Configurational temperature in dusty plasmas

The temperature of a dust ensemble in a dusty plasma is one of its most fundamental properties. Here, we present experiments using the configurational temperature as a for the temperature analysis in dusty plasmas. Using a model of the particle interactions, the configurational temperature allows us to determine the temperature of the dust ensemble from measurements of the particle positions, rather than particle velocities. The basic concept will be presented and the technique is applied to two-dimensional finite clusters as well as three-dimensional data from an extended dust cloud. Additionally, the configurational temperature can be used to derive the particle charge and the screening length from a comparison with the standard kinetic temperature.

Figure 1

(a) Experiment to confine a flat microparticle structure under gravity conditions. The field-of-view from a top-view camera covers all particles. An inverted measurement image is shown below the setup. (b) Symmetric discharge to confine a three-dimensional dust cloud under microgravity conditions. Four cameras observe a common field-of-view to retrieve the three-dimensional particle positions. An inverted measurement image is shown below the setup.

Figure 2

Configurational temperature map over a grid of different particle charges $Q$ and screening lengths ${\lambda }_{\mathrm{s}}$. The solid black line shows the contour of the surface at the kinetic temperature $T=800\mathrm{K}$ used in the simulation.

Figure 3

The plot shows curves in the $Q\text{−}{\lambda }_{\mathrm{s}}$ plane that yield the parameters of the simulated dust cluster. The dashed line represents the results from the mode analysis, the two solid lines are obtained by setting $T_{\mathrm{conf}}^{\mathrm{ind}}(Q,\lambda )=800\mathrm{K}$ and $T_{\mathrm{conf}}^{\mathrm{c}}(Q,\lambda )=800\mathrm{K}$. The crossmark is placed at the actual simulation parameter position (${\lambda }_{\mathrm{s}}=500\mu \mathrm{m}$ and $Q=12100e$). The dashed horizontal line indicates the mean interparticle distance.

Figure 4

Residual $x$ component of the force $F_x$ of particles as a function of distance from the cluster center in $x$ direction in a simulated dust cluster. The mean position of two particles are indicated by black circles and their respective forces are highlighted. It can be seen that the mean positions, where the particles are supposed to be in an equilibrium state, can be modeled well by a linear fit.

Figure 5

Residual $x$ component of the force $F_x$ of particles as a function of distance from the cluster center in $x$ direction in a measured dust cluster. The mean position of two particles are indicated by black circles and their respective forces are highlighted. The mean positions of the particles can not be modeled by a single linear fit (dashed line). Instead, a linear fit is made with every particle's mean position which is indicated for two particles by the two solid lines.

Figure 6

The cluster temperature is shown depending on the neutral gas pressure. The blue squares indicate the kinetic temperature with error bars, the yellow circles represent the mode temperature values.

Figure 7

${\lambda }_{\mathrm{s}}\left(Q\right)$ functions for a measured dust cluster at $p=8.2\mathrm{Pa}$. The solid curve is retrieved by intersecting the configurational temperature surface at the measured kinetic temperature of $493\mathrm{K}$. The thick dashed line is obtained from the mode analysis of the cluster. The thin dashed line indicates the measured mean interparticle distance.

Figure 8

The different ${\lambda }_{\mathrm{s}}\left(Q\right)$ curves are obtained from a dust cluster under different neutral gas pressures. The pressure is color-coded and increases from blue to yellow color just as in Fig. 9. The function values using the nearest-neighbor distances between the particles as a measure for ${\lambda }_{\mathrm{s}}$ are highlighted by squares.

Figure 9

The particle charge dependence on the neutral gas pressure. The color of the markers reflect the pressure accordingly.

Figure 10

Configurational temperature of central particles in a cuboid volume, depending on the total thickness of this volume.

Figure 11

Kinetic temperature in a section through a large dust cloud. The $x$ and $y$ positions of about 3000 detected particles from a single frame are shown as black dots. On the right side one can identify the particle free region in the center of the discharge (compare to Fig. 1).

Figure 12

Configurational temperature of a volumetric measurement in a dust cloud. The solid line indicates the ${\lambda }_{\mathrm{s}}\left(Q\right)$ function at a given temperature of $9540\pm 2450\mathrm{K}$.