circulation’ dynamo

in complex plasmas

• Introduction&motivationsIntroduction&motivations- Planetary atmospheric storms

- Tornado&lightning- Dust devils - The Devils of Mars- Vortices in experimental complex plasmas

• Experimental study of circulations in a complex plasma cloud Experimental study of circulations in a complex plasma cloud compensated against gravity by the thermophoretic forcecompensated against gravity by the thermophoretic force- Experimental setup- Observation conditions- Superimposed images- Regular waves in the cloud- Circulating particles- The interaction of waves and rotations

• Possible origin of circulationsPossible origin of circulations

- Governing equations- “Electrostatic dynamo”- “Thermophoretic dynamo”

• Breaking through the voidBreaking through the void - Particles outside of the clouds- Diagnostics of the void field

• SummarySummary

introduction&motivations

… Lets go to the Zoo, it’ll be great fun!...

John Galsworthy John Galsworthy “The Forsyte Saga”“The Forsyte Saga”

Atmospheric circulationAtmospheric circulation is the large-scale movement of air, and the means (together with the ocean circulation, which is smaller) by which heat is distributed on the surface of the Earth.

The larger storm is the famous Great Red Spot, while the smaller is a large white oval.

Source: NASA, wikimedia com.Source: NASA, wikimedia com.

Severe thunderstrom over Enschede, The Netherlands.

Giant Storm Systems Battle on Jupiter

planetary atmospheric storms

tornado&lightning

This picture of a tornado and lightning stroke over Lake Okeechobee was taken at about 10 PM on June 15, 1991. The photograph was taken by Mr. Fred Smith.

Source: www. fishingdog.comSource: www. fishingdog.com

Dust devils, even small ones Dust devils, even small ones (on Earth) can produce radio (on Earth) can produce radio noise and electrical fields noise and electrical fields greater than 10,000volts per greater than 10,000volts per metermeter

Source: WikipediaSource: Wikipedia

Dust Devil, El Mirage Dry Lake, Mojave Desert

dust devils

Dust devil in Ramadi, Iraq

Dust Devil in Johnsonville, South Carolina

A dust devil is a rotating updraft, ranging from small (half a meter wide and a few meters tall) to large (over 10 meters wide and over 1000 meters tall)

… a dust devil

… dancing devils

… a ghost or spirit of a Navajo

… a sand auger or dust whirl

… a willy willy

… a ghost's wind

the Devils of MarsWhen humans visit Mars, they'll When humans visit Mars, they'll have to watch out for towering have to watch out for towering electrified dust devils…electrified dust devils…

NASA is keen to learn more. How NASA is keen to learn more. How strong are the winds? Do dust devils strong are the winds? Do dust devils carry a charge? When does “devil carry a charge? When does “devil season” begin — and end? Astronauts season” begin — and end? Astronauts are going to want to know the answers are going to want to know the answers before they set foot on the red planet.before they set foot on the red planet.

An artist's concept illustrating what an electrified Martian dust devil might look like. The whitish glow near the bottom is the result of an electrical discharge.

Martian dust devils can be up to fifty times as wide and ten times as high as terrestrial dust devils, and large ones may pose a threat to terrestrial technology sent to Mars.

Source: NASASource: NASA

An artist's concept of a Martian dust storm, showing how electrical charge builds up as in terrestrial thunderstorms.

vortices in experimental complex plasmas

The ,driving force‘ inducing particles to circulate is claimed to be:- the ion drag force [Morfill et al PRL 1999]- the presence of a particle charge gradient [Fortov et al JETP Lett 2003]- a nonzero rotation of the net global force vector field [Goedheer et al PRE 2003] - gravitation induced Rayleigh–Taylor-like instability [Veeresha et al Phys. Plasmas 2005]- the voids [Mamun et al Phys. Plasmas 2004]- the shear instability [Rogava et al Phys. Plasmas 2004]

Complex plasmas reveal the ability to create and self-sustain large-scale dynamical structures, such as global Complex plasmas reveal the ability to create and self-sustain large-scale dynamical structures, such as global rotationsrotations

Particle size Vortex sise Angular velocity Damping rate citation

2a = 14.9μm 5mm not reported Morfill et al PRL 1999

2a = 3.7μm 1 ÷ 2mm not reported Morfill et al PRL 2004

a = 1.7μm <4mm 0.1–0.16 s−1 120–330 s−1 Fortov et al JETP Lett 2003

2a = 7.17μm2a = 7.17μm 8mm8mm 0.8 s0.8 s−1−1 26.5 s26.5 s−1−1 Rubin-Zuzic et al Rubin-Zuzic et al NJP 2007NJP 2007

… It is a capital mistake to theorize before one has data…

Sir Arthur Conan Doyle Sir Arthur Conan Doyle “A Scandal in Bohemia”“A Scandal in Bohemia”

experimental study of circulations in a complex

plasma cloud compensated against gravity by the thermophoretic force

experimental setup

The installation allows us to perform experiments in a wide range of parameters (gas pressure, temperature gradient, particle contamination)

Particles are injected into the plasma, charged negatively, and levitated above the lower electrode

Typical particle separation 300-400 m

The lower electrode is heated, so that an adjustable temperature gradient pointing downward is created in the chamber.

