K. Avinash1, S. J. Kalita2, R. Ganesh2, and P. Kaur21- Department of Physics, Sikkim University, Gangtok, Sikkim 737102, India2- Institute for Plasma Research, Bhat, Gandhinagar, 382428 Gujrat, IndiaAbstractIt is shown that the dust density regimes in dusty plasma are characterized by two complementary screening processes (a) the low dust density regime where the Debye screening is the dominant process and (b) the high dust density regime where the Coulomb screening is the dominant process. The Debye regime is characterized by a state where all dust particles carry an equal and constant charge. The high-density regime or the “Coulomb plasma” regime is characterized by (a) “Coulomb screening” where the dust charge depends on the spatial location and is screened by other dust particles in the vicinity by charge reduction (b) “quark” like asymptotic freedom where dust particles, which on an average carry minimal electric charge ( 0 d q ) , are asymptotically free (c) uniform dust charge density and plasma potential (d) dust charge neutralization by a uniform background of hot ions. Thus, the Coulomb plasma is essentially a one-component plasma (OCP) with screening as opposed to electron plasma which is OCP without screening. Molecular dynamics (MD) simulations verify these properties. The MD simulations are performed, using a recently developed Hamiltonian formalism, to study the dynamics of Yukawa particles carrying variable electric charge. A hydrodynamic model for describing the collective properties of Coulomb plasma and its characteristic acoustic mode called the “Coulomb acoustic wave” is given.
), with all N diagonal elements iib equal to unity. The matrix A can be inverted to give the solution of Eq. (31) as X = A-1B which then gives the values of N dust charges
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As can be appreciated, solving N-coupled nonlinear algebraic equations or N-coupled linear algebraic equations of the present model is computationally much simpler than solving a set of N-coupled nonlinear partial differential equations of the fully nonlinear model in Eq. (19) and (20). The YPVC model thus provides a computationally simple and a feasible method of simulating especially the Coulomb limit of dusty plasma. Thus in our model we solve Eq. (28) or (30) along with equations of motion in Eq. (21) and (22) to study the dynamical evolution of the system. In the next section, we construct a molecular dynamics simulation code based on the YPVC model. The results of this simulation will be compared with the corresponding fluid theory in Eq.(29). Next, we discuss the normalization scheme used in our simulations.The simulation is performed in a cubical box of dimension L and volume V. The box containes N dust particles 19 at given locations i.e., the
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.....3,2,1 at time t. The thi particle carries a normalized electric charge i . The velocity of the thi particle at time, is given by v = iv In our simulations, we solve the charging Eq. (28) or (30) along with equations of motion of N dust particles. These equations are given by Nijijdijsjdisididrrrrddrdtrdm/exp22 , Ni......3,2,1 (32). In these equations, we have eliminated pi from Eq. (27). The total energy of the system E, which is the sum of the potential and the kinetic energy, is a constant of motion given by the Hamiltonian H given in Eq. (21). In our simulations we use following normalization scheme. All lengths will be normalized by a which is the mean particles distance given by 3/14/3dna where dn is the global particle density given by VNnd/ and time is normalized by 2/122/Taqmd which is the typical time scale of particle motion. In terms of these units we have dn =3/4, dddccaa/1,/,/ .
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The normalized equations to be solved in simulations are Nijijrjciieiremmij2311ln21ln41 Ni,.....3,2,1 (33). In the Debye regime these equations are non linear in i while in the the Coulomb regime where i << 1 these equations reduce to a set of linear equations given by 20 , Nijijrjcieiremmij231ln41 , Ni,.....3,2,1 (34). The normalized equations of motion are given by Nijijrjiciirerdtrdij4229 Ni,.....3,2,1 (35). The total energy of N particles in normalized units is given by NiiiciKvE12221ln21612 (36), where tdrdvi/ . These equations are solved for given value of P which is determined by choosing appropriate values of c , d , the mass ratio eimm/ and given values of the positions ir and the velocities
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