×

A Huygens immersed-finite-element particle-in-cell method for modeling plasma-surface interactions with moving interface. (English) Zbl 1524.35666

Summary: Surface evolution is an unavoidable issue in engineering plasma applications. In this article an iterative method for modeling plasma-surface interactions with moving interface is proposed and validated. In this method, the plasma dynamics is simulated by an immersed finite element particle-in-cell (IFE-PIC) method, and the surface evolution is modeled by the Huygens wavelet method which is coupled with the iteration of the IFE-PIC method. Numerical experiments, including prototypical engineering applications, such as the erosion of Hall thruster channel wall, are presented to demonstrate features of this Huygens IFE-PIC method for simulating the dynamic plasma-surface interactions.

MSC:

35R05 PDEs with low regular coefficients and/or low regular data
35R37 Moving boundary problems for PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65T60 Numerical methods for wavelets

Software:

IFE-PIC
Full Text: DOI

References:

[1] Abashkin, V. V.; Gorshkov, O. A.; Lovtsov, A. S.; Shagaida, A. A., Analysis of ceramic erosion characteristic in hall-effect thruster with higher specific impulse, 30th International electric propulsion conference, Florence, Italy, 0336 (2007), IEPC
[2] Absalamov, S. K.; Andreev, V. B.; Colbert, T., Measurement of plasma parameters in the stationary plasma thruster (spt-100) plume and its effect on spacecraft components, 28th AIAA/ASME/SAE/ASEE joint propulsion conference and exhibit, Nashville, TN, 3156 (1992), AIAA
[3] Adjerid, S.; Ben-Romdhane, M.; Lin, T., Higher degree immersed finite element methods for second-order elliptic interface problems, Int J Numer Anal Model, 11, 3, 541-566 (2014) · Zbl 1499.65639
[4] Adjerid, S.; Guo, R.; Lin, T., High degree immersed finite element spaces by a least squares method, Int J Numer Anal Model, 14, 604-626 (2017) · Zbl 1429.65291
[5] Babuška, I., The finite element method for elliptic equations with discontinuous coefficients, Computing, 5, 3, 207-213 (1970) · Zbl 0199.50603
[6] Babuška, I.; Osborn, J., Can a finite element method perform arbitrarily badly?, Math of Comput, 69, 230, 443-462 (2000) · Zbl 0940.65086
[7] Barral, S.; Makowski, K.; Peradzyński, Z.; Gascon, N.; Dudeck, M., Wall material effects in stationary plasma thrusters. II. near-wall and in-wall conductivity, Phys Plasmas, 10, 10, 4137-4152 (2003)
[8] Birdsall, C. K.; Langdon, A. B., Plasma physics via computer simulation (1991), Institute of Physics Publishing: Institute of Physics Publishing New York
[9] Bramble, J. H.; King, J. T., A finite element method for interface problems in domains with smooth boundary and interfaces, Adv Comput Math, 6, 109-138 (1996) · Zbl 0868.65081
[10] Cao, H.; Chu, Y.; Wang, E.; Xia, G.; Zhang, Z., Numerical simulation study on barrel erosion of ion thruster accelerator grid, J Propul Power, 31, 6, 1785-1792 (2015)
[11] Cao, H.; Li, Q.; Shan, K.; Cao, Y.; Zheng, L., Effect of preionization on the erosion of the discharge channel wall in a hall thruster using a kinetic simulation, IEEE Trans Plasma Sci, 43, 1, 130-140 (2015)
[12] Cao, Y.; Chu, Y.; He, X.-M.; Lin, T., An iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity, J Comput Phys, 281, 82-95 (2015) · Zbl 1351.78045
[13] Cao, Y.; Chu, Y.; Zhang, X.; Zhang, X., Immersed finite element methods for unbounded interface problems with periodic structures, J Comput Appl Math, 307, 72-81 (2016) · Zbl 1382.78017
