Alfvén modes in a two-species magnetoplasma with anisotropic perturbation pressure-fluid and kinetic calculations

2007 ◽  
Vol 73 (4) ◽  
pp. 455-471
Author(s):  
C. ALTMAN ◽  
K. SUCHY
Keyword(s):  
Energy Flux ◽  
Acoustic Mode ◽  
Acoustic Energy ◽  
Moderate Increase ◽  
Pressure Tensor ◽  
Ion Temperature ◽  
Fluid Analysis ◽  
Dominant Component ◽  
Kinetic Calculations ◽  
Perturbation Pressure

AbstractThe octic fluid dispersion equation, the kinetic Boltzmann–Vlasov equation and the MHD (scalar pressure) analysis, programmed for a two-species collisionless magnetoplasma in a form permitting direct comparison between them, have been applied to the study of the Alfvén modes in both low- and high-β plasmas. In the low-βregime all methods give essentially the same solutions for the isotropic fast magnetosonic and the field-guided shear Alfvén modes. The real part of the refractive index of the field-guided slow magnetosonic acoustic mode is almost identical in the fluid and kinetic analyses, but is 50% too high in the MHD analysis owing to neglect of the trace-free part of the pressure tensor which drives almost half of the acoustic energy flux. The strong damping of the acoustic mode in both low- and high-β plasmas is drastically reduced by increase of electron temperature, whereas a moderate increase in the perpendicular ion temperature is sufficient to eliminate shear Alfvén damping in high-β plasmas and even to produce wave growth, the effect being more pronounced the higher the plasma β. The fluid analysis shows the electromagnetic energy flux to be negligible in the acoustic mode, in which the acoustic flux is driven both by the trace-carrying and trace-free parts of the pressure tensor, but is usually the dominant component in the (fast) magnetosonic mode.

Wave modes in a magnetoplasma with anisotropic perturbation pressure–fluid and kinetic calculations

2004 ◽  
Vol 70 (4) ◽  
pp. 463-479 ◽  
Author(s):  
C. ALTMAN ◽  
K. SUCHY
Keyword(s):  
Acoustic Mode ◽  
Anisotropic Pressure ◽  
Particle Interactions ◽  
Additional Information ◽  
Fluid Analysis ◽  
Quintic Equation ◽  
Kinetic Calculations ◽  
Perturbation Pressure ◽  
Good Agreement ◽  
Wave Modes

The fluid quintic dispersion equation and the full kinetic Boltzmann–Vlasov equation have been programmed for a one-species magnetoplasma in a form permitting direct comparison between them. The quintic equation yields five wave-modes, two electromagnetic, a Langmuir or Bernstein mode and two transversely polarized acoustic modes driven by the trace-free part of the anisotropic pressure tensor. The slower acoustic mode is found in the kinetic analysis to be evanescent, the other suffers appreciable Landau damping except in the first gyroharmonic band when its phase velocity approaches and even exceeds that of the Langmuir mode, with a resultant mixing of modal properties. The Langmuir or Bernstein mode refractive index surfaces found in the fluid and kinetic analyses are generally in good agreement, but gyroharmonic wave–particle interactions seen in the Bernstein modes are missed in the fluid analysis, such as resonant effects very close to the gyroharmonic frequencies and strong damping at all propagation angles when the wave frequency lies in a forbidden Bernstein region. In all cases the fluid analysis provides additional information on wave polarization and generalized energy fluxes–electromagnetic and acoustic–permitting easy identification of modes.

scholarly journals Nonequilibrium corrections in the pressure tensor due to an energy flux

1996 ◽  
Vol 54 (6) ◽  
pp. 6933-6935 ◽  
Author(s):  
Raquel Domínguez-Cascante ◽  
Jordi Faraudo
Keyword(s):  
Energy Flux ◽  
Pressure Tensor

Acoustic energy harvesting from vortex-induced tonal sound in a baffled pipe

2011 ◽  
Vol 225 (8) ◽  
pp. 1847-1850 ◽  
Author(s):  
R Hernandez ◽  
S Jung ◽  
K I Matveev
Keyword(s):  
Acoustic Pressure ◽  
Electrical Energy ◽  
High Amplitude ◽  
Acoustic Mode ◽  
Acoustic Energy ◽  
Electric Load ◽  
Mean Flow ◽  
Acoustic Resonators ◽  
Acoustic Energy Harvesting ◽  
Mean Flow Velocity

