COMPI,,PTATIONALMODEL OF SURFACE ABLATION FROM TOKAMAK DISRUPTIONS

Transcription

1 PAPER COMPI,,PTATIONALMODEL OF SURFACE ABLATION FROM TOKAMAK DISRUPTIONS David Ehst and Ahmed Hassanein Argonne National Laboratory 9700 S, Cass Avenue Argonne, IL USA The submitted manuscript has been authored by a contractor of the U.S. Government under contract No. W-31-10g-ENG-38.,... : Accordingly, the U. S. Government retains a. nonexclultve, rovaltv-free license to publish ".. or reproduce the Published form of this... ; ' _ contribution, or allow others to do so, for U. S. Government purposes. October 1993 * Work supported by the U.S. Department of Energy, Office of Fusion Energy, under Contract No. W Eng-38. Paper to be presented at the IEEE/NPSS 15th Symposium on Fusion Engineering, October 11-15, 1993, Hyannis, MA. 1_t_ DISTRIBUTION OF THIS DocUMENT IS UNLIMITED

2 I, Computational Model of Surface Ablation from Tokamak Disruptions* David Ehst and Ahmed Hassanein Argonne National Laboratory 9700 South Cass Avenue, Argonne, IL ABSTRACT Our computer code simultaneously solves these equations in a time-dependent manner, conserving energy and following Energy transfer to material surfaces is dominated by photon the evolution of the target vapor cloud. The code uses radiation through low temperature plasma vapors if tokamak simplified algorithms which eliminate many detailed atomic disruptions are due to low kinetic energy particles (_ 100 ev). physics calculations which have little bearing on the final Simple models of radiation transport are derived and result. As a consequence, we have achieved a very fastincorporated into a fast-running computer routine to model running routine which makes parametric studies practical for this process. The results of simulations are in fair agreement disruption modelling. Details of our atomic physics with plasma gun erosion tests on several metal targets, calculation compare well with more sophisticated computer codes, and the ablation predictions substantially agree with INTRODUCTION AND SUMMARY measurements of plasma gun erosion of targets such as Fe and Mo. Results reported in this paper are based on a stand-alone Observed damage to tokamak surfaces during thermal version of DESIRE, while more accurate simulations are disruptions has motivated bench tests (electron beams [e- possible by incorporating DESIRE as a subroutine to beams] and plasma guns) which simulate tokamak conditions; A'THERMAL. and also models of plasma-material interactions have been produced in order to better understand the nature of this EXAMPLE: HYDROGEN GUN ABLATION OF Mo erosion process. Computer studies with codes such as A'THERMAL [1] have shown that the ablation cloud itself Our computational model was tested by comparison with absorbs considerable energy from the thermal dump, and this observable parameters on several plasma gun experiments. As vapor shielding serves to mitigate the actual damage to the an illustration we model an experiment with the PLADIS gun solid surface. Vapor shielding of e-beams is easily calculated [2] at the University of New Mexico. We consider a hydrogen from the stopping power of high-energy electrons in the gun with proton and electron energies of 30 ev and 1 ev, vapor. We have recently developed a computer routine respectively, incident on a Mo surface, and we study the case DESIRE, which extends this analysis to sub-kev particles, with U I = 9.1 MJ/m 2 heat load over a 100 Its duration. more typical of thermal disruptions and plasma guns. Such low-energy particles suffer 90 scattering and create a thermal The gun hydrogen plasma radiation source and the plasma source in front of the vaporized target material. In this vaporized Mo target plasma are both followed in a time limit, energy is radiated as photons by the source plasma; this radiation is partly absorbed in the target vapor and partly dependent manner. transmitted through the target to the material surface. Under Fig. 1 shows the evolution of the source and target vapor typical conditions (10 MJ/m 2, <1 ms pulse width) the source temperatures, 0 S and 0T, and ionization degree, _S and q>t. impulse maintains both the source and target plasmas in the The target vapor is initially only barely ionized, as 0T = 0.45 Saha regime. For given densities and vapor temperatures the code computes the degree of ionization and the effective ev is well below the first ionization potential of Mo (Z1 = charge state of both zones. The heat capacity of each vapor, 7.1 ev), but _T increases rapidly as 0T rises due to the which can be a significant heat sink in this process, is found heating by the source vapor's radiation. The source vapor from particle kinetic energies along with the ionization and starts out and remains fully ionized until t = 10 Its. During excitation energy. The source and target plasmas respectively this first phase the hydrogen radiates inefficiently, but as 0s radiate and absorb radiation over a broad spectrum of eventually drops to -6 ev the recombination radiation wavelengths; and the optical depth of each zone is computed absorption edges arise, leading to a spike in the hydrogen at each wavelength by calculating the contributions from radiated power. As a consequence of this power loss the Bremsstrahlung (with ions and neutrals) and free-bound source temperature abruptly collapses. Beyond t-_- 30 Its the radiation. Finally, the equation of radiative transfer hydrogen radiative loss diminishes; and both source and target determines the photon power spectrum transmitted through the vapors are only partially ionized, with slowly dropping target vapor to the material surface, temperatures. Considerable energy is lost out the sides of the source Fig. 2 shows the spectral emissivity of the source plasma vapor zone; as this radiated power is directed away from the and transmissivity of the target vapor at t Its. The Lyman ablating surface, this two-dimensional effect further serves to and Baimer absorption edges are prominent for the hydrogen reduce ablation, source at -6 ev (during the radiative collapse). The effect of this free-bound radiative opacity is the two peaks in the source * Work supported by the USDOE/OFE, under contract No. emissivity, es, near rls = hc/kos_, = 0.6 and 2.3 in Fig. 2. W Eng-38. Note, however, es (1"1)is quite small compared to black body /