[14] Carter, G., Huygen’S wavelets and deterministic evolution of surfaces and interfaces, Vacuum, 48, 11, 925-931 (1997)
[15] Carter, G.; Nobes, M. J., Surface morphology evolution of sputtered, moving substrates, J Mater Sci Lett, 3, 6, 523-527 (1984)
[16] Chen, Z.; Wu, Z.; Xiao, Y., An adaptive immersed finite element method with arbitrary lagrangian-Eulerian scheme for parabolic equations in time variable domains, Int J Numer Anal Model, 12, 567-591 (2015) · Zbl 1499.65346
[17] Chen, Z.; Zou, J., Finite element methods and their convergence for elliptic and parabolic interface problems, Numer Math, 79, 2, 175-202 (1998) · Zbl 0909.65085
[18] Cheng, S. Y., Modeling of hall thruster lifetime and erosion mechanisms (2007), PhD dissertation, Massachusetts Institute of Technology
[19] Cho, S.; Komurasaki, K.; Arakawa, Y., Kinetic particle simulation of discharge and wall erosion of a hall thruster, Phys Plasmas, 20, 6, 063501 (2013)
[20] Chou, S., An immersed linear finite element method with interface flux capturing recovery, Discrete Contin Dyn Syst Ser B, 17, 7, 2343-2357 (2012) · Zbl 1262.65168
[21] Chou, S.; Kwak, D. Y.; Wee, K. T., Optimal convergence analysis of an immersed interface finite element method, Adv Comput Math, 33, 2, 149-168 (2010) · Zbl 1198.65212
[22] Chu, Y.; Cao, Y.; He, X.-M.; Luo, M., Asymptotic boundary conditions with immersed finite elements for interface magnetostatic/electrostatic field problems with open boundary, Comput Phys Commun, 182, 11, 2331-2338 (2011) · Zbl 1308.78006
[23] Chu, Y.; Han, D.; Cao, Y.; He, X.; Wang, J., An immersed-finite-element particle-in-cell simulation tool for plasma surface interaction, Int J Numer Anal Model, 14, 2, 175-200 (2017) · Zbl 1365.76112
[24] Coche, P.; Garrigues, L., A two-dimensional (azimuthal-axial) particle-in-cell model of a hall thruster, Phys Plasmas, 21, 2, 023503 (2014)
[25] D. Depew, D. Han, J. Wang, X.-M. He, T. Lin, Immersed-finite-element particle-in-cell simulations of lunar surface charging, #199, Proceedings of the 13th spacecraft charging technology conference, Pasadena, California, June 23-27, 2014.; D. Depew, D. Han, J. Wang, X.-M. He, T. Lin, Immersed-finite-element particle-in-cell simulations of lunar surface charging, #199, Proceedings of the 13th spacecraft charging technology conference, Pasadena, California, June 23-27, 2014.
[26] Dragnea, H.; Boyd, I.; Lee, B.; Yalin, A., Characterization of eroded boron atoms in the plume of a hall thruster, 33rd International electric propulsion conference, Washington, D.C, 158 (2013), IEPC
[27] Feng, W.; He, X.-M.; Lin, Y.; Zhang, X., Immersed finite element method for interface problems with algebraic multigrid solver, Commun Comput Phys, 15, 4, 1045-1067 (2014) · Zbl 1388.65177
[28] Gamero-Castano, M.; Katz, I., Estimation of hall thruster erosion using hphall, 29th International electric propulsion conference, Princeton, New Jersey, 303-312 (2005), IEPC
[29] Garrigues, L.; Hagelaar, G. J.M., Model study of the influence of the magnetic field configuration on the performance and lifetime of a hall thruster, Phys Plasmas, 10, 12, 4886-4892 (2003)
[30] Gong, Y.; Li, B.; Li, Z., Immersed-interface finite-element methods for elliptic interface problems with non-homogeneous jump conditions, SIAM J Numer Anal, 46, 472-495 (2008) · Zbl 1160.65061
