J. Plasma Fusion Res. SERIES, Vol.4 (2001) 309-3t2

Velocity Distributions and Density Profiles of Buffer-Gas
Gooled One Component Plasma in Toroidal RF lon Trap
ARAMAKI Mitsutoshi*, SAKAWA Youichi, SHOJI Tatsuo and HAYASAKA Kazuhirol
Department of Energy Engineering and Science, Nagoya university, Nagoya 464-8603, JapanI

Communications Re search Laboratory, Kobe 6 5 l -2492, J apan
(Received: 5 December 2000 / Accepted: 3 September 2001)

Abstract
Velocity and spatial distributions of calcium (Ca*) ions confined in a toroidal RF trap have beenmeasured by using laser-induced fluorescence method. Cat ion temperature in the toroidal direction
decreases from over 2000 K to about 500 K by collisions with He atoms when He pressure is increased
from 5 x 10-7 Torr to 5 x 10-5 Torr. The ion density, estimated from the fluorescence intensity of thetrapped ions, is roughly estimated as 105 cm-3. The Coulomb coupling parameter f, defined by the ratioof Coulomb energy to kinetic energy of ions, is about 10-4. Ca* ion temperature in poroidal cross-section
is estimated from the measured density profile. The velocity distributions and density profiles of thecooled ions are not deviated from those obtained from Boltzmann statistics.

Keywords:
toroidal RF ion trap, buffer-gas cooling, velocity distribution, density profile

1. Introduction

ion confinement time r from the decav curve of the LIF

Several types of ion trap have been used for precise

signal.

spectroscopical diagnostics ofions [] because they canconfine ions in a small space for long time. They arealso used to study one-component plasma physics suchas crystallization 12,31, nonlinear phenomena [4], andstatistical property [5] ofion or electron cloud. The aimof our experiment is to study the statistical property ofion cloud confined in a toroidal RF ion trap [6]. In thispaper, Ca* ion cloud is cooled by He buffer-gas cooling

2. Experimental
Figure I shows the top view of the experimental
setup. The toroidal RF ion trap, placed in a high-vacuum

chamber, is used to confine Ca* ions. Table 1 showsdimensions of the toroidal RF ion trap and experimental
parameters. Ca vapor is introduced into the ion trapfrom the oven placed under the ion trap, and ionized byelectron-beam bombardment. Velocity distributions andmethod, and He gas pressure Ps" dependence ofDoppler
spectra and density profile are measured by using laserinduced fluorescence (LIF) method. Since the toroidal

density profiles of the Ca* ion cloud are measured byusing LIF method. Electronic energy levels of Ca' areshown in Fig. 2. To pump up the energy levels of Ca* to
2Pr,r,397 nm (2S172 2P,r, transition)and 866 nm (2Dr,,-'Pr,, transition) light obtained by diode lasers arecollinearly overlapped and focused tangentially to theion cloud are irradiated tangentially by excitation lasers(397 nm and 866 nm) of Ca*, ion temperatures Z, intoroidal direction and Zo in the poroidal cross-section
are estimated from Doppler spectra and density profile,respectively. We also measure the Ps" dependence of*Corresponding author's e-mail: aramaki @ nuee.nagoya-u. ac.jp309@2001 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchAramaki M. et al., Velocity Distributions and Density Profiles of Buffer-gas Cooled One Component Plasma in Toroidal RF Ion Trap'P,,,
Fabry-Perotlnterferometer

866nm,D,,,
Beam Postion
Controller's,,,Fig. 2 Electronic energy levels of Ca..

ti>\oPue=1 x151cg

r=150 sPue=7x lOC(Jft=1 10 sc8€nrU)ro-.'Fig. 1 ExperimentalbII=

setup of the laser-induced

fluorescence measurement svstem.

0.01

R

400

Time [s]Table 1 Dimensions of the toroidal RF ion
trap and experimental parameters.
Main radius

100 200 300

Fig.3 He gas pressure dependence of the decay offluorescence intensity of Ca..

40 mm
4.5 mmMinor radiusRF voltage

ym250VRF frequency

O=2MHzDC voltage

Vrc

OV

Base pressure

PB

4 x 10-e Ton

He pressure

Pfu

l0'i - lO5 Ton

The 397 nm radiation from Ca' ion is collected by
optical lens, and detected by photomultiplier tube(PMT). The number of photon pulse-signal from thePMT is counted by the multi channel analyzer (MCA)
and stored in the computer (PC).

3. Results and Discussion
He buffer-gas is introduced into the vacuum
chamber at room temperature. Figure 3 shows Pg"
dependence of 397 nm fluorescence decay after thetoroidal ion cloud. The 397 nm UV light is obtained byfrequency doubling of 794 nm light of the diode laser.
The emission of 25r,, -2Puz(397 nm) transition is used
for the detection of Ca* ion fluorescence. To measure
the radial Ca'ion density profile, the beam focusing
positionis swept radially in a poroidal cross section with2S172
a fixed laser frequency. The Doppler broadening of-zPll2radiation is observed by detuning the UV laser

electron beam is turned off. The ion confinement time t
deduced from Fig. 3 is 70, ll0, and 150 s for Ps.= 6xlO-7, 7 x 10-7, andI x 10-6 Torr, respectively. Theseconfinement time are more than two-orders ofmagnitude longer than that of non-cooled Ar* ion [6].
The buffer-gas cooling of Ca* ions elongates tFigure 4 shows the P11" dependence of Doppler
spectra of Ca* ion cloud. The frequency of the UV laser

frequency around the resonance frequency at the centerof the ion cloud. Temperature of Ca* ion is estimatedfrom the density profile and the Doppler broadening.
310

