J. Plasma Fusion Res. SERIES, Vol. 8 (2009)

Effect of Plasma Rotation on Acceleration of Ions Along theMagnetic Field Line
Kenichiro TERASAKA, Tetsushi KATAHIRA, Shinji YOSHIMURA1) , Mitsutoshi ARAMAKI2) andMasayoshi Y. TANAKA3)Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka 816-8580, Japan
1) National Institute of Fusion Science, Gifu 509-5292, Japan
2) Department of Electrical Engineering and Computer Science, Nagoya University, 464-8603, Japan
3) Department of High Energy Engineering Science, Kyushu University, Fukuoka 816-8580, Japan(Received: 19 September 2008 / Accepted: 11 December 2008)

Supersonic ion flows accelerated from subsonic region have been observed in a weakly magnetized steadystate electron cyclotron resonance (ECR) plasma. The experiment revealed that the ions are accelerated by theelectrostatic field along the magnetic field line. The acceleration rate along the magnetic field has been examinedin terms of total angular momentum per unit mass and unit length. It is found that the acceleration rate is small
when the angular momentum is large and is independent of the direction of rotation. Control of plasma rotation
is important for the efficient acceleration of ions along the field line.
Keywords: ion acceleration, plasma rotation, directional Langumuir probe, ECR plasma

1. Introduction

In Sec. 2, the experimental apparatus and measurement method are shown. Section 3 shows the one dimensional momentum equation for ions to give the relation between plasma density and ion Mach number, which will becompared to the experimental results (Sec. 4). The total
angular momentum and the ion acceleration rate along theaxial direction are introduced to analyze the experimental
data, and the effect of rotation on ion acceleration along
the field line is clarified. The concluding remarks are summarized in Sec. 5.

Supersonic plasma flow plays an important role on developments of electric propulsion and is intensively studied so far. In a diverging magnetic field configuration, ionsare accelerated along the filed line to reach a subsonic orsupersonic velocity. According to the acceleration mechanism of a normal gas flow, a concept of “magnetic nozzle” has been proposed and the experimental studies havebeen also carried out.[1, 2] Magnetic nozzles have been
widely used because they do not need material walls andproduce supersonic flows efficiently. However, the acceleration mechanism including the electrostatic (and electromagnetic) field is not fully understood. In space plasmas,
there are many phenomena with supersonic plasma flows.
The astrophysical jets flowing from massive stars or proto
stars are considered to be fast flowing plasmas, however,
the acceleration mechanism is not fully understood yet.
In most of laboratory and space environments a magnetized plasma inevitably rotates around its axis due tothe radial electric field, however, the effect of rotation
on generation of axial flow has not been properly considered. When a plasma has an angular momentum, theparallel acceleration of ions may be different from thatof a non-rotating case, which is formulated by the variational principle with the constraints of axial mass flux andhelicity.[3, 4] In the experiments, on the other hand, theeffect of rotation has not been studied so far.
We have experimentally studied the effect of plasma
rotation on the axial acceleration of ions using directional
Langmuir probes (DLPs)[5], which can measure the radial, azimuthal and axial ion flow velocity. The objectivesof present study are as follows; (i) clarify the acceleration
mechanism along the magnetic field line and (ii) estimate
the effect of rotation on the ion acceleration.

2. Experimental Setup
The experiments are performed in the HYPER-I device at National Instiute for Fusion Science (NIFS), whichis shown in Fig. 1.[6] The HYPER-I device consists of acylindrical vacuum vessel (2.0 [m] in axial length and 0.3[m] in inner diameter) and 10 magnetic coils, which produce a weakly diverging magnetic field along the axis of
the chamber. A steady-state argon plasma is produced by
ECR heating using a microwave of 2.45 GHz frequency,
and sustained up to one minutes. Argon gas is used in thepresent experiments, and the pressure is 0.1-0.4 [mTorr].
The DLP has been used to measure the flow velocity
and is consists of a tungsten electrode and an insulatingtube (Al2 O3 ), which has a small hole (0.7-1.0 [mm] in diameter) on the side surface to collect a directed ion flux
normal to the hole opening. The Θ component of flow velocity is obtained by changing the hole (electrode) angle,
Θ, and is given byV
Iis (Θ + π ) − Iis (Θ)
cos Θ = α,CsIis (Θ + π ) + Iis (Θ)(1)

where, V , Cs and Iis are the ion flow velocity, ion acoustic
speed and ion saturation current, respectively. The quantity α is the correction factor, and is usually order unity.
When α = 2, Eq. (1) is identical to Stangeby’s model

author’s e-mail: tera-225@aees.kyushu-u.ac.jp

15©2009 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchK. Terasaka et al., Effect of Plasma Rotation on Acceleration of Ions along the Magnetic Field Line

here,

(Free Fall model [7]). In this experiment, the four radiallymovable DLPs and one axially-movable DLP are installedin the radial and axial ports, and all the DLPs are biased
at -90 [V]. The radially-movable DLPs are used to obtain
the azimuthal and axial flow velocities, and are located at
the axial positions: z = 1.175, 1.400, 1.555 and 1.828 [m]from the microwave injection point. The axially-movableDLP measures the axial and radial flow velocities. Since
the correction factor α depends on the probe geometry, wecompared an axial flow velocity measured with the axiallymovable DLP to that with the radially-movable DLP, andcorrected the factor α of axially-movable DLP.

