J. Plasma Fusion Res. SERIES, Vol. 3 (2000) 485-488

New Method of lon Injection into Helical Device with theUse of the Helical Ripple Loss ConeINAGAKI Shigeru*, MOTOJIMA Osamu and SHISHKIN Alexanderr
National Institute for Fusion Science, Toki, 509-5292, JAZAN,

llnstitute of Plasma Physics, NationalScience Center"Kharkov Institute of Physics and Technology", Kharkov-108, 310108, UKRAINE(Received: 18 January 2000 / Accepted: 27 June 2000)

Abstract
New physical mechanism of the ion injection into the helical device is proposed in which the natural
helical loss cone is used. We have shown that the ions with the energy W = 5 keV and small pitch-angle
VllV = 0.3 injected into the helical magnetic trap from outside of the confinement volume can penetratein the core of plasma. The particles with the transit orbits can reach the center of the confinement
volume. In addition we have clarified the possibility of generating the strong positive radial electric fieldin the bulk plasma within the framework of neoclassical theory.

Keywords:
Ion transportation, toroidal trap, helical ripple, loss cone, transit orbits, radial electric field

1. Introduc,tion

magnetic field. In the case of LHD, it is possible toIt is commonly understood that radial electric field,

utilize the existing loss cone orbit, which has aE, plays an important role in improving the confinement
properties of helical type magnetic traps like the Largereversible characteristic. Usually, these loss cone orbits

Helical Device (LHD) tll especially in a low collisional
regime under the physics picture of the neoclassicaltheory [2]. Moreover, some theories for turbulence
predict that the anomalous transport caused by plasma
fluctuations is influenced by the radial electric field

reduce direct particle loss and to increase thethrough its shear [3]. Thus, it is important to generate an
appropriate radial electric field. As one of possible ways
to control the E, a new idea is proposed to inject highenergy ions into the plasma core. If ions are injectedfrom helically trapped orbits to blocked ones [4].
Blocked particle means that it is no longer the helicallytrapped however it becomes toroidally trapped and its

should be minimized during field design optimization toconfinement capability. Therefore, we need to choose
the appropriate particles, which will possibly reach thecentral core of the plasma. The candidate orbit for thisscenario is the transit particle, which show transitions

velocity is only modulated by the helical magnetic field.
The senario to control the radial electric field,
which is demonstrated in this paper, is as follows: (i)The ions injected from a gun which is installed outsideof the last closed magnetic surface trace loss cone orbit.
(ii) These ions collide with thermal particles and aredeposited in the bulk plasma, and thus the radial current

into the plasma the positive E" will build up. Thepositive electric field is expected not only to improvethe confinement of bulk plasma, but also to protect theplasma center against the penetration of the impurity
ions from the periphery.

However, it is not easy to bring charged particles

freely into the core region across a strong toroidal*C o rr e sp ondin

I autho r' se -mail : ina g aki @ LH D. nifs. ac.j p
485@2000 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchInagaki S. er al., New Method of Ion Injection into Helical Device with the Use of the Helical Ripple Loss Coneis produced. (iii) The plasma compensates this radialcurrent by changing in E,.

axis of torus. Then r, rp and r9 are the radial variable, thetoloidal angle and the poroidal angle, respectively'

2. Transit Particle

into the core of plasma, Tp"n"n dtrd the time of theThe time necessary for the penetration of the ion
staying as the blocked particle there, 166"1"4, can be seen