Aramaki M. et al., Velocity Distributions and Density Profiles of Buffer-gas Cooled One Component Plasma in Toroidal RF Ion Trapis swept +3 GHz from the '5r,, - 2P,r, resonance

8 104

frequency. These Doppler broadening spectra agree withGaussian profiles. The ion temperature d in the toroidal
direction is obtained from the Doppler spectrum since

6a-the probing lasers are focused tangentially to theotoroidal ion cloud. d is estimated as 2600, 1200, and550 K for Pn"= 6 x 10-7, 2x10-6, and 3 x 10-s Torr,(J_(J.

cd+ro4coo

respectively. We roughly estimate the ion density n aslOs cm-3 from the measured number of photon by using
rate equation [7]. Here, we considered only the photonsof 2S,,, - 2Pu, transition, since the high-intensity 866 nm
laser repumps the ions in the metastable 2D32 state tothe2PtD state. Table 2 shows parameters of the photon
counting system. Here, V is observation volume, Q is
product of total transmittancy of optical system andquantum efficiency of PMT, dQ is solid angle of opticalsystem, and A is Einstein A coefficient. The Coulomb-c(Lo-2-1012
Laser Detuning at 755 THz [GHz]Fig. 4 Helium gas pressure dependence of the Doppler

spectrum ofthe ca* ion cloud.

Table2 Parameters of the photon counting system.

coupling parameter f , estimated from theseV = 0.65x10"m1
O=0'1
dO = 0.13 sr
A = 1.4 x 108 s-l

experimental results, is about l0'4. In order to obtain thelarger value of f for strongly-coupled plasma studies, itis necessaryto cool the ions by the laser-coolingtechnique.

Figure 5 shows the Ps" dependence of density
profile of the Cat ion cloud in the poroidal crosssection. The full width at half maximum of UV laser
spectrum is much narrower than that of the Doppler
spectrum of Ca* ion. The increase in the fluorescenceintensity by increasing Pr" is mainly caused by thedecrease in d by He buffer-gas cooling. The ion density
profile in the RF potential can be calculated from the@&+ 104#ooo2104cdifferential equation derived from Poisson equation andBoltzmann distribution of ions [8,9],.9o-c(Lt t\2'.n,_lr=J'r €okBTp,mrfrerk"T,-".
"?.r,_ + lr!!=_=0. (l)n *4_0-1.5 -1 -0.5 0 0.5 1

where e is elementary charge, es is permittivity in

1.5

Beam Position [mm]vacuum, ft" is Boltzmann constant, n is Ca* ion mass,and 7o is ion temperature in the cross section of ion
cloud. The measured density profiles (Fig. 5) are
Gaussian type, because the fourth term on the left-handside of Eq. (l) is much smaller than the fifth term in thisexperiment. Zo and full width at half maximum D of thedensity profile are estimated by curve-fitting the density
profile with Gaussian distribution as (1800 K, 0.9 mm),(1600 K, 0.8 mm), and (1400 K, 0.7 mm) for P"" - 5 x
l0'7,2 x 10-6, and 4 x 10-6 Torr, respectively. Both Zo
and D decrease by increasing Pn" due to He buffer-gas
cooling. Note that Zo has weaker dependence on PHs
than that of 7,. This weaker Pr1" dependence of Io may
be explained in terms of the ion heating by the radial RF

Fig.5 Helium gas pressure dependence of density
profile of the Ca' ion cloud in the poroidal crosssection.

field in the poroidal cross-section. In order to evaluate
the dependences of Z, and Zo on Pg" quantitatively,
precise treatment of non-adiabatic process of ion heating

inactual RF trap configuration is needed.

4. Conclusion
Ca' ions are trapped in a toroidal RF trap. The
velocity and spatial distributions of the ion cloud havebeen measured by using the LIF method. The Ca* ions3ll

Aramaki M. et aI., Velocity Distributions and Density Profiles of Buffer-gas Cooled One Component Plasma in Toroidal RF Ion Trap
are cooled by collisions with He atoms of the buffer gas.
We have estimated the ion density as 105 cm-3 from themeasured number of photon by using rate equation.
The estimated f from these experimental results is about

t3t I. Waki, S. Kassner, G. Birkl and H. Walther, Phys.
Rev. Lett. 68,2007 (1992).
t4t A. Kajita, M. Kimura, S. Ohtani, H. Tawara and Y.
Saito, J. Phys. Soc. Jpn. 60, 2996 (1991).

10-4. The velocity distribution and density profile of ionstsl D.H.E. Dubin and T.M. O'Neil, Rev. Mod. Phys.

cooled by He-buffer gas agree with those of7r,87 (1999).

Maxwellian. The deviation from the Boltzmann statistics
is hardly observed in this temperature region.

t61

M. Aramaki, Y. Sakawa and T. Shoji, Jpn. J. Appl.
Phys. 39, L246 (2000).

UI M. Hamamoto, M. Maeda, K. Muraoka and M.

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