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On the dispersion relation for the Buneman instability in spherically confined plasmas

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Plasma Physics and Controlled Fusion
Authors:
Johannes Gruenwald at Gruenwald Laboratories
Johannes Gruenwald
  • Gruenwald Laboratories
Catalin Teodorescu
Catalin Teodorescu
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Abstract and Figures

In this paper an analytically derived dispersion relation for the Buneman instability in spherically confined plasmas is presented. The calculations are based on plasmas with spherical symmetry in which the dependence of the dispersion relation is, thus, only radial. This article is supposed to give a solution for said dispersion relation as this has not been done for such a peculiar geometry. On the other hand, new research on electrostatic confinement fusion schemes shows that there are physical effects that are strongly connected with such instabilities in spherical plasma devices and have, hence, to be taken into account in order to get a proper scientific understanding of the underlying mechanisms.
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On the dispersion relation for the Buneman
instability in spherically confined plasmas
J Gruenwald
1
and C Teodorescu
2
1
Gruenwald Laboratories, Taxberg 50, A-5660 Taxenbach, Austria
2
American Institutes for Research, 1000 Thomas Jefferson St. NW, Washington, DC 20007, United States
of America
E-mail: jgruenwald@gmx.at
Received 26 September 2018, revised 24 November 2018
Accepted for publication 13 December 2018
Published 22 January 2019
Abstract
In this paper an analytically derived dispersion relation for the Buneman instability in spherically
confined plasmas is presented. The calculations are based on plasmas with spherical symmetry in
which the dependence of the dispersion relation is, thus, only radial. This article is supposed to
give a solution for said dispersion relation as this has not been done for such a peculiar geometry.
On the other hand, new research on electrostatic confinement fusion schemes shows that there
are physical effects that are strongly connected with such instabilities in spherical plasma devices
and have, hence, to be taken into account in order to get a proper scientific understanding of the
underlying mechanisms.
Keywords: instabilities, electrostatic confinement fusion, dispersion relation
(Some figures may appear in colour only in the online journal)
1. Introduction
Since the early works of Buneman and Farley [1–3]a lot of
investigations on the two stream instability in various plasmas
have been done [4–6]. However, the scientific works related
to the dispersion relation of the Farley–Buneman instability
were focused only on Cartesian geometries and no con-
siderations have been given to the derivation of a dispersion
relation in spherically confined plasmas. This has been done
despite the fact that the Farley–Buneman instability plays a
role in stars or the ionosphere of planets, which, of course, is
also shell of a hollow sphere [3]. A more recent example of
the occurrence of the Buneman instability in stars is, e.g. the
work by Gogoberidze et al [7]. Furthermore, taking into
account such spherical shapes has been found necessary in
recent work on electrostatic confinement fusion devices [8],
where a saturated Buneman instability was identified experi-
mentally. The instability in this work was excited in a sphe-
rical cathode with high electrical potential where the
frequency saturated and became independent of the ion mass.
Work on such a saturation of this instability has been done by
Ishihara et al in great detail [9], but again only in flat geo-
metry. This paper aims at deriving a dispersion relation for the
Buneman instability in spherically confined plasmas, which
can not only be found in inverted fireballs (FBs)or electro-
static confinement fusion devices but also in stars. Hence, this
investigation has importance in many fields of plasma phy-
sics, such as astrophysics, fusion science and technology and
low temperature plasma physics.
2. The model
It is known from measurements in spherically confined, non-
magnetized low temperature plasmas, so-called inverted FBs)
that the density profiles of electrons are independent on the
angles and, taking also into account the constant plasma
potential in such structures, this also holds for the ion density
profile due to quasineutrality [10,11]. Measured charge
density profiles have exhibited a Gaussian shape that is
determined by the density of electrons and ions at the
center n
c
:
nr nr n rexp . 1
ei ei ecic,, , 2
g¢= ¢» - ¢
() () · ( ) ()
Plasma Physics and Controlled Fusion
Plasma Phys. Control. Fusion 61 (2019)035007 (7pp)https://doi.org/10.1088/1361-6587/aaf949
0741-3335/19/035007+07$33.00 © 2019 IOP Publishing Ltd Printed in the UK1
... Since the first works on inverted fireballs (IFBs) were published in 2011 [1,2] several papers focussing on instabilities and basic plasma parameters in IFBs followed [3][4][5][6][7][8][9]. However, since 2014 a number of works have been devoted to the application of IFBs in PECVD deposition processes [10][11][12][13]. ...
... The first parameters that were measured were the radial profiles of the electron density n e as shown in Fig As can be seen in Fig. 2 the major part of n e follows an exponential decay towards the edge of the IFB. This is to be expected as this is the usual behaviour of the charge density in IFBs [3,8,9]. However, there is a distinct jump in the density close to the centre of the fireball plasma. ...
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