κ=z

yx

magnetic coils

� 2
�
M −1
ρi0= exp.
ρi2

B
plasmawave guide
DLPs

z(m)
1.5

210.5

3. Model Equations
We consider one dimensional fluid model for ions toclarify the ion acceleration mechanism along the magnetic
filed line. Here, the isentropic process along the flow line
is assumed for ions. Under the present experimental conditions, all the collision processes can be neglected, because
the mean free path for each collision processes is comparable to the device length. Since the electron temperature
is constant along the magnetic field (experimentally confirmed), the electrons are assumed to be isothermal. The
steady-state momentum equation is described byd pi
dVz=−+ eni Ez ,dzdz(6)Here, ρi0 means the mass density at the position whereM = 1. This formula corresponds that given in Ref. [2],though the electrostatic field term in the momentum balance equation is not considered. When Mach number increases, the mass density decreases to conserve the density
flux. In this case, the electric field in Eq. (2) is dominant,and the flow velocity is determined by the electrostatic potential, which is made by the fast moving electrons. Whenthe ion temperature is comparable to the electron temperature, we cannot analytically solve Eq. (2) because κ isgenerally a function of z. The solution obtained by the numerical method may be different from both the solutions
in limiting cases.
We apply the result of low ion temperature case since
the electron temperature is much larger than the ion temperature in the present experiment.

0Fig. 1 Schematic diagram of HYPER-I device.

ρiVz(5)The quantities M and γi are Mach number with respect toion acoustic speed and specific heat ratio of ions, respectively. In case of high ion temperature (i.e., Ti /Te � 1),
Eq. (4) can be easily solved, and its solution is exactly thesame as that of neutral gas cases[1, 2]. In other words, thepressure gradient term in Eq. (2) is dominant, and the flow
field is determined by the ions only.
In case of low ion temperature (i.e., Ti /Te � 1), Eq.
(4) can be also solved, and the relation between mass density and ion Mach number is given by

to pumpgas(Ti /Te ).
1 + (Ti /Te )(2)

where ρi , Vz , pi and ni mean the mass density, axial flow
velocity, pressure, and density of ions, respectively. The
quantities e and Ez are the electric charge and electrostatic
field in the axial direction, respectively. The subscription“i” stands for ions. The second term in the right-hand sideof Eq. (2) can be rewritten by using the Boltzmann’s relation for electrons and quasi-neutrality condition,eEz = −

Te dni,ni dz(3)where Te is the electron temperature expressed by energy
unit. Substituting Eq. (3) into Eq. (2), we obtainM

��dM
κ (γi − 1)M 2 + 2 1 d ρi=−,
dz
2
ρi dz

Fig. 2 Radial profiles of azimuthal ion flow velocity. Rotatingplasma cases (open symbols) and non-rotating plasmacase (closed symbol).

(4)

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K. Terasaka et al., Effect of Plasma Rotation on Acceleration of Ions along the Magnetic Field Line

4. Experimental Results
By carefully choosing the magnetic field intensity, anaxisymmetric rotating plasma and a non-rotating plasma
were obtained at the operational pressure 0.1 mTorr andwith the microwave power input of 6 [kW], which are
shown in Fig. 2. The data shown in the figure were measured by the radially-movable DLP at z = 1.175 [m]. The
positive sign of Vθ is counter-clockwise rotation around zaxis (see Fig. 1). Here, we assumed α = 2 in Eq. (1).
The quantities Ic means the coil current, and is proportional to the magnetic field strength. When Ic = 119.0 [A](B = 0.869 [T] at z = 1.175 [m]), the ions do not rotate in
the region of r ≤ 80 [mm]. When Ic = 120.0 and 121.0[A], on the other hand, the ions rotate. The velocity profiles exhibit rigid-body rotation at |x| < 40 [mm], and there
is a velocity shear in the outer region. The radial profiles ofdensity and axial flow velocity are almost flat (not shownin this figure), and there is no noticeable changes in thesequantities between the rotating plasma and the non-rotatingplasma. Thus, we can examine the effect of rotation on theparallel acceleration without changing other parameters.
Then, we measured the axial profiles of plasma density and axial flow velocity using the axially-movable DLP
at r = 0 to clarify the ion acceleration mechanism along
the field line, which are shown in Fig. 3. We obtained
the plasma density by averaging the ion saturation current
over the probe angle, and the symbol of the averaging isindicated by bracket of the vertical title in Fig. 3(a). In thisexperiment, we measured the ion saturation current at Θ =0, 90, 180 and 270 degrees. The density monotonically decreases in the axial direction, and the profiles are almostFig. 4 Density ratio as a function of Mach number. The closed
and open symbols mean the non-rotating plasma case andthe rotating plasma case, respectively. The data at r = 0,30 and 50 [mm] are presented by squared boxes, circles
and triangles, respectively.

