Abstract
In this paper, we have presented a comprehensive review of electron trapping in quantum plasmas. We have begun by giving a brief introduction of electron trapping in classical plasmas and then derived the expression of number density of trapped electrons for non-relativistic and relativistically degenerate cases and quantizing magnetic field. We have obtained the expression for Sagdeev potential for all these cases and explored the variation of solitary structures with the important plasma parameters. We have also derived the equations for drift ion acoustic and pure drift waves for spatially nonuniform quantum magnetoplasmas both in collisionless and collisional plasmas. The fundamental differences in trapping in classical and quantum plasmas have been enunciated in detail. The applications of the work in ultra-strong laser plasma interactions and white dwarf stars have also been pointed out.
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References
H. Abbasi, N. Tsintsadze, D. Tskhakaya, Influence of particle trapping on the propagation of ion cyclotron waves. Phys. Plasmas 6(6), 2373–2379 (1999)
S. Ali, P. Shukla, Streaming instability in quantum dusty plasmas. Eur. Phys. J. D 41(2), 319–324 (2007)
S. Ali et al., Linear and nonlinear ion-acoustic waves in an unmagnetized electron-positron-ion quantum plasma. Phys. Plasmas 14(8), 082307 (2007)
L. Ang, T. Kwan, Y. Lau, New scaling of Child-Langmuir law in the quantum regime. Phys. Rev. Lett. 91(20), 208303 (2003)
M. Ayub, H. Shah, M. Qureshi, Trapping effects in a self-gravitating quantum dusty plasma. Phys. Scr. 84(4), 045505 (2011)
S. Balberg, S.L., Shapiro, The properties of matter in white dwarfs and neutron stars. arXiv preprint astro-ph/0004317 (2000a)
Balberg, S., Shapiro, S.L., The properties of condensed matter in white dwarfs and neutron stars. In: Handbook of elastic properties of solids, liquids, and gases. 4. (2000b)
I.B. Bernstein, J.M. Greene, M.D. Kruskal, Exact nonlinear plasma oscillations. Phys. Rev. 108(3), 546 (1957)
D. Bohm, A suggested interpretation of the quantum theory in terms of" hidden" variables. I. Phys. Rev. 85(2), 166 (1952)
D. Bohm, D. Pines, A collective description of electron interactions: III. Coulomb interactions in a degenerate electron gas. Phys. Rev. 92(3), 609 (1953)
M. Cameron, Notes on the Burgers Equation (University of Maryland, 2011)
G. Chabrier, F. Douchin, A. Potekhin, Dense astrophysical plasmas. J. Phys. Condens. Matter 14(40), 9133 (2002)
S. Chandrasekhar, XLVIII. The density of white dwarf stars. Lond. Edinb. Dublin Philos. Mag. J. Sci. 11(70), 592–596 (1931)
P. Chatterjee et al., Effect of ion temperature on arbitrary amplitude ion acoustic solitary waves in quantum electron-ion plasmas. Phys. Plasmas 16(4), 042311 (2009)
A.-L. Chian, Effect of ion dynamics on relativistic nonlinear plasma oscillations. Plasma Phys. 24(1), 19 (1982)
J. Daniel, T. Tajima, Outbursts from a black hole via alfvén wave to electromagnetic wave mode conversion. Astrophys. J. 498(1), 296 (1998)
V. Demchenko, I. El-Naggar, On hybrid resonances in non-homogeneous magneto-active plasma. Physica 58(1), 144–160 (1972)
L. Demeio, Quantum corrections to classical BGK modes in phase space. Transport Theory Stat. Phys. 36(1–3), 137–158 (2007)
W. Dwarfs, N. Stars, The Physics of Compact Objects (Wiley, 1983)
B. Eliasson, P. Shukla, The formation of electrostatic shocks in quantum plasmas with relativistically degenerate electrons. EPL (Europhysics Letters) 97(1), 15001 (2011)
