The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

APPLICATION OF A PAUL TRAP
TO THE STUDY OF SPACE-CHARGE-DOMINATED BEAMS
ll : EXPERIMENT
Ryota Takai, Masao Kanou, Yoshio Wada, Kiyokazu Ito,
Hiromi Okamoto, and Atsushi Ogata
Department of Quantum Matter, Graduate School of Advanced Sciences of Matter,
Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan2Abstract
One-component plasmas confined in linear Paul traps are
physically almost equivalent to beam observed in the restframe. We can therefore study various behaviors of beams,
such as the space-charge effects and the beam halo formation, by using a compact trap device instead of a large accelerator. In such cases, the density of confined ions serves
as an important parameter. As the first step, we constructeda linear Paul trap, and succeeded in confinement of ionswith the density of 1.4 x 105 cm- 3 .

1 INTRODUCTION
The improvement of the beam quality (temperature, current, emittance) in accelerators used in science and in medical equipment has been increasingly demanded. It is necessary to understand behavior of the charged particles in accelerators for this purpose. However, it is difficult to study
it experimentally with accelerators, because the actual accelerators have several restrictions for the experiments.
In recent paper, Okamoto and Tanaka has proved that thedynamics of one component plasmas (OCP) in quadrupolerf field correspond with that of the charged particle beams
observed in the rest frame in an accelerator, and they indicate that the linear Paul trap can be applied to the experimental study of space-charge-dominated beams, such as
the space-charge effects and the beam halo formation [12]. Following this study, Kjrergaard and Drewsen proposed
numerical analysis about emulation of the stability of crystalline ion beams in storage rings by laser cooling ions, using a plasma stored in a pulse-excited linear Paul trap [3].
The experimental studies of beam physics using a linear
Paul trap are planed in Hiroshima University. When we apply the ion trap systems as a simulator for beam physics,
the density-to-temperature ratio of a plasma is important.
In this paper, we report an experimental trial to examine
the limit of the charge and the density which can be confined in the liner Paul trap system. The MAFIA code [4] isemployed to analyze the confinement potential.
The organization of this paper is as follows. The experimental configuration is given in Sec.2, and the Experimental results are given in Sec.3. We conclude the paper inSec.4.

EXPERIMENTAL CONFIGURATIONThe experimental configuration is illustrated schematically in Fig. 1. In a linear Paul trap, ions are confined radially by an rf quadrupole electric field and axially by astatic potential well. These potential fields were createdby biasing the four cylindrical electrodes and the end-plateelectrodes as shown in Fig. 2. We take the machine axis asz-axis with z = 0 at the mid-plane of the trap region.
The cylindrical electrodes with the radius of p =4. 75 mm and the length of L = 125 mm are arranged
at R = 4.11 mm from z-axis. The end-plate electrodes
are disks with the diameter of 30 mm and the thicknessof l·mm. The electrodes have holes with the diameter of
7 mm at the center to serve as the ion's path to the confinement region. They are placed at the both ends of thecylindrical electrodes. We can obtain an almost perfectquadrupole field in the radial direction and homogeneous
potential field in the axial direction in the trap region using
these electrodes configuration.
Ions are generated from residual gas, 2.6 x IQ-8 Torr,using the electron impact ionizer, and injected into the confinement region through several focusing electrodes and theend-plate on the ionizer side. Therefore, we consider thatthe major species of the generated ions is N:f. We estimate
the energy of the ions to be 3 eV from the experimental
result.
The amount of trapped charge is measured by an electron
multiplier on which the whole trapped ions are dumped..,rVacuum Chamber~--------------~

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Figure 1: Schematic view of the. experimental configuration. It consists of an electron impact ionizer, a linear Paultrap and an electron multiplier.

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Figure 2: Schematic configuration of a linear Paul trap. An rf potential and a static potential Vend is applied to the fourcylindrical electrodes and the two end-plate electrodes, respectively.
through the hole of the end-plate, as the bias voltage of theend-plate on the detector is turned off. The signals of theelectron multiplier are recorded on the digital oscilloscope.