Levitation position depends on temperature gradient

Type of discharge: cc-rf discharge at 13.56 MHz

M. Rubin-Zuzic, H. Thomas, S. Zhdanov, and M. Rubin-Zuzic, H. Thomas, S. Zhdanov, and G. Morfill. NJP (2007)G. Morfill. NJP (2007)

the PK-3 Plus rf plasma chamberthe PK-3 Plus rf plasma chamber

Argon, pressure 16 Pa

T = 61.5 C

MF microparticles of 7.17m 3% diameter M= 2.9 10−10 g

Particles are visualized with reflected light from a laser sheet (~100m thickness)

The cloud’s dynamics is recorded with a CCD camera at a rate of 17.34 Hz

observation conditions

superimposed imagesClouds of particles, edge vertices, vertical waves and ’void penetrator-particles’ are shown as a superposition of 42 colour-coded images consecutive in time. The field of view is 42.9 56.7 mm2.

The particle cloud has a complicated ’sandwichlike’ vertical structure of two dense slabs separated by a void. The top boundary of the bottom cloud is surprisingly flat.

The void is impenetrable for the bulk particles, but not for heavier and/or accelerated agglomerates, which may slide through the entire void. The penetrators are shown as long multi-coloured ’streaks’.

Circulations with closed particle trajectories concentrate at the edges.

regular waves in the cloud

More details about density waves:More details about density waves:

M. Schwabe, M. Rubin-Zuzic, H. Thomas, S. Zhdanov, M. Schwabe, M. Rubin-Zuzic, H. Thomas, S. Zhdanov, H.M. Thomas, and G. E. Morfill. PRL (2007)H.M. Thomas, and G. E. Morfill. PRL (2007)

Shown are five panels, which were obtained by superposition of eight images, temporally displaced by 2/17.34 s to demonstrate the propagation. The top of the cloud is almost motionless; the bright horizontal strips below demonstrate propagating waves:

λ = (2.2 ± 0.4)mm ν= (2.1 ± 0.3) Hz Vph = (4.6 ± 1.6)mms−1

Regular (density) waves propagate through the cloud (downwards for given experimental conditions) after a critical temperature gradient is established

circulating particles Since the particle clouds are extremely dense, and rotating particles vibrate quickly, only a few single particle trajectories could be traced (a).

First, we suppose that these particles go through similar stages, and their trajectories form a family of a simple fabric. We plotted the so called pedal curve, which was introduced first by Colin Colin MacLaurin (1718)MacLaurin (1718),, who first studied this group of curves. For the trajectories shown in figure (a), surprisingly, it turns out to be a simple circle (b).

Plotting the velocity profiles also supports this idea (c) and (d).

Simple fitting allows a quantitative characterization.

slopes of the velocity profiles: δVδVyy/δx /δx = −0= −0..62 s62 s−1−1, δV, δVxx /δy /δy = 0= 0..96 s96 s−1−1

angular velocity: ω ω = [|= [|δVδVyy/δx/δx| | | |δVδVxx/δy/δy|]|]11//22 ≈ 0 ≈ 0..8 rad s8 rad s−1−1

ellipticity factor: = [|= [|δVδVyy/δx/δx||||δVδVxx/δy/δy|]|]−1−1//22 ≈ 1 ≈ 1..22

the interaction of waves and rotations

Six consecutive snapshots represent two periods of shock propagations.

Periodic shocks move downwards inside the interaction area.

Shocks are 3–4 times faster than the rotations and the regular waves in the bulk of the cloud.

Estimates show that each individual shock particle has enough energy to drive 5–10 particles to rotate in the cloud, and hence the ‘perpetual’ motion could be self-sustained.

Still we need a mechanism (a dynamo), which triggers the circulations…Still we need a mechanism (a dynamo), which triggers the circulations…

possible origin of circulations

… in five minutes you will say that it is all so absurdly simple….

Sir Arthur Conan Doyle Sir Arthur Conan Doyle “The Dancing men”“The Dancing men”

== curl (V) curl (V)

∂∂tt + γ+ γ = = curlcurl ( (AA) )

curlcurl ((AA) = ) = curl curl ((VV ) − (Q/M)∇ ) − (Q/M)∇ ∇∇ − (α/M) ∇ − (α/M) ∇ T ∇T ∇ −−

−∇−∇γ γ v v − (ρ∇− (ρ∇ -1-1)) p∇p∇

governing equations

These equations establish the relationships between sources and losses of rotation. All the main forces, the electrostatic force (including the ion drag force), thermophoretic force, gravity, pressure and friction are taken into account.

