Simulation of electron kinetics in gas discharges

IEEE Transactions on Plasma Science

Volumn 34, Issue 3 PART 2, 2006, Pages 895-909

  Kolobov, Vladimir I ^a   Arslanbekov, Robert R ^a  

^a CFD RESEARCH CORPORATION   (United States)

Author keywords

Boltzmann; Capacitively coupled plasma; Electron kinetics; Fokker Planck equation; Inductively coupled plasma; Positive column; Striations; Vlasov equations

Indexed keywords

BOLTZMANN; CAPACITIVELY COUPLED PLASMA; ELECTRON KINETICS; POSITIVE COLUMN; STRIATIONS; VLASOV EQUATIONS;

BOLTZMANN EQUATION; DISTRIBUTION FUNCTIONS; ELECTRONS; FOKKER PLANCK EQUATION; GAS DISCHARGE TUBES; GASES; GLOW DISCHARGES; HARMONIC ANALYSIS; INDUCTIVELY COUPLED PLASMA; MAGNETIC FIELDS; PHOTORESISTS; PHYSICAL VAPOR DEPOSITION; PLASMA DIAGNOSTICS; PLASMA THEORY; PRASEODYMIUM COMPOUNDS; RECONNAISSANCE AIRCRAFT; TIMING JITTER;

TWO DIMENSIONAL ELECTRON GAS;

EID: 33846862145     PISSN: 00933813     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPS.2006.875850     Document Type: Conference Paper

References (120)

