Potential distribution around a test charge in a positive dust-electron plasma

Abstract

The electrostatic potential caused by a test-charge particle in a positive dust-electron plasma is studied, accounting for the dust-charge fluctuations associated with ultraviolet photoelectron and thermionic emissions. For this purpose, the set of Vlasov–Poisson equations coupled with the dust charging equation is solved by using the space–time Fourier transform technique. As a consequence, a modified dielectric response function is obtained for dust-acoustic waves in a positive dust-electron plasma. By imposing certain conditions on the velocity of the test charge, the electrostatic potential is decomposed into the Debye–Hückel (DH), wake-field (WF), and far-field (FF) potentials that are significantly modified in the limit of a large dust-charge relaxation rate both analytically and numerically. The results can be helpful for understanding dust crystallization/coagulation in twocomponent plasmas, where positively charged dust grains are present.

Keywords

dusty plasmas, dust charge fluctuations, positively charged dusty plasma, shielding and dynamical potentials

References

[1] T. Peter, Linearized potential of an ion moving through plasma, J. Plasma Phys. 44(02), 269 (1990)

[2] T. Peter and J. Meyer-ter-Vehn, Energy loss of heavy ions in dense plasma (I): Linear and nonlinear Vlasov theory for the stopping power, Phys. Rev. A 43(4), 1998 (1991)

[3] J. Neufeld and R. H. Ritchie, Passage of charged particles through plasma, Phys. Rev. 98(6), 1632 (1955)

[4] J. R. Sanmartin and S. H. Lam, Far-Wake structure in Rarefield plasma flows past charged bodies, Phys. Fluids14(1), 62 (1971)

[5] L. Chen, A. B. Langdon, and M. A. Lieberman, Shielding of moving test particles in warm, isotropic plasma, J. Plasma Phys. 9(03), 311 (1973)

[6] M. Nambu, S. V. Vladimirov, and P. K. Shukla, Attractive forces between charged particulates in plasmas, Phys. Lett. A 203(1), 40 (1995)

[7] S. V. Vladimirov and M. Nambu, Attraction of charged particulates in plasmas with finite flows, Phys. Rev. E 52(3), R2172 (1995)

[8] M. Salimullah and M. Nambu, Crystallization in a magnetized and inhomogeneous dusty plasma with streaming ions, J. Phys. Soc. Jpn. 69(6), 1688 (2000)

[9] M. Nambu, B. J. Saikia, and T. Hada, Wake potential around a test dust particulate in a magnetized plasma with streaming ions, J. Phys. Soc. Jpn. 70(5), 1175 (2001)

[10] M. Nambu, three-dimensional wake potential due to ion cyclotron waves in a flowing magnetized plasma, Phys. Scr. T98, 130 (2002)

[11] M. H. Nasim, Energy loss of charged projectiles in a dusty plasma, Ph.D. thesis, Quaid-i-Azam University, Islamabad, Pakistan, 1999

[12] H. Ikezi, Coulomb solid of small particles in plasmas, Phys. Fluids 29(6), 1764 (1986)

[13] J. H. Chu and I. Lin, Direct observation of Coulomb crystals and liquids in strongly coupled RF dusty plasmas, Phys. Lett. A 72(25), 4009 (1994)

[14] J. H. Chu, J. B. Du, and I. Lin, Coulomb solids and low-frequency fluctuations in RF dusty plasmas, J. Phys. D 27(2), 296 (1994)

[15] H. Thomas, G. E. Morfill, V. Demmel, J. Goree, B. Feuerbacher, and D. Möhlmann, Plasma crystal: Coulomb crystallization in a dusty plasma, Phys. Rev. Lett. 73(5), 652 (1994)

[16] Y. Hayashi and K. Tachibana, Observation of coulomb-crystal formation from carbon particles grown in a Methane plasma, Jpn. J. Appl. Phys. 33, L804 (1994)

[17] A. Melzer, T. Trottenberg, and A. Piel, Experimental determination of the charge on dust particles forming Coulomb lattices, Phys. Lett. A 191(3-4), 301 (1994)

[18] M. Nambu and H. Akama, Attractive potential between resonant electrons, Phys. Fluids 28(7), 2300 (1985)

[19] N. N. Rao and P. K. Shukla, Nonlinear dust-acoustic waves with dust charge fluctuations, Planet. Space Sci. 42(3), 221 (1994)

[20] J. X. Ma and P. K. Shukla, Compact dispersion relation for parametric instabilities of electromagnetic waves in dusty plasmas, Phys. Plasmas 1(5), 1506 (1995)

[21] R. K. Varma, P. K. Shukla, and V. Krishan, Electrostatic oscillations in the presence of grain-charge perturbations in dusty plasmas, Phys. Rev. E 47(5), 3612 (1993)

[22] P. K. Shukla, in: The Physics of Dusty Plasmas, edited by P. K. Shukla, D. A. Mendis, and V. W. Chow, Singapore: World Scientific, 1996

[23] F. Melandsc, T. Aslaksen, and O. Havnes, A new damping effect for the dust-acoustic wave, Planet. Space Sci. 41(4), 321 (1993)

