The Theory of Heating of the Solar Corona and Launching of the Solar Wind by Alfv\'en Waves

State-of-the-art MHD calculations reveal acceptable agreement with observational data for the height profile of the temperature $T(h)$ in the transition region of solar corona. Simultaneously, the velocity of the solar wind $U(h)$ has also been calculated. The developed method gives the possibility at given frequency dependent spectral density of Alfv\'en waves (AW) coming from chromosphere $\mathcal{W}(\omega)$ to calculate both height profiles $T(h)$ and $U(h)$. In agreement with the concepts of the self-induced opacity of plasma with respect of AW, the narrow width $\lambda$ of the transition region is determined by the fast temperature increase of the viscosity $\eta(T,B)$. After more than 70 years of development of Solar physics, the Alfv\'en hypothesis of heating of the solar corona by AW has remained without alternatives; none of other mechanisms can explain $ab$ $initio$ the value of $\lambda$. The performed MHD analysis explains the height dependence of the non-thermal broadening of the chromospheric spectral lines and predicts angular dependence of this broadening with respect of position in solar disc. One can expect significant impact of MHD analysis in the interpretation of the long expected data from Parker Solar Probe.Comment: University of Sofia PhD Thesis corrected and updated after defense, PhD advisor Prof. DSc Todor Mishonov, 122 pages total (6 added in this version), main text 74 pages (3 added in this version), bibliography 9 pages, appendices (source code) 29 pages, 31 figures (2 added in this version

Callen-Welton fluctuation dissipation theorem and Nyquist theorem as a consequence of detailed balance principle applied to an oscillator

We re-derive the Nyquist theorem and Callen-Welton fluctuation-dissipation theorem (FDT) as a consequence of detailed balance principle applied to a harmonic oscillator. The usage of electrical notions in the beginning makes the consideration understandable for every physicists. Perhaps it is the simplest derivation of these well-known theorems in statistical physics. The classical limit is understandable as a consequence of Waterston-Herapath equipartition theorem.Comment: 6 pages, 1 figur

Robust formula for NN-point Pad\'e approximant calculation based on Wynn identity

The performed numerical analysis reveals that Wynn's identity for the compass $1/(N-C)+1/(S-C)=1/(W-C)+1/(E-C)=1/\eta$ (here C stands for center, the other letters correspond to the four directions of the compass) gives the long sought criterion, the minimal $|\eta|$, for the choice of the optimal Pad\'e approximant. The work of this method is illustrated by calculation of multipoint Pad\'e approximation by a new formula for calculation of this best rational approximation. The work of the criterion for the calculation of optimal Pad\'e approximant is illustrated by the frequently seen in the theoretical physics problems of calculation of series summation and multipoint Pad\'e approximation used as a predictor for solution of differential equations motivated by the magneto-hydrodynamic problem of heating of solar corona by Alv\'en waves. In such a way, an efficient and valuable control mechanism for $N$-point Pad\'e approximant calculation is proposed. We believe that the suggested method and criterion can be useful for many applied problems in numerous areas not only in physics but in any scientific application where differential equations are solved. The solution of the Cauchy-Jacobi problem is illustrated by a Fortran program. The algorithm is generalized for the case of the first $K$ derivatives at $N$ nodal points.Comment: 12 pages, 6 figures, 2 appendix sections; Title and abstract precised, section Introduction restated, figure captions shortened and a new appendix section added, where the Cauchy-Jacobi problem is solved for the case of the first $K$ derivatives at $N$ nodal point

Comment on "Adiabatic Expansion of Electron Gas in a Magnetic Nozzle" by Kazunori Takahashi, Christine Charles, Rod Roswell, and Akira Ando, Phys. Rev. Lett. Vol. 120, 045001 (2018)

Heat capacities at fixed volume and pressure as a function of the degree of ionization are graphically depicted as functions of reciprocal temperature and ionization degree. The polytropic index is calculated as a function of the same variables; as it is not constant a partially ionized plasma can be only approximately polytropic fluid. In parallel, it is launched the idea that Alfv\'en waves can be used to heat the plasma in a propulsion jet with magnetic nozzle.Comment: 2 pages, 3 figure

Determination of magnon mass of neodymium magnet by temperature dependence of spontaneous magnetization

