Complex (Dusty) Plasmas – A new field of research under microgravity conditions

 

Plasmas (hot ionised gases) are sometimes referred to as the “fourth state of matter”. They are also the most disordered state. A “complex plasma” is a common electron/ion plasma enriched with microparticles (particles of µm size) [1, 2]. The different components of a complex plasma interact in many ways, in particular the continuous flux of electrons and ions to the particles’ surface leads to a net charge (see Figure 1). Due to the much higher mobility of the electrons, compared to that of the ions the charge is negative – typically thousands of elementary charges – provided secondary electron emission and photoemission are negligible. The microparticles are one of the components of the complex plasma – albeit a very heavy one – and their negative charge is screened by the spatial rearrangement of the positive ions. If the density of the microparticles in the plasma is sufficiently high they can interact via screened Coulomb forces. In the case that the Coulomb energy of two neighbouring particles, W_C, is larger than the thermal energy of the particles, W_th, the complex plasma is strongly coupled. The most interesting discovery in the last few years was the experimental proof the Coulomb interaction can be very strong and the complex plasma may undergo a transition from a disordered gaseous to the fluid and crystalline phase – the so called “plasma crystal” [3–8]. For this to happen, . G is the so-called Coulomb coupling parameter and is a measure of a reciprocal temperature. To describe the thermodynamics of complex plasmas a second parameter is needed, the so-called lattice parameter  [9]. k is a measure of the separation distance of the microparticles, D, normalised by the Debye screening length l_D.

 

Figure 1: A complex plasma consisting of electrons, ions and micronsized particles. The microparticles are exposed to the plasma and obtain a charge on their surface. This charge is highly negative and leads to a reorganisation of the surrounding plasma and a screening of the particles’ charge, mainly by ions.

The complex plasma has special properties:

1.      The micrometer-sized particles forming the liquid or crystalline state, respectively, are separated by tenths of mm and can be monitored individually. This allows plasma observations at the most elementary – the kinetic level – for the first time, giving the possibility to investigate the dynamics of the system in an unprecedented way. We expect many new insights into crystalline or fluid behaviours, especially phase transitions, and into plasma physics.

2.      Due to the relatively high mass of the microparticles, compared to that of the ions and electrons, the relevant time scales are slowed down. This opens up the possibility to perform measurements of plasma processes with a comparatively high time resolution – this is of paramount interest for plasma physics.

3.      The microparticles can be controlled and manipulated easily, e.g. with light pressure [10] or electromagnetic fields [11]. This makes it possible to perform active experiments, e.g. shock formation in complex plasmas, wave propagation etc., but it also promises application possibilities, e.g. in the manufacture of complex materials.

Gravity plays an important role in the formation of complex plasmas. The microparticles sediment due to their relatively high mass, compared to that of the ions, and have to be electrostatically levitated. This is possible only in  a small vertically limited region above the lower electrode of the experimental setup, in the plasma sheath. On the positive side, this opens up the possibility to study monolayers and small 3-dimensional systems in the laboratory. For example, we have investigated the interaction of single particles through head-on collisions [12, 13], the formation of molecules and small clusters by increasing the number of interacting microparticles step by step [14], we studied larger 2-dimensional crystals and their transition to the liquid and gaseous phases [6, 7], etc.

Under microgravity conditions larger 3-dimensional systems can be formed and investigated in much weaker electric fields than those necessary for the levitation on the ground. Since these fields have a strong influence on the formation of plasma crystals, we initiated a research program on complex plasmas under microgravity conditions in 1994, shortly after the discovery of plasma crystals in the laboratory. Since then we performed four parabolic flight campaigns and two sounding rocket experiments [15].

The overview of experiments under gravity and microgravity conditions presented in this paper will highlight the model character of a complex plasma and show its worth for fundamental physics. On the other hand complex plasmas are very interesting from an application point of view [16, 17]. For example, it is possible to grow nanoparticles in plasmas that may have special surface or volume properties. These particles can be extracted and used for e.g. catalysis or they can be deposited directly on surfaces leading to special coatings or they can be embedded in wafers while depositing amorphous silicon and so on. The latter has recently created a great deal of interest in the production of so-called polymorphous solar cells [18]. These solar cells, produced using “complex plasma technology”, have significantly higher efficiency and apparent no degradation with illumination, when compared to the commonly used amorphous solar cells - at comparable cost.

