Contrib. Plasma Phys. 38 (199s) 1/2,136-241

Asymmetry of the Electron Distribution Function in the PISCES-A Linear Divertor Simulator

L. Schmitz1 and 0. Batishchev2~3.~ Institute of Plasma and Fusion Research. University of California, Los Angeles. CA,USA

* Massachusetts Institute of Technology, Cambridge, MA, USA Lodestar Research Corporation, Boulder, CO 80301, USA Keldysh Institute for Applied Mathematics. Moscow 125047. Russia

I. Introduction In a dissipative divertor, the electron energy is strongly reduced near the divertor target due to inelastic electron collision processes such as ionization, dissociation, and line radiation as well as possibly recombination. Ion-neutral collisions can maintain a parallel plasma pressure gradient, and a sizable parallel electric field will develop due to this pressure gradient as well as due to the electron thermal force. It is well known that strong gradients of the plasma parameters parallel to the magnetic field can enhance non-local effects in a tokamak divertor [l]. As a result, the parallel electron energy distribution function can become asymmetric, as recently predicted by kinetic modeling, and the electron heat flux can be suongly affected. This asymmetry can affect plasma transport, plasma-neutral particle interactions, and the residual electron heat flux transmitted to the divertor target. Non-local effects thus have to be taken into account for predictive divertor modeling as well as for the correct interpretation of divertor probe data. In this paper, we discuss measurements and modeling results of the upstreanddownstream asymmetry of the electron distribution function in the PISCES-A linear divertor simulator. The PISCES-A detached plasma experiments [2] are modeled with the kinetic lD2V-code ALLA [3]. We present a preliminary comparison of code results and electron energy measurements in PISCES-A made by two-sided Langmuir probes.

II. Experiment The PISCES-A device is a linear reflex arc plasma source producing a magnetized (Bz10.02 T) plasma column of 1.3 m length [2]. The source plasma parameters (n 12x 1018 m-3, kTe S 20 eV) are similar to a typical tokamak scrape-off layer. The plasma is enclosed by a water-cooled, anodized aluminum tube simulating a closed (slot) divertor. Hydrogen can be introduced via a secondary gas feed near the divertor target. At four

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reference locations, the electron temperature has been measured by a two-sided probe with upstream and downstream tips which are mechanically insulated from each other. Detailed experimental results on plasma-neutral interactions and plasma detachment have been published elsewhere [4]. Fig. 1 shows the measured axial plasma density profile for a fully detached plasma, as measured by a plain Langmuir probe oriented towards the plasma source. The neutral pressure at the target is 180 mtorr, corresponding to a molecular hydrogen density of 1.5x1@1 m-3. For comparison, the neutral pressure at the (upstream) plasma source is about 1 mtorr. The bulk electron temperature decreases from 15 eV at the source to less than 3 eV at the target (Fig.3). In addition to the bulk electron population,

c' 4

4m) Fig. 1: a) Measured axial p h m a &nrity profile; b) axial profile of relative density

of primay (beam) clectronr.

there is an energetic (primary) electron population in this reflex arc discharge, accelerated by the cathode sheath potential to a beam energy of 60-100 eV, which is clearly discernible in the Langmuir probe characteristics. The beam energy decreases monotonically away from the plasma source to 20 eV at z = 0.2 m as a result of velocity space diffusion.

In. Kinetic Modeling with the Code ALL4

In order to accurately model dissipative divertor regimes, the effects of electron energy

and momentum losses due to ionization, H2 dissociation, and line radiation have recently

been included into the 1D2V Fokktr-Planck code ALLA [ 11. This code has been used to model the electron energy distribution function in the PISCES-A linear divertor simulator. Atomic and molecular neutral density profiles arc taken from measurements as well as fluid modeling reconstructions of PISCES-A experimental data [2]. Coulomb self-collisions of electrons are taken into account without approximation, while electron-

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ion collisions are linearized [3]. To facilitate a detailed comparison of code results and

experimental data, the effects of the energetic (primary) electron population produced in

the plasma nflex-arc source in PISCES-A have been included into the code. The plasma

evolution is described by the kinetic equation for the electron distribution function

f, 0, x. u, P) :

--+LIB-+-- & & 1 9 vp-f, +-- l-p2)-f, =c;+c;+c#! (2) b & ’ : ) v @ [ ( : ] Here x E [O,L] is the coordinate along to the magnetic field u is the modulus of the

velocity and jf is the cosine of the particle’s velocity pitch angle; e and me an the charge

and mass of electrons. EL is the parallel electric field calculated from the Braginskii

formula, Cl ,Cf are the e-e and e-i Coulomb collisional terms,C: is the electron-

neutrals collisional term (we take into account only inelastic collisions with hydrogen atoms and molecules). We assume the following boundary conditions: at x=L the distribution function is a superposition of two Maxwellians , f (for cold bulk and hot

The sheath potential A ~ Q , at the target, x=O, is evaluated using a logical sheath boundary

condition since the spatial scale is much bigger than Debye length. We equate the presheath fluid ion flux to the electron flux collected at the plate .

