Нелінійна взаємодія електромагнітних хвиль у жорстких надпровідниках у критичному стані

The suppression of magnetic moment under the action of a transverse magnetic field in hard superconductor / Fisher L.M., Il'enko K.V., Kalinov A.V., LeBlanc M.A.R., Pйrez-Rodrнguez F., Savel'ev S.E., Voloshin I.F., Yampol'skii V.A. // Phys. Rev. B. - 2000. - Vol. 61, № 22. - P. 15382 - 15391.

Ільєнко К.В. Нелінійна взаємодія електромагнітних хвиль у жорстких надпровідниках у критичному стані. - Рукопис.

Дисертація на здобуття наукового ступеня кандидата фізико-математичних наук за спеціальністю 01.04.22 - надпровідність. - Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України, Харків, 2000.

Розглянуто прояви нелінійності жорстких надпровідників у критичному стані у взаємодії радіохвиль. Вивчено взаємодію електромагнітної хвилі із статичним магнітним полем, що зумовлена нелінійною залежністю густини струму від магнітного та електричного полів. Запропоновано неконтактний спосіб визначення основних параметрів моделі E/E критичного стану. Теоретично передбачено та проаналізовано явище стрибків у часовій залежності поверхневого електричного поля в умовах взаємодії двох радіохвиль. Встановлено дві необхідні умови виникнення стрибків. Передбачено ефект колапсу статичного магнітного моменту зразка під дією змінного ортогонального магнітного поля. Проведено аналіз поведінки магнітного моменту пластини надпровідника у межах трьох існуючих моделей: моделі E/E критичного стану, моделі Клема-Гонзалеса та двошвидкісної гідродинамічної моделі.

Ключові слова: жорсткий надпровідник, критичний стан, критична густина струму, стрибок поверхневого електричного поля, однорідизація магнітної індукції, колапс магнітного моменту.

Ильенко К.В. Нелинейное взаимодействие электромагнитных волн в жёстких сверхпроводниках в критическом состоянии. - Рукопись.

Диссертация на соискание ученой степени кандидата физико-математических наук по специальности 01.04.22 - сверхпроводимость. - Физико-технический институт низких температур им. Б.И. Веркина НАН Украины, Харьков, 2000.

Рассмотрены проявления нелинейности жёстких сверхпроводников в критическом состоянии во взаимодействии радиоволн. Изучено взаимодействие электромагнитной волны со статическим магнитным полем, обусловленное нелинейной зависимостью плотности тока от магнитного и электрического полей. Предложен бесконтактный метод определения основных параметров модели E/E критического состояния. Теоретически предсказаны и проанализированы скачки во временнуй зависимости поверхностного электрического поля в условиях взаимодействия двух радиоволн. Установлены два необходимых условия возникновения скачков. Предсказан эффект коллапса статического магнитного момента образца под действием переменного ортогонального магнитного поля. Проведен анализ поведения магнитного момента пластины сверхпроводника в рамках трёх существующих моделей: модели E/E критического состояния, модели Клема-Гонзалеса и двухскоростной гидродинамической модели.

Ключевые слова: жёсткий сверхпроводник, критическое состояние, критическая плотность тока, скачок поверхностного электрического поля, однородизация магнитной индукции, коллапс магнитного момента.

Il'enko K.V. The nonlinear interaction of electromagnetic waves in hard superconductors in the critical state. - Manuscript.

Thesis for a degree of Doctor of Philosophy (Ph.D.) in physical and mathematical sciences by speciality 01.04.22 - superconductivity. - B. Verkin Institute for Low Temperature Physics and Engineering NAS of Ukraine, Kharkiv, 2000.

The thesis is devoted to studying implications of nonlinear interaction of radiowaves with different amplitudes, frequencies and an initial phase shift observed in hard superconductors being in the critical state. We use the electric field on a sample surface as a feedback of this interaction.

The first part of the thesis deals with a literature review. A place of the present investigation among current studies of high-temperature superconductors is established.