[31] Gong, Y.; Li, Z., Immersed interface finite element methods for elasticity interface problems with non-homogeneous jump conditions, Numer Math Theory Methods Appl, 3, 1, 23-39 (2010) · Zbl 1224.65266
[32] Han, D.; Wang, J.; He, X.-M., A non-homogeneous immersed-finite-element particle-in-cell method for modeling dielectric surface charging in plasmas, IEEE Trans Plasma Sci, 44, 8, 1326-1332 (2016)
[33] Han, D.; Wang, P.; He, X.-M.; Lin, T.; Wang, J., A 3D immersed finite element method with non-homogeneous interface flux jump for applications in particle-in-cell simulations of plasma-lunar surface interactions, J Comput Phys, 321, 965-980 (2016) · Zbl 1349.76212
[34] He, X.-M., Bilinear immersed finite elements for interface problems (2009), PhD Dissertation
[35] He, X.-M.; Lin, T.; Lin, Y., Approximation capability of a bilinear immersed finite element space, Numer Methods Partial Differential Equations, 24, 5, 1265-1300 (2008) · Zbl 1154.65090
[36] He, X.-M.; Lin, T.; Lin, Y., A bilinear immersed finite volume element method for the diffusion equation with discontinuous coefficients, dedicated to richard e. ewing on the occasion of his 60th birthday, Commun Comput Phys, 6, 1, 185-202 (2009) · Zbl 1364.65225
[37] He, X.-M.; Lin, T.; Lin, Y., Interior penalty bilinear IFE discontinuous galerkin methods for elliptic equations with discontinuous coefficient, dedicated to david Russell’s 70th birthday, J Syst Sci Complex, 23, 3, 467-483 (2010) · Zbl 1205.35010
[38] He, X.-M.; Lin, T.; Lin, Y., Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions, Int J Numer Anal Model, 8, 2, 284-301 (2011) · Zbl 1211.65155
[39] He, X.-M.; Lin, T.; Lin, Y., The convergence of the bilinear and linear immersed finite element solutions to interface problems, Numer Methods Partial Differential Equations, 28, 1, 312-330 (2012) · Zbl 1241.65090
[40] He, X.-M.; Lin, T.; Lin, Y., A selective immersed discontinuous galerkin method for elliptic interface problems, Math Methods Appl Sci, 37, 7, 983-1002 (2014) · Zbl 1292.65126
[41] He, X.-M.; Lin, T.; Lin, Y.; Zhang, X., Immersed finite element methods for parabolic equations with moving interface, Numer Methods Partial Differential Equations, 29, 2, 619-646 (2013) · Zbl 1266.65165
[42] Heron, A.; Adam, J. C., Anomalous conductivity in hall thrusters: effects of the non-linear coupling of the electron-cyclotron drift instability with secondary electron emission of the walls, Phys Plasmas, 20, 8, 082313 (2013)
[43] Ji, H.; Chen, J.; Li, Z., A symmetric and consistent immersed finite element method for interface problems, J Sci Comput, 61, 3, 533-557 (2014) · Zbl 1308.65198
[44] Jian, H.; Chu, Y.; Cao, H.; Cao, Y.; He, X.-M.; Xia, G., Three-dimensional IFE-PIC numerical simulation of background pressure’s effect on accelerator grid impingement current for ion optics, Vacuum, 116, 130-138 (2015)
[45] Kafafy, R.; Lin, T.; Lin, Y.; Wang, J., Three-dimensional immersed finite element methods for electric field simulation in composite materials, Int J Numer Meth Engrg, 64, 7, 940-972 (2005) · Zbl 1122.78018
[46] Kafafy, R.; Wang, J., A hybrid grid immersed finite element particle-in-cell algorithm for modeling spacecraft-plasma interactions, IEEE Trans Plasma Sci, 34, 5, 2114-2124 (2006)
[47] Kafafy, R.; Wang, J.; Lin, T., A hybrid-grid immersed-finite-element particle-in-cell simulation model of ion optics plasma dynamics, Dyn Contin Discrete Impuls Syst Ser B Appl Algorithms, 12, 1-16 (2005)
