J. Plasma Fusior Res. SERIES, Vol.5 (2002) 351-354

Possible Experiments with K" lons on Large Helical Device
to Simulate Alpha Particle Behavior
SHISHKIN Alexander, MORIMOTO Shigeyuki', YAMAZAKI Kozor,
MOTOJIMA Osamu' and INAGAKI Shigeru'
Institute of Plasma Physics, National Science Center "Kharkov Institute of Physics and Technology",
Kharkov-108, Ukraine
Department of Physics and Technology, Kharkov "V.N. Karazin" National University,
Kharkov-77, Ukraine

I Kanazawa Institute ofTechnology, Nonoichi 921-8501, Japan2National Institute for Fusion Science, Toki 509-5292, Japan(Received: 11 December 2001 / Accepted: 17 May 2OO2)

Abstract
New experiments are proposed with the K* ions on Large Helical Device to simulate the behavior ofalpha particles in fusion reactors. Some important physics issues: the penetration of the ions injected
outside the last closed magnetic surface into the core of the plasma confinement volume if they have thetransition orbits in order to control the electric field in plasma, the study of the cold alpha-particles

removal, the removal of the impurity ions from the confinement volume, - can be checked
experinrentally. Here one experiment to study loss cone transit particles is proposed.

Keywords:
ion transportation, alpha particle simulation, loss cone, transit orbit

1. lntroduction

effect when the blocked particle becomes the helicallytrapped one can be helpful to remove the impurity ionsor "cold" alpha particles from the center of theconfinement volume to outside.

Experiments with K+ ions on Large Helical Device
with the redtrced magnetic field can simulate thebehavior of hot alpha particles in fusion reactors
because of the similarity of the Larmor radius to plasma
minor radius ratios [1].
One of the possible experiments on LHD is
proposed here. The injection of K" ions outside the lastclosed magnetrc surface can be carried out in such waythat the ion penetrates into the core of the confinement
volume. This is the way to check the fundamental idea
[2,3] to use the particles with the transit orbits, which
belong to helical ripple loss cone for the penetration into
the helical devjce. This effect when the helically trapped
particle beconres the blocked particle can be used tocontrol the electric field in plasma [3]. The reverse

2. Main Equations and Magnetic Field Model
2.1 Main equations
For our consideration guiding center equations areused [4]*=v,4*4
dr 'B 82'IExB]
l,r\M,cl2V,i +Vil+_#tBxVBl.
2e,8"@2002 by The Japan Society of Plasma
C o rr e sp o ndin 8 aut ho r' s e - mai I : s hi s hkin @ v link. kharkov. ua

351

Science and Nuclear Fusion ResearchShishkin A. et al., Possible Experiments with K* Ions on Large Helical Device to Simulate Alpha Particle Behavior

tt

tt2 ^

trapped can be described with the equations Jn (r,8,Vn/V) = const, where ,Isl = $tu at is the longitudinal adiabatic
invariant of the particle in the corresponding state [2].
The starting points (with the coordinates re,ds) of'r dB-- dt+t"i28dt
dt ="EdrdWdp
dt

(2.r)

=0.

particles, which start outside the last closed magnetic
surface, cross the transition curve (at the point withcoordinates r,,8,) and should penetrate into the core ofconfinement volume (to the point with the coordinatesr",8"), can be found from the system of equations

Here r is the radius-vector of the particle trajectory, B is

the magnetic field, E is the electric field, V11 and Va are
the parallel and the perpendicular velocities, Mt and ei
are the mass and charge of the particle, Wis the kinetic

energy and p is the magnetic moment of the particle,I 1"'o (16, 8o,vn lv)= J ,n"'n (r,,d,, v/"\Itu- M,Vi' - t.
\' 28l11(3.1),lv),

I/ ll or*u"o (r.,8r,V ,/V1= 1 ,0,*u* (r",4, VrlV) , (3.2)

2.2 Main magnetic field

2=l+The main magnetic field (B = V<D) is modeled withthe use of the magnetic field potential

vz - ltBo+ pBo(r,l R ) cos rl,( .

