Buneman Instability, Pierce Instability, and Double-Layer Formation in a Collisionless Plasma

Abstract

Instabilities and double-layer formation are systematically investigated on a bounded collisionless system with electron beam penetrating through a plasma. The Buneman instability is observed at low beam currents. Above a critical current, there appears a sudden nonoscillatory potential drop due to the Pierce instability, which traps ions in the potential well. This collisionless ion trapping provides a new formation mechanism of the double layer, which is controlled by changing the speed of the potential drop.The Buneman instability (electron-ion twostream instability)' has been expected to be one of the most effective heating mechanisms in a current-carrying plasma. " To our knowledge, however, no clear-cut experiment on this instability has been published, except our preliminary report. It is a strong convective instability, and boundary effects are quite important for experiments on the instability. There are two types of boundary: a periodic boundary and a boundary of electron-beam injection. The former corresponds to the torus experiment of Hamberger and Jancarik, ' in which the spectrum of fluctuations was analyzed and the anomalous resistivity was said to be attributed to the Buneman instability. The latter situation was first realized by Nezlin etal. ' They observed unstabj. e oscillations and a virtual cathode due to the Pierce instability, ' although their theory is not suitable to the experiment as will be shown later. On the other hand, laminar' and turbulent' double layers were observed under this situation, where trapped electrons were, respectively, supplied externally and produced by the turbulent electron-electron two-stream instability. Trapped ions were also pointed out to be important for the double-layer formation. The mechanism of their initial production, however, was not explained clearly. In this Letter, we identify the Buneman instability in an electron beam-plasma system under a reasonable consideration of the boundary effect, and demonstrate a subsequent potential drop due to the Pierce instability, which provides a new mechanism of double-layer formation based on collisionless ion trapping. The dispersion equation in an infinite plasma with beam electrons is given by k'[1 -~,'/((u-kV)' -(u, .'/(u']+ k D' = 0, where kD (= &u, /v, ) is the Debye wave number of plasma electrons; U and v, are the electron-beam 3 3 MbL/m U I I (b), PI BI

Time-resolved measurements of double layer evolution in expanding plasma

“…Other instabilities, e.g., the Pierce instability, may trap ions in a narrow strongly varying potential and form a laminar DL. 41 Once formed, the charge separation of the DL can persist without the presence of the Pierce instability since the charge distribution of a DL is one of the solutions of the BGK equation. Ion-acoustic driven DLs, characterized by an ion hole on the low potential side and a potential difference equal to or less than the electron temperature, 42 are also observed to coincide with the existence of ion acoustic instabilities in computer simulations.…”

Numerical simulations on ion acoustic double layers

“…Furthermore, tlt^re are several laboratory experiments which succeeded in observing formation of double layers [Torven and babic, 1976;Torven and Anderson, 1979;Quon and Wong, 1976;Coakley and hershkowitz, 1979;Iizuka,et al, 1979].…”

Experimental Evidence of a Double Layer in a Large Volume Helicon Reactor

“…Since in situ measurements are difficult and costly in space, much of the current knowledge on DLs has been guided by laboratory experiments [7][8][9][10], theoretical work [8,11], and computer simulation [12 -14]. Historically, experimental regimes have fallen into two main categories, namely, double or triple plasma devices, which are voltage driven [15,16], and current driven discharges with an abrupt change in diameter [17], where the common thread was the requirement of an artificially induced current to drive the DL.…”