Condensation instability modes in dusty space and laboratory plasmas

A. Kopp, P. K. Shukla, B. Eliasson and Yu. Shchekinov†
Theoretische Physik IV, Ruhr-Universität Bochum, 44780 Bochum, Germany
†Department of Physics, University of Rostov, Rostov on Don, 344090, Russia
Abstract. In magnetized plasmas containing charged dust impurities, we study radiation condensation instabilities of lowfrequency
compressional electromagnetic waves. A new dispersion relation is derived and numerically analysed. For applications
to tokamak edges, we study the influence of charged dust grains on the growth rate of the instability and demonstrate
with numerical simulations how such an instability could work in the interstellar medium.
Keywords: dusty plasmas – multi-fluid – magnetohydrodynamics – interstellar medium
PACS: 52.30 Ex – 52.65 Kj – 98.38.Cp
Heating and cooling are fundamental processes in astrophysical as well in laboratory plasmas [1]. Of particular interest is the
radiation condensation (RC) instability, which was first discussed in the classical studies by [2] and [3]. It occurs in so different
scenarios as the solar corona [3], in the interstellar medium (ISM) [4], in the inner coma of a comet [5], or in tokamaks, where
so-called MARFEs (multifaceted asymmetric radiation from the edge) form [6, 7]. In laboratory plasmas [7, 8] as well as in the
ISM [9, 10], dust grains play an essential role.
A multifluid picture for dusty plasmas as first presented by [11, 12] was extended by [13] and used for the numerical simulation
code DENISIS [14] for a plasma consisting of dust, electrons, neutrals and ions. On this basis, [15] and [16] studied the RC mode
in dusty plasmas, [17] in addition took self-gravitation into account, [18] studied the RC in tokamak edges. In order to apply this
model to the ISM, we use the cooling rates by [19], which were considered by [20] in their famous cooling function, the heating,
in which the dust plays an important role, was formulated by [21]. We first review the results by [18] and then turn to numerical
simulations in the framework of a multifluid picture with application to the interstellar medium.
The plasma invesitigated here consists electrons (index e), ions (index i) and negatively charged dust (index d) and a neutral
component (index n). The dust charge number, Zd (note that Zd > 0 corresponds to negatively charged dust), is taken to be
constant. Moreover, we assume the dust as well as the neutrals to represent an immobile background, i.e. the dust velocity, ~vd,
and that of the neutrals,~vn. vanish. The equilibrium state (index 0) is homogeneous and at rest, the magnetic field points into the
z-direction of a Cartesian coordinate system, i.e. ~B0 = B0 ˆz. The plasma is quasineutral, so that the particle number densities fulfil
the condition
ni0−ne0−Zdnd0 = 0. (1)
The equilibrium densities are chosen in such a way that heating, H, and cooling by radiative losses, C, balance each other, so
that the energy loss function, L = H −C, vanishes.
This system is now perturbed (index 1, which is omitted in the velocities) perpendicular to the magnetic field (index ?), i.e.
in x and y-direction, where we consider low frequency waves on times scales, where the motion of dust and neutrals can be
neglected. If w is the frequency of these waves, we require |w|ne wce with ne being the electron collision frequency and
wce = eB0/(mec) the electron gyro frequency (e and me are charge and mass.

We performed numerical simulations in the framework of a multifluid picture. The numerical code is a further development
of DENISIS [14]. The consider an ISM with a degree of ionisation of 0.01 and a temperature around 7000K. The initial state is
homogeneous, where temperature and densities are chosen in such a way that heating and cooling are balanced. If we increase
the density at the origin (x = 0, y = 0) of a Cartesian coordinate system, the cooling should predominate in Eq. (19), and the
resulting lower temperature should increase the density, so that the system becomes unstable as derived above. That this can be
actually the case is illustrated in Figure 1, which shows the evolution of the electron temperature and density in the left and right
panel, respectively. All quantities are given in normalised units. These first results clearly show that the RC instability works in
principle: the perturbation leads to an (initially) exponentially growing cooling of the electrons in connection with an increase
in the density until a new stable state with a temperature of a few 10K is achived. This simulations demonstrate, how structure
forming in the ISM could work, more detailed and elaborated studies will follow.
ACKNOWLEDGMENTS
This work was supported by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 591 entitled “Universal
Behavior of Plasma far from Equilibrium: Heating, Transport, and Structure Formation”.
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