No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

The full text of this article is not currently available.

Chaoticity threshold in magnetized plasmas: Numerical results in the weak coupling regime

### Abstract

The present paper is a numerical counterpart to the theoretical work [Carati et al., Chaos 22, 033124 (2012)]. We are concerned with the transition from order to chaos in a one-component plasma (a system of point electrons with mutual Coulomb interactions, in a uniform neutralizing background), the plasma being immersed in a uniform stationary magnetic field. In the paper [Carati et al., Chaos 22, 033124 (2012)], it was predicted that a transition should take place when the electron density is increased or the field decreased in such a way that the ratio ω p /ω c between plasma and cyclotron frequencies becomes of order 1, irrespective of the value of the so-called Coulomb coupling parameter Γ. Here, we perform numerical computations for a first principles model of N point electrons in a periodic box, with mutual Coulomb interactions, using as a probe for chaoticity the time-autocorrelation function of magnetization. We consider two values of Γ (0.04 and 0.016) in the weak coupling regime Γ ≪ 1, with N up to 512. A transition is found to occur for ω p /ω c in the range between 0.25 and 2, in fairly good agreement with the theoretical prediction. These results might be of interest for the problem of the breakdown of plasma confinement in fusion machines.

© 2014 AIP Publishing LLC

Received 11 July 2013
Accepted 29 January 2014
Published online 12 February 2014

Lead Paragraph:
One of the most relevant open problems of plasma physics, particularly in connection with the operation of fusion machines, is the breakdown of magnetic confinement. Catastrophic events, called disruptions, occur when density exceeds a certain limit, and no general agreement seems to exist for an explanation.^{2} It is even under discussion, at a phenomenological level, on which parameters should the density limit depend, whether on the plasma current or on the imposed magnetic field (see Ref. 3, Fig. 6). In the work,^{1} the attention was restricted to the role of the imposed magnetic field *B*, and theoretical indications were given that a bold chaoticity involving all single electrons should take place for large enough electron density *n* _{ e } or small enough field *B*. In fact, the chaoticity border was predicted to be given by the relation (in Gauss units)(1)where *m* is the electron and *c* the speed of light, while **ω** _{ p } and **ω** _{ c } are the familiar plasma and cyclotron frequencies, to be defined later. In Ref. 1, it was also shown that law (1) fits pretty well a large set of experimental data for disruptions in actual fusion machines.The main idea leading to (1) as a chaoticity threshold for the motions of the electrons is as follows. Ordered gyrational motions induced by the field obviously prevail when the mutual interactions among the electrons are negligible, i.e., for small densities. On the other hand, perturbation increases with increasing density. Indeed the main perturbation is due to so-called microfield, namely, the sum of the Coulomb forces acting on each electron and due to all the other ones. This is a highly fluctuating quantity, whose typical intensity *E* was estimated long ago by Iglesias *et al.* ^{4} to be given, for a one–component plasma at temperature *T* and electron density *n* _{ e }, by(2)where *k* _{ B } is the Boltzmann constant. Thus, a threshold should occur when the microfield and the Lorentz force balance, i.e., when one has(3)where denotes transverse part. Using , with (2) and , this leads for the threshold to the condition (1), apart from a numerical factor of order 1.In the present paper, the results of numerical computations in the weak coupling regime are reported, which appear to confirm the theoretical prediction (1).

Acknowledgments:
The present paper is dedicated to Francesco Guerra (La Sapienza University at Rome) on the occasion of his seventieth birthday.

Article outline:

I. INTRODUCTION
II. THE MODEL AND ITS NUMERICAL IMPLEMENTATION
III. THE NUMERICAL RESULTS
IV. CONCLUSIONS

/content/aip/journal/chaos/24/1/10.1063/1.4865255

http://aip.metastore.ingenta.com/content/aip/journal/chaos/24/1/10.1063/1.4865255

Article metrics loading...

/content/aip/journal/chaos/24/1/10.1063/1.4865255

2014-02-12

2016-10-24

Full text loading...

###
Most read this month

Article

content/aip/journal/chaos

Journal

5

3

Commenting has been disabled for this content