Energy of high-amplitude sound that often appears in acoustic resonators with mean flow can be harnessed and converted into electricity for powering sensors and other devices. In this study, tests were conducted in a simple setup consisting of a pipe with a pair of baffles and a piezoelement. Tonal sound, corresponding to the second acoustic mode of the resonator, was excited due to vortex shedding/impinging on baffles in the presence of mean flow. Generated sound energy was partially converted into electrical energy by a piezoelement. About 0.55 mW of electric power was produced on a resistive electric load at acoustic pressure amplitudes in the pipe about 170 Pa and mean flow velocity 2.6 m/s.

Excitation of geodesic acoustic mode continuum by drift wave turbulence

2012 ◽  
Vol 78 (6) ◽  
pp. 651-655 ◽  
Author(s):  
JUN YU ◽  
J. Q. DONG ◽  
X. X. LI ◽  
D. DU ◽  
X. Y. GONG
Keyword(s):  
Growth Rate ◽  
Acoustic Mode ◽  
Kinetic Approach ◽  
Wave Turbulence ◽  
Ion Temperature ◽  
Drift Wave Turbulence ◽  
Acoustic Modes ◽  
Drift Wave ◽  
Radial Structure ◽  
Geodesic Acoustic Mode

AbstractExcitation of the geodesic acoustic mode continuum by drift wave turbulence is studied using the wave kinetic approach. For a model profile of weak non-uniform ion temperature, the forms of growth rate and radial structure of geodesic acoustic modes are obtained analytically. The growth rate is analyzed for several conditions for present-day tokamaks and compared with that for uniform ion temperature, as well as that given by the coherent mode approach for non-uniform ion temperature.

scholarly journals Disturbance energy transport and sound production in gaseous combustion

2012 ◽  
Vol 707 ◽  
pp. 53-73 ◽  
Author(s):  
Michael J. Brear ◽  
Frank Nicoud ◽  
Mohsen Talei ◽  
Alexis Giauque ◽  
Evatt R. Hawkes
Keyword(s):  
Energy Flux ◽  
Sound Production ◽  
Energy Transport ◽  
Source Term ◽  
Sole Source ◽  
Conservation Equation ◽  
Acoustic Energy ◽  
Far Field ◽  
Source Terms ◽  
Mean Flow

AbstractThis paper presents an analysis of the energy transported by disturbances in gaseous combustion. It extends the previous work of Myers (J. Fluid Mech., vol. 226, 1991, 383–400) and so includes non-zero mean-flow quantities, large-amplitude disturbances, varying specific heats and chemical non-equilibrium. This extended form of Myers’ ‘disturbance energy’ then enables complete identification of the conditions under which the famous Rayleigh source term can be derived from the equations governing combusting gas motion. These are: small disturbances in an irrotational, homentropic, non-diffusive (in terms of species, momentum and energy) and stationary mean flow at chemical equilibrium. Under these assumptions, the Rayleigh source term becomes the sole source term in a conservation equation for the classical acoustic energy. It is also argued that the exact disturbance energy flux should become an acoustic energy flux in the far-field surrounding a (reacting or non-reacting) jet. In this case, the volume integral of the disturbance energy source terms are then directly related to the area-averaged far-field sound produced by the jet. This is demonstrated by closing the disturbance energy budget over a set of aeroacoustic, direct numerical simulations of a forced, low-Mach-number, laminar, premixed flame. These budgets show that several source terms are significant, including those involving the mean-flow and entropy fields. This demonstrates that the energetics of sound generation cannot be examined by considering the Rayleigh source term alone.

scholarly journals Observational study of chromospheric heating by acoustic waves

2020 ◽  
Vol 642 ◽  
pp. A52
Author(s):  
V. Abbasvand ◽  
M. Sobotka ◽  
M. Švanda ◽  
P. Heinzel ◽  
M. García-Rivas ◽  
...  
Keyword(s):  
Energy Flux ◽  
Acoustic Waves ◽  
Acoustic Energy ◽  
Solar Chromosphere ◽  
Echelle Spectrograph ◽  
Quiet Sun ◽  
Non Local ◽  
Radiative Losses ◽  
Semi Empirical