The size of the loss cone depends on the magnetic
field spectrum in angular variables or, in other words,
the type of the modulation of the strength of magnetic
field along the magnetic force line. The LHD is a veryin Fig. 3. It is necessary for depositing the injected ionsthat they collide with thermal particles during theflexible device and different types of magnetic
configurations can be realized [5]. For our study, aspecial configuration is taken, in which the major radiusof the magnetic axis (R-) is shifted outside (R* = 3.9m) compared to the standard configuration (Ro, = J.JJ40m). The loss cone boundary of transit particle in theouter shifted configuration is shown in Fig. l. It wasmade clear that the outer shifted configuration isfavorable for the transition of the particles from the20
E3oN

helically trapped to the blocked, and even helps them tobe a passing particle in the core of the plasma. The-20

typical trajectory of transit deuterium ion with theenergy W = 5 keV is calculated by using a model-40

magnetic field and shown in Fig. 2. The ion is injectedfrom outside of the last closed magnetic surface andthen penetrates into the internal area, close to the centerof plasma. At the launching point the ion is helicallytrapped and it becomes the blocked particle. The
launching point coordinates are the following ro = 54.0
cm, 196 = 0.338, % = 2.27, and VllV = 0.356, where 16,350 370 390 410 430x(cm)Fig. 2 Trajectory of the tranqit ion from "loss cone" invertical cross-section.

196, {ft are the coordinates connected with the circular

HelicallyTrapped Blocked
1510slt^{r o0=0or(o) \ Losso0.4\\so0-D

LOSS-0.2-10-15-i0.2-0.5 0r/a0.5-0.4
100.5 1

1.5 2

2.5

Time ( ms )Fig. 1 Loss-cone boundary for ion. Here W, and 0o are
the perpendicular energy and the central plasma

Fig. 3 Time dependence of velocity of transit ion

potential. respectively.
486

Inagaki S. er a/., New Method of Ion Injection into Helical Device with the Use ofstaying time in the blocked state. When the density is of

the Helical Ripple Loss Coneis influenced by collision, and thus reduced with thedistance from launching point. For simplisity, we

the order of 1020 in-3 the effective collision time of
injected ions are of the order of I ms and comparable tothe staying time in the blocked state. Therefore it isexpected that the injected ions are detrapped from theripples (become passing state) and thermalized during

assume that all injected ions are deposited at 16l ao

el,o and e,o (sn) is the toroidal (helical) ripple at the outermost magnetic surface, where we employ sr = 0.148
and e1,o = 0.192. The total current is conserved in theregion of r > 16, and thereby J,b"o is writen as

the blocked state. If ions are injected into the plasma theradial electric field will build up positively.

3. The Behavior of the Radial Electric Field
Ambipolar Condition
When the loss mechanisms, which are not

J!^ = I*^r4n2 Rr, (r > r a)

intrinsically ambipolar, are present, the radial electricfield is determined by the condition that the total
particle flux is ambipolar in steady state. This condition

where I b"o^ is the injected beam current.

./,I*=o (r <ru)

(4)

The influences of ion iniection on the radial
electric field

can be written as

T,7E,1=f"(E,),-|+

0.5e - (2e)1t2. Here 16 is the loss cone boundary , t = E*/

The equilibrium of E, is determined by plotting the(l)left and right sides of Eq. (3) as a function of 8.. In thewhere /j (4) is ion (electron) particle flux. Thisequation is equivalent to J,(E,) = 0, where Jr is theradial current density. Each of these non-ambipolar
fluxes, such as the orbit loss of ions [6], the diffusion
flux introduced by helically trapped particles [7] and theflux due to the bulk ion viscosity [8] has a non-linear
dependence on the radial electric field, and hence a
drastic change of the radial electric field is expectedcase of no beam injection, the E, has only a small

solution as shown in Fig. 4 (see an intersection of thesolid curve and the broken curves). In low current
injection case, a drastic change in E, is not expected.

when the additional non-ambipolar fluxes are

When the beam current increases, E, can have threesolutions. In this situation, there is a possibility tointroduce the bifurcation ofE". Ifthe bifurcation occurs
andE, becomes large enough, the neoclassical particle
and heat flux are suppressed and thus confinement isintroduced. If ions are injected into the plasma, theimproved.

radial electric field is determined from the new

The E, profiles with and without the ion beam areshown in Fig. 5, where we assume that the central
temperatures of ion and electron are 4 keV and theambipolar condition
T, (E,)-4**( 8,) = f" ( E,),a)density is I x 1020 m-3. In the case that the ion beam
current exceeds 70 A, there is a possibility to bifurcate
in the core region and the width of this region increaseswhere lib"o'is the injected ion flux. This equation isequivalent toJ,(E)=1!^19,1.