+I v

05n,c, ( x = 0) = j ~ ’ p f ~ ( x = 0, u, p) dpdu (4) -I -

where u, =-,/-. The initial electron distribution is assumed to be a

MaxweUian with the experimental parameters. Eq.(l) is solved with a finite volume

technique on non-uniform grids in both real and velocity space, and combines a cubic spline technique for the free-streaming term with an implicit 9-points scheme for the Coulomb operator. The spatial resolution is around 3 cm. The velocity mesh varies from

0.01 Ur to 20 v, to resolve very energetic primary electrons coming from the cathode as

well as the cold bulk electrons. A typical grid size is 6 5 x 2 5 7 ~ 2 3 in 1.1. u and x

respectively.

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lV. Results

Fig.2 shows the modeling results of the electron energy distribution for the detached

plasma discussed above. Both inelastic electron-neutral collisions and a primary electron

source (np/np = 0.02 at a beam energy of 60 ev) have been included in the model. There

is a pronounced depletion of the upstream part of the energy distribution which persists

throughout the modeled domain (0 5 z S 0.95 m). This asymmetry is only in part due to

the beam electrons streaming towards the target. More importantly, electrons streaming towards the target with energies above the target sheath potential arc lost, while low energy electrons an reflected. The sheath potential in this case is about 12 eV (see Fig. 5 ) and the cutsff of the upstream distribution at energies above the sheath potential is clearly obvious in Fig.2b. Fig.3 shows a comparison of measured and calculated upstream and downstream electron energy. The bulk electron tcmperanue measured by the upstream tip is larger as compared to the downstream tip by up to 40%. The perpendicular electron temperam is substantially lower than the parallel component due to the predominance of small-angle scattering. In comparing experimental and modeling data. it is important to keep in mind that the probe is also sensitive to electrons with finite perpendicular energy and therefore does not measure the true parallel electron

energy. Thus it is not surprising that the parallel temperahue predicted by the code is above the measured electron energy (while the measured upstreamldownstream ratio is

well matched by the code results).

i ,J *m

u

Fig.2: Calculated 2 -0 electron energy dirtribution; a) near t h p b n a source (z = 0.94 m); b) at the rargrt (zoo).

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10

P s

ao u a4 a8 OA 1.0 4 m )

Fig. 3: Measured a d calcvhted upstream ad dowmtream electron energy vs. axicrl position (high pressure dctached plasma).

As expected, the sheath potential at the target is enhanced due to the energetic electron

component. Fig.4 shows the temporal evolution of the sheath potential for the detached

plasma simulation and for a reference case without hydrogen gas injection at the divertor

target. Since the energetic primary electrons an launched at the plasma source, the sheath potential at the target saturates on the time scale of the primary electron transit

time and is very sensitive to the energetic electron fraction ndnp In the detached

plasma, the primary electron-neutral mean fne path near the divertor target is smaller than the plasma length and the scale length of the electron temperature gradient.

Including inelastic electron-neutral collisions in the code thus results in increased velocity space diffusion of the primaq electrons and in a substantial reduction of the calculated sheath potential in steady state. The code results obtained in this way match the experimental data quite well as shown in Fig.5. The reference case without gas injection as well as two intermediate cases with lower target gas injection rates have been also

included in Fig.4.

HIGH PRESSURU 1

0.t 0 3 oa 0.4 0 1

t . m- Fig.4: Temporal evolution of the sheath potential for the detached phrmcr case w d

for a reference case without gas injection

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0 loo 200

Fig.5: Comparison of measured and calculated sheath potenrial as afvnction of target nevtml hydrogen pressure. I n c l d d me modeling results for a higher beam density (3%) and a case where neutr4LI have been neglected

P, (m

v. summary

We have demonstrated that both inelastic electron-neuual collisions and energetic primary electrons have to be taken into account to model the sheath potential and the

observed asymmetry of the electron distribution function in PISCES-A. For the detached plasma case discussed above, the primary electrons (Ue > 8 kTe) contribute about 50% of

the total electron heat flux near the target (in agreement with earlier experimental observations [4]). The measured and calculated asymmetry of the upstream/downstream

bulk electron energy is comparable. Inelastic electron-neutral collisions contribute substantially to velocity-space diffusion both for primary and bulk electrons, resulting in a lower target sheath potential. In conclusion, we have demonstrated that both electron- neutral collisions and non-Maxwellian features in the scrape-off layer plasma need to be taken into account self-consistently for comctly evaluating the sheath potential and the target heat flux in predictive divertor modeling.

*This Work supported by DOE pants DE-FG02-91ER54109 (MI;T), DE-FGOZ-88ER53263 (Lodestar) and DE-FG03-95ER5430 I (UCSD).

M. References [l] A.A.Batishcheva et al., Physics of Plasmas 3 (1996) 1634. [2] L. Schmitz et al., Physics of Plasmas 2 (1995) 3081. [3] O.V. Batishchev et al., Bulletin A P S Vo1.41, N7 (1996) 1483. [4] L. Schmitz et al., 20th EPS Conference, Vol.lI. (1993) 75 1.