25E03
On Analysis of Fluctuation Spectrum in Fine Particle Plasma
微粒子プラズマの揺動スペクトル解析について
Hiroo Totsuji1 and Chieko Totsuji2
東辻浩夫, 東辻千枝子
1Okayama University, 3-1-1, Tsushimanaka, Kitaku, Okayama 700-8530, Japan
Kogakuin University, 1-24-2, Nishishinjyuku, Shijyukuku, Tokyo 464-0073, Japan1
岡山大学，〒700-8530 岡山市北区津島中3-1-1
2
工学院大学，〒163-8677 新宿区西新宿1-24-2

2

Among various kinetic level information obtained in fine particle plasma experiments, the density
fluctuation spectrum is one of most interesting data to understand collective phenomena in stronglycoupled charge systems. In comparing observational results with those of theoretical predictions, we haveto take into account the effects of the dimensionality of observations and the non-uniformity of theobserved systems which are closely related. Based on the numerical simulation of observations, we discussthese effects and possible relations to observations in PK-3+ on the International Space Station.

1. Introduction
In fine particle plasmas, various phenomena
related to the strong coupling between particles
can be observed directly through images of CCD
cameras. Since these data give us kinetic level
information, one of most interesting quantities
may be those related to the collective phenomena
such as critical fluctuations. The possibility ofcritical point in fine particle plasmas associatedwith the divergence of the isothermal
compressibility of one-component plasmas has
been pointed out[1].
2. Two- and three-dimensional observations andnon-uniformity
The observations by CCD cameras are usually
performed under the illumination of sheet laser
beam. Three-dimensional (3d) positions ofparticles are captured by scanning vertically tothe plane of laser beam. We may have, however,cases where the latter is not available. We haveshown that 3d pair correlation function and thestructure factor can be restored fromtwo-dimensional (2d) ones[2,3].
Our basic assumption is that the system isuniform and isotropic: Otherwise, it is clearlyimpossible. Conversely, if the system is uniform
and isotropic, the same amount of information isincluded in 2d observations. Mathematically, 2dfunctions are given by integral transforms from3d ones and they can be inverted.
We have inversion formulas as expansions withrespect to a parameter. These transformations arecompared with simulations where both 2d and 3dfunctions are obtained exactly. Examples areshown in Figs.1 and 2.

In Fig.2, we have the apparent increase oflong-wavelength fluctuations in 2d observation incontrast to the real behavior S(k; 3d)~0: In 2d
observations of a part of the uniform system, thenon-uniformity is effectively enhanced.
Non-uniformity seems to have similar effects
to fluctuation spectrum. Possible relations to theresults of PK-3+ observations will be discussed inthe presentation.

Fig.1. Pair distribution function. Dots are simulations
and the solid line is the restoration formula.

Fig.2. 2d (left) and 3d (right) structure factors. Notethat S(K, 2d) is finite at K~0, while S(k, 3d) ~0.
References[1] For example, H. Totsuji: Phys. Plasmas
15(2008)072111.
[2] H. Totsuji: J. Phys. Soc. Japan 78(2009)065004.
[3] H. Totsuji: J. Phys. Soc. Japan 79(2010)064002-1.