In the second part of the thesis we investigate response of hard superconductors to irradiation by electromagnetic wave in the presence of static magnetic field in the framework of the critical state model E/E. The dc and ac magnetic fields are collinear and parallel to the surface of specimens of two typical geometries - a slab and a circular cylinder. For slabs symmetrical two-sided excitation is considered. In zero dc magnetic field, the graph of surface electric field exhibits different stages of ac magnetic field penetration into the bulk sample. In particular, there exists an amplitude of ac magnetic field when additional extrema of the surface electric field arise. A subsequent growth of ac magnetic field leads to appearance of additional inflection point. The analysis of surface electric field allows us to put forward a simple method for determination of main parameters of the critical state model E/E. Nonlinear interaction of ac magnetic field with a radiowave inside the sample takes place only because of dependence of the critical current density on the magnetic induction. A non-zero magnetic field breaks the symmetry of curves for the surface electric field under the substitution t for (p /w - t). Similar to the case of zero dc magnetic field, the rise of ac signal in non-vanishing dc magnetic field causes the appearance of additional extrema and inflection point. However, the static magnetic field influences the amplitude of ac magnetic field at which they emerge. Besides that, because of nonlinear dependence of the critical current density on the magnetic induction, the existence of dc magnetic field moves the additional extrema to greater (lower) values of time for the first (second) halfperiod of ac signal. The formulae obtained for the surface electric field are actually valid not only for an arbitrary dependence of the critical current density on the magnetic induction but also for any temporal dependence of the modulus of magnetic field on the sample surface.

The third part of the thesis deals with interaction of two radiowaves. Magnetic fields of radiowaves are collinear and parallel to the sample surface. We again consider samples of slab and cylindrical geometries. We predict an unusual phenomenon - jumps in the temporal dependence of surface electric field. This theoretically derived and subsequently experimentally verified phenomenon reflects a unique nonlinearity specific to hard superconductors in the critical state. Notably, it occurs even if the critical current density is taken to be independent of magnetic induction. Absence of superposition principle enables configurations of magnetic induction distribution, which produce the jumps of surface electric field. Appearance of the jumps may be regarded as a serious test for the critical state model E/E. We also find two necessary conditions for the presence of the jumps. These conditions place certain restrictions on the amplitudes, frequencies and initial phase shift of interacting radiowaves.

Collapse of static magnetic moment for a slab sample being in the critical state, which is placed in orthogonal ac and dc magnetic fields parallel to its surface, is predicted in the fourth part of the thesis. Consider the sample put in a dc magnetic field parallel to its surface. Let us turn on an orthogonal ac magnetic field. According to the critical state model E/E, a current screening the ac magnetic field must appear. Then, suppression of current, which was screening the dc magnetic field, takes place in those regions where the ac field has penetrated. The reason for such suppression lies in the fact that, because of the critical state model E/E, the total current in these regions flows in the direction of the existing electric field. If the amplitude of radiowave is large enough in order that the ac signal penetrates whole sample, then, the static magnetic moment vanishes completely. We call this process homogenization of the static component of magnetic induction. It has been observed in a number of carefully designed experiments. Albeit its numerous successes in predicting new electrodynamical phenomena in hard superconductors in the critical state, the phenomenological critical state model E/E lacks firm microscopic foundations. Until recently, the only model with such foundations applicable to calculations of distributions of magnetic induction in situations when the direction of external magnetic field changes had been the Clem-Gonzalez double critical state model. It accounts not only for pinning of flux vortices but also for cutting flux lines with different orientations. Quite unexpectedly, this microscopical model does not successfully explain the experiments on the collapse of magnetic moment. Using the notion of homogenization, a two-velocity hydrodynamical model was developed. In this part of the thesis, we investigate the pertinence of the Clem-Gonzalez critical state model and the two-velocity hydrodynamical model to the description of behaviour of magnetic moment of a slab in parallel to its surface orthogonal dc and ac magnetic fields. It turns out that the Clem-Gonzalez critical state model describes the evolution of the sample magnetic moment qualitatively well only for the first quarter-period of ac magnetic field. To the contrary, the two-velocity hydrodynamical critical state model provides an adequate description of main features of the collapse of magnetic moment for arbitrary starting conditions. We examine different evolution scenarios of flux system in the sample based on the latter model.

Key words: hard superconductor, critical state, critical current density, jump of surface electric field, homogenization of magnetic induction, collapse of magnetic moment.

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