Frank Melandsø

Lattice waves in dust plasma crystals

Techniques previously known from solid state physics are used to look at linear and weak non‐linear wave propagation in dust lattices. These expansion techniques include only electrostatic interactions between neighbor particles in addition to assuming small vibrations in the dust lattice. As a simple model for the dust lattice, a one‐dimensional Bravais lattice is considered. For this particular lattice, expressions for the linear phase velocity are compared to a quasi‐particle simulation. The word quasi here means that only the dust particles are represented as diffuse objects, while the plasma is treated as a fluid. The simulation is also used to study the breakdown of the analytical theory and to investigate non‐linear dust lattice waves. A very good agreement is found between the analytical expressions and the particle simulations, for cases where the average dust separation a is of the order of or larger than the plasma Debye length λD. This is a condition which very often applies to dust crystal in...

A new damping effect for the dust-acoustic wave

Abstract We have computed the dispersion relation for low-frequency dust-acoustic waves including dust charge variation. A phase difference between the dust charge variation and the wave can lead to a strong damping of the wave. We present analytical expressions for the wave dispersion and the damping rate for dust acoustic waves in a not too dense dusty plasma and discuss possible applications of the theory for dust waves in planetary dust rings.

Levitation and dynamics of charged dust in the photoelectron sheath above surfaces in space

Bodies in space subject to solar ultraviolet flux will emit photoelectrons. At steady state the current of escaping photoelectrons is balanced by an influx of particles from the surrounding plasma. When the photoelectrons dominate the space charge close to the surface, it has previously been shown that two steady state potential distributions can exist, one in which the potential decreases from the surface value to zero monotonically and one in which it decreases to a negative minimum and then increases to zero. It has been suggested that the nonmonotonic distribution is the stable one. By assuming planar geometry and a Maxwellian distribution of the emitted photoelectrons the charging of isolated dust particles in the plasma sheath is calculated for both the monotonic and nonmonotonic potential distribution. By increasing photoemission from the surface from zero a transition from an ordinary Debye sheath above a nonilluminated surface to a photoelectron sheath is simulated. Dynamical properties of the dust particles such as oscillations, damping, stability, and trapping are investigated. After being injected into the sheath or electrostatically levitated, dust may be stably suspended above illuminated surfaces in space, even in the case of zero gravitation. However, the smallest particles may escape completely from the body. For all sheath types an unstable layer exists close to the surface where dust cannot collect. The theory is applied to bodies in the solar wind and to the spokes of Saturn.

A kinetic model for dust acoustic waves applied to planetary rings

We have derived a kinetic model for the propagation of low-frequency waves in a dusty plasma containing dust particles and drifting plasma particles. The model includes Landau damping or growth and damping from charge variation on the dust particles, and is applied to dust-acoustic waves in planetary rings. Analytic expressions for the dispersion function are used to examine the stability of this wave mode. The dispersion properties are also found numerically for dense dust clouds or large drift velocities, where the analytical expressions are not applicable. We show how the stability condition depends on the density of dust particles and the wavelength, for plasma and dust parameters which may apply to Saturns F ring, G ring, and E ring, and to Jupiters ring.

Charged dust in the Earth's mesopause; effects on radar backscatter

We discuss to what extent small scale density inhomogeneities in the dust distribution may influence radar backscatter in the summer mesopause. We show for a reasonable range of parameters that falling dust interacting with a neutral gas vortex cannot penetrate to the centre of the vortex. The size of the hole in the dust space density distribution around the vortex centre depends on the vortex size and rotation speed and on the free fall velocity of the dust. If the dust contains a non-negligible fraction of the space charge (this requires that the dust is charged by the photoelectric effect), a substantial gradient in the positive charge density across the dust hole edge results. The positive charge density profile in the thin boundary layer will depend on the size distribution of the dust grains. A corresponding gradient in the electron density will appear and we discuss the conditions under which it will lead to a radar reflection of the magnitude observed in the summer polar mesosphere (PMSE - Polar Mesospheric Summer Echoes). This mechanism appears to have the potential of explaining the observed characteristics of the radar echoes such as the strong wavelength dependence and the narrow and sometimes complex and composite spectral signal profiles.

