Qiao K, Hyde T W
Center for Astrophysics, Space Physics, and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Oct;68(4 Pt 2):046403. doi: 10.1103/PhysRevE.68.046403. Epub 2003 Oct 22.
The formation of a two-dimensional (2D) Coulomb crystal in a typical experimental environment was simulated with a computer code called BOX_TREE. The dispersion properties of a novel dust lattice wave (DLW) mode, the out-of-plane transverse wave, were obtained. The dispersion relation was determined to be an opticlike inverse dispersion when wave number k is lower than a critical value k(critical), and a positive dispersion when k>k(critical). The negative group velocity of the wave for k<k(critical) depends on the kappa value (with kappa=a/lambda(D), where a is the interparticle spacing and lambda(D) is the Debye length) and the positive group velocity for k>k(critical) depends on the propagation direction. The value of k(critical) depends on both kappa and propagation direction, but changes very little for all propagation directions and the range of kappa investigated. An analytical method has also been used to derive the dispersion relations assuming a hexagonal 2D lattice and Yukawa interparticle potential. These dispersion relations compare favorably with the simulation results. The dispersion relation for a 1D string was also obtained via BOX_TREE simulation and shown to agree with the analytical result given by Vladimirov [Physica A 315, 222 (2002)]. Comparison shows that the out-of-plane transverse DLW in a 2D lattice when k<k(critical) has a negative group velocity much larger than that of the 1D string, given the same particle parameters and operating environment. Again k(critical) for 1D string and 2D lattice are in the same range.
利用名为BOX_TREE的计算机代码模拟了典型实验环境中二维（2D）库仑晶体的形成。获得了一种新型尘埃晶格波（DLW）模式，即面外横波的色散特性。确定当波数k低于临界值k(critical)时，色散关系为类光学逆色散，而当k>k(critical)时为正色散。对于k<k(critical)，波的负群速度取决于κ值（其中κ = a/λ(D)，a为粒子间距，λ(D)为德拜长度），对于k>k(critical)，正群速度取决于传播方向。k(critical)的值取决于κ和传播方向，但在所研究的所有传播方向和κ范围内变化很小。还使用一种解析方法，假设为六边形二维晶格和 Yukawa 粒子间势来推导色散关系。这些色散关系与模拟结果吻合良好。通过BOX_TREE模拟还获得了一维弦的色散关系，并表明与Vladimirov给出的解析结果一致[《物理学报A》315, 222 (2002)]。比较表明，在相同的粒子参数和操作环境下，当k<k(critical)时，二维晶格中的面外横DLW的负群速度比一维弦的负群速度大得多。同样，一维弦和二维晶格的k(critical)处于相同范围内。
