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