J. Plasma Fusion Res. SERIES, YoL.4 (2001) 69-'14

Field-Aligned Plasma-Potential Structure Formed by
Local Electron Cyclotron Resonance
HATAKEYAMA Rikizo*, KANEKO Toshiro and SATO Noriyoshi
Graduate School of Engineering, Tohoku [,lniversity, Sendai 980-8579, Japan(Received: 5 December 2000 / Accepted:27 August 2001)

Abstract
The significance of basic experiments on field-aligned plasma-potential structure formed by local
electron cyclotron resonance (ECR) is claimed based on the historical development of the investigation
on electric double layer and electrostatic potential confinement of open-ended fusion-oriented plasmas. In
the presence of a single ECR point in simple mirror-type configurations of magnetic field, a potential dip(thermal barrier) appears around this point, being followed by a subsequent potential hump (plugpotential) along a collisionless pJasma flow. The observed phenomenon gives a clear-cut physics to theformation of field-aligned plug potential with thermal barrier, which is closely related to the double layer
formation triggered by a negative dip.

Keywords:
field-aligned structure, local electron cyclotron resonance, plug/barrier potential, effective confinement

1. Introduction

barrier potential formation [2] simultaneously required a

The formation and control of plasma potential

neutral beam injection (NBI) producing sloshing ionsand two ECR points in each cell. This scenario wasdemonstrated by the TMX-U [3] and GAMMA l0 [4]along magnetic-field lines has attracted general attention
in laboratory, space and fusion-oriented plasmas because
the potential structure holds the key of wave-nonlinear
development, charged-particle acceleration, plasma

experiments in 1984 and 1985, respectively.
In this stage, however, we pointed out that theconfinement and heat-transport reduction. In that

underlying physics of the above-mentioned idea isrelated to double-layer formation [5] triggered by asmall potential dip inducing current limitation. Actuallyin a laboratory experiment in 1980, we could alreadyfind the potential dip and rise like the plug/barrier in aconnection, local electron cyclotron resonance (ECR) as

a typical principle of radio-frequency heating ininhomogeneous magnetic fields is endowed with
important attribute, because it is supposed to induce
intemrption of field-aligned electron flow, resulting in
the formation of local plasma-potential structure under
the charge neutrality condition. This process can be

DC-discharge positive column [6]. The same was foundapplied to heat-flux control in diverted torus plasmas,
where the combination of VB along a divertor channel
and ECR heating (ECRH) could yield thermal dikeformation [1]. It can also be applied to improved
confinement in tandem-mirror plasmas. Historicallyspeaking, the original tandem-mirror scenario for plug/

plug/barrier formation. Thereafter, our basic*

in a particle simulation in 1980 [7]. Therefore, we
claimed that only a single ECR point is sufficient for theexperiments have demonstrated this novel scenario [8].

On the other hand, recent GAMMA l0 experiments
have shown in 1995 that the plug/barrier potential isformed without NBI in the presence of the two ECRCorre sponding author' s e-mail : hatake @ ecei.tohoku.ac jp69@2001 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchHatakeyama R. et al., Field-Aligned Plasma-Potential Structure Formed by Local Electron Cyclotron Resonancea circular waveguide at the other end of the machine (z= -150 cm), propagating toward the hot plate (2 = lfg

points in each cell [9]. Furthermore, only fundamental
ECRH, i.e., the single ECRH is now used to produce theplug/barrier potential in the GAMMA l0 experimentscm). The subscript 0 stands for the parameters in thecase of Pp = 0 W.

t101.

