Chairman:R. Henne
J.F. Coudert


Hiroshi Kikuchi

Nihon University, College of Science and Technology, 8, Kanda Surugadai, l-chome, Chiyoda-ku, Tokyo 101, Japan

Dusty and dirty plasmas may be considered a plasma environment, fully or partially ionised, collisionless or collisional, containing dust grains or aerosols, charged and/or uncharged. In such environments, electric rather than magnetic processes are taking place predominantly involving electric charging and discharge, ionisation and recombination, particle coalescene, and space charge transport. For these phenomena; conventional hydrodynamics (HD) or magnetohydrodynamics (MHD) breaks down, and even conventional plasma physics is not relevant, since they usually ignore the effects of space charges, electric and gravitational fields. Furthermore, most of their environments are considered neither conducting fluids, fully ionised gases nor collisionless plasmas. They may be partially ionised, collisional gases, semiconducting or dielectric fluids where electrohydrodynamics (EHD) or more generally electromagnetohydrodynamics (EHD) transport processes are taking place significantly rather than HD or MHD processes.

The present paper updates the work on these EHD and EMHD processes involving new electric and space charge transport in addition to conventional fluid vortex and magnetic field transport. For such an EHD or EMHD regime, a new equation of electric field transport in a charged one-component fluid is presented, including space charge, ponderomotive (electric), and gravitational forces, and is supplemented by the equations of fluid vorticity, magnetic field, energy transport, and heat transfer extended also for this new regime. This is the so-called 'single EHD or EMHD fluid model' analogous to the conventional single MHD model. The `electric Reynolds number', RE = emuL/T ( e: dielectric constant; m: permeability; u: fluid velocity; L: characteristic length; T: characteristic time) newly introduced, analogous to the Reynolds and magnetic Reynolds numbers, plays an important role in the EHD or EMHD regime as a criterion of relative importance of convection, diffusion, dissipation, propagation, and radiation.

While the generalised equations of fluid vorticity and magnetic field transport recover the well-known Kelvin-Helmholtz theorem; holding the source-free frozen in field concept in the HD and MHD regimes; respectively for high Reynolds and high magnetic Reynolds numbers, it is similarly shown that the new equation of electric field transport also satisfies the Kelvin-Helmholtz equation for high electric Reynolds numbers, namely RE>l, indicating that the frozen in field concept still holds for the electric displacement D in a dielectric fluid just like the magnetic flux density B in a conducting fluid. In other words, when space eharges are frozen-in to a dielectric fluid, we have the EHD or EMHD relation, H* = H - u * D~0 in a dielectric flow which corresponds to the well-known MHD relation, E* = E + u * B~0 in a conducting flow.

Although a single EHD or EMHD fluid model may be relevant as a continum for dusty and dirty plasmas, particularly for collisional gases, dust particles in tenuous cosmic plasmas can often be highly charged as a result of collisons to background plasma electrons and ions, photoelectron, secondary electron emission and so on. For such cases, the environment needs to be considered a multi-component plasma or fluid, composed of electrons, ions, charged (negatively or positively) or uncharged dust, and specifications to a multi-component fluid model for such plasmas are given of basic features of cosmic dusty plasmas such as electrostatic charging and physical effects of dust, namely coagulation, disruption, and levitation.

While the phenomena of field line merging-reconnection are well-known for fluid vortex merging-reconnection in the HD regime and for magnetic reconnection in the MHD regime, its electric version has never been pointed out in spite of rather common and ubiquitous phenomena in cosmos and atmospheres and even in our daily life. Such a basic novel physical concept is introduced and is descnbed on the basis of EHD and EMHD.

Electric reconnection is a phenomenon in which electric field lines in one direction tend to connect to other adjacent field lines in the opposite direction and by which energy stored in electric fields is released rapidly to be transferred to other kinds of energy such as kinetic energy of particles, if dust particles are present in the environment. Electric cusp and reconnection is analogous to magnetic cusp and reconnection familiar to plasma physicists as well as geo-astro physicists, and offers a basic concept and a variety of applications to EHD and EMHD. Surprisingly, however, such an electric version of field line merging-reconnection has never been discussed as yet except my preliminary reports (for instance, [1]).
While it is well known that the conversion from magnetic to flow energy causes solar or auroral flares by magnetic reconnection in the MHD regime, it is newly shown that the conversion from electric to kinetic or flow energy causes significant atmospheric phenomena such as natural and triggered lightning by electric field line merging-reconnection in the EHD or EMHD regime. Its theory is updated on the basis of the equation of electric field transport in relation to the Kelvin-Helmholtz theorem, and at the same time, physically on the basis of a new but more specific space-charge related frozen-in concept than the conventional source-free frozen-in concept. Thus, the source-origin of electric merging-reconnection is an electric cusp across which electric field reversal occurs and which is a bifurcation as well as a saddle point in terms of electric potential and field, necessarily being capable for a source-origin of chaos. In addition, for electric merging-reconnection to occur, non-zero space charge and low electric Reynolds number are required to cause a local breakdown of the frozen-in field concept. It is emphasized through a couple of examples that electric merging-connection in the EHD or EMHD regime may play an important role in dusty and dirty plasmas.

