Ion acoustic shock wave propagation in plasma in the presence of non-uniform magnetic field

Document Type : Research Article


Department of Physics, Bojnourd Branch, Islamic Azad University, Bojnourd, Iran.


The propagation of nonlinear waves such as ion acoustic, electron acoustic, dust acoustic in the plasma media have been studied in different equilibrium and non-equilibrium conditions. Meanwhile, the study of these waves in magnetized plasmas, due to the effect of the external magnetic field on the plasma with different angles of wave propagation has been less addressed. There are extensive studies on the propagation of acoustic waves in magnetized plasma, which show that when the intensity of the magnetic field is constant, these waves propagate as soliton waves with a stable profile in the plasma. In fact, the uniform magnetic field does not interfere with the fluctuations of the plasma particles to produce dilute and dense regions and wave propagation, and for this reason, the harmonic soliton wave is propagated in the plasma. We know factors such as heating, particles collision and viscosity that cause perturbation in plasma particles fluctuations. In this situation, the propagation of the acoustic wave will no longer be in the soliton form and a shock wave may appear. On the other hand, we know that in actual conditions, the magnetic field governing laboratory plasmas such as tokamaks and also astrophysical and space plasmas are not constant at all. As a realistic example, the Earth's magnetic field intensity varies from 30000 nT in 0 (latitude): +60 (altitude) to 45000 nT in 10 (latitude): +90 (altitude), where the magnetic field is almost horizontal. Therefore it would interesting to study the presence of a non-uniform magnetic field. For this purpose, we considered an ion-electron magnetized plasma model and numerically investigate the ion acoustic wave behavior in this medium, while the strength of the magnetic field is not the same in different parts of the plasma. In this situation, for simplicity in calculations, we assume the direction of the magnetic field to be constant. We use the second order Runge-Kutta method and by numerically solving the basic equations of the ion acoustic wave, it is shown that the stable behavior of the solitonic wave is perturbed in the presence of varying magnetic field and in this case, the wave propagates as a shock wave. Now we can introduce the non-uniform magnetic field along with factors such as viscosity, heating, collision etc. as the new sources of producing the acoustic shock waves in plasmas. We also studied the cases where the collisional terms and gyro frequencies of the particles are considered. In this condition, the effects of the non-uniform magnetic field are different. This subject can also be considered for other acoustic waves in different temperature and density models, various non-thermal plasmas and other features in astrophysical and laboratory plasmas.


Main Subjects

Andersen, H. K., D’Angelo, N., Michelsen, P., & Nielsen, P. (1967). Investigation of Landau-damping effects on shock formation. Phys. Rev. Lett., 19(4), 149-151.
Biskamp, D. (1973). Collisionless shock waves in plasmas. Nucl. Fusion, 13 (5). 719-740.
Casanova, M., Larroche, O., & Matte, J. P. (1991). Kinetic simulation of a collisional shock wave in a plasma. Phys. Rev. Lett., 67 (16). 2143-2146.
Chan, C., Khazei, M., Lonngren, K. E., & Hershkowitz, N. (1981). Excitation of multiple ion‐acoustic shocks. Phys. Fluids 24, (8), 1452-1455.
Hu, P. N. (1972). Collisional Theory of Shock and Nonlinear Waves in a Plasma. Physics of Fluids, 15 (5). 854–864.
Keilhacker, M., Kornherr, M., Steuer, K. H, (1969). Observation of collisionless plasma heating by strong shock waves. Zeitschrift für Physik A Hadrons and nuclei, 223(4). 385–396.
Laedke, E. W., & Spatschek, K. H. (1982). Nonlinear ion‐acoustic waves in weak magnetic fields. Phys. Fluids 25, 985 (6), 985-989.
Li, F. O., & Havnes, O. (2001). Shock waves in a dusty plasma. Phys. Rev. E, 64 (6). 066407 –6.
Luo, Q. Z., D’Angelo, N., & Merlino, R. L. (1999). Experimental study of shock formation in a dusty plasma. Phys. Plasmas 6, (9). 3455-3458.
Luo, Q. Z., D’Angelo, N., & Merlino, R. L. (2000). Ion acoustic shock formation in a converging magnetic field geometry. Phys. Plasmas 7, (6). 2370-2373.
Mandea, M., & Korte, M. (2011). Geomagnetic Observations and Models, IAGA Special Sopron Series Vol. 5, edited by M. Mandea and M. Korte (Springer, British Geological Survey, 2011).
Misra A. P., Adhikary N.C., & Shukla P. K. (2012). Ion-acoustic solitary waves and shocks in a collisional dusty negative-ion plasma. Phys. Rev. E, 86 (5). 056406.
Nakamura, Y., Bailung, H., & Shukla, P.K. (1999). Observation of Ion-Acoustic Shocks in a Dusty Plasma. Phys. Rev. Lett., 83 (8).1602-1605.
Niu, K. (2009). Shock waves in gas and plasma. Laser and Particle Beams, 14 (10). 125 – 132.
Pakzad, H.R. (2010). Kadomstev–Petviashvili (KP) equation in warm dusty plasma with variable dust charge, two-temperature ion and nonthermal electron. Pramana, J. Phys., 74(4). 605-614.
Pakzad, H.R. (2011). Dust acoustic shock waves in plasmas with strongly coupled dusts and superthermal ions. Can. J. Phys., 89(2). 193-200.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P., & Metcalf, M. (1996). Numerical Recipes in Fortran 90., Vol. 2, (Cambridge University Press).
Sagdeev, R. Z. (1966). in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 4, 23–91.
Shah, A., & Saeed, R. (2009). Ion acoustic shock waves in a relativistic electron–positron–ion plasmas, Phys. Lett. A, 373(45). 4164-4168.
Washimi, H., & Taniuti, T. (1966). Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett., 17 (19). 996-998.
Yashvir, Bhatnagar, T. N., & Sharma, S. R. (1984). Nonlinear ion-acoustic waves and solitons in warm-ion magnetized plasma. Plasma Physics and Controlled Fusion, 26, (11), 1303-1310.
Yu, M. Y., Shukla, P. K., & Bujarbarua, S. (1980). Fully nonlinear ion-acoustic solitary waves in a magnetized plasma. Phys. Fluids, 23(10). 2146-2147.