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Abstract

The magnetoacoustic heating of a plasma by harmonic or periodic saw-tooth perturbations at a transducer is theoretically studied. The planar fast and slow magnetosound waves are considered. The wave vector may form an arbitrary angle θ with the equilibrium straight magnetic strength. In view of variable θ and plasma-β, the description of magnetosound perturbations and relative magnetosound heating is fairly difficult. The scenario of heating depends not only on plasma-β and θ, but also on a balance between nonlinear attenuation at the shock front and inflow of energy into a system. Under some conditions, the average over the magnetosound period force of heating may tend to a positive or negative limit, or may tend to zero, or may remain constant when the distance from a transducer tends to infinity. Dynamics of temperature specifying heating differs in thermally stable and unstable cases and occurs unusually in the isentropically unstable flows.

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Authors and Affiliations

Anna Perelomova
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Abstract

Nonlinear excitation of the entropy perturbations by magnetosonic waves in a uniform and infinite plasma model is considered. The wave vector of slow or fast mode forms an arbitrary angle θ (0≤θ≤π) with the equilibrium straight magnetic field, and all perturbations are functions of the time and longitudinal coordinate. Thermal conduction is the only factor which destroys isentropicity of wave perturbations and causes the nonlinear excitation of the entropy mode. A dynamic equation is derived which describes excitation of perturbation in the entropy mode in the field of dominant magnetosonic mode. Effects associatiated with temperature dependent and anisotropic thermal conduction are considered and discussed.
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Bibliography

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18. Perelomova A. (2006), Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound, Physics Letters A, 357: 42–47, doi: 10.1016/j.physleta.2006.04.014.
19. Perelomova A. (2008), Modelling of acoustic heating induced by different types of sound, Archives of Acoustics, 33(2): 151–160.
20. Perelomova A. (2018a), Magnetoacoustic heating in a quasi-isentropic magnetic gas, Physics of Plasmas, 25: 042116, doi: 10.1063/1.5025030.
21. Perelomova A. (2018b), Magnetoacoustic heating in nonisentropic plasma caused by different kinds of heating-cooling function, Advances in Mathematical Physics, 2018: Article ID 8253210, 12 pages, doi: 10.1155/2018/8253210.
22. Perelomova A. (2020), Hysteresis curves for some periodic and aperiodic perturbations in magnetosonic flow, Physics of Plasmas, 27(10): 102101, doi: 10.1063/5.0015944.
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Authors and Affiliations

Anna Perelomova
1

  1. Gdansk University of Technology, Faculty of Applied Physics and Mathematics, Gdansk, Poland
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Abstract

The dynamics of slightly diverging two-dimensional beams whose direction forms a constant angle θ with the
equilibrium straight magnetic strength is considered. The approximate dispersion relations and corresponding links which specify hydrodynamic perturbations in confined beams are derived. The study is dedicated to the diffraction of a magnetosonic beam and nonlinear thermal self-action of a beam in a thermoconducting gaseous plasma. It is shown that the divergence of a beam and its thermal self-action is unusual in some particular cases of parallel propagation (θ = 0) and has no analogues in the dynamics of the Newtonian beams. The nonlinear attenuation of Newtonian beams leads to their defocusing in gases, whereas the unusual cases correspond to the focusing in a presence of magnetic field. The examples of numerical calculations of thermal self-action of magnetoacoustic beams with shock fronts are considered in the usual and unusual cases of diffraction concerning stationary and non-stationary self-action. It is discovered that the diffraction is more (θ = 0) or less (θ = π/2) manifested as compared to that of the Newtonian beams. The beams which propagate oblique to the magnetic field do not reveal diffraction. The special case, when the sound and Alfvénic speeds are equal, is discussed. This magnetosonic beams incorporate acoustic and Alfvénic properties and do not undergo diffraction in this particular case.
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Bibliography

Botha G.J.J., Arber T.D., Nakariakov V.M., Keenan F.P. (2000), A developed stage of Alfvén wave phase mixing, Astronomy and Astrophysics, 363(3): 1186–1194.

Callen J.D. (2003), Fundamentals of Plasma Physics, Lecture notes, University of Wisconsin, Madison.

Chin R., Verwichte E., Rowlands G., Nakariakov V.M. (2010), Self-organization of magnetoacoustic waves in a thermal unstable environment, Physics of Plasmas, 17: 032107, doi: 10.1063/1.3314721.

Duck F.A. (2002), Nonlinear acoustics in diagnostic ultrasound, Ultrasound in Medicine & Biology, 28(1): 1–18, doi: 10.1016/S0301-5629(01)00463-X.

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Nakariakov V.M., Mendoza-Briceño C.A., Ibáñez M.H. (2000), Magnetoacoustic waves of small amplitude in optically thin quasi-isentropic plasmas, The Astrophysical Journal, 528(2): 767–775, doi: 10.1086/308195.

Rudenko O.V., Sapozhnikov O.A. (2004), Self-action effects for wave beams containing shock fronts, Physics-Uspekhi, 47(9): 907–922.

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Yufeng Z. (2015), Principles and Applications of Therapeutic Ultrasound in Healthcare, Taylor & Francis Inc.