[48] Katardjiev, I. V., Simulation of surface evolution during ion bombardment, J Vac Sci Technol A, 6, 4, 2434-2442 (1988)
[49] Katardjiev, I. V.; Carter, G.; Nobes, M. J., The application of the huygens principle to surface evolution in inhomogeneous, anisotropic and time-dependent systems, J Phys D Appl Phys, 22, 12, 1813-1824 (1989)
[50] Katardjiev, I. V.; Carter, G.; Nobes, M. J.; Smith, R., Precision modeling of the mask-substrate evolution during ion etching, J Vac Sci Technol A, 6, 4, 2443-2450 (1988)
[51] Kim, V., Main physical features and processes determining the performance of stationary plasma thrusters, J Propul Power, 14, 5, 736-743 (1998)
[52] Kiriakidis, G.; Carter, G.; Whitton, J. L., Erosion and growth of solids stimulated by atom and ion beams, 112 (1986), Martinus Nijhoff Publishers: NATO ASI Series
[53] Kwak, D. Y.; Wee, K. T.; Chang, K. S., An analysis of a broken \(p_1\)-nonconforming finite element method for interface problems, SIAM J Numer Anal, 48, 6, 2117-2134 (2010) · Zbl 1222.65125
[54] Li, Y.; Yu, D., Reconstruction of ionization density distribution in hall thruster channel from ion energy spectrum of plasma jet, Plasma Sci Technol, 8, 666-669 (2006)
[55] Li, Z., The immersed interface method using a finite element formulation, Appl Numer Math, 27, 3, 253-267 (1997) · Zbl 0936.65091
[56] Li, Z.; Lin, T.; Lin, Y.; Rogers, R. C., An immersed finite element space and its approximation capability, Numer Methods Partial Differential Equations, 20, 3, 338-367 (2004) · Zbl 1057.65085
[57] Li, Z.; Lin, T.; Wu, X., New cartesian grid methods for interface problems using the finite element formulation, Numer Math, 96, 1, 61-98 (2003) · Zbl 1055.65130
[58] Lin, M.; Lin, T.; Zhang, H., Error analysis of an immersed finite element method for euler-Bernoulli beam interface problems, Int J Numer Anal Model, 14, 822-841 (2017) · Zbl 1375.74088
[59] Lin, T.; Lin, Y.; Rogers, R. C.; Ryan, L. M., A rectangular immersed finite element method for interface problems, (Minev, P.; Lin, Y., Advances in Computation: Theory and Practice, Vol. 7 (2001), Nova Science Publishers, Inc.), 107-114 · Zbl 1019.65092
[60] Lin, T.; Lin, Y.; Zhang, X., Partially penalized immersed finite element methods for elliptic interface problems, SIAM J Numer Anal, 53, 2, 1121-1144 (2015) · Zbl 1316.65104
[61] Lin, T.; Sheen, D.; Zhang, X., A locking-free immersed finite element method for planar elasticity interface problems, J Comput Phys, 247, 228-247 (2013) · Zbl 1349.74328
[62] Lin, T.; Wang, J., An immersed finite element electric field solver for ion optics modeling, Proceedings of AIAA joint propulsion conference, Indianapolis, IN, July, 2002-4263 (2002), AIAA
[63] Lin, T.; Wang, J., The immersed finite element method for plasma particle simulation, Proceedings of AIAA aerospace sciences meeting, Reno, NV, Jan, 2003-0842 (2003), AIAA
[64] Manzella, D.; Yim, J.; Boyd, I., Predicting hall thruster operational lifetime, 40th AIAA/ASME/SAE/ASEE joint propulsion conference and exhibit, Fort Lauderdale, Florida, 04-3953 (2004), AIAA
[65] Oleson, S.; Sankovic, J., Advanced hall electric propulsion for future in-space transportation, 3rd International Conference on Spacecraft Propulsion, Cannes, France, 717-726 (2000)
[66] Peterson, P.; Manzella, D., Investigation of the erosion characteristics of a laboutatory hall thruster, 39th AIAA/ASME/SAE/ASEE Joint propulsion conference and exhibit, Huntsville, AL, 5005 (2003), AIAA
