Abstract
Threedimensional plasma crystals under microgravity condition are investigated by taking into account an external magnetic field. The wavedispersion relations of dust lattice modes in the body centered cubic (bcc) and the face centered cubic (fcc) plasma crystals are obtained explicitly when the magnetic field is perpendicular to the wave motion. The wavedispersion relations of dust lattice modes in the bcc and fcc plasma crystals are calculated numerically when the magnetic field is in an arbitrary direction. The numerical results show that one longitudinal mode and two transverse modes are coupled due to the Lorentz force in the magnetic field. Moreover, three wave modes, i.e., the high frequency phonon mode, the low frequency phonon mode, and the optical mode, are obtained. The optical mode and at least one phonon mode are hybrid modes. When the magnetic field is neither parallel nor perpendicular to the primitive wave motion, all the three wave modes are hybrid modes and do not have any intersection points. It is also found that with increasing the magnetic field strength, the frequency of the optical mode increases and has a cutoff at the cyclotron frequency of the dust particles in the limit of long wavelength, and the mode mixings for both the optical mode and the high frequency phonon mode increase. The acoustic velocity of the low frequency phonon mode is zero. In addition, the acoustic velocity of the high frequency phonon mode depends on the angle of the magnetic field and the wave motion but does not depend on the magnetic field strength.
The authors are grateful to Professor Xiaogang Wang for helpful discussions. This work is supported by National Nature Science Foundation of China with Grant Nos. 11075030, 11005015, and J1103110 and supported by FRFCU(DUT12ZD201).
I. INTRODUCTION
II. WAVEDISPERSION RELATION
III. MAGNETIC FIELD PERPENDICULAR TO WAVE VECTOR
A. Waves propagating in the direction
B. Waves propagating in the direction
C. Waves propagating in the direction
IV. MAGNETIC FIELD IN ARBITRARY DIRECTIONS
V. SUMMARY
Key Topics
 Magnetic fields
 74.0
 Plasma waves
 32.0
 Dispersion relations
 31.0
 Acoustic wave velocity
 16.0
 Plasma crystals
 15.0
Figures
Sketch diagram of characteristic directions.
Sketch diagram of characteristic directions.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to the (1,0,0) direction and the magnetic field is perpendicular to with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to the (1,0,0) direction and the magnetic field is perpendicular to with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to the (1,1,1) direction and the magnetic field is perpendicular to with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to the (1,1,1) direction and the magnetic field is perpendicular to with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to (1,1,0) direction, and the magnetic field is parallel to (0,0,1) direction with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to (1,1,0) direction, and the magnetic field is parallel to (0,0,1) direction with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to (1,1,0) direction, and the magnetic field is parallel to (1,−1,0) direction with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to (1,1,0) direction, and the magnetic field is parallel to (1,−1,0) direction with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to the (1,0,0) direction and the magnetic field is parallel to with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
Dependence of the dispersion relation on the magnetic field for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to the (1,0,0) direction and the magnetic field is parallel to with the screening parameter . Black lines are for and red lines are for . (a1) and (b1) are the dispersion relations and the mode mixing parameters P in the bcc lattice, respectively. (a2) and (b2) are the dispersion relations and the mode mixing parameters P in the fcc lattice, respectively.
The wave frequency and the mode mixing parameters P as a function of the cyclotron frequency for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to the (1,0,0) direction andthe magnetic field is parallel to with the screening parameter and the wavenumber .
The wave frequency and the mode mixing parameters P as a function of the cyclotron frequency for the OM (solid line), HPM (dashed line), and LPM (dotted line) when the wave vector is parallel to the (1,0,0) direction andthe magnetic field is parallel to with the screening parameter and the wavenumber .
The acoustic velocity of HPM as a function of for the screening parameter (solid line), (dashed line), and (dotted line) when the wave vector is parallel to the (1,0,0) direction.
The acoustic velocity of HPM as a function of for the screening parameter (solid line), (dashed line), and (dotted line) when the wave vector is parallel to the (1,0,0) direction.
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