas, A)-, 1 (11). SoHd-state plasmas or... 

According to his deduction the common finding of ellipsoidal deformation of the reflections is indicative for affine deformation. Moreover, he arrives at an equation that permits to determine with high accuracy the microscopical draw ratio, Xd, of the structural entities from the ellipticity of the deformed Debye sphere. This value can be compared to the macroscopical draw ratio. Even the intensity distribution along the ellipsoidal ridge is predicted for a bcc-lattice of spheres, and deviations of experimental data are discussed. 

XD, in centimeters, and (-) Debye sphere volume, IVp, in cubic centimeters. The plasma frequency is given on the right-hand axis. Condensed-state... 

Although both these types of analyses are well exploited, more information may be gleaned by comparing the experimental data with simulations made using a model, based either on a molecular structure expressed in the form of Debye spheres to facilitate calculation of model data, or a model constructed ab initio. This approach is especially favored when determining protein structure and has been used to great effect by Svergun and coworkers to obtain detailed structural information about proteins in solution. ... 

Inside the Debye sphere, strong electron acceleration takes place. The electrical field that surrounds the ion current channel accelerates the electrons toward the filaments where they are deflected on the induced magnetic field. The scenario is depicted in fig. 2. It have previously been shown that the ion filaments are generated in a self-similar coalescence process (Medvedev et al., 2004) which implies that a spatial Fourier decomposition exhibits power law behavior. As a result, the electrons are accelerated to a power law distribution function (fig. 3) as shown by Hededal et al., 2004. 

The Debye radius gives the characteristic plasma size scale required for the shielding of an external electric field. The same distance is necessary to compensate the electric field of a specified charged particle in plasma. In other words, the Debye radius indicates the scale of plasma quasi-neutrality. There is the correlation between the Debye radius and plasma ideality. The non-ideality parameter F is related to the number of plasma particles in the Debye sphere, For plasma consisting of electrons and positive ions,... 

The number of electrons and ions in the Debye sphere is usually large 1),... 

Modelling strategies based on 7(2) data are based initially on the values for V (or Mf) and Rq (Sections 2.5 and 2.6 Table 8), together with the values of 7 xs and 7 th and their related parameters if available, and the maximum particle dimension (Section 2.10). More detailed modelling involves direct comparisons between experimental and calculated 7(2) curves (Fig. 7). These can involve the use of 7(2) calculated from simple triaxial bodies (above). The most powerful and general method is to use smdl Debye spheres in three-dimensional arrangements to refine and extend the curve fits of 7(2)- The shape under consideration can be directly... 

Another modelling strategy is based on the use of spherical harmonics, where the excess scattering density p(r) - pg is expanded as a finite series of multipoles in order to approximate the shape of the particle [57]. While the experimental and calculated 1(Q) curves can be compared in this way, it has not yet been shown that the particle shape can be readily visuahzed in the way that is possible by computer displays of Debye spheres. 

With sufficient information on the location of the subunits, more detailed models of the ribosomal quaternary structure can be tested by neutron scattering. Thus an early analysis of the 30S ribosomal particle was performed by comparing experimental neutron contrast variation curves with models based on Debye spheres set at two density levels to correspond to a V-shaped 16S RNA moiety, together with the putative locations of the 21 ribosomal proteins [441]. More recently, the triangula-tion of the 19 30S ribosomal proteins shows that they are not uniformly distributed about the RNA in the 30S subunit, as once believed. The use of deuterated RNA within the 30S ribosomal particle showed an asymmetry in the RNA and protein distribution to confirm this result, where a separation A of 2.5 nm between their centres was calculated [446]. 

The ratio rc/rp plays a crucial role in the description of plasmas. When this ratio is small, charged particles are dominated by one another s electrostatic influence more or less continuously, because many particles are inside the virtual sphere available for a particle, and their kinetic energies are small compared to the interaction potential energies. Such plasmas are termed strongly coupled. On the other hand, when this ratio is large, strong electrostatic interactions between individual particles are occasional and relatively rare events. A typical particle is electrostatically influenced by all of the other particles within its Debye sphere, but this interaction very rarely causes any sudden change in its motion. Such plasmas are termed weakly coupled. 

Here, e and refer to the electron number density and electron Debye length, respectively. The meaning of the plasma parameter is clear if it is large, then the Debye sphere is heavily populated (this is the case of the weakly coupled plasma), whereas if it is small, then the Debye sphere is only sparsely poptilated and the plasma is strongly coupled. Some authors define the plasma parameter as 1/3 of the value in O Eq. (6.12). In this case, the plasma parameter is exactly the number of particles inside the Debye sphere, whereas in the definition given by O Eq. (6.12), it is only proportional to it. The plasma parameter is defined for the electrons only. One could, in principle, define a plasma parameter for the ions also, but that is not common. 

A subtle but important point in the above introduction of the plasma parameter is that its expression with the Debye radius is only valid as long as the Debye radius has a meaning at all. The above introduction of the Debye radius is valid if the number of particles inside the Debye sphere is statistically significant, and this number does not fluctuate too much. If there are very few particles inside the Debye sphere, and so the plasma is very strongly coupled, the above formulas must be modified. Very strongly coupled plasmas, however, are outside the scope of this chapter. 

The physical meaning is as follows in a plasma, an ion attracts electrons, which form a cloud aroimd it and thereby act as a screen, decreasing its potential. The resulting electron sphere is the Debye sphere, and its radius is. ... 

CO = vq = v (q] + q2 Q3) surface of constant frequency is a sphere of radius q, the Debye sphere. Since v j = v and J dS = 4Trq, we obtain from (3.86) by summing over the three acoustic branches for the Debye density of states... 

---