(3)

We consider the ion-root plasma [9] as a target because
the high density plasma is favorable for the deposite of
the ion beam. We are interested in the generation ofstrong positive E" in the bulk plasma and thus the flux
due to the bulk viscosity and the loss cone loss of thetoroidally trapped particles are not important. The loss_____+b€amN

trcone loss of the helically trapped particles are small
compared to the diffusion flux introduced by helicallytrapped particles in this collisionality regime. We thus
consider the diffusion flux induced by helically trapped
particles only as the non-ambipolar flux. We choose thebeam energy, the pitch angle and launching point so thatthe ion can penetrate the core region and assume theweak dependence of J,b"* on E". The injected ion beam'*w/o beam

E-p= O.27 |10E, ( kV/m )15 "E* 20Fig. 4 The left side and the right side of Eq. (a) versus E.
487

Inagaki S. er al., New Method of Ion Injection into Helical Device with the Use of the Helical Ripple Loss Conecalculation, this is the case of the ions belonging to

the "loss cone", namely, the case in which
trajectories are the "transit orbits". It is possible toE

launch helically trapped particles from the outside of

the magnetic confinement volume and thenJtransform them into blocked particles in the centerof the confinement volume.

t{\ -102. The injected ions can stay in the core of the plasma

40^30
F(b) [with Bifurcation- w/o bea;20504
704
904

310

r.l- 0-10

long enough before retrapping occurs. It is sufficient
to produce a non-ambipolar flux across the magnetic
surfaces and which generates the radial electric field.

3. The ion beam injection has a strong possibility totrigger the bifurcation ofE,in the core region of theLHD plasma.
References

0 0.2 0.4 0.6 0.8[]

Motojima, O., Fusion Eng. Des. 39-40 (1998) 91.
[2] Gateev, A.A. and Sagdeev, R.2., Reviews ofPlasma Physics (Edit. by Acad. M.A. Leontopvich)
vol.7,1979, Consultants Bureau New York-Lon-1pFig. 5 Change in radial profiles of the radial electric fieldwith ion beam injection. Without bifurcation case(a) and with bifurcation case (b) are shown.

don, p. 251-343.
[3] Biglari, H., Diamond, P.H. and Terry, P.W., Phys.
Fluids 82 (1990) l.

[4] Sanuki, H., Todoroki, J. and Kamimura, T., Phys.

with increases in the beam current. The j:""^ increase
with decreases in radius as shown in eq. (4), and hence
the center region is easy to achieve the critical

Fluids 82 (1990\2155.
[5] Shishkin, A.A., Watanabe, K.Y., Yamazaki, K.,
Motojima, O., Grekov, D.L., Smirnova, M.S. andZolotukhin. A.V.. "Some Features of Particle Orbit
Behavior in LHD Configurations", Research Reportcondition. When the E. is bifurcated, the large E shear isgenerated. In this case the shear suppression of thefluctuation can be expected.

NIFS-211, March 1993, Nagoya, Japan.
[6] Shaing, K.C. and Crume, Jr. E.C., Phys. Rev. Lett.

4. Summary

63 (1989\ 2369.
[7] Shaing, K.C., Phys. Fluids 27 (1984) 1567.
t8l Shaing, K.C., Phys. Rev. Lett. 76 (1996) 4364.
[9] Hastings, D.E., Houlberg, W.A. and Shaing, K.C.,

As the result of our study, it is possible to conclude
the following.

l. The penetration of ions to the core of the plasma in aNucl. Fusion 25 (1985\ 445.

helical device is demonstrated by the drift orbit

488