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  • KT 5720 Our study has focused on charged particle fluxes

    2018-11-05

    Our study has focused on charged particle fluxes in a small neighborhood of the plane of symmetry, which allowed approximately calculating the spatial distribution of the field structure; for this we employed the well-known expansion in powers of the small quantity z:
    The study in the degree of accuracy of the three-dimensional potentials obtained by formula (16) and their applicability to calculating charged particle fluxes near the plane of symmetry with a varying number of series terms has been carried out earlier, and the results are published in Ref. [11]. The error in defining the three-dimensional potential by several series terms of expansion (16) instead of an infinite number of them is within the accuracy required when fabricating electrodes of a complex-shaped system. The fields were calculated with an approximation to sixth-power members including z. To put the calculated system into practice, it is preferable to select equipotential surfaces forming a closed area. Such surfaces with the values φ** = −0.001 and φ** = −10 are suitable for this purpose. Fig. 3 presents the electrodes of the system determining the field and the trajectory set in it. Variant 2. Let the mapping be expressed by the formula
    Particle trajectories in this field are shown in Fig. 4. Variant 3. In the most general form, mapping (17) can be represented as
    The flux of charged particles in field (20) assumes the configuration shown in Fig. 5.
    The questions of practical implementation Alternative options could include tailoring a transformation function which would generate a field structure satisfying the sufficient criterion of trajectory KT 5720 in the median plane [12] or using an additional conformal mapping that transforms unstable solutions into stable.
    Conclusion
    Acknowledgments
    Introduction Determining the physical causes of the formation of the corrections to the collision term of the Boltzmann kinetic equation that are associated with the phenomenon of quantum interference is one of the most interesting and challenging subjects in the field of particle scattering. This problem has been studied both in its classical wave aspect and from the quantum perspective, especially since the start of the trend to derive the kinetic Boltzmann equation from the quantum equation for the density matrix. As it turns out, describing radiative transfer based on wave equations and based on conventional transport theory does not always yield matching results. This difference is most evident when describing the backscattering of electromagnetic waves from inhomogeneous media [1–6]. An increased probability of such scattering and the manifestation of weak localization of electrons in disordered media have the same physical cause. Explaining these effects from the perspective of the particles is related to their quantum transport. Quantum transport of electrons means that they experience collisions while moving in a medium, with each subsequent collision starting before the previous one has ended. This motion can occur both under the action of an applied external field, and because of the initial kinetic energy stored by the electrons. The aspect of quantum transport associated with the phenomenon of weak localization is universal; it manifests itself in the well-known problems of conductivity theory and in problems on radiation and mass transfer. If the motion of electrons or photons occurs in a disordered medium, such interference leads not only to quantitative corrections to the results obtained with the help of the Boltzmann equation, but to qualitatively new effects. In the best-known case, these effects are related to Anderson localization [7,8]. Electrons with energies ranging from tens of eV to a few keV clearly exhibit a new type of quantum transport, as shown in Refs. [3,9,10]. This is due to the fact that, in contrast to the normal weak localization corresponding to an increase in electron backscattering into a very narrow range of solid angles of about , the preferential scattering of electrons occurs in a wide range of angles: . Here is the de Broglie wavelength, l is the electron mean free path, E is the electron energy, ℏω is the energy lost by the electron.