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Authors and Affiliations

Anna Perelomova
1

  1. Gdansk University of Technology, Faculty of Applied Physics and Mathematics, Gdansk, Poland
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Abstract

Excitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoretically considered in this work. The dynamic equation for an excess density which specifies the entropy mode, has been obtained by means of the method of projections. It takes the form of the diffusion equation with an acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient is proportional to the thermal conduction, and the acoustic force is proportional to the total attenuation. Theoretical description of instantaneous heating allows to take into account aperiodic and impulsive sounds. Acoustic heating in a half-space and in a planar resonator is discussed. The aim of this study is to evaluate acoustic heating and determine the contribution of thermal conduction and mechanical viscosity in different boundary problems. The conclusions are drawn for the Dirichlet and Neumann boundary conditions. The instantaneous dynamic equation for variations in temperature, which specifies the entropy mode, is solved analytically for some types of acoustic exciters. The results show variation in temperature as a function of time and distance from the boundary for different boundary conditions.

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Authors and Affiliations

Anna Perelomova
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Abstract

The nonlinear interaction of magnetoacoustic waves in a plasma is analytically studied. A plasma is an open system. It is affected by the straight constant equilibrium magnetic flux density forming constant angle with the wave vector which varies from 0 till π. The nonlinear instantaneous equation which describes excitation of secondary wave modes in the field of intense magnetoacoustic perturbations is derived by use of projecting. There is a diversity of nonlinear interactions of waves in view of variety of wave modes, which may be slow or fast and may propagate in different directions. The excitation is analysed in the physically meaningful cases, that is: harmonic and impulsive exciter, oppositely or accordingly directed dominant and secondary wave modes.
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Authors and Affiliations

Anna Perelomova
1

  1. Gdansk University of Technology, Faculty of Applied Physics and Mathematics, Gdansk, Poland
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Abstract

The diversity of wave modes in the magnetic gas gives rise to a wide variety of nonlinear phenomena associated with these modes. We focus on the planar fast and slow magnetosound waves in the geometry of a flow where the wave vector forms an arbitrary angle θ with the equilibrium straight magnetic field. Nonlinear distortions of a modulated signal in the magnetic gas are considered and compared to that in unmagnetised gas. The case of acoustical activity of a plasma is included into consideration. The resonant three-wave non-collinear interactions are also discussed. The results depend on the degree of non-adiabaticity of a flow, θ, and plasma-β.

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Authors and Affiliations

Anna Perelomova
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Abstract

The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differential form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.

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Authors and Affiliations

Anna Perelomova
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Abstract

Graphs in the thermodynamic plane acoustic pressure versus excess acoustic density representing acoustic hysteresis, are considered as indicators of relaxation processes, equilibrium parameters of a flow, and kinds of wave exciters. Some flows with deviation from adiabaticity are examined: the Newtonian flow of a thermoconducting gas, the flow of a gas with vibrational relaxation, the flow of liquid electrolyte with a chemical reaction, and the Bingham plastic flow. The total range of characteristic frequencies of a harmonic exciter is taken into account. The impulsive sound is considered as well. The peculiarities of hysteretic behaviour are discussed in dependence with the kind and degree of deviation form adiabaticity. Examples of acoustically active flows are discussed.
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Authors and Affiliations

Anna Perelomova
1

  1. Gdansk University of Technology, Faculty of Applied Physics and Mathematics, Gdansk, Poland
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Abstract

Thermal self-action of an acoustic beam with one discontinuity or several shock fronts is studied in a Newtonian fluid. The stationary self-action of a single sawtooth wave with discontinuity (or some integer number of these waves), symmetric or asymmetric, is considered in the cases of self-focusing and self- defocusing media. The results are compared with the non-stationary thermal self-action of the periodic sound. Thermal self-action of a single shock wave which propagates with the various speeds is considered.
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Authors and Affiliations

Anna Perelomova
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Abstract

This study is devoted to the instantaneous acoustic heating of a shear-thinning fluid. Apparent viscosity of a shear-thinning fluid depends on the shear rate. That feature distinguishes it from a viscous Newtonian fluid. The special linear combination of conservation equations in the differential form makes it possible to derive dynamic equations governing both the sound and non-wave entropy mode induced in the field of sound. These equations are valid in a weakly nonlinear flow of a shear-thinning fluid over an unbounded volume. They both are instantaneous, and do not require a periodic sound. An example of a sound waveform with a piecewise constant shear rate is considered as a source of acoustic heating.

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Authors and Affiliations

Anna Perelomova
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Abstract

The distribution of perturbations of pressure and velocity in a rectangular resonator is considered. A resonator contains a gas where thermodynamic processes take place, such as exothermic chemical reaction or excitation of vibrational degrees of a molecule’s freedom. These processes make the gas acoustically active under some conditions. We conclude that the incident and reflected compounds of a sound beam do not interact in the leading order in the case of the periodic sound with zero mean pressure including waveforms with discontinuities. The acoustic field before and after forming of discontinuities is described. The acoustic heating or cooling in a resonator is discussed.
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Authors and Affiliations

Anna Perelomova
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Abstract

Nonlinear phenomena of the planar and quasi-planar magnetoacoustic waves are considered. We focus on deriving of equations which govern nonlinear excitation of the non-wave motions by the intense sound in initially static gaseous plasma. The plasma is treated as an ideal gas with finite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. This introduces dispersion of a flow. Magnetoacoustic heating and streaming in the field of periodic and aperiodic magnetoacoustic perturbations are discussed, as well as generation of the magnetic perturbations by sound. Two cases, corresponding to magnetosound perturbations of low and high frequencies, are considered in detail.