3EXPERIMENTAL RESULTS

In this experiment, we chose an rf frequency D/27f
2.25 MHz and an amplitude Vrf = 175 V to create thetransverse confinement field. This operating point is lo, cated within the stability region. A de voltage biasing theend-plate electrodes to provide axial confinement potential
is Vend = 12 V which is optimized experimentally.
Typical output signals of the electron multiplier are
shown in Fig. 3. In each figure, the upper line represents
the signal from the electron multiplier and lower line indicates the bias voltage of the end-plate on the detector side.
Figure 3(a) shows the observed signal when the end-platesare biased positively. We do not observe any change ofthe signal level from the electron multiplier. On the otherhand, after turning off the voltage of the end-plate, a decrease of signal level is observed for several ms as shownin Fig. 3(b). The decrease of the signal is caused by theions which was confined in the trap region. The area of
this component of the output signal is proportional to theamount of the trapped charge. By taking account of theamplification rate of the electron multiplier, we can calculate the absolute value of the charge.
We experimentally examine the upper limit of the charge
amount which can be confined in this trap system. Figure 4
shows the charge amount as a function of the ion accumulation time. The charge amount increases with the increasing
accumulation time until it reaches 180 seconds. However,the charge amount saturates at 6.8 x w- 15 C. We expectthat it indicate the limit in this trap system. If we assume
that the all ions are
we can estimate the number of theions as 4.3 x 104 .
To examine the density of the trapped ions, we estimate
the volume of the confined plasma. First, we estimate theaxial length of the plasma. Figure 5 shows the potential
distribution along z-axis generated by the applied voltages.

This distribution is calculated by MAFIA code. The endplates are placed at z = ±64 mm. The axial potential
is homogeneous around the mid-plane, and it increase in
the vicinity of the end-plates. We estimates that the axial length of a column of the confined plasma is typically
120 mm from this vacuum-field configuration and the ion
energy of 3 e V.
Next, we estimate the transverse spread of the trapped
ions. Here we introduce an assumption that the plasma is(a)~500kS/s Run D: 3.00ms Smpl
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Ni,Figure 3: Typical signal from the electron multiplier.
(a)Ions are not detected when the end-plates are biased.
(b )Ions are detected immediately after turning off the voltage of the end-plate on the detector.

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The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

806X

80160240320400

4805606400Accumulation time [sec]6.8 X 10- 15 C.
stationary. Then, the relationship among the rms radius a 0 ,the line density n 1 and the transverse temperature T 1_ of theplasma is obtained as [5],(1)

where r P is the classical particle radius, A = 27rc/D is thewavelength of an rf field. kB, c and mare the Boltzmann
constant, the speed of light and the rest mass of ions, respectively. Here, up is the betatron phase advance per unitcell,

eVrt (R.\)/21rmc2

2203040506070z [mm]Figure 4: Total amount of trapped charge vary with theaccumulation time of ions. The total charge is limited touP =10

Figure 5: Axial profile of the confinement potential on zaxis calculated by MAFIA code.
sideration of the previous result of laser cooling [7] and themelting point.

4 CONCLUSIONAs the preliminary experiment to apply the ion trap systems as a simulator for beam physics, we examined thelimit of the density which was able to be confined in thelinear Paul trap. It turned out that the present density limit
is 1.4 x 105 em - 3 . Because it is not high enough to simulate accelerator beams, we are planning to laser cool theions in the trap.

5 REFERENCES(2)

where e is the charge state of ions.
Owing to the flat distribution of the vacuum-field potential in the trap region with axial length Lp, we canapproximate that the actual line density is represented by
n 1 = N / LP, where N is the observed maximum numberof trapped ions. The line density of the plasma then becomes n 1 = 3. 5 x 10 2 mm - 1 . Moreover, we suppose thatthe plasma has reached the thermal equilibrium. We canobtain T 1_ ~ T 11 = 3 eV from this assumption. Therefore,
we obtain the a 0 = 0.9 mm by substituting these value into
Eqs.(l) and (2).
Here, we assume that the plasma distribution is homogenous along the column with the radius of a0 and the lengthof Lp· As a result, the number density of trapped ions are
estimated as 1.4 x 105 em - 3 using the maximum ion number, 4.3 x 104 .
This density is much smaller than the density required
for the experimental study of beam physics, 10 10 em - 3 . In
order to improve this situation, it is required to decrease thetemperature of the trapped plasma. Laser cooling must be
the most effective means to accomplish this purpose.
We are planning to introduce an atomic oven ion sourcein order to inject a variety of ions, with lower initial temperature [6]. At the present, magnesium is planned in con-[1] H. Okamoto and H. Tanaka, Nucl. lustrum. Meth. 437, 178(1999).
[2] M. Kanou, R. Takai, et al., reported in this symposium.
[3] N. Kjrergaard and M. Drewsen, Phys. Plasmas 8, 1371
(2001).

[4] See, e.g., http://www.cst.de[5] H. Okamoto, Y. Wada and R. Takai, submitted to Nucl. Instrum. Meth. (2001).
[6] K. J. Ross and B. Sonntag, Rev. Sci. lustrum. 66, 4409
(1995).
[7] M. Drewsen, C. Brodersen, L. Homekrer, and J. S. Hangst,Phys. Rev. Lett. 81, 2878 (1998).

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