the same for both cases. The axial flow velocity increases
in 1.175 [m] < z < 1.6 [m], and saturates at z > 1.6 [m].
In the acceleration region, the axial Mach number (Vz /Cs )exceeds the unity near z = 1.4 [m] in both cases. Here, it
should be noted that there exists a finite difference in axial
flow velocity between the rotating and non-rotating cases.
The axial Mach number in the non-rotating plasma case increases more rapidly than that in the rotating plasma case,in the acceleration region. The maximum value of the axial flow velocities are 1.1 and 1.25 for the rotating case andthe non-rotating case, respectively.
Figure 4 shows the comparison of experimental datain accelerating region with Eq. (6) (solid line). The closed
and open symbols show the non-rotating plasma and therotating plasma cases, respectively. The three different
symbols mean the data at different radial positions. The
quantity n0 is taken at the position M = 1 by interpolating the axial flow velocity in Fig. 3(b). The experimental
data show a good agreement with the theoretical result. At
the saturation region, the experimental data deviate fromthe theoretical curve, which will be discussed in the lastsection.
We also measured the radial profiles of the radial ion
flow velocity in the acceleration region using the axiallymovable DLP, the results of which are shown in Fig. 5.
The discharge condition in this figure is the same as thatin the non-rotating plasma case. The shaded regions in thefigure mean outflow. As seen in the figure, the radial flow
velocity at z = 1.2 [m] is virtually zero at all radial positions. In the downstream region (z > 1.4 [m]), the radialflow velocity increases with the axial position (z), and also
the each radial profile is proportional to the radius It is interesting to note that when the plasma flow starts expansion(z ≥ 1.6 [m]) due to diverging magnetic field, the axial flow
velocity saturates.

Fig. 3 Axial profiles of the density (a) and the axial flow velocity(b). The square with sold lines is for a rotating plasmacase, and the open circle with dashed line is for a nonrotating plasma case.

17K. Terasaka et al., Effect of Plasma Rotation on Acceleration of Ions along the Magnetic Field LineHere, we introduce two quantities to estimate the effect of rotation on ion acceleration along the magnetic fieldline. One is the total angular momentum per unit mass, L,
and other is the ion acceleration rate along the axial direction, ΔM, which are defined as
L ≡ 2πΔM ≡� rs0(rVθ ) rdr ,M1 − M0,Δz(7)(8)

where, the quantities rs is the plasma size under consideration. The quantities M0 and M1 are ion Mach number at
z0 and z1 , respectively, and Δz = z1 − z0 . Figure 6 shows
the acceleration rate as a function of L , where rs = 0.08[m], z0 = 1.175 [m] and Δz = 0.325-0.425 [m]. The closed
symbols are taken under the same experimental conditions
as in Fig. 2, and the rectangles, closed circles and triangles
are for Δz = 0.325, 0.38 and 0.425 [m], respectively. The
open circles correspond the different experimental conditions with operation gas pressure of 0.2-0.4 [mTorr], microwave input power of 5-10 [kW] and Δz = 0.38 [m]. It isfound in the figure that when the total angular momentumis small (i.e., non-rotating plasma case), the acceleration
rate is large. It is also noted that the sign of L does notaffect the acceleration rate.

Fig. 6 L dependence of the acceleration rate. The closed andopen symbols mean the experimental conditions at 0.1[mTorr] and 0.2-0.4 [mTorr], respectively.

In the saturation region, however, the theoreticalmodel does not well describe the experimental data, which
may be attributable to the effect of recombination process
and neutral backflow near the end wall. To explain the acceleration mechanism near the end wall region, the modelequation should be modified so as to include the effect ofcollisions, which is left for future works. We have alsomeasured the radial ion flow velocity, and found that it increases in the saturation region.
The behavior of axial ion flow velocity is different between the rotating plasma and the non-rotating plasma. To
estimate the effect of rotation on ion acceleration, we introduce the total angular momentum per unit mass and ion
acceleration rate along the axial direction. Under the various discharge conditions, we have obtained the relation
between two quantities. It is found that the acceleration
rate becomes maximum for the non-rotating case, and linearly decreases with increasing the total angular momentum. This may cause deceleration of ions along the fieldeven in a diverging magnetic field. It may be concluded
that control of plasma rotation is an important issue to efficiently accelerate the ions. Further understanding of theeffect of rotation on the plasma acceleration is left for future work.

5. Conclusions
We have measured the radial, azimuthal and axial ion
flow velocities using DLPs in a diverging magnetic field,
and observed a supersonic ion axial flow accelerated fromsubsonic regime. The relation between mass density andion Mach number has been derived from the momentum
balance equation to clarify the ion acceleration mechanism
along the field line. In the acceleration region, the experimental data well agree with the theoretical result of low
ion temperature limit. This indicates that the ions are accelerated by parallel electrostatic field established by thefast moving electrons.

Acknowledgment

This work is supported by collaboration program atNIFS (NIFS06KOAP016). The authors would like to thank
ECW group for useful comments.
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Fig. 5 Radial profiles of radial flow velocity at different axialpositions.

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K. Terasaka et al., Effect of Plasma Rotation on Acceleration of Ions along the Magnetic Field Line

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