J. Plasma Fusion Res. SERIES, Vol.4 (2001) 57O-573

Shock Formation by a Velocity-Modulated lon-Beam Injection
in a Magnetized Plasma with Negative lons
GOHDA Takuma, NAGAOKA Hiroshi, IIZUKA Satoru and SATO Noriyoshi
Tohoku University, Aramaki aza-Aoba 05, Aoba-ku, Sendai 980-8579, Japan(Received: 5 December 2000 / Accepted: 14 September 2001)

Abstract
Nonlinear evolutions of density pulses excited by a velocity-modulated ion beam injected into aplasma with negative ions are investigated. A ramp modulation of ion beam velocity gives rise to adensity perturbation of the ion beam, which grows as a result of bunching, then a shock like structure isformed eventually. The front slope of the perturbation during the evolution is dependent on the density
ratio e of negative to positive ions. When e is small, positive slope is steepening. On the other hand,when e is large, it is observed that a density perturbation with negative slope is steepening.

Keywords:
velocity modulation, ion beam, shock formation, negative ion, SF;

1. lntroduction

phenomena are ascribed to a reduction of the electronshielding. This effect was well demonstrated for prop-

The behaviors of modulated ion beam in plasmas
are of current interest, particularly in connection withplasma instability and heating. Spatial evolution ofdensity perturbations produced in an ion beam-plasma
system is demonstrated by Sato et al., using a doubleended Q machine plasma []. In case of sinusoidal
modulation, initial growth and subsequent amplitude
oscillation are observed and explained by the linear
wave theory with fast and slow beam modes. Ramp
modulations also give rise to an initial growth of theperturbations, which evolve into a single pulse propagating along the ion beam. However, the behaviors of
the ion perturbations in case of large amplitude
modulation have not been investigated together with theeffect of negative ions.
Negative ion plasmas, which include negative ionsin addition to electrons and positive ions [2], are of
crucial importance in space plasmas, fusion-oriented
plasmas, and material-processing plasmas which some-agating and damping of linear ion acoustic waves in acollisionless negative ion plasma with SF; [3].
Nonlinear propagations of ion acoustic waves innegative ion plasmas were also investigated by Takeuchi

et al. L4l in a single-ended Q machine plasma. The
positive and negative density jumps have been evolved
into compressive and rarefactive ion acoustic shocks,
respectively, depending on the density ratio e ofnegative to positive ions. The critical ratio t", observed
between positive and negative steepening is well
explained on the basis of the KdV equation.
In this paper, we investigate the characteristics ofnonlinear evolution of perturbations excited by avelocity-modulated ion-beam in a plasma with negativeions.

2. Experimental Apparatus
The experiment is carried out in a double-ended Qmachine with a vacuum chamber of 20.8 cm in diametertimes include dust particles charged up negatively. Mostof the important effects of negative ions on plasma

02001 by The Japan Society of Plasma

Corresponding author's e-mail: plasm0S@ ec.ecei.tohoku.ac.jp
570

Science and Nuclear Fusion ResearchGohda T. er a/., Shock Formation by a Velocity-Modulated Ion-Beam Injection in a Magnetized Plasma with Negative IonsOJPuJoFIo_VuFzulElozo2tctJ

Fig. 1 Experimental apparatus.

Fig.2 Evolutions of perturbations when the beamenergy is positively modulated in a plasma withno negative ions at V- = 0.5 V.

and 167 cm long. Potassium ion plasmas produced bycontact ionization at hot 52-mm-diam tungsten plates(HP) of 2300 K, placed at both ends of chamber underelectron-rich condition, are confined by axial magnetic
field of 2 kG, as shown schematically in Fig.l. TheThe current perturbations are detected through a resisterto ground and the resulting voltage perturbations are
displayed on a digital oscilloscope which is externiilly
triggered by the signal generator.

machine is operated as a double plasma (DP) device [5].
One of them, the "driver plasma", is surrounded by asmall metal cylinder connected electrically to the hot
plate HPp. The other hot plate HP1 in the "target
plasma" is grounded. Electrons of the two plasmas areturbations when the beam velocity is positively

separated from each other by a negatively biased grid ofmodulated by applying ramp voltage V.* (= Vr + V_) to100 mesh/inch. By applying positive bias V5 to Hpp,ions of the driver plasma flow into the target plasma asa beam. The ramp modulation bias V- is -5 - 15 V andthe HPo in case of no negative ions. Here, c is 20 psec,

3. Experimental Results and Discussions
Figure 2 shows the evolutions of ion density per-initial beam energy V5 is 4 V, and V. is 0.5 V. Typicalbunching position is defined by / = vp2tl(v2 - v1),

the rise time z is 5 - 20 psec. When V_ > 0, compressional pulses with positive density slope are exited.

where v1 and v2 are the velocities of ions before andafter the modulation, respectively. When V- = 0.5 V andOn the other hand, when V- < 0, rerafactive pulses withnegative density slope are generated. Plasma densities ofthe driver and target plasmas are 5 x 108 - I x lOe cm-3and the electron temperatures Z" are about 0.2 eV. The
positive ion temperture is almost equal to e.
In order to produce a negative ion plasma, SF6 gas