 

Most scientific experiments are performed in a low temperature radiofrequency (rf) discharge, although other plasmas (e.g. dc discharge, inductive, combustion [19, 20]) have also been used already. A typical sketch of an rf-system is shown in Figure 2. The plasma is excited between the two electrodes and the particles are injected into the plasma through a specially designed particle dispenser. The particles that are used in our experiments are monodispersive particles from Melamine-Formaldehyde in the micrometer range. In the plasma the particles are charged and levitated in the sheath of the lower electrode. The microparticles are illuminated with a laser and the reflected light is observed at 90° by a CCD-camera.

 

Figure 2: Typical sketch of an rf-parallel plate discharge. The plasma is excited between two electrodes. Microparticles are injected through a dispenser mounted as a piston into one of the electrodes. The microparticles are illuminated by a sheet of laser light perpendicular to the electrode surface and the scattered light is observed in 90° by a CCD-camera. The field of view of an overview camera is shown in the sketch. Laser and optics can be moved in the y-direction to obtain particle positions in 3-D.

 

The determination of the interaction potential of charged particles that are embedded in a plasma is of fundamental importance in the physics of complex plasmas. It plays a role in astrophysics, in planetary magnetospheres, ionospheres, lightning as well as colloid physics and plasma technology. This potential is determined by the influence of the particle charge on the surrounding plasma and vice versa. The plasma influence on the particle interaction, for instance, changes the effectiveness of coagulation processes and, it determines the collective behaviour of plasma crystal structure and dynamics, which have received great attention in recent years. To describe these physical mechanisms (and others) in a complex plasma, the potential around a single dust particle is normally assumed to be a screened Coulomb potential, as mentioned above:

                                                                                                                  (1)

with an effective charge Q [9] and a screening length l_D. To obtain an experimental input into this long-standing problem, we investigated head on collisions between two microparticles in the sheath of an rf-Argon discharge [12, 13]. Analogous to the nuclear collision experiments it can be shown that it is possible to calculate the interaction potential between two microspheres from their trajectories during head on collisions. For the plasma conditions used in these experiments the interaction potential is in agreement with a screened Coulomb potential over the studied parameter range (see Fig. 3). 

Figure 3: The interaction energy between two colliding particles in the sheath of an rf-discharge dependent on their relative distance. The solid line is a fit to a screened Coulomb potential.

 

Further it is shown that head on collisions can be used to calculate an effective charge as well as a screening length for the particle interaction with high accuracy, and they can be used to determine the neutral gas friction and the shape of the confining potential (see Fig. 4). In the experimental configuration used, the latter is parabolic. Of considerable interest in the future will be the quantitative deviations of derivations from this screened Coulomb potential (e.g. for larger particles, aspherical particles, extended parameter range). In addition, particle trajectory analysis of particles with different sizes and densities may provide an attractive direct probe method to study the spatial properties of plasma sheaths in detail.

Figure 4: The confining potential measured from single particle oscillations. The solid line is a fit to a parabolic potential.

The next step in the investigation of complex plasmas is the study of small 2-D Coulomb clusters formed in the measured parabolic potential in the sheath of an rf-discharge [14]. By adding single particles, step by step, and waiting for the system to attain thermal equilibrium, we were able to analyse the formation of clusters of particles, starting with binaries, triangles, then pentagons, hexagons and septagons, as well as larger systems, including the details of closed shell structures and the formation of new shells. The structures of the small microparticle Coulomb clusters are shown in Figure 5. An obvious feature from the observations is the tendency to form circular configurations in contrast to the typical hard-sphere configurations that are mainly triangular. 

Figure 5: Experimental data of the structure of 2-D Coulomb clusters consisting of 1-19 particles.

 

Comparison of the experimental data with numerical simulations (using screened Coulomb potentials) described elsewhere [14] show good agreement. Hence, complex plasmas may be used as experimental model systems for investigating cluster physics at the kinetic level. Of particular interest, too, is the transition from clusters to 2-D crystals. One would expect that the circular confining potential provided by a ring on the lower electrode will imprint a circular geometry on the outer perimeter of the system. This is indeed what happens in larger “clusters” – the outer shells tend to be circular while the center shows hexagonal structure. The transition from circular to hexagonal geometry  is provided by dislocation chains as can be seen in Fig. 6.

 

Figure 6: The transition from 2-D clusters to monolayers with 948 particles. Shown is the triangulation of the experimental data. Non-sixfold symmetries are marked with different colors (5-fold: blue, 7-fold: red, 8-fold: green).

