Abstract
The plasma kinetic theory with Vlasov–Poisson model is taken into account to study the dispersion relation and dam** rate of one of the fundamental longitudinal low-frequency mode, i.e., ion-acoustic waves (IAWs) in a hybrid Vasyliunas–Cairns distributed plasma using the 3D Vasyliunas–Cairns distribution function (VCDF) for non-thermal electrons. The longitudinal dielectric response function for ion-acoustic waves in non-thermal plasmas is calculated by considering the electrons as Vasyliunas–Cairns distributed while the ions are taken to be Maxwellian. Both the dispersion and dam** rate of IAWs are significantly swayed by the simultaneous presence of two non-thermality parameters \(^{\prime }\alpha ^{\prime }\) and \(^{\prime }\kappa ^{\prime }\). It is found that the dam** rate of IAWs is remarkably higher for Maxwellian distributed electron plasmas in comparison to non-thermal Vasyliunas–Cairns distributed plasmas. The analytical expression of dam** rate of IAWs is obtained under weak dam** approximation, while numerical plots of strong dam** rates (when ion temperature become almost equal to electron temperature) are also obtained using Newton–Raphson method from exact solution of dispersion relation equation obtained from dielectric response function. The results are applicable to space plasma regions where highly energetic particles having VCDF exist.
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This manuscript has associated data in a data repository. [Authors comment : The data that support the findings of this study are available from the corresponding author upon reasonable request.]
References
D.A. Gurnett, A. Bhattacharjee, Introduction to Plasma Physics with Space and Laboratory Applications (Cambridge University Press, Cambridge, 2005)
F.F. Chen, Introduction to Plasma Physics and Controlled Fusion, 3rd edn. (Springer, Switzerland, 2016)
A.Y. Wong, N.D. Angelo, R.W. Motley, Propagation and dam** of ion acoustic waves in highly ionized plasmas. Phys. Rev. Lett. 9, 415 (1962). https://doi.org/10.1103/PhysRevLett.9.415
B.D. Fried, Roy W. Gould, Longitudinal ion oscillations in a hot plasma. Phys. Fluids 4, 139 (1961). https://doi.org/10.1063/1.1706174
A. Rehman, M. Ahmad, M.A. Shahzad, Revisiting some analytical and numerical interpretations of Cairns and Kappa-Cairns distribution functions. Phys. Plasmas 27, 100901 (2020). https://doi.org/10.1063/5.0018906
W.D. Jones, Sound Waves in Plasmas—A Basic Phenomenon and a Simple Diagnostic Tool (Oak Ridge National Laboratory Operated by Union Carbide Corporation for the U. S. Atomic Energy Commission, Oak Ridge, 1967)
L. Liyan, D. Jiulin, Ion acoustic waves in the plasma with the power-law-distribution in nonextensive statistics. ar**v:0804.3732
L. Ding, Chen Yinhua et al., Plasma Physics (Higher Education Press, Bei**g, 2006)
J. Xu, S. **, Plasma Physics (Nuclear Energy Press, Bei**g, 1981)
N.P. Abraham, S. Sebastian, G. Sreekala, R. Jayapal, Ion-acoustic instabilities in a multi-ion plasma. Hindawi Publ. Corp. J. Astrophys. 2013, 838534. https://doi.org/10.1155/2013/838534
L. Tonks, I. Langmuir, Oscillations in ionized gases. Phys. Rev. 33, 195 (1929). https://doi.org/10.1103/PhysRev.33.195
R.W. Revans, The transmission of waves through an ionized gas. Phys. Rev. 44, 798 (1933). https://doi.org/10.1103/PhysRev.44.798
I. Alexeff, R.V. Neidigh, Observations of ionic sound waves in plasmas: their properties and applications. Phys. Rev. 129, 516 (1963). https://doi.org/10.1103/PhysRev.129.516
E.T. Sarris, S.M. Krimigis, A.T.Y. Lui, K.L. Ackerson, L.A. Frank, D.J. Williams, Relationship between energetic particles and plasmas in the distant plasma sheet. Geophys. Res. Lett. 8, 349 (1981). https://doi.org/10.1029/GL008i004p00349
D.J. Williams, D.G. Mitchell, S.P. Christon, Implications of large flow velocity signatures in nearly isotropic ion distributions. Geophys. Res. Lett. 15, 303 (1988). https://doi.org/10.1029/gl015i004p00303