[24] M. H. Nasim, P. K. Shukla, and G. Murtaza, Effect of dust charge fluctuations on energy loss of a test dust charged particulate in a dusty plasma, Phys. Plasmas 6(5), 1409 (1999)

[25] M. H. Nasim, A. M. Mirza, G. Murtaza, and P. K. Shukla, Energy loss of a test charge in dusty plasmas: collective and individual particle contributions, Phys. Scr. 59(5), 379 (1999)

[26] S. Ali, M. H. Nasim, and G. Murtaza, Effects of dust-charge fluctuations on the potential of an array of projectiles in a partially ionized dusty plasma, Phys. Plasmas 10(11), 4207 (2003)

[27] M. Horanyi, G. E. Morfill, and E. Griin, Mechanism for the acceleration and ejection of dust grains from Jupiter’s magnetosphere, Nature 363(6425), 144 (1993)

[28] O. Havnes, J. Trøim, T. Blix, W. Mortensen, L. I. Næsheim, E. Thrane, and T. Tønnesen, First detection of charged dust particles in the Earth’s mesosphere, J. Geophys. Res. 101(A5), 10839 (1996)

[29] V. E. Fortov, A. P. Nefedov, O. F. Petrov, A. A. Samarian, and A. V. Chernyschev, Particle ordered structures in a strongly coupled classical thermal plasma, Phys. Rev. E 54(3), R2236 (1996)

[30] A. A. Samarian, O. S. Vaulina, A. P. Nefedov, V. E. Fortov, B. W. James, and O. F. Petrov, Positively charged particles in dusty plasmas, Phys. Rev. E 64, 056407 (2001)

[31] M. Rosenberg and D. A. Mendis, UV-induced Coulomb crystallization in a dusty gas, IEEE Trans. Plasma Sci. 23(2), 177 (1995)

[32] P. K. Shukla and D. Resendes, Dust acoustic waves with dust charge fluctuations — revisited, Phys. Plasmas 7(5), 1614 (2000)

[33] P. K. Shukla, Dust acoustic wave in a thermal dusty plasma, Phys. Rev. E 61, 7249 (2000)

[34] S. Ghosh, Dust acoustic shock waves in two-component dusty plasma, New J. Phys. 5, 142 (2003)

[35] M. Horanyi, B. Walch, S. Robertson, and D. Alexander, Electrostatic charging properties of Apollo 17 lunar dust, J. Geophys. Res. 103(E4), 8575 (1998)

[36] C. K. Goertz, Dusty plasmas in the solar system, Rev. Geophys. 27(2), 271 (1989)

[37] G. L. Delzanno, G. Lapenta, and M. Rosenberg, Attractive potential around a thermionically emitting microparticle, Phys. Rev. Lett. 92(3), 350021 (2004)

[38] S. K. Paul, IJCIT 2, 25 (2012)

[39] P. K. Shukla and A. A. Mamun, Introduction to Dusty Plasma Physics, Bristol, U.K.: Institute of Physics Publishing Ltd., 2002

[40] M. Sodha and S. Guha, Physics of Colloidal Plasmas, Adv. Plasma Phys. 4, 219 (1971)

[41] M. Rosenberg, D. A. Mendis, and D. Sheenan, UV-induced Coulomb crystallization of dust grains in high-pressure gas, IEEE Trans. Plasma Sci. 24(6), 1422 (1996)

[42] S. A. Khrapak, A. P. Nefedov, O. F. Petrov, and O. S. Vaulina, Dynamical properties of random charge fluctuations in a dusty plasma with different charging mechanisms, Phys. Rev. E 59, 6017 (1999)

[43] D. B. Fried and S. D. Conte, The Plasma Dispersion Function, New York: Academic Press, 1961

[44] N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics, New York: McGraw-Hill, 1973

[45] X. G. Wang and Q. B. Luan, Low frequency Whistler waves excited in fast magnetic reconnection processes, Front. Phys. 8(5), 585 (2013)

[46] Z. H. Hu, M. D. Chen, and Y. N. Wang, Current neutralization and plasma polarization for intense ion beams propagating through magnetized background plasmas in a two-dimensional slab approximation, Front. Phys. 9(2), 226 (2014)

[47] D. Montgomery, G. Joyce, and R. Sugihara, Inverse third power law for the shielding of test particles, Plasma Phys. 10(7), 681 (1968)

[48] S. A. Khrapak and G. Morfill, Waves in two component electron-dust plasma, Phys. Plasmas 8(6), 2629 (2001)

[49] P. Debye and E. Hückel, The theory of electrolytes (I): Lowering of freezing point and related phenomena, Phys. Z. 24, 185 (1923)

[50] M. Rosenberg and P. K. Shukla, On beam-plasma interaction in a dust-electron plasma, IEEE Trans. Plasma Sci. 29(2), 202 (2001)

[51] P. K. Shukla and N. N. Rao, Coulomb crystallization in colloidal plasmas with streaming ions and dust grains, Phys. Plasmas 3(5), 1770 (1996)

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