Thus, in order to systematically clarify essential

features of the problem, it has been required to

3. Experimental Results and Discussion

investigate details of potential formation and control due
to local ECR under simplified configurations. Here,three kinds of basic experiments are carried out using apoint resonance in symmetric magnetic-well

The first experiment is concerned with a singleconfigurations as shown in the lower figure in Fig. l.

single-ended Q machine. Secondly, a comparison
between our results and GAMMA l0 results is made.
Thirdly, a particle-in-cell (PIC) computer simulation is

The bottom of the magnetic well is located at themachine center. A mirror ratio R- is defined as the ratio

performed.

for R- = 1.68 is typically used in the following

2. Experimental Apparatus
A collisionless plasma is produced by surface

experiment. The microwave propagates toward the righthand side in the region of ala"" < I and the ECR takes
place in the vicinity of lila". = | (a""127t: electronof B around z = +100 cm to that at z - 0 cm. The profile

cyclotron frequency) denoted by the arrow at z = 0 cm.
Figure 2 shows typical profiles of plasma potentialofR. = 1.68 and Pp@ and electron density n" in the caseto the timewhich
corresponds
msec
0.5
W
at
t
0.6
=
=
necessary for the plasma flow to arrive at the ECR
region. The potential structure consists of a potential dip

ionization of potassium atoms on a hot tungsten plate
under an electron-rich condition and is confined by amagnetic field B of a few kG in the Q1-Upgrade
machine, as shown schematically in the upper figure in
Fig. l. A plasma-flow pulse is injected along themagnetic field (t = 0) by applying a step potential @, to anegatively-biased grid in front of the hot plate. A small
Langmuir probe is used to measure plasma parameters

A0o (< 0) formed around the ECR point and asubsequent potential hump A@o (> 0) along the plasma

flow. n" gradually decreases toward the downstream

and their axial profile. The plasma density, electron andion temperatures, and ion flow energy are- ns= 1 x 10e

cm-3, 2"0 = 0.2 eY, Tio a T.o' and E1s = 107"0,
respectively. A background gas pressure is 4 x 10-7 Torr.
A microwave with frequency ol2n = 6 GHz andpower Pu = 0 - I W is launched into the plasma through

-".r"

-1

f^t

Z-z
+
--5T"s / e

-3

^Qd

4
t)

El
o

l0

40
-100

0

100

Z(cm)

-20

0

20

40

Z(cm)

Fig. 2 Spatial profiles of plasma potential @ and electron

density ne at t= 0.6 msec with B- = 1.68 for Pp =Fig. 1 Schematic of experimental setup and symmetric

0.5 w.

magnetic-well configuration.
70

Hatakeyama R. et al., Field-Aligned Plasma-Potential Structure Formed by Local Electron Cyclotron Resonanceregion due to an ambipolar diffusion. However, a3

stagnation of electrons is generated in the ECR region
and the steep density drop is subsequently formed.
Namely, the plasma flow is observed to be drasticallyplugged by the potential structure formed by the ECR.

2

The electron temperature Z" increases \p to T./T"s = 25

e 0

- 30 around the ECR region, and the I" difference

between the upstream and downstream regions ismaintained. A@o is of the order of the ion flow energy
and large enough to plug ions, so called, "plug-1

potential". -Ap6 is about five times Z.e, preventing cold
electrons supplied by the plasma source from merging
with hot electrons in the ECR region, so called, "thermal
barrier potential". Such values of A@o and A@6 areplotted as functions of P, with R- kept constant as given
in Fig. 3, and instead R. with P, kept constant [see Fig.
4(b): cross marksl. In any case, both A@o and -A@6
increase at first, gradually saturating for larger P, or R-.
It is to be remarked that the saturation value of A@o isalways of the order of the ion flow energy d6, plugging
most of the ions so as not to pass through the magnetic
well region. This is because the electrons are welltrapped and -4@6 is large enough for most of theelectrons to be reflected for large P, or R- under the
charge neutrality condition.
Let us present results in the second case of a single-

-2

00.5

1

Pp (W)
Fig. 3 Potential dip A@oand hump A,Qovs Prat t= 0.6
msec with F- = 1.68.

(a)
4
3

tt2

point resonance in asymmetric magnetic-wellconfigurations. The aim of this experiment is to clarify

which mirror ratio between upstream (R,) anddownstream (R6) ones is more effective in the plug/-100

barrier potential formation due to local ECR. Firstly, we(b)change R6 with Ru kept constant 1.30 as shown in Fig.