The effective mass of a magnon in a neodymium magnet is evaluated using Bloch temperature dependence of spontaneous magnetization. We used the Hall effect magnetometer and thermo-couple thermometer for measuring of the temperature of the water in which the encapsulated commercial magnet is immersed. The experiment can be repeated in every school and methodological remarks for experimental data processing are given with great detail and attention. The purpose of the paper is to illustrate the simple relation between the quantum spectrum of magnons and the easily measured magnetic field of a permanent magnet.Comment: Second version manuscript - comparison with previous papers, 7 pages, 4 figures, 21 Ref

Predicted electric field induced surface magnetization of vortex phase of superconductors

We predict a new effect in condensed matter surface magnetization of the vortex phase of a superconductor induced by electric field. The magnetized superconductor should be one of the plates of a plane capacitor on which a voltage has to be applied. Applying alternating voltage to the capacitor, electrostatic induction leads to oscillations of the magnetic moment which has to be measured by electromotive force inducted in a detector coil. The derived explicit formula for the magnetization contains the effective mass of Cooper pairs and a systematic investigation of the predicted magnetization will lead to a creation of an effective Cooper pair mass spectroscopy. For cleaved superconductors this effective mass is a property of the bulk material.Comment: 4 pages, 1 enhanced figure, changes in abstract, final journal version, to see discussions with referees delete %-sign before first \end{document

Determination of Boltzmann constant by equipartition theorem for capacitors

A new experimental set-up for Boltzmann constant measurement is described. Statistically averaged square of voltage \left is measured for different capacitances $C$. Boltzmann constant is determined by the equipartition theorem C\left=k_{_\mathrm{B}}T. For fixed capacitance, voltages could be measured for different temperatures. The set-up consists of low-noise high frequency operational amplifiers ADA4898-2. An instrumental amplifier is followed by an inverting amplifier, square of the voltage is created by an analog multiplier AD633 and finally the averaged signal is measured by a multimeter.Comment: 14 pages, 8 figures, 3 tables, 2 appendice

An undergraduate laboratory experiment on measuring the velocity of light with a catastrophic machine

An experimental setup for electrostatic measurement of $\varepsilon_0$, separated magneto-static measurement of $\mu_0$ and determination of the velocity of light $c=1/\sqrt{\varepsilon_0 \mu_0}$ according to Maxwell theory with percent accuracy is described. No forces are measured with the experimental setup therefore there is no need of a scale and the experiment price less than \pounds20 is mainly due to the batteries used. Multiplied 137~times, this experimental setup was given at the fourth open international Experimental Physics Olympiad (EPO4) and a dozen high school students did very well. This article, however, focuses on the catastrophe theory, which is the basis of the methodology.Comment: 13 pages, 4 figures, 1 table. Referee recommendations are taken into accoun

Simple do-it-yourself experimental set-up for electron charge qeq_e measurement

A simple experiment for the electron charge $q_e$ measurement is described. The experimental set-up contains standard electronic equipment only and can be built in every high-school lab all around the world with pocket money budget for several days. It is concluded that it is time such a practice to be included in the regular high-school education. The achieved 13\% accuracy is comparable to the best student university labs. The measurement is based on Schottky noise generated by a photodiode. Using the criterion dollar per accuracy for the electron charge $q_e$ measurement, this definitely is the world's best educational experiment. An industrial replica can be easily sold across the globe.Comment: 10 pages, 9 figures, 3 tables, last version corresponds to the published version in Eur. J. Phys, Eq. (15-17) have been corrected and minor typographical improvements have been mad

Problem of the 8th Experimental Physics Olympiad, Skopje, 8 May 2021 Determination of Planck constant by LED

This is the problem of the 8$^\mathrm{th}$ International Experimental Physics Olympiad (EPO). The task of the EPO8 is to determine Plank constant $\hbar=h/2\pi$ using the given set-up with LED. If you have an idea how to do it, do it and send us the result; skip the reading of the detailed step by step instructions with increasing difficulties. We expect the participants to follow the suggested items -- they are instructive for physics education in general.Only the reading of historical remarks given in the first section can be omitted during the Olympiad without loss of generality. Participants should try solving as much tasks as they can without paying attention to the age categories: give your best.Comment: 27 pages (10 main text), 11 figures, 3 tables, 18 references, 1 appendix of scanned solution (16 pages); latex source files in Bulgarian and Macedonian languages included as auxiliary files. arXiv admin note: text overlap with arXiv:1912.0736