A Two-Fluid Approach to Study the Dynamics of Finite Size Plasmas

A non-relativistic cold electrostatic model incorporating a two-fluid approach has been investigated to study the behavior of normal modes motivated by microdroplet plasmas [1]. Particularly, for a finite-size plasma medium, the behavior of normal modes is expected to differ from those in an infinite plasma medium [2, 3] due to the inhomogeneous plasma edge. For our study [5], we used a package of Flux Corrected Transport (FCT)[4] algorithm, and we found that even a small perturbation in the charge density causes concentrated oscillations at the plasma’s edge. Although the simulation breaks down when the oscillations become too sharp, it provides a useful estimate of wave-breaking time even when the initial electrostatic field is below the wave-breaking limit [2,3]. Our study shows that wave breaking via phase mixing happens primarily due to the density gradient in the plasma edge and, therefore, occurs earlier with a sharper density gradient. Also, the dissipative effects, such as diffusion, are observed to relax the sharp structures in the density profiles.

[1] Anand, M., Gibbon, P. and Krishnamurthy, M., 2007.  Europhysics Letters, 80(2), p.25002.

[2] Dawson, John M.  Physical review 113.2 (1959): 383.

[3] Davidson, R. W. C., and P. P. J. M. Schram.  Nuclear Fusion 8.3 (1968): 183.

[4] Boris, J. P., Landsberg, A. M., Oran, E. S., & Gardner, J. H. (1993). (No Title).

[5] Bag, Subhasish, Vikrant Saxena, and Amita Das. arXiv preprint arXiv:2404.06786 (2024).