24P136-P
Parallel Energy Distribution of an Electron Vortex During E×B Drift Rotation
E×Bドリフト周回運動をする電子渦糸のエネルギー分布計測
Tetsuya Mimura, Yukihiro Soga, Yasutada Kato, Yonsu Paku, Keiichi Kamada, Yosuke Kawai*,
Tetsuya Takada* and Yasuhito Kiwamoto*
三村徹也, 曽我之泰，加藤泰禎，朴 英樹，鎌田啓一，河井洋輔，高田哲也，際本泰士
Kanazawa University
Kakuma-machi, Kanazawa 920-1192, Japan
金沢大学 〒920-1192 金沢市角間町*Graduate School of HES, Kyoto University
Yoshidanihonmatsu-cho, Sakyo-ku, Kyoto 606-8501, Japan
京都大学大学院人間環境学研究科 〒606-8501 京都市左京区吉田二本松町
Investigations of energy distribution of a pure electron plasma column rotating around the axis ofcylindrical vessel due to an E×B flow are presented. An abrupt relaxation of energy distribution wasobserved in an electron string trapped for a few microseconds after injection from an electron emitter. A
macroscopic E×B drift rotation of the single electron column is mainly dominated by their microscopic
energy distribution determining an each position of reflection, namely, a radial electric field attributed toan external trap potential exerted on the particle.

1. IntroductionMany features of dynamics in 2D Euler fluids
have been examined experimentally by using
electron plasmas confined in Malmberg-Penning
trap [1]. The macroscopic dynamics in an electron
plasma, trapped axially by an electrostatic potential
and radially by a strong homogeneous magnetic
field, is isomorphic to that of two-dimensional (2D)
inviscid fluid, as long as the axial bouncing motionof the electrons is much faster than the transverse
E×B drift motion of their guiding centers. In thepresence of the electric field E = −∇φ(x,y) undera uniform magnetic field B = Boez, the flow velocityof the guiding centers is given by vd = E×B/Bo2 =ez×∇φ(x,y)/Bo . Here, ez is the unit vector parallelto the machine axis.
An electron column is expected to rotate aroundthe center of the cylindrical vessel under theinfluence of the radial electric field from the image
charge and from the bounce-averaged confining
field. Here, we report experimental verifications ofa mechanism of an E×B rotation using a single
electron column by a measurement of time resolved
parallel energy distribution.
2.

Experimental apparatus and method
The electron plasma is confined in aMalmberg-Penning trap that combines radialconstraint with a homogeneous magnetic field of
Bo= 0.1 T and axial reflections between -80 V
potential dips at both ends. As shown in Fig. 1, thepotential is created by negatively biasing the end

cylindrical electrodes and by axially aligned 9conducting cylindrical electrodes.
350mm
40121234678

9 1011Phosphor&Electron Collector

Electron Vortex

Bo=0.1T

E×B Drift
Rotation

CathodeCCD Camera
5.0kV-80V
To Pump-8~10 Torr-80V

OscilloFig.1. Schematic configuration of the electron plasma
trap.

Among the 11 electrodes, which are numbered from
1 to 11 from the cathode side, the 3th, 6th, 9th,electrodes are azimuthally divided into four sectors
with a uniform separation of 90o. We generate theelectron string by injecting electrons from acathode.
A system to measure the image current is shownin Fig. 2. We connect one of 6th sectored electrodes
to the virtual ground of a current amplifier througha small resistance 15 kΩ. It is known thatunbalanced grounding or even careless connectionof a high gain amplifier can cause unstableoscillations of the electron column [2]. We shouldcarefully adjust resistance of the sector while allother electrodes are directly grounded to thevacuum chamber wall.

16B

14Image
Current

12Enegy [eV ]E×B Drift
Rotation

AMP
Oscillo1086

6th Electrode

4Fig.2. System of image current monitor and 6thelectrode.

2010 - 6-610 -5-10 - 45

3. Parallel Energy Distribution
When electron plasma is injected, the plasma isgenerally not near thermal equilibrium but showsthe sharp distribution at 13 eV corresponding with
the injection energy (blue in Fig.3). Time for which
an electron column is confined is defined as aholding time. Parallel energy distribution showsthat a loosely expanded distribution from low
energy to high energy “36 eV” at holding time 1
usec for which the electrons reflect three or fourtimes between -80V potential dips at both ends anddoesn’t rotate mostly. This result shows that energy
distribution rapidly expands when electron plasma
is confined. We speculate that switching potentialof an end electrode partially accelerated injectedelectrons.
A peak-energy rapidly decreases while theelectron column is rotating once or more times forholding time from 100 usec to 1 msec, and stabilize
at 1 eV after 2 msec as shown in Fig.4. An averageenergy slowly decreases during 1 sec due tocyclotron radiation.
1.6

Energy Distribution

1.4
1.2
1.0
0.8
0.6

10 - 1100101Fig.4. Average energy <E> is calculated by <E>=∫dEEf(E), E_max is maximum energy of f(E) .

5.

E×B Rotation Frequency
The measured E×B rotation frequency  exp of asingle electron column plotted in Fig.5 (■) is ingood agreement with the calculated frequency
 cal2 (■) mainly contributed by abounce-averaged
external electric field Eexp. A rotation due to anelectric field Ei of the image charge (indicatedby symbols ● in Fig.5) doesn’t affect themacroscopic rotation  exp .
15Rotation Frequency [kH z]

After plasma is confined for few seconds, theelectron column is dumped by a lowered, butnonzero, confinement potential. The electrons movealong magnetic field lines and are collected
phosphor screen. We get total electron number andluminosity distribution. This procedure is repeatedwith several potentials. So, we measured Parallel
energy distribution [3].

10 - 310 - 2
Holding Time [sec]
<E>
E_max



105

0
10 - 410 - 310 - 2
Holding Time [sec]

w

wcal1

10 - 1

100

wcal2

Fig.5. E×B drift rotation frequency versus holding time.
Experimental result is ■, calculated result is ● and ■, theformer is consist of Ei, latter is Ei+Eext

6. Summary
In summary we investigated a mechanism of an
E×B rotation using a single electron column by ameasurement of parallel energy distribution. The
macroscopic E×B drift rotation of the single
electron column is mainly dominated by theirmicroscopic energy distribution determining aneach position of reflection, namely, a radial
electric field attributed to an external trap potential
exerted on the particle.

0.4
0.2
0.0
05
beam

101520Electron energy [eV]
1usec
3msec
1sec

2530
5sec

Fig.3. Parallel energy distribution of electron vortex.

References[1] Y.Kiwamoto, K.Ito, A.Sanpei, A.Mohri: Phys. Rev.
Lett. 85 (2000) 3173.
[2] I. Kiyokazu, Y. Kiwamoto, and A. Sanpei: J. J. Appl.
Phys. 40 (2001) 2558.
[3] D. L. Eggleston and C. F. Driscoll, B. R. Beck, A. W.
Hyatt and J. H. Malmberg: Phys. Fluids. B. 4 (1992)
3432.