25E04
Coulomb screening in laser-cooled strongly-coupled plasma
レーザー冷却強結合プラズマ中のクーロン遮蔽
Mitsutoshi Aramaki, Satoshi Kameyama, Yoichi Sakawa, Tatsuo Shoji, and Akihiro Kono
荒巻光利, 亀山聡，坂和洋一，庄司多津男，河野明廣
Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
Institute of Laser Engineering, Osaka University, Yamadaoka, Suita, Osaka, 565-0871, Japan
名古屋大学工学研究科 〒464-8603 名古屋市千種不老町
大阪大学レーザーエネルギー学研究センター 〒565-0871 大阪府吹田市山田丘 2-6
A non-intrusive probe laser induced fluorescence (LIF) system has been developed to observe laser-cooledstrongly-coupled plasma. Quantitative evaluation of the spectrum shape becomes possible by using theprobe-LIF system. The ion temperature is derived from the Doppler component, and the Coulomb coupling
parameter Γ is determined. In this experiment, we have succeeded to control Γ over the range of 0.1 to 10.
The variation of Coulomb interaction in the transitional region between the weakly coupled state and thestrongly coupled state has been studied. The Γ dependence of the collisional broadening shows that theDebye screening assumption already breaks down at the transitional region.

1. Introduction
An rf trap (Paul trap) is a device that confines
ions using a quadrupole rf electric field. The
trapped ions are referred to as ideal one component
plasma. We aim to experimentally study theinfluence of the correlation among the trapped ionson the nature of the strongly coupled plasma. The
correlation among the ions is indicated by theCoulomb coupling parameter Γ defined as the ratioof the Coulomb interaction energy to the thermalenergy of ion. Most of laboratory plasmas arecharacterized by Γ<<1, and called as weakly
coupled plasmas. On the other side, the plasma
which Γ is larger than one is called strongly coupledplasma. In the case of Γ>1, the number of existingions into the Debye sphere is less than unity,
therefore, the breakdown of the Debye screening
assumption is predicted. Many elementaly
processes are affected by the change of theCoulomb screening mechanism [1].
We have developed a non-intrusive probe laser
induced fluorescent (LIF) method for laser-cooled

RF Electrode

Ca OvenEnd Electrodee-gunFig. 1 Linear ion trap

ions in a linear RF trap. The undeformed LIF
spectra of laser cooled plasma were observed, andthe variation of the shape was systematicallystudied at the boundary region between the weakly
and strongly coupled state. From the analysis of theline shape, the ion temperature and the change ofthe elementally process in the cooled plasma wasclarified.
In the following sections, the experimental setup
and the probe laser LIF system are explained in
section 2. The results of the probe LIF
measurements are discussed in section 3.
2. Experiment
Figure 1 shows a linear ion trap equipped with acalcium ion source. The assembly is installed in astainless steel chamber evacuated to less than
4×10-10 Torr. The linear rf trap is composed of thefour cylindrical rf electrodes and the two dc
end-electrodes. The ions are confined in the radial
direction by the oscillating quadrupole electric field.
Confinement of the ions in the axial direction isachieved by the electrostatic field generated by theend electrodes. Calcium vapor created by the Caoven is introduced to the trap center through the gap
between the rf electrodes and ionized by electron
bombardment. The trapped ions are cooled using
the Doppler laser cooling techniques. Oncesufficient numbers of ion are loaded into the trap,
the calcium oven and e-gun are turned off. Since theconfinement time of the cooled ions is long enough,the number of ions is roughly constant during themeasurements.
40Ca+ ions are used in this work, since all thetransitions of the 40Ca+ laser-cooling cycle can be

94%

6%
866nm

Lorentz Width [MHz]

P1/2

D3/2

Metastable State

397nm

S1/2
Ground StateFig. 2 Relevant energy levels of 40Ca+ laser coolingICCDFPIPC

103102101010 -1
10100

101Fig. 4 The dependence of Lorentz width on Γ.

Cooling Laser

PBS

866nm
10 mW
794nm 397nm

PBSSHG

PC

PMTPC

inFPI

Gated Photon
Counter

Probe Laser

794nm 397nm
PC

refoutChopper

SHG

FPI

AOM

80MHz

Fig. 3 Schematic diagram of the non-intrusive
measurements of the laser cooled plasma.

driven by laser diodes. Figure 2 shows the relevantenergy levels of 40Ca+ laser cooling. The LIF
emitted by the de-excitation of the P1/2 state to theS1/2 state is used for ion detection. A part of the ionsin P1/2 state falls into the meatastable D3/2 state;
therefore a 866-nm laser is used for repumping theions in the D3/2 state to the P1/2 state.
We propose here a non-intrusive observation
method for the cooled ions. Figure 3 shows theschematic diagram of the experimental setup. The
second 397-nm laser is introduced for probing theLIF spectrum. The ion temperature is controlled by
the cooling lasers, and the LIF spectrum is probed
by sweeping the frequency of the probe laser. The
power of the probe laser is weak enough to avoid
deforming the LIF spectrum. Here, the probe
measurements are performed with probe laser
power of 15 W. The power of the cooling laser
and repumping laser lights are 500 W and 2 mW,respectively. The probe laser was chopped at 1 kHz
by an optical chopper and introduced from 0° to thetrap axis. The weakly modulated LIF signal isdetected by a photomultiplier tube and a gatedphoton counter synchronized to the chopping
frequency.
3. Results and Discussion
The observed spectrum is decomposed into
Gaussian component and Lorentzian component byfitting to the Voigt function. The ion temperature iscalculated using the Doppler width, and then Γ isalso calculated. Here, the low temperature limit
approximation is adopted for the ion density
calculation. We note that the Lorents width is muchlarger than the natural line width 23 MHz of theS1/2-P1/2 transition. Since the experiments areperformed in the chamber evacuated to less than
4×10-10 Torr, the pressure broadening by thecollision with background particles is negligible.
The Stark broadening generated by the electric
microfield is also very small (~6 mHz).
Collisional broadening by ion-ion interaction is acandidate of the broadening mechanism. Figure 4
shows the dependence of Lorentz width on Γ. The
natural line width is subtracted from the Lorentz
width before plotting. The residual Lorentz widths
are well fitted by Γ-1/2; therefore it is proportional toT1/2. Since the Coulomb collision frequency basedon Debye screening assuption is proportional toT-3/2, the dependence of the collision frequency on
the ion temperature is not consistent with the trend
shown in Fig. 4. On the other hand, the collisionalfrequency based on the ion-sphere model is
proportional to T1/2 [2]. Although the experiments
are performed with plasmas which are moderately
coupled state, the experimental results show that theDebye screening assumption already breaks down
and the ion-sphere model is appropriate for thecooled plasmas.
Acknowledgments
The authors would like to thank Drs. M. Y.
Tanaka and K. Hayasaka for valuable advices anddiscussions. This work was partially supported by
the Ministry of Education, Science, Sports andCulture, Grant-in-Aid for Scientific Research (C).
References[1] B.L. Whitten, N.F. Lane, J.C. Weisheit: Phys. Rev. A,
29 (1984) 945.
[2] S. Ichimaru: Statistical Plasma Physics Vol.1,