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Authors and Affiliations

Anna Perelomova
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Abstract

Dynamics of a weakly nonlinear and weakly dispersive flow of a gas where molecular vibrational relaxation takes place is studied. Variations in the vibrational energy in the field of intense sound is considered. These variations are caused by a nonlinear transfer of the acoustic energy into energy of vibrational degrees of freedom in a relaxing gas. The final dynamic equation which describes this is instantaneous, it includes a quadratic nonlinear acoustic source reflecting the nonlinear character of interaction of high-frequency acoustic and non-acoustic motions in a gas. All types of sound, periodic or aperiodic, may serve as an acoustic source. Some conclusions about temporal behavior of the vibrational mode caused by periodic and aperiodic sounds are made.

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Authors and Affiliations

Anna Perelomova
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Abstract

Diagnostics and decomposition of atmospheric disturbances in a planar flow are considered in this work. The study examines a situation in which the stationary equilibrium temperature of a gas may depend on the vertical coordinate due to external forces. The relations connecting perturbations are analytically established. These perturbations specify acoustic and entropy modes in an arbitrary stratified gas affected by a constant mass force. The diagnostic relations link acoustic and entropy modes, and are independent of time. Hence, they provide an ability to decompose the total vector of perturbations into acoustic and non-acoustic (entropy) parts, and to establish the distribution of energy between the sound and entropy modes, uniquely at any instant. The total energy of a flow is hence determined in its parts which are connected with acoustic and entropy modes. The examples presented in this work consider the equilibrium temperature of a gas, which linearly depends on the vertical coordinate. Individual profiles of acoustic and entropy parts for some impulses are illustrated with plots.

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Authors and Affiliations

Sergey Leble
Anna Perelomova
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Abstract

The sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting of boiling water and its vapor under different temperatures, are evaluated as functions of mass concentration of the vapor. The relations analogous to that in the Riemann wave in an ideal gas are obtained in a fluid obeying an arbitrary equation of state. An example concerns the van der Waals gases. An excess pressure in the reflected wave, which appears when standard or nonlinear absorption in a fluid takes place, is evaluated in an arbitrary fluid.

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Authors and Affiliations

Anna Perelomova
Paweł Wojda
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Abstract

Weakly nonlinear sound propagation in a gas where molecular vibrational relaxation takes place is studied. New equations which govern the sound in media where the irreversible relaxation may take place are derived and discussed. Their form depends on the regime of excitation of oscillatory degrees of freedom, equilibrium (reversible) or non-equilibrium (irreversible), and on the comparative frequency of the sound in relation to the inverse time of relaxation. Additional nonlinear terms increase standard nonlinearity of the high-frequency sound in the equilibrium regime of vibrational excitation and decrease otherwise. As for the nonlinearity of the low-frequency sound, the conclusions are opposite. Appearance of a non-oscillating additional part which is a linear function of the distance from the transducer is an unusual property of nonlinear distortions of harmonic at the transducer high-frequency sound
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Authors and Affiliations

Anna Perelomova
Magdalena Kusmirek
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Abstract

Instantaneous acoustic heating of a viscous fluid flow in a boundary layer is the subject of investigation. The governing equation of acoustic heating is derived by means of a special linear combination of conservation equations in the differential form, which reduces all acoustic terms in the linear part of the final equation but preserves terms belonging to the thermal mode. The procedure of decomposition is valid in a weakly nonlinear flow, it yields the nonlinear terms responsible for the modes interaction. Nonlinear acoustic terms form a source of acoustic heating in the case of the dominative sound. This acoustic source reflects the thermoviscous and dispersive properties of a fluid flow. The method of deriving the governing equations does not need averaging over the sound period, and the final governing dynamic equation of the thermal mode is instantaneous. Some examples of acoustic heating are illustrated and discussed, and conclusions about efficiency of heating caused by different waveforms of sound are made.

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Authors and Affiliations

Anna Perelomova
Weronika Pelc-Garska
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Abstract

Standing waves and acoustic heating in a one-dimensional resonator filled with chemically reacting gas, is the subject of investigation. The chemical reaction of A → B type, which takes place in a gas, may be reversible or not. Governing equations for the sound and entropy mode which is generated in the field of sound are derived by use of a special mathematical method. Under some conditions, sound waves propagating in opposite directions do not interact. The character of nonlinear dynamics of the sound and relative acoustic heating or cooling depends on reversibility of a chemical reaction. Some examples of acoustic heating in a resonator are illustrated and discussed.
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Authors and Affiliations

Anna Perelomova
Weronika Pelc-Garska

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