THE REDUCTION OF DIFFUSION BY PLASMA ROTATION AND ION DISSIPATIVE EFFECTS

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THE REDUCTION OF DIFFUSION BY PLASMA ROTATION AND ION DISSIPATIVE EFFECTS

J.J.A.M. van der Mullen, B. Pots, D. Schram, B. van der Sijde

To cite this version:

J.J.A.M. van der Mullen, B. Pots, D. Schram, B. van der Sijde. THE REDUCTION OF DIFFUSION

BY PLASMA ROTATION AND ION DISSIPATIVE EFFECTS. Journal de Physique Colloques,

1979, 40 (C7), pp.C7-283-C7-284. �10.1051/jphyscol:19797139�. �jpa-00219112�

JOURNAL DE PHYSIQUE CoZZoque C7, suppldment au n07, Tome 40, ~ u i Z Z e t 1979, page C7- 283

THE REWCTION OF DIFFUSION BY PLASMA ROTATION AND ION DISWATIVE EFFECTS

J.J.A.M. Van der Mullen, B.F.M. Pots,,D.C. Schrarn and 6. van der Sijde.

Eindhoven University o f Technoloqy, Eindhoven, the Netherlands.

Introduction.

Many studies have been conducted on particle transport and pressure enhancement in magnetized arcs

I.

The magnetic field reduces the transverse electron heat conduction and particle diffusion (at least classical), leading to higher axisvalues of Te and ne. In addition the Nernst effect reduces

1

I

also the particle transport

.

In many of these treatments the effects of ion- viscosity and ion-neutral friction have been ignored.

~ l h b e r 21 realized, that in these arcs rotational

trodes : at the cathode the plasma is hotter and more dense than at the anode. It is the aim of this contribution to show, as well theoretically as expe- rimentally that because of these effects the par- ticle confinement may be appreciably better than

"Nernst classical", i.e. classical including the Nernst-effect; in many cases the pressure-built up can be explained by the rotational confinement rather than by the Nernst effect.

Theoretical prediction.

velocities are relatively large and may even 2kT.

approach the ion thermal velocity

---;L;

the rota- tion (caused by radial electro field E M, ) is connec- ted with the presence of radial current. At the cathode it tends to be positive (Er < 0, directed inward), at the anode negative (Er > 0); the exact potential distribution depends also on geometry

(cf. fig. 1). We will show that the combined effects of rotation and ion-viscosity and ion-neutral fric- tion can reduce the particle transport substantially for positive rotation (cathode side and in our case for most of the arc length) and can enhance the transport for negative rotation (close to the anode).

Consequently, there exists a weak axial gradient even in a cylindrical geometry with identical elec-

.02 .01 0 .01 a02

V thi

z

We have investigated elongated quasi-cylindrical arcs with axial dimensions (typical gradient length L) much longer than radial dimensions (A). The rate of the two scale lengths is supposed to be in the order ot the Hall parameter R T which is supposed

e e'

to be large (L/A% R T >> 1; Re, electroncyclotron

,,

e e

frequency; T ~ , electron-ion collision time). The radial diffusion velocity, wriC1, is much smaller than rotational velocity, wei. If we assume 'I, that the radial electric field is in the order of the temperature over the radial scale length A:

E(A) %

x,

kT we can estimate w to be : w %a(r)rQi,

ei 0 i

with a(r) s vthi2/~2Ri2. Furthermore, with

w % b(r)rRi, one can show that for classical dif- r i

fusion w ri/wei = b(r)/a(r) s I/Re~e.

The analysis cif the momentum equations for ions and electrons with systematic ordering in l/R T and

e e l i i / ~ (Aii = v ~ ~ ~ T ~ ) , yields the following diffusion flux 3l:

The second term contains contributions of viscosity

( v . ~ ~ ) ,

ion neutral friction, Ria, and momentum transfer connected to a finite source term M S ; we consider the case R.T. < 1.