1. U. Kortshagen and L. D. Tsendin, Eds., Electron Kinetics and Applications of Glow Discharges. New York: Plenum Press, 1998.
2. V. I. Kolobov and V. A. Godyak, "Nonlocal electron kinetics in collisional gas discharge plasmas," IEEE Trans. Plasma Sci., vol. 23, no. 4, pp. 503-531, Aug. 1995.
3. G. E. Geoghiou, A. P. Papadakis, R. Morrow, and A. C. Metaxas, "Numerical modeling of atmospheric pressure gas discharges leading to plasma production," J. Phys. D., vol. 38, p. R303, 2005.
4. R. E. Robson, R. D. White, and Z. L. Petrovic, "Colloquium: Physically based fluid modeling of collisionally dominated low-temperature plasmas," Rev. Mod. Phys., vol. 77, p. 1303, 2005.
5. G. J. M. Hagelaar and L. C. Pitchford, "Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models," Plasma Sources Sci. Technol., vol. 14, p. 722, 2005.
6. L. D. Tsendin, "Electron kinetics in nonuniform glow discharge plasmas," Plasma Source Sci. Technol., vol. 4, p. 200, 1995.
7. V. Godyak, "Hot plasma effects in gas discharge plasma," Phys. Plasmas, vol. 12, p. 055501, 2005.
8. M. A. Liberman and A. J. Lichtenberg, Principles of Plasma Discharges and Material's Processing, 2nd ed. New York: Wiley, 2005.
9. Y. B. Golubovskii, A. A. Kudryavtsev, V. O. Nekuchaev, I. A. Porokhova, and L. D. Tsendin, Electron Kinetics in Non-Equilibrium Gas Discharge Plasmas (in Russian). St. Petersburg, Russia: St. Petersburg Univ. Press, 2004, 248p.
10. V. E. Fortov, Ed., Encyclopedia of Low Temperature Plasmas (in Russian). Moscow, Russia: Nauka, 2000.
11. R. Winkler et al., "Progress of the electron kinetics in spatial and spatiotemporal plasma structures," Contrib. Plasma Phys., vol. 44, p. 437, 2004.
12. H. C. Kim, F. Iza, S. S. Yang, M. Radmilovic-Radjenovic, and J. K. Lee, "Particle and fluid simulations of low temperature plasma discharges: Benchmark and kinetic effects," J. Phys. D, vol. 38, p. R283, 2005.
13. A. Bogaerts, K. de Bleecker, I. Kolev, and M. Madani, "Modeling of gas discharge plasmas: What can we learn from it?," Surface Coatings Technol., vol. 200, p. 62, 2005.
14. J. P. Verboncoeur, "Particle simulation of plasmas: Review and advances," Plasma Phys. Control. Fusion, vol. 47, p. A231, 2005.
15. M. Shiozawa and K. Nanbu, "Coupling of plasma and flow in materials processing," Thin Solid Films, vol. 457, p. 48, 2004.
16. C. Cercignani, The Boltzmann Equation and Its Applications. New York: Springer-Verlag, 1988.
17. E. M. Lifshitz and L. P. Pitaevsky, Course of Theoretical Physics: Physical Kinetics. New York: Pergamon, 1981, vol. 10.
18. P. P. J. M. Schram, Kinetic Theory of Gases and Plasmas. New York: Kluwer, 1991.
19. V. P. Vstovsii, "Kinetics of a weakly ionized plasma in external field," Sov. J. Plasma Phys., vol. 12, p. 856, 1986.
20. I. Shkarofsky, T. Johnston, and M. P. Bachinski, The Particle Kinetic of Plasmas. Reading, MA: Addison-Wesley, 1981, 452p.
21. U. Kortshagen, C. Busch, and L. D. Tsendin, "On simplifying approaches to the solution of the Boltzmann equation in spatially inhomogeneous plasmas," Plasma Sources Sci. Technol., vol. 5, p. 1, 1996.
22. R. D. White, R. E. Robson, B. Schmidt, and M. A. Morrison, "Is the classical two-term approximation of electron kinetic theory satisfactory for swarms and plasmas," J. Phys. D, vol. 36, p. 3125, 2003.
23. P. Degond, "An infinite system of diffusion equations arising in transport theory: The coupled spherical harmonics expansion model," Math. Models Methods Appl. Sci., vol. 11, p. 903, 2001.
24. L. M. Biberman, V. S. Vorobév, and I. T. Yakubov, Kinetics of Nonequilibrium Low-Temperature Plasmas. New York: Springer, 1987.
25. E. M. Epperlein, "Fokker-Planck modeling of electron transport in laser-produced plasmas," Laser Particle Beams, vol. 12, p. 257, 1994.
