Microwaves in dispersive magnetic composite media

Review discusses some special questions of physics of composite media (metamaterials), which are formed by elements made from natural materials of two kinds. The first ones are “carriers of permittivity” and are presented by plasma-like media and semiconductors. The second ones are “carriers of permeability” — they are presented by ferromagnets. Among such ferromagnets are ferrodielectrics (ferrites) and manganite-perovskite compounds. In the first chapter of the review some principal aspects of the electrodynamics of periodical structures — magnetophotonic crystals are considered. The questions of zone structure and possible violations of periodicity (Tamm states, defect mode) as well as the influence of external magnetic field on the spectral characteristics of magnetophotonic crystals are considered. The second chapter of the review is devoted to the electrodynamics of left-handed media (left-handed metamaterials). Different versions of composite left-handed media are considered. Particular attention is paid to features of electrodynamics of artificially synthesized lefthanded media, the doped lanthanum manganites-perovskites, which in a certain concentrations of doping element and temperature range can serve as an example of natural left-handed media. The Appendix describes the details of experimental techniques radiophysical research. Note that the research and design of the metamaterials listed above in a range of low temperatures are particularly important. This is due to the fact that at low temperatures a main disadvantage of artificial materials mentioned above (quite large losses) becomes less noticeable. At the same time the main their advantage (namely the possibility to control their frequency dispersion) remains. Thus it seems that the most prospective areas of application and further study of the magnetic metamaterials lie at low temperatures

The velocity of slow nuclear burning in the two-group approximation

The velocity of slow nuclear burning was obtained in the two-group approximation. Two groups of neutrons were considered: the group of thermal (slow) neutrons and the group of fast neutrons; each group being described with its diffusion equation. It was shown that in the case of heavy moderators the obtained expression for the two-group velocity had the same structure as the one-group velocity studied by authors before if new effective diffusion and multiplication coefficients were introduced. The expressions for corresponding effective coefficients are presented

High-gradient fields in magnets with giant anisotropy

The gradient of strong stray fields generated by various systems of permanent magnets with giant magnetic anisotropy has been calculated. It is shown that the gradient values near singular points are characterized by the dependence ∇H ≈ AMs(1/r), where A is a constant for this system of magnets, Ms is the saturation magnetization of the magnet material, r is the distance from the singular point. The field gradient in those areas may reach about 10⁶ to 10⁸ Oe/cm. The indicated gradient level is comparable with maximum values achieved in superconducting solenoids supplied with the conical tips produced of soft magnetic material with high Ms. It is established that the volume forces with the specific density of f ≈ 4Ms²/r arise near singular points in the magnet material being in high-gradient field. The mechanical stress in a magnet caused by these forces is characterized by the dependence σ ≈ 4πMs²ln(a/Xmin) and may reach 2-3 kg/mm².Обчислено градієнт сильних полів розсіяння, що генеруються різними системами з постійних магнітів з гігантською магнітною анізотропією. Показано, що величина градієнта поблизу сингулярних точок характеризується залежністю ∇H ≈ AMs(1/r), де А - певна стала для даної системи магнітів. Градієнт поля може сягати значень порядку 10⁶-10⁸ Е/см. Вказаний рівень градієнта є порівнянним з граничними його величинами, які досягаються у надпровідних магнітах з конічними наконечниками, виготовленими з магнітом'яких матеріалів з високою індукцією. Встановлено, що у високоградієнтному полі у матеріалі магніту поблизу сингулярних точок виникають об'ємні сили з питомою густиною f ≈ 4Ms²/r. Механічні напруги у магніті, пов'язані з цими силами, характеризуються залежністю σ ≈ 4πMs²ln(a/Xmin) і можуть досягати значень 2-3 кг/мм².Рассчитан градиент сильных полей рассеяния, генерируемых различными системами из постоянных магнитов с гигантской магнитной анизотропией. Показано, что величина градиента вблизи сингулярных точек характеризуется зависимостью ∇H ≈ AMs(1/r), где А - некоторая постоянная для данной системы магнитов. Вблизи сингулярных точек I∇HI может достигать значений I∇HI ≈ 10⁶-10⁸ Э/см. Указанные значения градиента поля сравнимы с предельными его величинами, которые достигаются в сверхпроводящих магнитах с коническими наконечниками, изготовленными из материалов с высокой индукцией. Установлено, что в высокоградиентном поле в материале магнита вблизи сингулярных точек возникают объёмные силы с удельной плотностью f ≈ 4Ms²/r. Механические напряжения в магните, связанные с этими силами, характеризуются зависимостью σ ≈ 4πMs²ln(a/Xmin) и могут достигать значений 2-3 кг/мм²

Distribution peculiarities of stray fields and magnetization near magnet singularities

Distributions of both magnetization and stray fields near singularities of a permanent magnet with high uniaxial anisotropy have been studied. On the basis of calculations it is shown that in magnets with high magnetic anisotropy, strong stray fields H > 4πMs occurring near the edge of a magnet do not practically result in deviation of magnetization from easy axis if the quality factor of the magnetic material g = K/(2πMS²) is g > 10. In such magnet systems, the distribution of magnetization is close to homogeneous, and it is possible to use the method of "magnetic charges" for calculations of stray fields. It is shown that the stray field near an edge of a magnet takes finite values, and the presence of a singularity at the dependence of the tangent component of the stray field Hτ ~ Ms-ln(a/r) at r → 0 is related to macroscopic characteristics generally accepted in magnetism, namely the surface density of "magnetic charges" σ