A. Fayyaz et al., Nonlinear drift ion acoustic waves in degenerate plasmas with adiabatic trapping. Phys. Scr. 95(4), 045609 (2020a)
A. Fayyaz et al., Coupled drift ion acoustic shock waves with trapped electrons in quantum magnetoplasma. Phys. Scri. 95(8), 085602 (2020b)
G. Fontaine, P. Brassard, The pulsating white dwarf stars. Publ. Astron. Soc. Pac. 120(872), 1043 (2008)
S. Ghosh, G. Lakhina, Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas. Nonlinear Process. Geophys. 11(2), 219–228 (2004)
P. Goldreich, W.H. Julian, Pulsar electrodynamics. Astrophys. J. 157, 869 (1969)
A. Gurevich, Distribution of captured particles in a potential well in the absence of collisions. Sov. Phys. JETP 26(3), 575–580 (1968)
F. Haas, Quantum Plasmas: An Hydrodynamic Approach, vol. 65 (Springer Science & Business Media, 2011)
F. Haas, S. Mahmood, Nonlinear ion-acoustic solitons in a magnetized quantum plasma with arbitrary degeneracy of electrons. Phys. Rev. E 94(3), 033212 (2016)
F. Haas, G. Manfredi, M. Feix, Multistream model for quantum plasmas. Phys. Rev. E 62(2), 2763 (2000)
Q. Haque, H. Saleem, Ion acoustic vortices in quantum magnetoplasmas. Phys. Plasmas 15(6), 064504 (2008)
H. Haug, S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific Publishing Company, 2009)
M. Iqbal et al., Nonlinear density excitations in electron-positron-ion plasmas with trapping in a quantizing magnetic field. Phys. Plasmas 24(1), 014503 (2017)
I.U.R.L.V. Klimontovich, Concerning the Spectra of Systems of Interacting Particles (US Atomic Energy Commission, 1952)
D. Koester, G. Chanmugam, Physics of white dwarf stars. Rep. Progress Phys. 53(7), 837 (1990)
H. Kuehl, C. Zhang, Effect of ion drift on arbitrary-amplitude ion-acoustic solitary waves. Phys. Fluids B Plasma Phys. 3(3), 555–559 (1991)
L. Landau, E. Lifshitz, Statistical physics Pergamon (Elsevier, 1980)
N.C. Lee, C.R. Choi, Ion-acoustic solitary waves in a relativistic plasma. Phys. Plasmas 14(2), 022307 (2007)
M. Leontovich, Reviews of Plasma Physics (Springer Science & Business Media, 2012)
A. Luque, H. Schamel, Electrostatic trapping as a key to the dynamics of plasmas, fluids and other collective systems. Phys. Rep. 415(5–6), 261–359 (2005)
A. Luque, H. Schamel, R. Fedele, Quantum corrected electron holes. Phys. Lett. A 324(2–3), 185–192 (2004)
J.H. Luscombe, A.M. Bouchard, M. Luban, Electron confinement in quantum nanostructures: self-consistent Poisson-Schrödinger theory. Phys. Rev. B 46(16), 10262 (1992)
S. Mahmood, W. Masood, Electron acoustic solitary waves in unmagnetized two electron population dense plasmas. Phys. Plasmas 15(12), 122302 (2008)
S. Mahmood, A. Mushtaq, Quantum ion acoustic solitary waves in electron–ion plasmas: a Sagdeev potential approach. Phys. Lett. A 372(19), 3467–3470 (2008)
A. Mamun, Effects of ion temperature on electrostatic solitary structures in nonthermal plasmas. Phys. Rev. E 55(2), 1852 (1997)
G. Manfredi, How to model quantum plasmas. Fields Inst. Commun. 46, 263–287 (2005)
G. Manfredi, M. Feix, Theory and simulation of classical and quantum echoes. Phys. Rev. E 53(6), 6460 (1996)
G. Manfredi, P.-A. Hervieux, Autoresonant control of the many-electron dynamics in nonparabolic quantum wells. Appl. Phys. Lett. 91(6), 061108 (2007)
P.A. Markowich, C.A. Ringhofer, C. Schmeiser, Semiconductor Equations (Springer Science & Business Media, 2012)
W. Masood, Obliquely propagating low frequency electromagnetic shock waves in two dimensional quantum magnetoplasmas. Phys. Plasmas 16(4), 042314 (2009a)
