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F.M.H. CheungSchool of Physics, University of Sydney, NSW 2006, Australia
Rotation of Fine Plasma Crystal in Axial Magnetic Field
Rotational Motion of Dust Plasma Crystals
Information provided by the Crystal’s Rotation
Approximation Model for Crystal’s Rotation
Rotation of Fine Plasma Crystal in Electric Field
B
Introduction
Dust Plasma Crystal is a well ordered and stable array of highly negatively charged dust particles suspended in a plasma
Dust Plasma Crystal consisted of one to several number of particles is called Fine Plasma Crystal
Dust Plasma Crystal Fine Plasma Crystal
Experimental Apparatus
Argon PlasmaMelamine Formaldehyde Polymer SpheresDust Diameter = 6.21±0.9mPressure = 100mTorr
Voltage RF p-p = 500mV at 17.5MHz
VoltageConfinement = +10.5VMagnetic Field Strength = 0 to 90GElectron Temperature ~ 3eVElectron Density = 1015m-3
Crystals of 2 to 16 particles, with both single ring and double ring were studied
Interparticle distance 0.4mm
Rotation is in the left-handed direction with respect to the magnetic field.
Crystal Configuration & Stability
Number of
Particles
Stability Factor (SF)
2 4.4
3 1.6
4 2.6
5 -
6 1.4
7 2.2
8 5.0
9 1.9
10 1.7
11 1.5
12 1.9
=199±4m
=406±4m
=495±2m
=242±2m
=418±4m
=487±1m
=289±3m
=451±3m
=492±3m
Planar-2
Planar-6 (1,5)
Planar-10 (3,7)
Planar-3
Planar-7 (1,6)
Planar-11 (3,8)
Planar-4
Planar-8 (1,7)
Planar-12 (3,9) =454±4m
Planar-9 (2,7)
Stability Factor (SF) is:Standard Deviation of Crystal Radius
Mean Crystal Radius
Pentagonal (Planar-6) structure is most stable
or
B x
Circular Trajectory of Crystals
02.9.00AD
Video is running at 5x actual speed
Trajectory of the crystals were tracked for a total time of 6 minutes with magnetic field strength increasing by 15G every minute (up to 90G)
Circular Trajectory of Crystals
Particles in the crystal traced out circular path during rotation
Periodic Pause/ Uniform Motion
Crystal maintains their stable structure during rotation (shown by constant phase in angular position)Planar-2 is the most difficult to rotate with small B field and momentarily pauses at a particular angle during rotation. Other crystals, such as planar-10, rotate with uniform angular velocity (indicated by the constant slope)
increases with increasing magnetic field strength
increase linearly for planar-6 and -8
For double ring crystals, the rate of change in increases quickly and then saturate
Angular Velocity
Threshold Magnetic Field
Ease of rotation increases with number of particles in the crystal, N
Magnetic field strength required to initiate rotation is inversely proportional to N2
Planar-2 is the most resistant to rotation
We attempted to model the previously shown vs B plot by assuming:
= Bk
where and k are constants
However, both and k were discovered to be dependent on N
Taking threshold magnetic field into account, the final derivation became:= e(-22.83/N) x B -4/N4(8.27/N3/2)
Approximation Model of vs B
The above vs B plot shows how the graph change as the number of particles in the crystal N increases
= Bk
Driving Force & Ion Drag
The driving force FD for the rotation must be equal but opposite to the friction force FF due to neutrals in the azimuthal direction (FD = -FF)
FF is given by the formula:
Estimation value of the driving force for such rotation is 1.7 x10-16N for driving force (ion drag force ~ 9.6 x 10-18N)
Nonuniform Space Charge Driver
Non-uniformity in charge variation dusty plasma systems might be a possible mechanism for rotation
Electrons confined by magnetic field more than ions because of smaller mass (Bq/m)
2V = -/o
~ ni + ne
Magnetic field modifies the radial profile of electron and ion density, presumably due to the magnetization of the electrons
Magnetic field might affect electric potential
A change in shape of the potential might make particle to rotate
VV
rr
Ratio of electron gyrofrequency to frequency of electron-neutral collisions ~1.5 (for ions, this ratio <0.01)
Change of radial distribution of ne (ni) can lead to an increase in dust charge spatial gradient r = Z(r)/r. The angular velocity of rotation can be estimated from
where Fnon is the non-electric force, Z is the dust particle charge, and fr is the collisional frequency
Thermophoretic force Fth(r) = where is the heat conductivity. Estimation value of the charge gradient r/<Z> which would be sufficient to drive the rotation can be found by substituting the above expression for Fth into equation:
Temperature gradient in sheath is about 0.5 K/cm. Therefore r /<Z>= 0.2, 0.14, 0.06 cm-1 for large, annular and small crystals respectively.
Change of potential?
r
Ta
T
mn
2
815
32
= Fnonr/2mdZfr
Experimental Setup
Melamine formaldehyde – 6.13 μm ± 0.06 μm Melamine formaldehyde – 6.13 μm ± 0.06 μm
Argon plasma TArgon plasma Te e ~ 2 eV, V~ 2 eV, Vp p =50V &=50V & nne e ~ 10~ 1099 cm cm-3-3