4(a), where R6 and Ru are defined as ratios ofB around z= -70 cm and z = 100 cm, respectively, to that at z = 0
cm. The values of the plug and barrier potentials

L1

increase with an increase in the downstream mirror
ratio, saturating for larger R6 for Pu = 0.8 W, as seen in
Fig. a@). Next, we change the upstream mirror ratiowith Ro kept constant 1.68. In this case, however, nochanges of the plug and barrier potentials are observed
for any Ro larger than unity. Thus, the downstream
mirror ratio is predominant in the plug/barrier potential
formation, and only the downstream mirror ratio isneeded to be increased for the confinement performance.
The third experiment is concemed with two-points
resonances in symmetric magnetic-well configurations.

e

-1

-2

11.52
Rd

Fig. 4 (a) Asymmetric magnetic-well configuration. (b)Potential dip L,Qo and hump L.Qrvs Ro at t = 0.6
msec for Pp=0.8 W, Crosses denote results with

When we decrease an average magnetic-field strength of
the symmetric configuration (a), instead of the single

R" = Ro.

ECR point, two ECR points appear in (b) and (c)configurations as shown in Fig. 5. In accordance with7l

Hatakeyama R. et al., Field-Aligned Plasma-Potential Structure Formed by Local Electron Cyclotron Resonancethe configuration variation, the measured potential
greatly varies in profile as demonstrated in Fig. 6.
Although not so appreciable change is noticed in theplug-potential value, a very deep and widespread-100

potential well is formed as an interval of the ECR points
becomes longer. Pay attention to the ordinate-scaledifference (one order of magnitude difference) between(a) and (c) configurations in Fig. 6. In the configuration(c) the plug and barrier potential values are measured
with the microwave power (P p = O - 1 W) as aparameter. The barrier potential depth greatly increases0

Z (cm)

without saturating, being different from the plugpotential height. The same tendency is obtained whenR* is increased with P, kept constant in the presence ofFig. 5 Symmetric magnetic-well configuration with twopoints resonances.

two-points resonances.
Such a strongly-modified potential profile in thebarrier region is explained by an additional
experimental-result in diverging magnetic-field
configurations [ 1]. When ECR takes place at a position
in a diverging-B-gradient region, the electron magnetic
moment kG mull2$ increases, being accompanied by-Lt"YllB acceleration of electrons. Then the strong ion-

-1

e

_1

acceleration potential is formed so as to maintain the
charge neutrality condition.

In case of closing this section, it is to beemphasized that the potential-formation mechanism isbased only on the selective electron trapping due toperpendicular Z. heating in the magnetic well andelectrostatic ion trapping resulted self-cosisitently tosatisfy the charge-neutrality condition. Such a formationeof the potential structure with a positive potential region
and a local minimum is the same phenomenon as a
double layer formation due to the reflection of electrons

in a current-carrying plasma ll2,l3l. Then theeconventional scenario for the tandem mirror devices is
not necessary, which needs two ECR points: the one forbarrier formation and the other for plug formation. A
single ECR is sufficient to provide the plug/barrierI

potential structure.

4. Gomparison with GAMMA 10 Results
Here we compare our basic results with results of-100 -50

050

the GAMMA 10 experiments, where only the

100

Z(cm)

fundamental ECRH is applied to the B-gradient tegionof the plug/barrier mirror cell. The representative

Fig. 6 Potential profiles in the magnetic configurationsof Fig. 5 at f = 0.6 msec for Pr = 0.5 W.

parameters are as follows. A@o = 0 - 2.5 V for Q7-U,

0-1.3 kV (0-0.6 kV) for GAMMA lO. n" = I x 10e cm-3
for Q1-U and 5 x l0rr cm-3 (5 x l0rr cm-3; in the plugregion for GAMMA 10. Eig - 2 eV for Q1-U and theion temperature parallel to the magnetic field 4rr - 300
72

