_____________________________________________________________________________________ The paper deals with generation of Alfvén plasma disturbances in magnetic flux P.A. Prokopov, Yu.P. Zakharov, V.N. Tishchenko, E.L. Boyarintsev, A.V. Melekhov, A.G. Ponomarenko, V.G. Posukh, I.F. Shaikhislamov 20 INTRODUCTIONThe problem of heating of the solar corona is well known in solar research. The temperature of the solar surface (the photosphere) is approximately 5800 °C, whereas the temperature of the solar corona exceeds it by several orders of magnitude [Prist, 1985]. There are different hypotheses explaining the corona heating up to so high temperatures. One of the hypotheses assumes that energy is transferred from the solar surface to the corona by Alfvén waves (AW) or slow magnetosonic waves propagating in plasma. These waves propagate inside the plasma in the external magnetic field. Plasma particles move predominantly along magnetic field lines and, given sufficient field strength, form the so-called magnetic plasma tube along a magnetic field line.This paper presents the results of experimental simulation of plasma processes in tubes that begin and end in the photosphere, but are largely situated in the solar atmosphere (in the corona). The simulation experiments are generally used to study the generation of Alfvén and slow magnetosonic waves (and perhaps of accompanying shock waves) at the stand KI-1 with laser plasma blobs injected in a cone with ~1 sr opening and its axis along the magnetic field B 0 (initial configuration of the laser plasma (LP) cloud is a directional explosion). This is characteristic for generation and propagation of Alfvén and slow magnetosonic waves in the solar atmosphere. In addition, these experiments have provided data on fast high-frequency disturbanceselectron whistlers propagating in magnetic flux tubes at a velocity higher than the Alfvén velocity and preceding Alfvén and slow magnetosonic waves.One of the main objectives of these simulation experiments is to explore the possibility of generating torsional Alfvén waves (TAW) and their propagation in plasma structures imitating magnetic flux tubes in the solar atmosphere. Such waves induced by torsional movements (in azimuth) on the surface of the photosphere [Antolin, Shibata, 2010] are nowadays considered to be one of the most effective sources of corona heating [De Moortel, Nakaryakov, 2012;Antolin et al., 2015;Okamoto et al., 2015]. The new simulation experiments at the stand KI-1 have been initiated by calculations [Tishchenko, Shaikhislamov, 2010, 2014Tishchenko, et al. 2014 Tishchenko, et al. , 2015 of formation of cylindrical channels along a magnetic field (like a magnetic flux tube) with LP blobs propagating inside (together with their generated Alfvén and magnetosonic waves), as well as by results of previous experiments with LP [Antonov et al., 1985;Zakharov et al., 2006; Shaikhislamov et al., 2015] in simulation of different nonstationary processes in space plasma [Vshivkov et al., 1987;Brady et al., 2009;Dudn...

Рассмотрены вопросы, связанные с построением и областью применения численной модели гидроволновой лаборатории как инструмента, позволяющего в некоторых ситуациях отказаться от физического моделирования и заменить его численным, удешевить и ускорить ряд этапов проектных работ в гидротехническом строительстве. Представлены математические модели и численные алгоритмы, которые могут войти в состав численной лаборатории и использоваться для численного моделирования процессов генерации поверхностных волн, их распространения и взаимодействия с прибрежными и морскими сооружениями. Перечислены требования к программному обеспечению численной модели гидроволновой лаборатории, выполнение которых позволит эффективнее использовать этот инструмент инженерами-гидротехниками при проектировании гидротехнических сооружений. In the design of hydraulic structures and facilities of the coastal infrastructure, one of the main methods of confirming the claimed characteristics of the constructed facilities is the implementation of physical modelling in special hydrowave laboratories. However, the use of physical modelling as a tool for determining the most rational characteristics and parameters of hydraulic structures is very limited due to the high cost and, as a rule, the high complexity of the relevant studies. For this reason, it is virtually impossible to resort to this type of study in situations where a significant number of different project options need to be sorted out. The way out of the situation is the use of numerical modelling methods that allow you to choose the most suitable option. In fact, there is a need for a numerical model of the hydrowave laboratory, which allows abandoning the physical modelling in appropriate situations and replacing it with a numerical one. In this case, it will be possible to achieve important advantages: to reduce the cost and speed up the process of choosing the rational parameters of the design solution in hydraulic engineering, to give sufficient justification for the decision before its final verification by physical modelling. Thus, the combination of numerical studies of the proposed design solutions and physical modelling of the final result in order to confirm compliance with the requirements meets the needs of design studies in hydraulic engineering. In this paper, we consider the issues related to the construction and the domain of the numerical model of the hydrowave laboratory, as a tool that allows in some situations to abandon the physical modelling and replace it with a numerical one. Mathematical models and numerical algorithms that can be included in the numerical laboratory and used for numerical simulation of the processes of generation of surface waves, their propagation and interaction with coastal and marine structures are presented. The requirements are given for the software of the numerical model of the hydrowave laboratory, the implementation of which will ensure the effective use of this tool by hydraulic engineers in the design of hydraulic structures. Examples of successful use of mathematical technology to improve the efficiency of laboratory research are given.

The paper deals with generation of Alfven plasma disturbances in magnetic flux tubes through exploding laser plasma in magnetized background plasma. Processes with similar effect of excitation of torsion-type waves seem to provide energy transfer from the solar photosphere to corona. The studies were carried out at experimental stand KI-1 represented a high-vacuum chamber of 1.2 m diameter, 5 m long, external magnetic field up to 500 Gs along the chamber axis, and up to 2·10–6 Torr pressure in operating mode. Laser plasma was produced when focusing the CO2 laser pulse on a flat polyethylene target, and then the laser plasma propagated in θ-pinch background hydrogen (or helium) plasma. As a result, the magnetic flux tube of 15–20 cm radius was experimentally simulated along the chamber axis and the external magnetic field direction. Also, the plasma density distribution in the tube was measured. Alfven wave propagation along the magnetic field was registered from disturbance of the magnetic field transverse component Bφ and field-aligned current Jz. The disturbances propagate at near-Alfven velocity of 70–90 km/s and they are of left-hand circular polarization of the transverse component of magnetic field. Presumably, Alfven wave is generated by the magnetic laminar mechanism of collisionless interaction between laser plasma cloud and background. The right-hand polarized high-frequency whistler predictor was registered which have been propagating before Alfven wave at 300 km/s velocity. The polarization direction changed with Alfven wave coming. Features of a slow magnetosonic wave as a sudden change in background plasma concentration along with simultaneous displacement of the external magnetic field were found. The disturbance propagates at ~20–30 km/s velocity, which is close to that of ion sound at low plasma beta value. From preliminary estimates, the disturbance transfers about 10 % of the original energy of laser plasma.