3 r IL emissivity. The target vapor at I ev exhibits the absorption at Eio = 31)eV is in good agreement with the data at UI < 12 edge of Mo + recombination into the Mo ground state; the MJ/m 2, while it underestimates erosion at 16 MJ/m 2. This is corresponding wavelength of 0.17 Itm is at rls = I.! for a additional evidence suggesting the plasma gun produces source temperature 0 s = 6.1 ev. Due to the small line- higher ion kinetic energies at large U I. averaged density of vaporized Mo, the target vapor is optically thin, with the target transmissivity nearly equal to the source The agreement of the DESIRE model with the emissivity, experiment, shown in Fig. 4, is much better than the MAGFIRE result [3] which found 5 = 10.7 Itm r,t U 1 = 8.3 Despite the transparency of the target vapor, relatively little of the plasma gun energy arrives at the Mo surface; the MJ/m 2. This emphasizes the importance of the additional fraction is only Y = 0.45 MJ/9.1 MJ = Most of the heat sinks incorporated in our treatn'tent, which constitutes a incident energy is radiated by the source vapor sideways (6.8 distinct improvement relat:ive to earlier calculations. MJ/9.1 MJ) and backward (0.55 MJ/9.1 MJ). At the end of the pulse tb.e source vapor also stores considerable energy Molybdenum targets were tested with both U.S. and density due to its heat capacity (Us/UI = 1.2 MJ/9.! MJ). The Russian plasma guns, and the experimental data, in Fig. 5, again show [4,5] how typically there is a scatter of results target vapor stores relatively little energy density and losses under similar conditions. The horizontal error bars from little to sideways radiation. Due to these sundry heat sinks the VIKA are a measure of uncertainty in the energy content vapor shielding is quite effective, the ablation depth being delivered in the plasma pulse, and the vertical scatter of only 5 = 0.29 I-_mfor Mo with 9 = 9000 kg/m 3, PLADIS points indicate a certain lack of reproducibility in these experiments. Some difference between the two DESIRE CODE COMPARISON WITH institutional results may be attributed to subtle geometric PLASMA GUN DATA differences; for example, VIKA had a gun-to-target distance of 3.0 m but PLADIS had gun electrodes much closer to the Code validation is best achieved by comparison with target. The DESIRE results shown treated both geometries experiments, which we have done for various metal surfaces the same. Our calculated erosion with Eio ev - 50 ev is and different plasma gun conditions. The calculations assume in approximate agreement with the data. Time-of-flight a sine-shaped wave form for the heat load, of total length 100 measurements on PLADIS suggest the leading edge of the gun Its. pulse is populated by protons at a few tens of electron volts, which is perhaps a bit lower than Eio = 30 ev - 75 ev Fig. 3, adapted from [2], shows three data points of reported on VIKA. measured energy transmission fraction to a tungsten calorimeter through the vapor clouds generated under Erosion of tungsten was likewise measured on both VIKA specified heat loads. The gun energy density, noted by the and PLADIS, and the results are shown in Fig. 6 along with abscissa, was determined from discharges into a deep copper the DESIRE calculations. In the experiments tungsten appears bucket calorimeter, which accounted for total plasma energy, including sideways-radiated losses. When the DESIRE code more robust than Mo under the same heat pulse conditions. is run with a fixed initial ion kinetic energy from the plasma Both experiment [4] and the DESIRE theoretical model gun, Eio = 30 ev, the calculation shows Y decreasing as U1 show beryllium to suffer more erosion than the three metals increases from 6 MJ/m 2 to 16 MJ/m 2. Yet the data suggest Y discussed above, which is evident from Fig. 7. A noteworthy increases with U l; so we conclude that Eio may be increasing point illustrated in the graph is that the central dcpth of the with U1. (This is not unreasonable, as, for a fixed pulse damage crater is roughly triple the average depth, as inferred width, e.g., 100 Its, the experimental set-up keeps the bank from mass loss measurements. The nonuniform crater depth capacitance constant and increases UI by raising the voltage may be associated with a depression in the melt layer, possible on the bank.) Whereas Eio = 30 ev agrees with the data at U1 redeposition or splashing of the melt toward the edges, and = 6 MJ/m 2, apparently Eio _, 100 ev would be needed to nonuniform heat deposition by the gun plasma. Such details duplicate the data at 16 MJ/m 2. are not included in the present DESIRE model. Target erosion is an obvious test for DESIRE. The CONCLUSIONS experimental data (points) in Fig. 4 [2] display the average Although our atomic physics models are very simplified ablation depth of steel found at four different values of U1. we are able to duplicate many observed features of plasma There is a wide, inconsistent scatter of results with only slight gun ablation experiments with a reasonable accuracy. Besides differences in target composition, so we cannot expect energy transmission fraction and erosion depth, our model DESIRE to fully explain the observed erosion. However, it is agrees well with measured vapor temperatures, pressures, and evident, in the experiment and from the DESIRE results for spatial extent as seen in experiments [4-6]. pure Fe, that minimal erosion occurs below U MJ/m 2. Yet substantial erosion occurs for UI _" 10 MJ/m 2. The code The main shortcoming of our model presently is its results show this onset of erosion is associated with an limitation to a pure hydrogen plasma source with Eio + Eeo 2: ablation threshold, which is a characteristic of the thermal 50 ev. We hope that by extending the code capability to properties of metal surfaces. Note also that the DESIRE curve