Va = 4 Y, I = 23 cm, which is about the middle of theexperimental region between the grid and Hp1. The
perturbations excited grow gradually with propagating
along the beam. Since the modulation amplitude ofbeam energy is small, the evolution of perturbation isinterpreted by the linear wave theory as in Ref.[l]. On
the other hand, when the modulation amplitude of beamenergy is V- - 5 V, a large amplitude density pulse isgenerated around a bunching position of I= 12 cm,
accompanied by a steepening of the front slope asshown in Fig.3. Finally, a shock-like structure withpositive density slope (positive shock) is formed andpropagates with an almost constant velocity comparable
to the average speed of ion beam, v6 = (v1 + v2)12.

is introduced into the Q machine. The SF6 has a large
electron attachment cross section at T" I 0.2 eV toproduce SF; ions. The SF6 gas pressure is varied in therange 0 - I x 10-a Torr, yielding r= 0 - 0.99, density
ratio of negative to positive ions. The negative ion
temperature is estimated to be approximately 0.03 eVfrom SF6 gas temperture. Under our condition, collision
mean free paths ofcharged particles are longer than theplasma column length.

Figure 4(a) shows the spatial evolutions of

The evolutions of perturbations are measured byaxially movable mesh probe (6-mm-diam, 200 mesh/inch) which is biased negatively to detect ion current.

perturbation amplitude with modulation amplitude V- as
a parameter. The perturbation amplitude increases until
a beam bunching position indicated by an arrow ands71Gohda T. er al., Shock Formation by a Velocity-Modulated Ion-Beam Injection in a Magnetized Plasma with Negative Ions(")

36d!tiqllJD€nsity Ralio eoWO
^ 0.25o0.50

a 0.77o 0.95o-oaa
Fzotro6l!Oo4
PROPAGATION DISTANCE
Fig. 3 Evolutions of perturbations when the beam(b)energy is positively modulated in a plasma withno negative ions at V. = 5.0 V.

t=1'-:v 4lg!t(a)1z. 7 =10[ zsecl, Vrr=4.o[VlVr[Vl t Buncfiing Position (theory)
lo.eul
11Y79ofF'=oz>oo.;

a'5'o.

o.

IIo +o'r0.5zoEuo0oOYYvtroEFig.5 Spatial variations of the front slope of theperturbations at (a) V- = 5.0 V and (b) y- - -5.0 V;
9o.z -& 0.5
5.0
3+10.0 /E90.1(t,a 0.77o 0.95

PROPAGATIONDISTANCE z[cm]'with eas a Parameter.

30
PROPAGATION DISTANCE z[cm]10WO. r=VrUl&0.25^ 0.50trzoffoaat20Fig.a@). The saturation amplitude of the perturbationsyn.
increases with V., but is not simply proportional to(b)IIJoW/OFoIUJ3odl1l"'rn : 3l--EEIA 5.015.0?o.aRatio €ltJo 0.5rz[cm],1, Bunching

The spatial evolutions ofthe slope ofperturbationsin the presence of negative ions are shown in Figs.5(a)Poeition (theory)and (b), where the beam velocity is positively andnegatively modulated, respectively, with density ratio ofnegative to positive ions t = n,ln, as a parameter. As eincreases, both saturation amplitudes for positive and+15.O t/ /{idnegative modulations are decreased. But, in case of
positive modulation, it is found that the front slopes fortoorrorouol%N

I = 0 increase with the propagation. On the other hand,when € = 0.95, the slope does not increase markedly. On
the contrary, in case of negative modulation, the front
slope steepens during the propagation when e = 0.95,
but no remerkable steepening is observed when e = 0.
In our experiment the motion of negative ions SF;

DrsrffcE rl"rfo

Fig. 4 Spatial variations of (a) saturation amplitude and(b) front slope with y- as a parameter.

is negligible because of the large mass compared withpositive ions K*. Therefore, negative ion density isthen the growth is saturated subsequently. It is foundthat the slope of the wave front also increases and isalmost undisturbed along the beam. Under thissaturated around the bunching position as shown in572

Gohda T' er a/" Shock Formation by a velocity-Modulated

Ion-Beam Injection in a Magnetized plasma with Nesative

condition, the following model is presumed. When V. >0, compressive part with lower € slows down inaccordance with C,* - C./{l=, then front slope
decays. Reversely, when V_ < 0, rarefactive part withhigher e propagates faster, then front slope steepens.

Jons

Acknowledgements
We are grateful to Dr. S. Ishiguro, NIFS, for his
encouragement and Mr. H. Ishida for his experimental
advice.

This effect is dominant when e approaches l.

References

tll N. Sato, H. Sugai and R. Hatakeyama, phys. Rev.

4. Gonclusions
Evolutions of perturbation excited by large
amplitude velocity-modulation have been investigated ina negative ion plasma and shock_like structures areformed in a saturation state. The structure of the shocks
depends on the density ratio e of negative to positiveions. When e is small, positive slope is steepening. On

the other hand, when e is large, negative slope issteepening. The method of velocity modulation is quite
effective for generating positive and negative density
perturbations in negative ion plasmas.

Lett.34,93r (1975).

t2l N. D'Angelo, S.V. Goeler and T. Ohe, phys. Fluids
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t3l B. Song, N. D'Angelo and R.L. Merlino, phys.
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[5] Taylor R.J. and Coroniri, phys. Rev. Lett. 29,34(r97T.

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