26. M. O. M. Mahmoud and M. Yousfi, "Boltzmann equation analysis of spatiotemporal swarm development," J. Appl. Phys., vol. 81, p. 5935, 1997.
27. L. D. Tsendin, "Electron distribution function of weakly ionized plasmas in nonuniform electric fields. I Weak fields," Sov. J. Plasma Phys., vol. 8, p. 96, 1982.
28. J. R. Albritton, "Laser absorption and heat transport by non-Maxwell-Boltzmann electron distribution," Phys. Rev. Lett., vol. 50, p. 2078, 1983.
29. A. Kudryavtsev and L. D. Tsendin, "Cathode boundary conditions for fluid models of gas discharges on the righ-hand branch of the Pashen curve," Tech. Phys. Lett., vol. 28, p. 621, 2002.
30. F. Sigeneger and R. Winkler, "Response of the electron kinetics on spatial disturbances of the electric field in non-isothermal plasmas," Contrib. Plasma Phys., vol. 36, p. 551, 1996.
31. H.-H. Choe, N. S. Yoon, S. S. Kim, and D.-I. Choi, "A new unconditionally stable algorithm for steady-state fluid simulations of high density plasma discharges," J. Comp. Phys., vol. 170, p. 550, 2001.
32. E. P. Hammond, K. Mahesh, and P. Moin, "A numerical method to simulate radio-frequency plasma discharges," J. Comp. Phys., vol. 176, p. 402, 2002.
33. V. I.Kolobov, "Fokker-Planck modeling of electron kinetics in plasmas and semiconductors," Comput. Mater. Sci., vol. 28, p. 302, 2003.
34. G. J. M. Hagelaar and G. M. W. Kroesen, "Speeding up fluid models for gas discharges by implicit treatment of the electron energy source term," J. Comp. Phys., vol. 159, p. 1, 2000.
35. F. Alouani-Bibi, M. M. Shoucri, and J.-P. Matte, "Different Fokker-Planck approaches to simulate electron transport in plasmas," Comp. Phys. Comm., vol. 164, p. 60, 2004.
36. V. I. Kolobov and R. R. Arslanbekov, "Deterministic Boltzmann solver for electron kinetics in plasma reactors for microelectronics applications," Microelectronic Eng., vol. 69, p. 606, 2003.
37. V. I. Kolobov and R. R. Arslanbekov, "Four-dimensional Fokker-Planck solver for electron kinetics in collisional gas discharge plasmas," Comput. Phys. Comm., vol. 164, p. 195, 2004.
38. R. J. Kingham and A. R. Bell, "An implicit Vlasov-Fokker-Planck code to model nonlocal electron transport in 2-D with magnetic fields," J. Comp. Phys., vol. 194, p. 1, 2004.
39. R. Winkler, V. A. Maiorov, and F. Sigeneger, "Impact of magnetic fields on the spatial relaxation of electrons," J. Appl. Phys., vol. 87, p. 2708, 2000.
40. I. A. Porokhova and Y. B. Golubovski et al., "Two-dimensional nonlocal model of axially and radially inhomogeneous plasma of cylindrical magnetron discharge," Phys. Rev. E, vol. 68, p. 016401, 2003.
41. Z. L. Petrovic, Z. M. Raspopovic, S. Dujko, and T. Makabe, "Kinetic phenomena in electron transport in radio-frequency fields," Appl. Surf. Sci., vol. 192, p. 1, 2002.
42. E. Pohn, M. Shoucri, and G. Kamelander, "Eulerian Vlasov codes," Comput. Phys. Comm., vol. 166, p. 81, 2005.
43. V. A. Godyak, R. B. Piejak, and B. M. Alexandrovich, "Experimental setup and electrical characteristics of an inductively coupled plasma," J. Appl. Phys., vol. 85, p. 703, 1999.
44. V. A. Godyak, R. B. Piejak, and B. M. Alexandrovich, "Electron energy distribution function measurements and plasma parameters in inductively coupled argon plasma," Plasma Sources Sci. Technol., vol. 11, p. 525, 2002.
45. A. V. Vasenkov and M. J. Kushner, "Electron energy distributions and anomalous skin depth effects in high plasma density inductively coupled discharges," Phys. Rev. E, vol. 66, p. 066411, 2002.