Hatakeyama R. et al., Field-Aligned Plasma-Potential Structure Formed by Local Electron Cyclotron ResonanceeV (350 eV) for GAMMA 10. The upstream-region
electron temperature 2"" = 0.35 eV for Qr-U and

Q7-U case and Z;11 in the GAMMA case. Although thenormalized A@o increases with an increase in thenormalized Z" and appears to saturate for larger T"/T."ina similar way in both devices, the normalized A@o in the
GAMMA 10 attains to a value between two and fourtimes as much as that in the Q7-U. This is due to thedifference between the ion velocity distributions and thelarge A,Q, is expected to be necessary to plug the tailcomponent ions in the GAMMA 10, the detail of whichcentral-cell electron temperature Tu = 60 - 80 eV (60 80 eV) for GAMMA 10. In the GAMMA l0 case boththe two operation modes, i.e., ECRH startup [14,15] andhot ion [10], are referred, and the values written in theparentheses described just above are obtained from theexperiment of the hot ion mode.

In order to be in line with the GAMMA l0
situation, on the other hand, our magnetic configuration

is discussed later.
When the normalized A@o is plotted as a function ofis determined as shown in Fig. 7(a), where the ECR
point is located in a B-gradient region. As expected,

P, normalized by n"S (S: plasma cross section), thealmost the same potential profile as described so far isexperimentally confirmed. It is to be noted that there is adifference of ion velocity distribution functions between
the Q1-U and GAMMA 10 plasmas: a truncated half-

normalized P, in the Q7-U, which is required to makeA,Qo large enough to plug most of the ions, is smaller

than that in the GAMMA 10. This may be caused by thehigher heating efficiency of the ECR in the collisionlessplasma of Q1-U while a part of the microwave power isused for a plasma production in the GAMMA 10. It is tobe remarked that A@o in our work plays the same role onion confinement parallel to the magnetic field as in theMaxwellian for Q1-U and a Maxwellian for GAMMA
10. Figure 7(b) gives the summarized result, where theplug(ECR)-region Z" at the abscissa is normalized by7.", and A@o at the ordinate is normalized by d6 in the

GAMMA 10, although A@o and E16 in the Q7-U aremuch smaller than A@o and Zilq in such a big fusionoriented device as the GAMMA 10.

(a) 3
ECR
.?

5. PIC Computer Simulation
In order to understand physical details of the

9-9-se--2potential formation such as a A@o difference between

JI

Q7-U and GAMMA 10 experiments, a PIC computer
simulation with a two-and-a-half dimensional
electrostatic code is performed based on a Q-machine
emitter model [6]. There is a reservoir of the plasma
particles at z = 0 and x = 0.3L, - 0.7L,, from whichelectrons and ions are emitted toward a floatingcollector nt z = 7, and ; = 0 - L,. An externally applied

I
0

(b) 5
?
l-

4

0

-50

Z(cm)

s0

electromagnetic wave with right-hand circular. Qr-UPGRADE

polarization propagates along -z toward the reservoir,
coming across a resonance point on the way. Typicalsimulation parameters are as follows. The charge tomass ratio: -1.0 (electron), 0.0025 (ion). The system
length: l. = 5I21o.s, L,= l28Lr*s (2.p"s: Debye length).
The step length: o)r"sLt = 0.02 (r4"5: electron plasma
frequency). The wave electric-field strength: El(T"sleLe.r; = 0.2. The subscript S stands for the parameters

O GAMMA IO(ECRH)O GAMMA l0(HotIon)

!v3
o
UJ

\t

g d2
1

0L
0

l0

at the reservoir.

20

Figure 8 presents a typical result on the potential,
electron- and ion-density profiles at arest = 2400 under
the symmetric magnetic-well configuration of R^ = 2
with the single-point resonance at zlLo"s = 256 such as
in Fig. 1. The simulation convincingly confirms theexperimental result on the plug (Af")/barrier (A@6)

Te / Tec
Fig. 7 (a) Magnetic configuration corresponding to the

GAMMA 10 situation. (b) Comparison of
normalized potential hump A@o vs normalized

electron temperature I in the ECR region.
73

Hatakeyama R. et al., Field-Aligned Plasma-Potential Structure Formed by Local Electron Cyclotron Resonanceresonance, the following conclusions are obtained.

