Density-Step-Excited Ion Acoustic Solitons

Abstract

Highly nonlinear ion acoustic solitons are produced by the superposition of a 15\ Dwide photoionized plasma slab on a dc background. The Mach number increases with the initial step ratio R up to M » 1,95 for R « 10. Above M « 1.8, R^6, however, the profiles diffuse rapidly as they propagate. For Mach numbers M&1.8, a linear interaction is observed in the collision of two solitons traveling in opposite directions, whereas two solitions moving in the same direction exhibit a nonlinear interaction.A plasma composed of isothermal electrons and cold ions was first shown by Moiseev and Sagdeev 1 to be capable of supporting a symmetric solitary pulse, a soliton. Subsequent analysis of soliton formation and interaction, for small but finite amplitudes via the Korteweg-de Vries equation, was carried out by several authors. 2 " 5 Recently, large-amplitude solitons have been treated by computer numerical and simulation techniques. 6 " 9 Mason 7 has considered soliton formation from an initial slug of plasma (in close analogy with our experimental method). Further, soliton interactions have been considered for two important cases: (a) two solitons of different amplitude moving in the same direction with the larger catching up to the smaller, and (b) the collision of two oppositely directed solitons. Sakanaka 8 has considered case (a) with the assumption of isothermal electrons and warm ions. Using the fluid equations for cold ions and isothermal electrons, Biskamp and Parkinson 9 have treated cases (a) and (b). Ikezi et al}° have experimentally studied the reversible interactions in cases (a) and (b) for Mach numbers M% 1.2. The present experiment examines the formation of solitons with Mach numbers 1.24<M^1.95, and the interaction of solitons for Mach numbers up toM~1.8.Large-amplitude solitons were produced by the same technique as collisionless electrostatic shocks in this device, 11 i.e., by the superposition of a photoionized plasma slab on a dc background. The plasma slab, initially ~15A D (5 mm) wide, establishes an electric field which launches two solitonlike structures, symmetric about the original slab center, propagating in opposite directions. 7 The dc plasma was maintained by ionizing electrons emitted from an array of filaments distributed around the chamber periphery; and the photoplasma slab was obtained by collimating a l-/isec burst of photons from a vacuum spark. The minimum slab width was limited to 5 mm since narrower collimator widths did not result in appreciably narrower density profiles. Photon scattering from the collimator edges probably accounted for this lower limit. Photoplasma densities were on the order of 10 9 cm" 3 in a background argon pressure of 5x 10" 4 Torr. The electron temperature throughout the experimental volume was controlled between 1 and 4 eV by positive potentials applied to a secondary anode 11 ' 12 ; and the ion temperature was approximately 0.1 eV. Planar Langmuir probes were used to monitor the soliton structure, and all oscilloscope traces plot electron random current, pr...

A high resolution wave propagation scheme for ideal Two-Fluid plasma equations

“…These solutions are in the strongly nonlinear regime and hence cannot be described with a standard KdV equation. Similar structures have been observed experimentally [27]. Numerical simulations of density slug induced solitons were carried out by Baboolal [24] who assumed an isothermal electron fluid and an adiabatic ion fluid with adiabatic index c = 3.…”

Boundary conditions and numerical fluid modelling of time-evolutionary plasma sheaths

“…In one scenario, we create a flow towards the boundary by allowing a Gaussian 'slug' in the densities to expand freely, on the background level (12), i.e. with system centre x c we take the densities as…”

“…This can also occur with fluid models allowing for transfer terms due to collisions. Our particular choice of initial driving mechanism has, for instance, been used in experiments [12] and simulations [11,13] to generate soliton structures in similar models.…”

“…Thereafter, the entire non-linear structure decays smoothly, towards a steady state as indicated in figure 1(f ) corresponding to our particular choice of ionization rate. In a second scenario, we disturb the plasma of uniform densities (12), i.e. with no slug perturbation, by applying, e.g.…”

“…Such a sheath can be generated by applying a potential difference at the ends. For example, we set φ L = −2.0 and φ R = +2.0 with the same initial conditions as in (12). On the left boundary we apply the usual quadratic extensions as before, but on the right (x = L x ) we employ the Neumann conditions [14], ∂n e ∂x = ∂n i ∂x = 0, together with v e and v i obtained by quadratic extrapolation as before.…”