J.T. Gosling, J.R. Asbridge, S.J. Bame, W.C. Feldman, R.D. Zwickl, G. Paschmann, N. Sckopke, R.J. Hynds, Interplanetary ions during an energetic storm particle event: the distribution function from solar wind thermal energies to 1.6 MeV. J. Geophys. Res. [Space Phys.] 86, 547 (1981). https://doi.org/10.1029/JA086iA02p00547
J.M. Liu, J.S. De Groot, J.P. Matte, T.W. Johnston, R.P. Drake, Measurements of inverse bremsstrahlung absorption and non-Maxwellian electron velocity distributions. Phys. Rev. Lett. 72, 2717 (1994). https://doi.org/10.1103/PhysRevLett.72.2717
D. Debnath, A. Bandyopadhyay, Combined effect of Kappa and Cairns distributed electrons on ion acoustic solitary structures in a collisionless magnetized dusty plasma. Astrophys. Space Sci. 365, 72 (2020). https://doi.org/10.1007/s10509-020-03786-6
V. Vasyliunas, A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3. J. Geophys. Res. 73, 2839 (1968). https://doi.org/10.1029/JA073i009p02839
S. Olbert, R.L. Carovillano, J.F. McClay, H.R. Radoski, Summary of experimental results from MIT detector on IMP-1, in Physics of the Magnetosphere: Based Upon the Proceedings of the Conference held at Boston College, 19–28 June 1967 (Springer, Boston, 1968)
R.A. Cairns, R. Bingham, R.O. Dendy, C.M.C. Nairn, P.K. Shukla, A.A. Mamun, Ion sound solitary waves with density depressions. J. Phys. 5, C6-43 (1995). https://doi.org/10.1051/jp4:1995608
K. Aoutou, M. Tribeche, T.H. Zerguini, Electrostatic solitary structures in dusty plasmas with nonthermal and superthermal electrons. Phys. Plasmas 15, 013702 (2008). https://doi.org/10.1063/1.2828073
A. Rehman, M.A. Shahzad, S. Mahmood, M. Bilal, Numerical and analytical study of electron plasma waves in nonthermal Vasyliunas–Cairns distributed plasmas. J. Geophys. Res. Space Phys. 126, e2021JA029626 (2021). https://doi.org/10.1029/2021JA029626
D. Summers, R.M. Thorne, The modified plasma dispersion function. Phys. Fluids B 3, 1835 (1991). https://doi.org/10.1063/1.859653
V. Pierrard, M. Lazar, Kappa distributions: theory and applications in space plasmas (2010). https://doi.org/10.1007/s11207-010-9640-2
P.O. Dovner, A.I. Eriksson, R. Bostrom, B. Holback, Freja multiprobe observations of electrostatic solitary structure. Geophys. Res. Lett. 21, 1827 (1994). https://doi.org/10.1029/94GL00886
R. Bostrom, Observations of weak double layers on auroral field lines. IEEE Trans. Plasma Sci. 20, 756 (1992). https://doi.org/10.1109/27.199524
G. Sarri, M.E. Dieckmann, I. Kourakis, M. Borghesi, Shock creation and particle acceleration driven by plasma expansion into a rarefied medium. Phys. Plasmas 17, 082305 (2010). https://doi.org/10.1063/1.3469762
D. Darian, S. Marholm, M. Mortensen, W.J. Miloch, Theory and simulations of spherical and cylindrical Langmuir probes in non-Maxwellian plasmas. Plasma Phys. Control. Fusion 61, 085025 (2019). https://doi.org/10.1088/1361-6587/ab27ff
L.F. Ziebell, R. Gaelzer, F.J.R. Simões Jr., Dispersion relation for electrostatic waves in plasmas with isotropic and anisotropic Kappa distributions for electrons and ions. J. Plasma Phys. 83, 905830503 (2017). https://doi.org/10.1017/S0022377817000733
R. Gaelzer, M.C. de Juli, L.F. Ziebell, Effect of superthermal electrons on Alfvén wave propagation in the dusty plasmas of solar and stellar winds. J. Geophys. Res. 115, A09109 (2010). https://doi.org/10.1029/2009JA015217
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Shahzad, M.A., Aman-ur-Rehman, Mahmood, S. et al. Kinetic study of ion-acoustic waves in non-thermal Vasyliunas–Cairns distributed plasmas. Eur. Phys. J. Plus 137, 236 (2022). https://doi.org/10.1140/epjp/s13360-022-02463-7
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DOI: https://doi.org/10.1140/epjp/s13360-022-02463-7