46. V. I. Kolobov, R. R. Arslanbekov, N. Zhou, and V. A. Godyak, "Comparison of spatially resolved experimental and calculated electron distribution functions and other plasma parameters in inductively coupled argon plasma," in Proc. 56th Annu. Gaseous Electronics Conf. 2003, vol. 58, no. 6, p. 18.
47. U. Kortshagen, I. Pukropski, and L. D. Tsendin, "Experimental investigation and fast two-dimensional self-consistent kinetic modeling of a low pressure inductively coupled rf discharge," Phys. Rev. E vol. 51, p. 6063, 1995.
48. G. Mumken, "Spatial profiles of a planar inductively coupled discharge in Argon," J. Phys. D, vol. 32, p. 804, 1999.
49. U. Kortshagen and B. Heil, "Kinetic modeling and experimental studies of large scale low pressure RF discharges," J. Tech. Phys., vol. 41, p. 325, 2000.
50. R. Piejak, V. Godyak, B. Alexandrovich, and N. Tishchenko, Plasma Sources Science Technol., vol. 7, p. 590, 1998.
51. M. W. Kiehlbauch and D. B. Graves, "Modeling argon inductively coupled plasmas," J. Appl. Phys., vol. 91, p. 3539, 2002.
52. V. E. Golant, A. P. Zhilinskii, and I. E. Sakharov, Fundamentals of Plasma Physics. New York: Wiley, 1980.
53. S. Djurovic, J. R. Roberts, M. A. Sobolevski, and J. K. Olthoff, "Absolute spatially and temporally resolved optical emission measurements of rf glow discharges in argon," J. Res. NIST, vol. 98, p. 159, 1993.
54. U. Czarnetski and V. A. Kadetov, "Optical time modulation spectroscopy," in Proc. XXVI ICPIG, Greifswald, Germany, 2003.
55. A. Mareska, K. Orlov, and U. Kortshagen, "Experimental study of diffusive cooling of electrons in a pulsed inductively coupled plasma," Phys. Rev. E, vol. 60, p. 056405, 2002.
56. V. A. Godyak and B. M. Alexandrovich, "Plasma parameter evolution in a periodically pulsed ICP," in Proc. XXVII ICPIG, Eindhoven, The Netherlands, 2005.
57. V. I. Demidov, C. A. DeJoseph, Jr, and A. A. Kudryavtsev, "Anomalously high near-wall sheath potential drop in a plasma with nonlocal fast electrons," Phys. Rev. Lett., vol. 95, p. 215002, 2005.
58. V. A. Godyak, Soviet Radio Frequency Discharge Research. Falls Church, VA: Delphic, 1986.
59. Y. P. Raizer, M. N. Shneider, and N. A. Yatsenko, Radio-Frequency Capacitive Discharges. Boca Raton, FL: CRC Press, 1995.
60. G. Gozadinos, M. M. Turner, and D. Vender, "Collisionless electron heating by capacitive RF sheaths," Phys. Rev. Lett., vol. 87, p. 135004, 2001.
61. G. Chen and L. Raja, "Fluid modeling of electron heating in low-pressure, high-frequency capacitively coupled plasma discharges," J. Appl. Phys., vol. 96, p. 6073, 2004.
62. N. Xiang, "Effects of electron inertia in capacitively coupled radio-frequency discharges," Phys. Plasmas, vol. 11, p. 4213, 2004.
63. A. A. Howling et al., "Probe measurements of plasma potential nonuniformity due to edge assymmetry in large area radio-frequency reactors: The telegraph effect," J. Appl. Phys, vol. 97, p. 123308, 2005.
64. P. Chabert et al., "Inductive heating and E to H transition in capacitive discharges," Phys. Rev. Lett., vol. 95, p. 205001, 2005.
65. Y. P. Raizer, Gas Discharge Physics. New York: Springer, 1991.
66. G. G. Lister, J. E. Lawler, W. P. Lapatovich, and V. A. Godyak, "The physics of discharge lamps," Rev. Mod. Phys., vol. 76, p. 541, 2004.
67. J. E. Lawler and U. Kortshagen, "Self-consistent Monte Carlo simulations of the positive column of gas discharges," J. Phys. D vol. 32, p. 3188, 1999.
68. E. Kawamura and J. H. Ingold, "Particle in cell simulations of low pressure small adius positive column discharges," J. Phys. D, vol. 34, p. 3150, 2001.
69. L. L. Alves, G. Gousset, and C. M. Ferreira, "Self-consistent solution to the spatially inhomogeneous electron Boltzmann equation in a cylindrical plasma positive column," Phys. Rev. E, vol. 55, p. 890, 1997.