.\l/2ltBo €,.^ \e' + n' )'(3.3)

where(D= Bolo,- L l e,.^(r / )^'-A -?E,.^-1,€''^ sin n rl, ,aI

sin(nrl -me)+e,,orsinrll ,

(3.4)

(2.2)

B =21''n El-^

where 86 is the magnetic field at the circular axis, R andalare the major and minor radii of the helical winding;
r,8,rp are the coordinates connected with the circularaxis of the torus, r is the radial variable, I and tp are the"orn,l,,

We can use the configurations with the different setsof parameters. The sets of parameters with the different
signs and values of the coefficients before the harmonics
of the angular variables are responsible for the shift ofthe magnetic axis (outward or inward), the shape of themagnetic surfaces and the modulation of the magnetic
field absolute value along the magnetic field line.

angular variables along the minor and major circumference of the torus, d increases in the direction opposite to

the main normal of the circular axis of the torus; metriccoefficients are the following: h,= l, ho= r, hq = R + r
cos:D1' m is the number of the magnetic field periods

along the torus, / is the helical winding pole number.
The index ,? assumes the values n = l, I - l, I + l; en.^are the coefficients of the harmonics of the maenetic

4. Penetration of Potassium lons in theGenter of the Confinement Volumefield.

K'ions in the inward shifted magnetic configuration.
As the test particle the K+ ion with the energy I7 = 1
keV is taken. One typical trajectory of the transit

In this paper we concentrated on the study of theFor the results presented in Section 4 theparameters of the Large Helical Device [5] are taken as

follows: l=2,m = 10, Bo= 1.5 T, R = 390 errr,a6=
97 .5 cm; the values of €,.^ are taken in such a way thatparticle is shown on Figs. I (vertical cross-section) andthe magnetic surfaces, the magnetic field modulation
along the force line and other properties coincide withthe results of Ref. [6]. For the configuration with theinward shift of the magnetic axis the parameters are t2,p= 0.79, ezto = -0.032, €1,r0 = -0.056 and t1,s = 0.045.

found here with the rule of the orbit reversal. Under thestarting point coordinat€s 16 = 60.537 cm, ds = O.l25l
rad, tps = 1.035 rad, V11lV = --0.4 the test ion starts as thehelically trapped particle and then becomes the blocked
one and stays as the blocked one during the time ?5ro"p"6= 6 ms. The period of the particle staying in the blocked
state can be seen on Fig. 3. The 3-D trajectory of such test

2 (hotizontal cross-section). The starting points are3. Properties of lon Transit Orbit
The particle starts its motion as the blocked onethen crosses the transition curve and becomes thehelically trapped one. The trajectory of the particle inthe blocked state and then in the state of the helicallyion is seen on Fig. 4. One can see the parts ofthe trajectorywhen the test ion is the helically trapped one and when

it becomes the blocked (toroidally trapped) one.

352

Shishkin A. et al., Possible Experiments with K* Ions on Large Helical Device to Simulate Aloha Particle Behavior

4OO320390.{00Fig.4 3-D trajectory ofthe test ion460

R(cm)5. Discussion

Fig. 1 Vertical projection of the test ion trajectory on thebackgror-rnd of the magnetic surfaces

The described effect - the penetration of the ionsinjected outside the last closed magnetic surface into thecore of the confinement volume, can be reversed. Itmeans that the impurity ions with transit orbits (coldalpha particles, particularly) can be removed from thecore of the confinement volume to the periphery ofplasma.

6. Gonclusions{|to-2l/D

025t

With the use of K* ion gun it is possible to carryout the experiment for the study of the penetration of
injected ions, which belong to the helical ripple loss
cone into the helical device. This is one of the possible
experiments to simulate the alpha-particle behavior.

5rn

The starting points are outside the last closed
magnetic surfaces. The starting points can be chosen insuch way that it is suitable to place the ion gun.
This experiment can be carried out in the vacuum

X (Gm)

Fig. 2 Horizontal projection of the test ion trajectory

configuration and can open the way for the experimental
0.6

study other physics effects such as estafette ofresonances [7] for the removal of the test particle.

0.4

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a function of time353

Shishkin A. et a/., Possible Experiments with K* Ions on Large Helical Device to Simulate Alpha Particle Behavior

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