  

Moving from 2-D systems to 3-D, it is possible (in principle) to analyse the lattice structure of plasma crystals by measuring the particle positions exactly in three dimensions. Since 1994, when plasma crystals where observed for the first time in experiments [3-5], there have been many publications about the crystal structure and phase transitions [7, 8]. However, due to constraints imposed by gravity it had not been possible to “manifacture” 3-D plasma crystals with more than ~10 horizontal layers. Recently, some advances have been made by careful plasma chamber design and we would like to report on new 3-D plasma crystals observations [21]: The crystal consists of 19 horizontal lattice planes (19 layers normal to the Z-axis). The 3-D particle coordinates in the whole crystal are directly measured. The particle number per unit length in vertical direction, as well as the total number of particles in each layer is presented in Fig. 7. We clearly see that the distribution of particles in each layer is rather narrow, so that we can easily distinguish neighbouring planes. The particle density in a given plane increases the closer the plane is to the lower electrode, so that the interparticle distance in a lattice plane decreases from the top to the bottom (see Fig. 7). It follows also from Fig. 7 that the thickness of the layers diminishes to the bottom. Thus, layers become more and more compressed by the particles above, and the coupling between particles in each layer increases. This provides a high ordering of particles in the lower and medium layers (see Fig. 8 b,c) with just a few dislocations. Particles in the upper layer are comparatively disordered (see Fig. 8 a). Note, the interplane distance changes rather slowly in z direction and attains a minimum in the lower part of the crystal (see Fig. 7).  

Figure 7: Particle number statistics of a 19 layer plasma crystal. The solid line shows the histogram of the particle distribution in the vertical direction, and the symbols mark the number of particles in each layer.

 

The detailed analysis of the 19-layer plasma crystal, containing about 16,000 particles shows a mixture of fcc and hcp structure, respectively, distributed in “domains” exhibiting no apparent layer structural order within the observed volume. The relative distribution (fcc/hcp) is 3/2. The first step to determine the lattice type in any local region of the crystal is to superpose three consecutive horizontal layers. By doing that it is found that only two types of symmetry (and their mixture) coexist in the crystal. Figure 9 illustrates these two cases. The particle positions of the three consecutive layers are marked in green (third layer, A), blue (second layer, B), and red (first layer, C). Triangulation is shown for the third (upper) plane. Comparison with ideal lattices shows that the sample in Fig. 9a obviously represents an hcp lattice. The sample in Fig. 9b corresponds either to fcc or bcc type with the (111) lattice plane parallel to the electrode. Further analysis presented elsewhere [21] – the 3-D pair correlation function and a rotation of the system through the Euler-angle to the (100) crystal direction - show that this structure is fcc. 

 

 

Figure 8: Three layers of the plasma crystal from the top (left), middle (middle) and bottom (right) of the crystal. Shown is a Voronoi-analysis with non-sixfold symmetries marked in different greyscales.

 

Figure 9: Three consecutive horizontal layers of the plasma crystal marked with different symbols showing hcp (a) and fcc (b) structures.

 

The inhomogeneous structure found in the 3-D experiment shows the influence of gravity on the complex plasma. Gravity introduces a preferred direction as well as shear forces to the plasma crystal, leading to the observed higher order in the lower planes and low order in the top planes. Hence, to understand and avoid the effects of gravity we performed experiments on parabolic flights and sounding rockets [15].

The experiments use a symmetrically driven rf-discharge as shown already in Fig. 2. The particles are injected into the plasma through a specially designed dispenser incorporated in one of the electrodes. They are charged in a fraction of a second and then interact with each other via their screened Coulomb potentials and with the global electrical field. A typical distribution of microparticles under microgravity conditions can be seen in Fig. 10. Here, the trajectories of the individual particles forming the complex plasma are followed, color-coded from red at the beginning of the trajectory to blue at its end (following the rainbow colors). The figure shows the particle motion between the two rf-electrodes – observed is only a quarter of the total field and this is mirrored for a better understanding of the geometry. The centre of the system is particle free. In the absence of gravity, microspheres can in principle be embedded in the main plasma, where the major bulk forces - electric fields, QE, thermophoresis, F_th, density gradients F_gr, ion drag, F_i, and neutral drag, F_n – are much smaller. F_th and F_i are directed outwards, QE and F_gr into the main plasma, and F_n is a friction force slowing the particles down. In the main plasma, the ion drag force is due to subsonic drifts, v_i, governed by collisions with neutrals at the rate n_in. Throughout the subsonic ion drift regime of the main plasma we get the interesting result that the ratio of the bulk forces for a particle at rest is