The paper proceeds to the behaviour and roles of dust in an electric cusp. When a dust particle is invading an electric cusp, some of adjacent electric field lines in the opposite direction tend to merge toward the particle, inducing or polarizing tiny quadrupole-like charges and producing large local electric fields on its surface, thus electric forces being exerted on the grain. Now subsequent processes are divided into two cases, depending on whether the local electric fields on the grain surface are below or beyond the breakdown threshold of the background gas (or free space). For the former case, some of the electrostatic energy tend to be converted into the kinetic energy of the particle, leading to its rapid acceleration. For the other case, local surface discharge may take place due to sufficiently high local electric fields, forming a corona around the dust or object and producing critical ionization flow in the form of streamer and leader followed by eventual main discharge, or rarely by a plasma layer formation around the dust grain, thus some of the electrostatic energy being converted into ionisation and flow energy.

For both cases, there are a number of meteorologico-electric atmospheric and cosmic phenomena that have never been properly explained by any models [2]. Examples of the former case include the formation of diffusive dust layers or dust distributions over a wide range of altitudes between the clouds and the ionosphere as a result of gravito-electrodynamic motion of dust in electric cusps and electric mirrors with electric reconnection in the presence of thunderclouds or a horizontal electrification, causing a variety of pre-earthquake atmospheric and ionospheric effects such as appearance or increase of Es layers and additional layers, spread phenomena on bottom side ionograms, sometimes large scale variations of electron density in F-layer, strong plasma depletion in the upper atmosphere over the region of the preparing earthquake, emanation of aerosol particles with a large content of metals by the crust before and some time after the earthquake and so on observed recently [3]. On the other hand, examples of the latter case are also plenty, including natural and triggered lightning, tornadic thunderstorms, ball lightmng, cloud-to-ionosphere discharges, nebular lightning, a new universal elecric-cusp type plasma reactor and so on [2].


  • H. Kikuchi, (ed.), Dusty aizd Dirty Plasmas, Noise, aizd Chaos in Space and in the Laboratoiy, Plenum, New York, 1994: `EHD and EMHD Transport Processes in Dusty and Dirty Plasmas', pp.139 148, `Electric Reconnection and Chaos in Dusty and Dirty Plasmas', pp.535-544.
  • H. Kikuchi, `Roles of Dust or Object Perturbing an Electric Cusp in Electric Reconnection and Consequent Electric Discharge or Lightning', Physics and Chemistry of the Earth, 21, 549-557, 1996.
  • S. A. Pulinets, A.D. Legen'ka, and V. A. Alekseev, `Pre-Earthquake Ionospheric Effects and Their Possible Mechanisms' in [1], 1994, pp.545-557.


Geert C. Dijkhuis

Zeldenrust Steelant College and Convectron N.V., Terneuzen The Netherlands

ABSTRACT This paper models turbulent vorticity in shearing plasma layers as strings of identical helix units smoothly joined at their junctions. We present scaling versions of vortex stretching, breaking and reconnection at high Reynolds number breeding chiral vortex loops as in phase slippage events in superfluids. In state diagrams for conduction electrons in cool, dense discharge plasma we find a subdomain for cavitation and a triple point with zero chemical potential for equilibrium of fermi and bose systems. The phase space geometry for entropy of vortex crystals and tangles favours self-organization of vortex plasma with negative temperatures for their chiral degree of freedom at high energies.

Vortex plasmoids from ablation plasmas

We review plasma conditions in erosive discharge plasma shearing along circuit breaker electrodes, supersonic nozzle walls, resonant microwave cavities, or from oblique lightning impact. We consider electrode configuration and circuit parameter domains associated with creation of long-lived laboratory plasma formations. We compare their observed characteristics with high-energy microplasmoids, charged vortex rings and tangles in superfluid helium, and with statistics of ball lightning.

