[Show abstract][Hide abstract] ABSTRACT: Lagrangian variables are used to describe both surface and volume nonlinear oscillations of spatially bounded plasmas. Simple exact, or nonperturbative, solutions can often be obtained for complicated problems. Here, several recent analytical results on nonlinear standing waves in bounded systems are reviewed. These include temperature effects on nonlinear standing waves, oscillations of expanding multi-species plasma, and phase locking and transition to chaos. The analytical solutions are in good agreement with that from particle-in-cell simulation. The exact solutions are also useful as starting point and verification for novel perturbation or numerical schemes, as well as stability analysis. They are of particular interest with respect to electromagnetically trapped nonneutral as well as freely expanding plasmas.
Physica Scripta 04/2006; 2004(T113):9. DOI:10.1238/Physica.Topical.113a00009 · 1.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An analytical model for breathing oscillations in a nonuniform non-neutral plasma slab is developed. The plasma is relatively small and warm with the smallest dimension only of several Debye lengths. Nonuniformity in the equilibrium results in a frequency shift associated with pressure and boundary effects. The plasma size and temperature, being related to the frequency shift, can therefore be evaluated from frequency measurements. In particular, for small nonuniform plasmas the frequency of the breathing mode is twice that predicted by the cold fluid theory. Nonlinear oscillations are also considered and the pressure is shown to have an important effect on the dynamics. Analytical solutions for linear and nonlinear oscillations are obtained and compared with that from one-dimensional particle-in-cell simulations. Good agreement is found.
[Show abstract][Hide abstract] ABSTRACT: Lagrangian variables are used to describe linear and nonlinear oscillations of a magnetized non-neutral plasma slab in a harmonic trap, for slab width larger or comparable to the Debye length. The plasma particles move along the magnetic field lines, so that the oscillations are one-dimensional. The oscillation spectrum is found analytically, and the thermal corrections to the frequencies are calculated in a nonperturbative manner. Simple exact nonlinear solutions for the low-order modes are also obtained.
Physics of Plasmas 01/2003; 10:1239-1242. DOI:10.1063/1.1569488 · 2.14 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An analytical model for nonlinear volume oscillations in a bounded cold plasma is developed. Although here the familiar propagating wave solutions do not exist, exact nonlinear standing waves subject to appropriate boundary conditions can nevertheless be found. The behaviors of the electrons and ions are described self-consistently in terms of Lagrangian variables. The analytical solutions are compared with that from particle-in-cell simulations. Good agreement is found in the regimes of interest.
[Show abstract][Hide abstract] ABSTRACT: A non-neutral plasma column in an asymmetric trapping field is considered in this paper. It is shown that nonlinearly interacting bulk plasma oscillations and quadrupole surface waves allow an exact analytical description. The absence of symmetry leads to nonintegrability and other nonlinear phenomena, such as passage through different resonances and phase locking. These phenomena should be observable in experiments involving elliptical traps and rotating walls and can affect the latters' applications.
[Show abstract][Hide abstract] ABSTRACT: In several experiments atom-like dust clusters with parabolic confining potential were observed [1–3]. Here we present a general theory of 2D clusters confined by (1/2)m dω02r2 potential with arbitrary pair interaction potential depending on the inter-dust distance. It describes the equilibrium conditions, normal modes, their frequencies and possible instabilities of clusters with arbitrary N number of grains. The mono-layer clusters can have 2N frequencies of oscillations in the cluster plane among which 3 modes are trivial (ω = 0 and double degenerate frequency of oscillation in the potential well). The 2N - 3 non-trivial modes are considered. For example, for square dust cluster with potential V(r) the equilibrium is described by ω02 = −(4/m) [V′(2R) + V′(2R)], the frequency of radial oscillations is ω2 = (16R2/m) [V″(2R) + 2V″(2R)], the two single modes frequencies are ω2 = (32R2/m)V″(2R); ω2 = (16R2/m)V″(2r) and one double degenerated mode frequency is ω2 = (1/m) [V′2R) − V′(2R) + 4R2V″(2R)] where ′ corresponds to the differentiation of the potential V(r) with respect to r. The general stability criterion was found and investigated for N ⩾ 4. The pair interaction potential V(r) is considered as a sum of different attraction and repulsion terms , including that which describe the non-screened collective and non collective attraction, the screened non-Coulomb interaction and the non-screened repulsion. The collective non-screened potential causes the absence of equilibria at certain dust cluster sizes. For screened Coulomb potential Vc(r) = (Zd2e2αscr/r)exp(−r/λscr) the clusters with the size R are considered. The pentagon cluster is found to be stable for R < 3.3λscr and the clusters with N ⩾ 6 are found to be always unstable. The measurements of the frequencies of the cluster modes, the thresholds of cluster equilibria and the stability of the clusters can be used for detection of the dust-dust interactions and for comparison of the theory of 2D dust clusters and the observations.
[Show abstract][Hide abstract] ABSTRACT: A monolayer dusty crystal can be observed in the glow discharge. In particular, a small number of dusty grains form simple atom-like plane clusters. Stability and oscillations of the polygonal cluster are considered. For the simplest stable clusters normal displacements and frequencies are found for an arbitrary form of mutual interaction. The measurement of these modes can help to give in detail the form of the potential function.
[Show abstract][Hide abstract] ABSTRACT: It is shown that inhomogeneous heating of the dust grain by ion flow in a glow discharge results in a photophoresislike force. According to our estimations, this radiometric force can be comparably-valued with the ion-drag force under the conditions of microgravity dusty plasma experiments.
[Show abstract][Hide abstract] ABSTRACT: A uniform density ellipsoid is an equilibrium state of a low-energy non-neutral plasma confined in a harmonic trap. Normal modes of this plasma can be detected; they provide a nondestructive diagnostic tool. The low-order quadrupole modes are particularly simple. They can be calculated analytically even in a nonlinear regime. In general, nonlinear coupling leads to the complicated stochastic dynamics. In special cases, regular solutions can be found. It is shown that the behavior of an elongated ellipsoid oriented along the trap symmetry axis is nearly integrable. The study results in simple analytical expressions for frequencies and ellipsoid semiaxes.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 08/2000; 62(1 Pt B):1215-23. DOI:10.1103/PhysRevE.62.1215 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The stability of polygonal patterns composed of a set of N point charges in a potential well is studied. It is shown that a right polygon is stable for N
Physical Review A 04/1999; 59(4):3098-3100. DOI:10.1103/PhysRevA.59.3098 · 2.81 Impact Factor