Aims. Our aim is to investigate the role of acoustic and magneto-acoustic waves in heating the solar chromosphere. Observations in strong chromospheric lines are analyzed by comparing the deposited acoustic-energy flux with the total integrated radiative losses. Methods. Quiet-Sun and weak-plage regions were observed in the Ca II 854.2 nm and Hα lines with the Fast Imaging Solar Spectrograph (FISS) at the 1.6-m Goode Solar Telescope on 2019 October 3 and in the Hα and Hβ lines with the echelle spectrograph attached to the Vacuum Tower Telescope on 2018 December 11 and 2019 June 6. The deposited acoustic energy flux at frequencies up to 20 mHz was derived from Doppler velocities observed in line centers and wings. Radiative losses were computed by means of a set of scaled non-local thermodynamic equilibrium 1D hydrostatic semi-empirical models obtained by fitting synthetic to observed line profiles. Results. In the middle chromosphere (h = 1000–1400 km), the radiative losses can be fully balanced by the deposited acoustic energy flux in a quiet-Sun region. In the upper chromosphere (h >  1400 km), the deposited acoustic flux is small compared to the radiative losses in quiet as well as in plage regions. The crucial parameter determining the amount of deposited acoustic flux is the gas density at a given height. Conclusions. The acoustic energy flux is efficiently deposited in the middle chromosphere, where the density of gas is sufficiently high. About 90% of the available acoustic energy flux in the quiet-Sun region is deposited in these layers, and thus it is a major contributor to the radiative losses of the middle chromosphere. In the upper chromosphere, the deposited acoustic flux is too low, so that other heating mechanisms have to act to balance the radiative cooling.

Energetically Consistent Computation of Combustor Stability with a Model Consisting of a Helmholtz-Fem-Domain and a Low-Order Network

2021 ◽  
Author(s):  
Gerrit Heilmann ◽  
Christoph Hirsch ◽  
Thomas Sattelmayer
Keyword(s):  
Boundary Conditions ◽  
Energy Flux ◽  
Fundamental Problem ◽  
Acoustic Energy ◽  
Special Treatment ◽  
Transfer Matrices ◽  
Mean Flow ◽  
Acoustic Damping ◽  
Spatially Resolved ◽  
Low Order

Abstract An efficient approach for the detection of the acoustic damping of gas turbine combustors is the combination of spatially resolved FEM approaches based on the Helmholtz equation with low-order networks for all elements leading to acoustic damping. A fundamental problem of such hybrid approaches is that the flow is considered in the networks, but not in the spatially resolved FEM area. Without special treatment of the boundary conditions this leads to serious errors in the calculation of the damping rate. The purpose of the paper is the derivation of the required correction procedures, which allow the energetically consistent formulation of such hybrid models and lead to correct damping rates. The time averaged equation of acoustic energy flux is expressed in terms of reflection coefficients and compared to the equivalent formulation for vanishing mean flows. An existing transformation for boundary conditions to obtain equal energy flux at the interface between network and Helmholtz domain is analyzed in detail. The findings are then used to derive energetically consistent transformations of transfer matrices to couple two FEM domains via a network model. The relevance of energetically consistent transfer matrices for stability analysis is demonstrated with a generic test case. The central partition is acoustically characterized via low order models considering mean flow. The resulting acoustic two-port is transformed to obtain an energetically consistent transfer matrix for a subsequent FEM discretized eigenvalue analysis of the remaining geometry. The eigenvalues of energetically consistent calculations are finally compared to eigenvalues of energetically inconsistent setups.

Characteristics of collisional damping of surface ion-acoustic mode in Divertor Plasma Simulator-2 (DiPS-2)

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
Myoung-Jae Lee ◽  
In Sun Park ◽  
Sunghoon Hong ◽  
Kyu-Sun Chung ◽  
Young-Dae Jung
Keyword(s):  
Decay Constant ◽  
Argon Plasma ◽  
Acoustic Mode ◽  
Experimental Simulation ◽  
Landau Damping ◽  
Ion Temperature ◽  
Ion Acoustic ◽  
Collisional Damping ◽  
Weakly Ionized ◽  
The Given