METER-SCALE VARIATIONS OF THE CHARGE CARRIED BY MESOSPHERIC DUST

Abstract Results from the first direct rocket probe measurements of the currents due to impacting mesospheric dust are reported. The observations which are corrected for production of secondary electrons during impact show that dust is a major charge carrier during polar mesosphere summer echo (PMSE) conditions and that the charge density of the dust can vary strongly over a vertical distance of several meters only. The dust is negatively charged in the reported case.

The effect of a dust-size distribution on dust acoustic waves

Using a kinetic model for low-frequency dust acoustic waves (DAW) in a dusty plasma, we have examined the effects of a dust-size distribution on their propagation and damping. Both Landau damping and damping due to dust-charge variation are included. We consider Gaussian and power-law dust-size distributions. In accordance with earlier results of Melandso et al ., we find that the dust Landau damping dominates at short wavelengths. At wavelengths longer than the Debye length λ D 0 , the dust-charge variation is generally dominant. It is always dominant for the power-law size distributions that we have studied. We also find that if the upper and lower size limits of the dust are chosen so that the average dust size remains constant, regardless of the power-law exponent γ, the wave properties are practically identical to those of a monosize distribution of the average dust size. For a Gaussian dust-size distribution, Landau damping may be the dominant damping mechanism if the dust plasma is tenuous ( P [Lt ]1) and the width of the distribution is large.

Probing the properties of planetary ring dust by the observation of Mach cones

Compressive dust acoustic waves can be excited in dusty plasmas. Big boulders in planetary rings move at the Keplerian velocity, while smaller dust particles move at a slightly different velocity due to the action of the Lorentz force. If the difference in velocity Δυ is larger than the dust acoustic wave velocity, αd, a wake will be formed with an opening angle of 2θ where sin θ = |αd/Δυ|. The discovery of wakes and the measurement of their opening angles by the space experiment Cassini to Saturn will yield added information on the dusty plasma conditions in regions through which Cassini will not pass. We find that in some regions the waves that are excited by the boulders may be weak because a large fraction of the interacting dust is absorbed rather than deflected by the boulder. For a given dust size the most favourable conditions for the observations of wakes exist in two fairly narrow regions, one inside and one outside the corotation radius. The favorable regions are closest to the corotation radius for the smallest dust particles and progressively further away for larger dust particles.

Collisionless braking of dust particles in the electrostatic field of planetary dust rings

We show that a dust test particle moving in a periodic orbit in electrostatic fields, as those due to planetary rings, will experience a net deceleration also in the absence of any dust-dust collisions. The varying charge on the moving dust, as it moves in and out of regions of differing electron and ion densities (due to changes in the ring electrostatic potential), will be out of phase with the equilibrium charge in a way which leads to a net braking of the particle. This effect has been shown to damp the coherent oscillations of electrostatically supported dust rings [1] and to damp the oscillatons of levitated dust particles in plasma sheaths at surfaces of solid bodies [2]. We show that this effect will lead to a damping of internal random velocities in a planetary ring, at a rate which in many cases can be much faster than that due to dust-dust collisions. For moderate radial motions of dust test particles relative to a ring we also find that there can be an efficient braking and pick-up of particles already at the ring edges. We conclude that when the collisionless braking of random velocities dominates over dust-dust braking, an increased rate of collapse of the ring to its minimum electrostatic thickness may occur and possibly also an increased radial stability of the ring. The pick-up effect at the ring radial edges is a potentially imortant factor in forming their structure.

Diagnostic of dusty plasma conditions by the observation of Mach cones caused by dust acoustic waves

The theory of dust acoustic waves in dusty plasmas is well developed for conditions with monosized dust particles. It was proposed [O. Havnes et al., J. Geophys. Res. 100, 1731 (1995)] that such waves may be generated in planetary dust rings by boulders moving through the dust at a velocity that is somewhat higher than the dust acoustic velocity. In this manner Mach cones can form with an opening angle that is dependent on the boulder velocity and the local dust acoustic velocity. Measurements of this opening angle will therefore provide additional information on dusty plasma conditions since the dust acoustic velocity can be determined when the boulder velocity is known. We suggest that this method may also be applied under laboratory conditions if a suitable controlled disturbance can be made and we discuss how the dust acoustic velocity and resulting Mach cones are affected if the dusty plasma have a distribution of dust sizes.