Knot classification of vortex loops

We model vorticity in turbulent flow as strings of identical helix units joined smoothly on a scaling lattice with fractal dimension inverting to Von Karman's universal shear layer constant. We calculate pitch and domain for closure of helix strings into smooth vortex loops circum-+scribing the regular polyhedra with uniform curvature and torsion. We collect their invariant coordinate transformations in multiplication tables of their respective symmetry groups. Using Reidemeister's rules we classify possible helix loop topologies as various torus knots, links or braid types. We discuss critical helix pitch values for self-intersection separating parameter domains with knot-free, self-linked or braided string loops. A picture gallery of doublet loops illustrates knots, double links, Borromean ring and Möbius band topologies serving as lattice units for planar and 3D helical vortex packing.

Vortex lattices for string loops

For a single straight vortex line our helix strings models transition to turbulence as a random sequence of left- and right-handed, but otherwise identical helix units. For planar shear zones near transition we reproduce Bernal and Roshko's topology of streamwise vortex tubes with helix strings arranged into staggered rows of hairpin vortices. Local balance of right-and left-handed helicity packs vortex lines into chiral polarization patterns as seen in numerical large-eddy simulations, and in direct numerical flow simulation of jets. Swirling flow from an orifice ties helix strings into torus knots or braids with chiral charge. And random helix string sequences packed on a 3D lattice model vortex tangles and plasmoids formed by capillary flow of liquid helium and sliding sparks.

Triple point for chiral cavitation

We treat cavitation as two-phase circulation of liquid in thermodynamic equilibrium with saturated vapour in hollow vortex cores. The string model ensures equipartition of circulation energy along slender helical cavitation loops with uniform cross section and surface tension of their liquid-vapour interfaces. We compare empirical data for critical temperature, vapour pressure and surface tension of water with estimates for liquid helium and dense plasma from state equations for ideal bose and non-ideal fermi systems. And we discuss observable effects of quantum statistics modified by the loss of reflection and time reversal symmetry in helical flux tubes.

Random strings on scaling grids

For rapid non-equilibrium vortex deformation we include breaking and reconnection of flux loops by opposing friction torques from sideward motion. A recursive deformation cycle packs vortex loops with neutral, monopolar and bipolar chirality on a scaling lattice with decreasing mesh size. With reversible mesh refinement in isothermal fluid, total string length and circulation energy share common growth factors by conservation of angular momentum. We discuss loop abundances and chiral cavitation patterns on planes, cylinders and spheres minimizing shear between adjacent cells. And we compare fractal versions of the chiral lattice with fractal structure of micron-size polymeric threads in erosive discharge plasma blown into air through a capillary, and with fractal models for ball lightning.

Plasma vortex crystals

From Hamiltonian vortex dynamics we obtain a microcanonical ensemble average for entropy favouring self-organization of aligned vortex rings into a single loop. With two-level interaction energy between nearest string units, vortex packings include realizations with negative temperatures overpopulating high-energy states as in maser or laser plasmas and in Joyce- Montgomery vortex flow on flat grids. We illustrate 3D packings with a picture gallery of vortex crystals constructed from straight tubes, line-centered chiral strings and chiral loops on a cubic lattice.


Formation of long-lived plasma formations in air arises naturally from self-organizing vortex dynamics in sheared arc plasma with significant exchange interaction between its conduction electrons. Their state diagram includes a triple point for thermodynamic equilibrium
between non-ideal fermions and ideal bosons at zero chemical potential. With surface tension from bosonic condensate lining hollow vortex tubes, progressive mesh refinement of cavitation readily accelerates plasma circulation beyond the virial constraint set by ambient pressure. Our smooth chains of helical vortex units with periodic or random orientation and chirality on linear, planar and spatial grids model ordered as well as tangled vortex structures in capillary flow, shear layers and free convection zones. With Ising-type interaction energy, the chiral degree of freedom of helix packings has negative temperature in high-energy vortex plasmoids.


  • Kikuchi, H., In: Handbook of Atmospheric Electrodynamics, Vol. 1, Ed. H. Volland, CRC Press, Boca Raton, 1995.
  • Moiseev, S., and Onischenko, O., In Proceedings of the International Symposium on Heat and Mass Transfer under Plasma Conditions, Ed. P. Fauchais, Begell House, New York, 1995.
  • Dijkhuis, G. C., Constructions for Scale-invariant and Kink-free Vortex Stretching, Physica B, Vol. 228, pp. 144-152, 1996.
  • Chorin, A.J., Vorticity and Turbulence, Springer-Verlag, 1998.

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