W. Masood, Drift ion acoustic solitons in an inhomogeneous 2-D quantum magnetoplasma. Phys. Lett. A 373(16), 1455–1459 (2009b)
W. Masood et al., Coupled nonlinear drift and ion acoustic waves in dense dissipative electron-positron-ion magnetoplasmas. Phys. Plasmas 16(11), 112302 (2009)
W. Masood, N. Jehan, A.M. Mirza, A new equation in two dimensional fast magnetoacoustic shock waves in electron-positron-ion plasmas. Phys. Plasmas 17(3), 032314 (2010)
W. Masood et al., A nonlinear model for magnetoacoustic waves in dense dissipative plasmas with degenerate electrons. Phys. Plasmas 21(10), 102311 (2014)
F.C. Michel, Theory of pulsar magnetospheres. Rev. Mod. Phys. 54(1), 1 (1982)
S. Mola, G. Manfredi, M. Feix, Expansion of a quantum electron gas. J. Plasma Phys. 50(1), 145–162 (1993)
A. Mushtaq, A. Qamar, Parametric studies of nonlinear magnetosonic waves in two-dimensional quantum magnetoplasmas. Phys. Plasmas 16(2), 022301 (2009)
A. Mushtaq, H. Shah, Study of non-Maxwellian trapped electrons by using generalized (r, q) distribution function and their effects on the dynamics of ion acoustic solitary wave. Phys. Plasmas 13(1), 012303 (2006)
Y. Nejoh, Double layers, spiky solitary waves, and explosive modes of relativistic ion-acoustic waves propagating in a plasma. Phys. Fluids B Plasma Phys. 4(9), 2830–2840 (1992)
P. Norreys et al., Intense laser-plasma interactions: new frontiers in high energy density physics. Phys. Plasmas 16(4), 041002 (2009)
J.A. Orosz et al., An optical precursor to the recent X-ray outburst of the black hole binary GRO J1655–40. Astrophys. J. Lett. 478(2), L83 (1997)
J.P. Ostriker, Recent developments in the theory of degenerate dwarfs. Annu. Rev. Astron. Astrophys. 9(1), 353–366 (1971)
D. Pines, Quantum plasma physics. J. Nucl. Energy Part C Plasma Phys. 2(5), 5 (1961)
L. Pitaevskii, E. Lifshitz, Physical kinetics, vol. 10 (Butterworth-Heinemann, 2012)
A. Pointon, Introduction to Statistical Physics (Longman, London and New York, 1980)
H. Ren et al., Electrostatic drift modes in quantum dusty plasmas with Jeans terms. Phys. Plasmas 16(10), 103705 (2009)
R. Sagdeev, M. Leontovich, Reviews of Plasma Physics (Consultants Bureau New York, 1966)
O. Sah, J. Manta, Nonlinear electron-acoustic waves in quantum plasma. Phys. Plasmas 16(3), 032304 (2009)
A. Saha, B. Pradhan, S. Banerjee, Bifurcation analysis of quantum ion-acoustic kink, anti-kink and periodic waves of the Burgers equation in a dense quantum plasma. Eur. Phys. J. plus 135(2), 1–13 (2020)
B. Sahu, R. Roychoudhury, Electron-acoustic solitary waves and double layers in a relativistic electron-beam plasma system. Phys. Plasmas 11(5), 1947–1954 (2004)
B. Sahu, R. Roychoudhury, Electron acoustic solitons in a relativistic plasma with nonthermal electrons. Phys. Plasmas 13(7), 072302 (2006)
H. Shah, M. Qureshi, N. Tsintsadze, Effect of trapping in degenerate quantum plasmas. Phys. Plasmas 17(3), 032312 (2010)
H. Shah et al., Effects of trapping and finite temperature in a relativistic degenerate plasma. Phys. Plasmas 18(10), 102306 (2011)
H. Shah et al., Effect of trapping in a degenerate plasma in the presence of a quantizing magnetic field. Phys. Plasmas 19(9), 092304 (2012)
H. Shah, W. Masood, Z. Ali, Adiabatic trapping in coupled kinetic Alfvén-acoustic waves. Phys. Plasmas 20(3), 032301 (2013)
H. Shah et al., Drift solitary structures in inhomogeneous degenerate quantum plasmas with trapped electrons. Astrophys. Sp. Sci. 350(2), 615–622 (2014)