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5 energies > I00 ev we will be better able to duplicate the 100,, experimental data, such as shown in Figs. 3and7. _, [ I [, ], I I- [ I ] ', _ l:_ VIKA [BARABASH] ACKNOWLEDGMENTS o PLADIS [GAHL] - We are indebted to R.R. Peterson for many enlightening conversations, and to J.M. Gahl, J.T. Bradley, III, and J.F. Crawtbrd for access to their plasma gun data REFERENCES "_" : _ [I] A. M. Hassanein, "Simulation of plasma disruption "-" induced melting and vaporization by ion or electron,o beam," J. Nucl. Mater. 122&123 (1984) _ J_50 [2] S. Suzuki, J. F. Crawford, J. T. Bradley, III, and J.M. 1.0 o- _ELf --_ Gahl, "Experimental study of pulse plasma heat flux,_ absorption and ablation measurements of materials during _ the simulation of the thermal quench phase of tokamak - n _ m plasma disruption," J. Nucl. Mater. 20 f10 (1993)265. -Eio (ev) [3] J. Gilligan, D. Hahn, and R. Mohanti, "Vapor shielding of DESIRE surfaces subjectedtohighheatfluxesduringaplasma 0.1 ' I, I, I, I, I, 1, disruption," J. Nucl. Mater !64 (1989) a a [4] J.M. Gahl, private communication. ENERGYDENSITY (Md/m2) [5] V. R. Barabash et al., "Damage of refractory metals and Fig. 6 Ablation of W (100 Its) by H plasma guns. carbon-based materials under simulation of the thermal influence at plasma disruption," Fusion Eng. and Design I..88(1991) ' 1 ' I ' I ' I ' I ' I ' [6] V.M. Strunnikov, private communication. -m - A m _oo_' I ' I ' I ' I ' I ' I ' - - o - E)-----El VlKA [BARABASH] O -- - O PLADIS [GAHL] - _ O _ m m - - v'_ '-- _ 'Q EIo(eV)- 30 [)ESIRE,o O 1.o- o _5o z_maximumcraterdepth(profilometry) E: EP o_3_f_5_ 40 _ - o AVERAGE DEPTH (MASS LOSS) - - DESIRE- 0."' I' 1, I, I t I., I, - 0 _._ ,,,,,,.,.,.,,,--i) Eio(eV)= 30 o,, I, I, I, I, I, I, ENERGY DENSITY (MJ/m 2) Fig. 5 Ablation of Mo (tu = 100 Its) by H plasma guns. ENERGY DENSITY (Md/m 2) Fig.7 Ablationof Be (I00Its)by H plasmagun. DISCLAIMER This report was prepared as an account of work sponsored.by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed hereto do not necessarily state or reflect those of the United States Government or any agency thereof.

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