[67] Popok, V. N.; Barke, I.; Campbell, E. E.B.; Meiwes-Broer, K. H., Cluster-surface interaction: from soft landing to implantation, Surf Sci Rep, 66, 10, 347-377 (2011)
[68] Saikia, P.; Kakati, B.; Saikia, B. K., Study on the effect of target on plasma parameters of magnetron sputtering discharge plasma, Phys Plasmas, 20, 10, 103505 (2013)
[69] Shan, K.; Chu, Y.; Li, Q.; Zheng, L.; Cao, Y., Numerical simulation of interaction between hall thruster cex ions and smart-1 spacecraft, Math Probl Eng, 2015, 1-8 (2015)
[70] Sommier, E.; Allis, M.; Cappelli, M., Wall erosion in 2d hall thruster simulations, 29th International electric propulsion conference, Princeton, New Jersey, 1-11 (2005), IEPC
[71] Szabo, J. J., Fully kinetic numerical modeling of a plasma thruster (2001), PhD dissertation
[72] Taccogna, F.; Longo, S.; Capitelli, M., Plasma sheaths in hall discharge, Phys Plasmas, 12, 9, 093506 (2005)
[73] Tverdokhlebov, O. S.; Karabadzhak, G. F., Tal relative erosion rate real-time measurements through analysis of its emisson spectra, 28th International electric propulsion conference, Toulouse, France, 133 (2003), IEPC
[74] Vallaghè, S.; Papadopoulo, T., A trilinear immersed finite element method for solving the electroencephalography forward problem, SIAM J Sci Comput, 32, 4, 2379-2394 (2010) · Zbl 1214.92046
[75] Vassallo, E.; Caniello, R., Removing of mixed coatings by plasma discharges, J Fusion Energy, 32, 6, 642-644 (2013)
[76] Wang, J.; Chang, O.; Cao, Y., Electroncion coupling in mesothermal plasma beam emission: full particle pic simulations, IEEE Trans Plasma Sci, 40, 2, 230-236 (2012)
[77] Wang, J.; He, X.-M.; Cao, Y., Modeling spacecraft charging and charged dust particle interactions on lunar surface, Proceedings of the 10th spacecraft charging technology conference, Biarritz, France (2007)
[78] Wang, J.; He, X.-M.; Cao, Y., Modeling electrostatic levitation of dusts on lunar surface, IEEE Trans Plasma Sci, 36, 5, 2459-2466 (2008)
[79] Wang, J.; Polk, J.; Brophy, J.; Katz, I., Three-dimensional particle simulations of ion-optics plasma flow and grid erosion, J Propul Power, 19, 6, 1192-1199 (2003)
[80] Yamamura, Y.; Itikawa, Y.; Itoh, N., Angular dependence of sputtering yields of monatomic solids, Nagoya University Institute of Plasma Physics Report, Article IPPJ-AM-26 (1983)
[81] Yamamura, Y.; Tawara, H., Energy dependence of ion-induced sputtering yields from monatomic solids at normal incidence, Atom Data Nucl Data Tables, 62, 2, 149-253 (1992)
[82] Yang, J.; Yokotav, S.; Kaneko, R.; Komurasaki, K., Diagnosing on plasma plume from xenon hall thruster with collisional-radiative model, Phys Plasmas, 17, 103504 (2010)
[83] Yim, J.; Keidar, M.; Boyd, I., A hydrodynamic-based erosion model for hall thrusters, 29th International electric propulsion conference, Princeton, New Jersey, 013-022 (2005), IEPC
[84] Yu, D.; Li, Y., Volumetric erosion rate reduction of hall thruster channel wall during ion sputtering process, J Phys D Appl Phys, 40, 2526-2532 (2007)
[85] Yu, D.; Li, Y.; Song, S., Ion sputtering erosion of channel wall corners in hall thrusters, J Phys D Appl Phys, 39, 2205-2211 (2006)
[86] Zhang, X., Nonconforming immersed finite element methods for interface problems (2013), Ph.D. Dissertation
[87] Zhu, L.; Zhang, Z.-Y.; Li, Z.-L., The immersed finite volume element method for some interface problems with nonhomogeneous jump conditions, Int J Numer Anal Model, 13, 368-382 (2016) · Zbl 1347.65163
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.