1-D PIC Simulation of Localized Langmuir Field Structures

Induced by Sharp Density Gradients

K.D.Kang, M.D.McFarland, and A.Y.Wong

Department of Physics, University of California, Los Angeles, California 90024

 Abstract

Experimental measurements[1] show that the relative intensity of spiky field structures driven by a cold electron beam correlates with the reciprocal of the density gradient scale length. In this work one dimensional PIC(Particle-In-Cell) simulation is performed to analyze the interaction of beam-driven electrostatic waves with a sharp density gradient to compare with the experimental results. The simulation parameters are selected to closely match the experimental situation. The ratio of beam density to plasma density is about h=n_b/n_p ~1%, where n_b is the beam density and n_p is the background plasma density. Beam velocity parameters, v_b,drift=30v_th, v_b,th=0.5v_th, are chosen to simulate the cold electron beam, (DKE_beam/KE_beam)^1/2 << h^1/3. The zero order density function, n_po(z), is chosen to

where n_top is the plasma density at the top of gradient, Dn_p is the difference between the high density and low density regions, and z_c is the center location of the density gradient. The density gradient scale length is defined as L_c= n_top/( ¶ n_po/¶ z) evaluated at the inflection point.

The simulation are done using the BEPS1(Bounded 1D Electrostatic Particle Simulation) code[2] which has been modified for beam injection at the left boundary and beam absorption at the right boundary. 1280 beam particles and 128000 plasma particles are used in the simulations which run typically for 90 plasma periods(w_po^-1) with time step Dt of 0.2w_po^-1.

The simulation results show that the spiky field structures develop at the transition region between high plasma density and low plasma density as measured in the experiment. When the ES waves interact with a sharp, downward-going density gradient which has a scale length on the order of L~l_ES the spiky structures reach their largest amplitude and sharpest definition. The average of the electric field intensity and the background plasma density is shown in Fig. 1. Analysis of the spiky field structures evident in 1(a) and 1(b) reveals a standing wave pattern produced by the interaction of the forward traveling wave with a backward wave produced by reflections at the sharp density gradient. When the gradient is steep the reflected wave is strong producing the large spiky structures and as the gradient is reduced beyond L~4l_ES the reflected wave is weak and the structures do not form. The beam phase space diagram and the time history of beam velocity distribution function will also be discussed to demonstrate the kinetic effects of the beam-plasma interaction.

Fig.1 E²(upper plot) and n_po(z)/n_top(lower plot) vs axial position. Fig (a) is for L@ l_ES, (b) is for

L@ 2l_ES, (c) is for L@ 4.5l_ES, while in (d) the gradient is flat.

References

[1] M.D.McFarland, and A.Y.Wong, submitted to Physical Review Letters.

[2] V.K.Decyk, and J.M.Dawson, J. Comput. Phys., 30, 407 (1979); V.K.Decyk, and J.E. Slottow, Comput. Phys., March, 50 (1989).