Generation of a vortex is only possible if the source terms are not vanishing, and are intense enough to overcome the frictional dissipation.

Note that a possible reason for inhomogeneity is the particle size dispersion (particles used in the experiment have a 3% dispersion).

∼ ∼ {{EE⊥⊥//EE||||}} { {g/γLg/γLQQ} } {{δa/aδa/a}}

EE⊥⊥//EE|||| ∼ ∼LL||||/2L/2L⊥⊥

“electrostatic dynamo”

(Gravity and the electrostatic force are dominating in the balance)

Symbols || and mark vertical and horizontal components, ⊥ 22LL⊥⊥/L/L|||| is the ratio of horizontal to vertical size of the cloud. LLQQ is the scale of vertical inhomogeneity of charge distribution.

For our geometry this yields EE⊥⊥/E/E|||| 0∼ 0∼ ..0808. Since LLQQ ≈ 8mm≈ 8mm, δa/a , δa/a = 0= 0..0303, we estimate that 0∼ 0∼ ..1 rad/s1 rad/s, much less than the measured value expexp ~ ~

00..8 rad/s8 rad/s .

Therefore, this mechanism is not powerful enough in our conditions; the charge inhomogeneity mainly affects the particle oscillations, rather than creating intense rotations.

∼ ∼ {{g/γLg/γLQQ} } {{δa/aδa/a}}

“thermophoretic dynamo”Experimentally, it is well known that particle clouds containing particles of different sizes tend to sediment in such a way that larger particles are accumulated mainly at the outside edges. This can create horizontal gradients of charge and/or mass density as well.

Assuming that the inhomogeneity scale is of the order of the circle size, LLQQ

∼ ∼ RRcc 3–4mm∼ 3–4mm∼ , we can estimate at which steady-state level of size variations it is possible to create the needed rotation ∼ ∼ ω ω ≈ 0≈ 0..8 rad/s8 rad/s. This turns out to be

δa/a δa/a 0∼ 0∼ ..01 01 < < 00..0303.

Since it is lower than 3% of the levels guaranteed by the manufacturer for these particles, it seems reasonable that this mechanism could be responsible for the creation of particle circulation.

breaking through the void

…Down, down, down. There was nothing else to do…

Lewis Carroll Lewis Carroll “Alice’s Adventure in Wonderland”“Alice’s Adventure in Wonderland”

The unique feature of the given experiment is a great opportunity to observe in situ the interaction of agglomerates with complex plasma clouds. A heavier particle appears first in the upper cloud (above the void), then penetrates into the void and slides through, collides with the lower cloud beneath the void and damages it to create caverns.

particles outside of the clouds

A simple analysis demonstrates that sliding particles lose energy along theirs trajectory, but it is less than that predicted by standard gas drag theory. We suppose that this kind of ‘ super super fluidityfluidity’ is due to acceleration by the oscillatory field induced by the dynamics of the void plasma. To test if this is the case, we fitted the velocity distributions of traced particles by the sum of the zeroth, first and second harmonics:

diagnostics of the void field

VV00,,11,,22 are the amplitudes of the harmonics constituting the velocity fit: are the amplitudes of the harmonics constituting the velocity fit:

Trajectory:Trajectory: 1 1 2 2 33

VV00 ((mm/smm/s)) −18−18..6 ± 06 ± 0..6 6 −18−18..3 ± 03 ± 0..4 4 00..21 ± 021 ± 0..1616

VV11 ((mm/smm/s) ) 1111..5 ± 05 ± 0..6 6 1717..1 ± 01 ± 0..4 4 3030..5 ± 05 ± 0..22

VV22 ((mm/smm/s) ) 55..5 ± 05 ± 0..7 7 11..7 ± 07 ± 0..6 6 99..5 ± 05 ± 0..55

ω (ω (rad/srad/s)) 88..8 ± 08 ± 0..6 6 88..8 ± 08 ± 0..5 5 1010..2 ± 02 ± 0..11

Oscillations:

ννoscosc = 1= 1..4–1.6 Hz4–1.6 Hz

Waves:

ννwavewave= = ((22..1 ± 01 ± 0..33) ) HzHz

summary

… Funny how things turn out so differently from what you expect….

Patricia Cornwell Patricia Cornwell “Predator”“Predator”

We have investigated dynamical properties of a complex plasma cloud compensated against gravity by the thermophoretic force

We have found the dynamical activity in such a cloud: an excitation of circulations (rotations) and regular waves

We proposed a possible mechanism which would produce such a ‘circulation’ dynamo’ based on the non-Hamiltonian character of complex plasmas

Having traced the particles inside the void (above the cloud), we also have shown that there could be a correlation between the dynamic activity inside the cloud and the behaviour of the particle trajectory through the void

We have experimentally measured the parameters of different dynamical activities and demonstrated a fairly good agreement between them

Thank you very Thank you very much for your much for your

attention!attention!