B. Shokri, S. Khorashady, Pramana (2003). https://doi.org/10.1007/BF02704506
B. Shokri, A. Rukhadze, Quantum surface wave on a thin plasma layer. Phys. Plasmas 6(9), 3450–3454 (1999a)
B. Shokri, A. Rukhadze, Quantum drift waves. Phys. Plasmas 6(12), 4467–4471 (1999b)
P.K. Shukla, B. Eliasson, Recent developments in quantum plasma physics. Plasma Phys. Control. Fusion 52(12), 124040 (2010a)
P.K. Shukla, B. Eliasson, Nonlinear aspects of quantum plasma physics. Phys. Usp. 53(1), 51 (2010b)
P. Shukla, B. Eliasson, Colloquium: Nonlinear collective interactions in quantum plasmas with degenerate electron fluids. Rev. Mod. Phys. 83(3), 885 (2011)
P.K. Shukla, L. Stenflo, New drift modes in a nonuniform quantum magnetoplasma. Phys. Let. A 357(3), 229–231 (2006)
N. Shukla et al., Ion streaming instability in a quantum dusty magnetoplasma. Phys. Plasmas 15(4), 044503 (2008)
P. Shukla, A. Mamun, D. Mendis, Nonlinear ion modes in a dense plasma with strongly coupled ions and degenerate electron fluids. Phys. Rev. E 84(2), 026405 (2011)
H. Siddiqui, H. Shah, N. Tsintsadze, Effect of trapping on vortices in plasma. J. Fusion Energy 27(3), 216–224 (2008)
R. Silvotti et al., Search for p-mode oscillations in DA white dwarfs with VLT-ULTRACAM-I. Upper limits to the p-modes. Astron. Astrophys. 525, A64 (2011)
V.O. Strasser, Relativistic arbitrary-amplitude electrostatic solitons in a plasma. Phys. Rev. E 53(5), 5194 (1996)
N.-D. Suh, M.R. Feix, P. Bertrand, Numerical simulation of the quantum Liouville-Poisson system. J. Comput. Phys. 94(2), 403–418 (1991)
Tsintsadze, L.N. Quantization and excitation of longitudinal electrostatic waves in magnetized quantum plasmas. In: AIP Conference Proceedings, vol 1306 (American Institute of Physics, 2010), pp. 89
N. Tsintsadze, E. Tsikarishvili, Parametric instabilities in relativistic plasma. Astrophys. Sp. Sci. 39(1), 191–199 (1976)
N. Tsintsadze, D. Tskhakaya, On the theory of electrosound waves in a plasma. Sov. Phys. JETP 72, 480 (1977)
N. Tsintsadze et al., Nonlinear screening effect in an ultrarelativistic degenerate electron-positron gas. Phys. Plasmas 16(11), 112307 (2009)
Tyshetskiy, Y.O., Vladimirov, S., Kompaneets, R. Unusual physics of quantum plasmas. Boпpocы aтoмнoй нayки и тexники, (2013)
H. Van Horn, Dense astrophysical plasmas. Science 252(5004), 384–389 (1991)
M.A. Wahab, Solid State Physics: Structure and Properties of Materials (Alpha Science Int’l Ltd., 2005)
J. Weiland, Collective Modes in Inhomogeneous Plasmas: Kinetic and Advanced Fluid Theory (CRC Press, 1999)
D. Winget, S. Kepler, Pulsating white dwarf stars and precision asteroseismology. Annu. Rev. Astron. Astrophys. 46, 157–199 (2008)
E. Witt, W. Lotko, Ion-acoustic solitary waves in a magnetized plasma with arbitrary electron equation of state. Phys. Fluids 26(8), 2176–2185 (1983)
M. Yahia, I. Azzouz, W. Moslem, Quantum effects in electron beam pumped GaAs. Appl. Phys. Lett. 103(8), 082105 (2013)
M. Yalabik et al., Quantum mechanical simulation of charge transport in very small semiconductor structures. IEEE Trans. Electron Devices 36(6), 1009–1013 (1989)
M. Zobaer et al., K-dV and Burgers’ equations on DA waves with strongly coupled dusty plasma. Astrophys. Sp. Sci. 346(2), 351–357 (2013)
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Masood, W., Shah, H.A. & Qureshi, M.N.S. Trapping in quantum plasmas: a review. Rev. Mod. Plasma Phys. 6, 11 (2022). https://doi.org/10.1007/s41614-022-00072-6
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DOI: https://doi.org/10.1007/s41614-022-00072-6