1 1 -

In the experimental case considered, we may ne- glect the pinch- and ion-terms in the first term of

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797139

nwri which can be written as nw = D with

ri ar

classical diffusion coefficient DC1 = kTe e B The second term of nwri "rotational o 'eTe '

diffusion", is multiplied by ile~e and can be very large. All three contributions depend on wgi; if the ion rotation is positive (cathode side) the rotational diffusion is inward, if it is negative then the diffusion is outward. For our experimental conditions (and the estimate of wgi as above), the rotation-viscosity contribution and the ion-neutral friction are in the same order as classical trans-

3

I

port

.

Anomalous diffusion.

For large values of Sle~, and B we observe also a high level of turbulence. These fluctuations (k%l/A) may give rise to anomalous (Bohm) diffusion and enhance the transport. The anomalous diffusion co- efficient, Dan, can be estimated as

-

:

D~~ = D" Q T ( E ) , if we ignore here the effect e e n

of rotation.

The turbulence level is measured 41 by probing the plasma-light-fluctuations with two photodiodes

(f < 1 MHz). Of the three classes of observed waves

(rotational instabilities, drift waves, ion waves, all propagating transverse to B ) we assume that the drift waves are mainly responsible for the ano- malous transport, the spectrum is relatively broad- band, with f

;

ni/2n, and k % ]/pi. An anomalous enhancement of transport may occur for large values of Q e ~ e and

-.

n

Experimental arrangement and procecure.

We analysed the argon plasma of a hollow cathode arc (length 1.4 m, diameter .03 m). The magnetic field is varied between .05 and .4 Tesla, the plasma- current between 20A and 200 A. The electron density, ne, and temperature, Te, were measured with Thomson- scattering (.2

lo2'

< ne < 2.10~'; 2,5 eV <

<

^{< 5eV).}

The neutral density, na, is obtained from line inten- sities (4p

-

4s transition 696.5 nm) and a colli- sional radiative model of the Ar I-system 51. Ion- and neutral temperatures follow from the Doppler broadening of Ar I1 and Ar I lines. For the experi- mental determination of the ion transport we need the

source term S.. As the axial gradients are weak and the axial component of the ion systematic velocity w is small (though nonzero 61) we may write from

zi

the ion mass balance (recombination can be neglected):

Results and discussion.

In fig. 2 the measured diffusion coefficient D~~~ is compared with classical transport, D" as a function of the Hall parameter,

9 ~ ~ .

The measure- ments refer to the plasma near the axis at a loca- tion halfway the electrodes. It is observed that for several conditions the diffusion is remarkably reduced as compared to classical transport. We con- clude, that for these conditions rotation with ion- friction improves plasma confinement apprecially.

However, for large values of (and increasing values of the fluctuation. level) the improvement deteriorates contrary to the expectations based on the rotational reduction only. The fluctuation levels are typically between <I0 -3 (for low values of Qeh) UP to >10 -2 (for larger values of %.re)

.

We observe indeed an anomalous diffusion with va- lues which are in agreement with the expectations.

We may conclude that anomalous .-, transport takes over for large values of

( a

e e T ) n

-.

ⁿ

Acknowledgement.

We gratefully acknowledge the assistance of Mr.

van der Sande. This work is partly supported by the foundation FOM.

.<eferences

.

1

]

G. Venus, Z. Physik 259 (1973) 437.

2 ] 0. ~liiber, 2. ~ a t u r f z c h .

25a

(1970) 1583,

27a (1972) 652.

3 1 J.J.A.M. van der Mullen, B.=. 'pots, D.C.

Schram, to be published.

4

j

B.F.M. pots et al., Qroc. 3rd Int. Conf. Waves and Instab. Plasmas, Palaiseau France, 1977, p 88-4B4.

5lJ.J.A.M. van der Mullen et al., Proc. 13th ICPIG, Berlin, 1977, p. 323-324.

6lP.A.W. Tielemans, B. van der Sijde, private communications.

71P. Janssen, to be published (thesis 1979).

anomalous A diffusion

riffusion X

X

*