 

       ½ F_i/QE ½ = 8.06 × 10^-12 (n_i/P_mbT₃₀₀) a_mf_e º x                       (2)

 

i.e. it depends only on neutral gas pressure (P_mb in millibar), ion temperature (in units of 300 K), ion density (cm^-3) and particle size a_m (in microns). f_e is the cross section enhancement due to ion-microsphere Coulomb collisions. Hence for particles in the micron size range, it should be possible under microgravity conditions to adjust the system to be largely force free (x = 1) provided F_th and F_gr can be kept small. If (2) is smaller than unity, the microspheres will then aggregate in the main plasma under the external confining force QE, and can thus then be controlled easily. For the conditions of Fig. 10 equation (2) is larger than unity, leading to the void in the centre.

The second information that can be drawn from Figure 10 is that the particles in the outer part of the cloud show a convective type of motion. This might be due to the fact that the ions are moving outwards from the centre along the electrical field. The strength of the field is weaker in the radial direction compared to the axial direction. This leads to a net force on the particle cloud and a collective motion in the outer part.  In the central part of the cloud the structure is very stable and no collective motion could be observed. For this stable part we made a 3-dimensional analysis of the particle positions by moving the laser sheet and the optics (CCD-camera) in depth as in the experiment described above. The 3-D particle positions projected into the X-Z plane are shown in Figure 11. The particles form layers parallel to the electrode in the lower part of the cloud but lose symmetry towards the centre. This could indicate that the nucleation of the crystallisation occurs close to the electrodes and then spreads over the total volume. From laboratory experiments we found that crystallisation takes some minutes - which were not available in the sounding rocket experiment. 

 

Decreasing the rf-plasma power could decrease the size of the void in the centre in Fig. 10. This leads to the following changes:

·        The plasma density (electron and ion density) is decreased – as a consequence the screening length increases, which in turn results in a larger particle separation.

·        The  plasma potential is decreased – this leads to a weaker electric field from the centre towards the electrodes and therefore to a weaker ion drag force on the microparticles.

By decreasing the rf-power more and more we were able to fill the whole void with particles, that means that equation (2) became <1. But at the same time an instability occurred, which produced a cyclic motion of the particles towards and away from the centre with a frequency of 1.5 Hz. A possible cause of this instability might be electron depletion, i.e. the effect, that the microparticles diminish the density of the electrons by a factor , where n_e is the electron density and n_p is the microparticle density. From the single particle experiments discussed at the beginning we know that the charge Q on a microparticle can be very high, up to 10⁴ e^-. For a particle density of about n_p ~ 10⁵/cm³  this would imply that practically all electrons (for a typical electron density of  10⁹/cm³) would be located on the microparticles. To sustain the rf-discharge, however, free electrons are required. If these are removed (onto the particles) the plasma production is stopped. The system adjusts by expelling microspheres from some region (creating a “void”), where upon the plasma production can increase again. The microspheres may return, and when this occurs continuously it results in what we called the “heart-beat-instability”.

 

The first (time-limited) experiments with complex plasmas under microgravity conditions showed the potential of this new field of research. New effects and phenomena could be observed, helping to understand the physics of complex plasmas in greater detail. This should be very important for the possible future applications of this new field of research mentioned in the beginning.

The continuation of the work in space is one of the major milestones in the field of complex plasmas. It complements the laboratory work of this growing new field. We will perform a series of longer-duration experiments (of about 40h total experimental time) on the Russian Service Module of the International Space Station ISS at the end of 2000 – one of the first scientific experiments aboard. It is a Russian-German collaboration with an American Co-I. The aim of this stand-alone experiment is to explore strongly coupled complex plasmas over a large parameter range and to form large 3-D plasma crystals for the first time.

The next step currently investigated, is a long-term facility for the research on complex plasmas under microgravity conditions – the International Microgravity Plasma Facility, IMPF [2]. A large and growing community of plasma scientists, interested in both fundamental and application oriented physics, and coming from all over the world, supports this unique project.

 

This work was supported by the German Aerospace Research Centre (DLR):

 

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[22]      for information see: www.microgravity.net