The dissipation of ion-acoustic surface waves propagating in a semi-bounded and collisional plasma which has a boundary with vacuum is theoretically investigated and this result is used for the analysis of edge-relevant plasma simulated by Divertor Plasma Simulator-2 (DiPS-2). The collisional damping of the surface wave is investigated for weakly ionized plasmas by comparing the collisionless Landau damping with the collisional damping as follows: (1) the ratio of ion temperature $({T_i})$ to electron temperature $({T_e})$ should be very small for the weak collisionality $({T_i}/{T_e} \ll 1)$ ; (2) the effect of collisionless Landau damping is dominant for the small parallel wavenumber, and the decay constant is given as $\gamma \approx{-} \sqrt {\mathrm{\pi }/2} {k_\parallel }{\lambda _{De}}\omega _{pi}^2/{\omega _{pe}}$ ; and (3) the collisional damping dominates for the large parallel wavenumber, and the decay constant is given as $\gamma \approx{-} {\nu _{in}}/16$ , where ${\nu _{in}}$ is the ion–neutral collisional frequency. An experimental simulation of the above theoretical prediction has been done in the argon plasma of DiPS-2, which has the following parameters: plasma density ${n_e} = (\textrm{2--9)} \times \textrm{1}{\textrm{0}^{11}}\;\textrm{c}{\textrm{m}^{ - 3}}$ , ${T_e} = 3.7- 3.8\;\textrm{eV}$ , ${T_i} = 0.2- 0.3\;\textrm{eV}$ and collision frequency ${\nu _{in}} = 23- 127\;\textrm{kHz}$ . Although the wavelength should be specified with the given parameters of DiPS-2, the collisional damping is found to be $\gamma = ( - 0.9\;\textrm{to}\; - 5) \times {10^4}\;\textrm{rad}\;{\textrm{s}^{ - 1}}$ for ${k_\parallel }{\lambda _{De}} = 10$ , while the Landau damping is found to be $\gamma = ( - 4\;\textrm{to}\; - 9) \times {10^4}\;\textrm{rad}\;{\textrm{s}^{ - 1}}$ for ${k_\parallel }{\lambda _{De}} = 0.1$ .

Stability analysis for the onset of thermoacoustic oscillations in a gas-filled looped tube

2014 ◽  
Vol 741 ◽  
pp. 585-618 ◽  
Author(s):  
H. Hyodo ◽  
N. Sugimoto
Keyword(s):  
Wave Equation ◽  
Stability Analysis ◽  
Temperature Gradient ◽  
Energy Flux ◽  
Diffusion Layer ◽  
Wave Mode ◽  
Frequency Equation ◽  
Acoustic Energy ◽  
Tube Length ◽  
Thermoacoustic Oscillations

AbstractThis paper develops a stability analysis for the onset of thermoacoustic oscillations in a gas-filled looped tube with a stack inserted, subject to a temperature gradient. Analysis is carried out based on approximate theories for a thermoviscous diffusion layer derived from the thermoacoustic-wave equation taking account of the temperature dependence of the viscosity and the heat conductivity. Assuming that the stack consists of many pores axially and that the thickness of the diffusion layer is much thicker than the pore radius, the diffusion wave equation with higher-order terms included is applied for the gas in the pores of the stack. For the gas outside of the pores, the theory of a thin diffusion layer is applied. In a section called the buffer tube over which the temperature relaxes from that at the hot end of the stack to room temperature, the effects of the temperature gradient are taken into account. With plausible temperature distributions specified on the walls of the stack and the buffer tube, the solutions to the equations in both theories are obtained and a frequency equation is finally derived analytically by matching the conditions at the junctions between the various sections. Seeking a real solution to the frequency equation, marginal conditions of instability are obtained numerically not only for the one-wave mode but also for the two-wave mode, where the tube length corresponds to one wavelength and two wavelengths, respectively. It is revealed that the marginal conditions depend not only on the thickness of the diffusion layer but also on the porosity of the stack. Although the toroidal geometry allows waves to be propagated in both senses along the tube, it is found that the wave propagating in the sense from the cold to the hot end through the stack is always greater, so that a travelling wave in this sense emerges as a whole. The spatial and temporal variations of excess pressure and mean axial velocity averaged over the cross-section of a flow passage are displayed for the two modes of oscillations at the marginal state. The spatial distribution of mean acoustic energy flux (acoustic intensity) over one period is also shown. It is unveiled that the energy flux is generated only in the stack, and it decays slowly in the other sections by lossy effects due to a boundary layer. Mechanisms for the generation of the acoustic energy flux are also discussed.

Sign in / Sign up

Export Citation Format

Share Document