The plug/barrier potential is well formed andcontrolled with a single ECR point in mirror-type

ao

A0p

configurations of magnetic field. The scale length of the\0
eopotential structure is of the order of the ion Debye
length around the ECR point. The barrier potential
formation is enhanced by electron trapping and/or ion
acceleration due to 1tYB. The plug potential is

A0odetermined by the ion kinetics (self consistently formed
so as to reflect ions including a higher-tail component in

the velocity distribution function). The GAMMA 10-ne/nes----ni / nis

results are consistent with our simple scenario supportedby the basic experiments ( quantitative agreement tocosome extent).

q
Acknowledgements
We thank M. Inutake and many scientists in the
GAMMA 10 group for their useful discussion and
0

512

384

256

z | ?ts,,s128

comments. The authors are indebted to S. Ishiguro for
his cooperation and H. Ishida for his assistance.

0

References

Fig.8 Profiles of potential {. electron n" and ion n,[1] T. Ohkawa, J. Plasma Fusion Res. 64, 305 (1990).
[2] D.E. Baldwin and B.G. Logan, Phys. Rev. Lett.43,

densities in the PIC simulation ot @"05t = 2400 with
B-=2.0 (single ECR point) for EllT"rld"*"1 =0.2.

l3r8 (1979).

t3l D.P. Grubb er al., Phys. Rev. Leu. 53,783 (1984).
t4l M.Inutake et al.,Phys. Rev. Lett.55,939 (1985).

potential formation. In addition, the simulation for the
first time clarifies a spatial deviation of the electron- andion-density profiles, generating a charge separation toform the plug/barrier potential. This is because electrons
are trapped at the B-well bottom and ions stagnate due

t5l N. Sato, Proc. (Invited Papers) Symp. Plasma
Double Layers, Roskilde, 1982 (Risg National
Laboratory, Roskilde, 1982) p.1 16.

[6] J.S. Levine and F.W. Crawford, J. Plasma Physics
24,3s9 (1980).

to the potential deceleration. The separation distance Az(= 401D"s) almost corresponds to the estimated deviationof the ion plasma oscillation around the trappedelectrons, i.e., the ion Debye length (= 2lLo'1).

t1l T.Sato and H. Okuda, Phys. Rev. Lett. 44,74O(1980).

[8] T. Kaneko et al., Phys. Rev. Lett. 80, 2602 (1998)

In order to investigate effects of the ion energy

and J. Phys. Soc. Jpn. 69,2060 (2000).

distribution function on the potential formation, the[9] T. Tamano, Phys. Plasmas 2,2321 (1995).

distribution ahead of the reservoir exit is systematicallychanged. When the ion-flow energy is increased with
the ion temperature kept almost constant and on thecontrary the latter is increased with the former kept
almost constant, the plug potential is correspondingly

t10l K. Yatsu e/ a/., Nucl. Fusion 39,1707 (1999).
I l] T. Kaneko et al.,IEEE Trans. Plasma Sci.2E, 1747

increased and found to be always formed so as to reflect

tl3l A. Hasegawa and T. Sato, Phys. Fluids 25, 632(2000).

[2] S. Torvdn et al., Plasma Phys. Control. Fusion 27,
143 (l985).

even the high-energy tail component in the ion(1982).

[4] T. Saito er al., Proc. Int. Conf. Open Plasma

distribution. This result consistently explains the A@Ddifference between the Qr-U and GAMMA 10.

Confinement Systems for Fusion, Nobosibirsk, 1993

(World Scientific, Singapore, 1993) p.l2l.
[15] I. Katanuma et al., Phys. Plasmas 3,2218 (1996).
[16] S. Ishiguro et al., Phys. Plasmas2,327l (1995).

6. Conclusions
According to the basic experiments on the potential

formation and control due to local electron cvclotron
74