70. Y. B. Golubovskii, I. A. Porokhova, J. Behnke, and J. F. Behnke, "A comparison of kinetic and fluid models of the positive column of discharges in inert gases," J. Phys. D., vol. 32, p. 456, 1999.
71. J. L. Guiliani, G. M. Petrov, J. P. Apruzese, and J. Davied, "nonlocal radiation transport via coupling constants for the radially inhomogeneous Hg-Ar positive column," Plasma Sources Sci. Technol. vol. 14, p. 236, 2005.
72. G. Mumken, H. Schluter, and L. D. Tsendin, "Formation mechanisms of radial electron fluxes in a positive column," Phys, Rev E, vol. 60, p. 2250, 1999.
73. R. R. Arslanbekov, V. I. Kolobov, E. A. Bogdanov, and A. A. Kudryavtsev, "Simulations of plasmas of positive column in rare gases," in 31th IEEE Int. Conf. Plasma Sci., IEEE Conf. Records - Abstracts 3P46, 2004, p. 249.
74. W. J. M. Brok, J. van Dijk, M. D. Bowden, J. J. A. M. van der Mullen, and G. M. W. Kroesen, "A model study of propagation of the first ionization wave during breakdown in a straight tube containing argon," J. Phys. D., vol. 36, p. 1967, 2003.
75. G. M. Petrov and C. M. Ferreira, "Numerical modeling of the constriction of the dc positive column in rare gases," Phys. Rev. E vol. 59, p. 3571, 1999.
76. A. Bogaerts, R. Gijbels, and J. Vlcek, "Collisional-radiative model for an argon glow discharge," J. Appl. Phys., vol. 84, p. 121, 1998.
77. R. R. Arslanbekov, V. I. Kolobov, E. A. Bogdanov, and A. A. Kudryavtsev, "Nonmonotonic excitation rates in argon positive column," Appl. Phys. Letters, vol. 85, p. 3396, 2004.
78. L. D. Tsendin, E. A. Bogdanov, and A. A. Kudryavtsev, "Paradoxical nonmonotonic behavior of excitation-rate spatial profiles in bounded plasmas," Phys. Rev. Lett., vol. 94, p. 015001, 2005.
79. Y. B. Golubovskii, V. I. Kolobov, and L. D. Tsendin, "Two-dimensional theory of ionization waves in a contracted discharge in an inert gas," Sov. Phys. Tech. Phys., vol. 31, p. 31, 1986.
80. Y. B. Golubovskii, V. O. Nekuchaev, and E. B. Pelyukhova, "Bifurcation analysis of contraction in inert gases," Tech. Phys., vol. 41, p. 1011, 196.
81. P. S. Landa, N. A. Miskinova, and Y. V. Ponomarev, "Ionization waves in low temperature plasmas," Sov. Phys. Usp., vol. 23, p. 813, 1980.
82. R. R. Arslanbekov and V. I. Kolobov, "2-D Simulations of striations in direct current glow discharges in argon," IEEE Trans. Plasma Sci. vol. 33, p. 354, 2005.
83. R. R. Arslanbekov, "Two-dimensional simulations of the transition from Townsend to glow discharge and subnormal oscillations," J. Phys. D vol. 36, p. 2986, 2003.
84. Y. B. Golubovskii et al., "Kinetic resonances and stratification of the positive column of a discharge," Phys. Rev. E, vol. 72, p. 026414, 2005.
85. T. Ruzicka and K. Rohlena, "On non-hydrodynamic properties of the electron gas in the plasma of a dc discharge," Czech. J. Appl. Phys. B, vol. 22, p. 906, 1972.
86. L. D. Tsendin, "Electron distribution function of weakly ionized plasmas in nonuniform electric fields. II strong fields," Sov. J. Plasma Phys., vol. 8, p. 228, 1982.
87. L. D. Tsendin, "Ionization kinetics and ionization waves in neon," Sov. Phys. Tech. Phys., vol. 27, p. 407, 1982.
88. V. A. Shweigert, "Electron distribution function in inert gas in slightly modulated static electric field," Sov. J. Plasma Phys., vol. 15, p. 714, 1989.
89. D. Loffhagen, "Impact of electron-electron collisions on the spatial electron relaxation in non-isothermal plasmas," Plasma Chem. Plasma Proc., vol. 25, p. 519, 2005.
90. R. Winkler, V. A. Maiorov, and F. Sigeneger, "Impact of magnetic fields on the spatial relaxation of electrons," J. Appl. Phys., vol. 87, p. 2708, 2000.
91. I. A. Porokhova and Y. B. Golubovski et al., "Kinetic simulation model of magnetron discharges," Phys. Rev. E, vol. 63, p. 056406, 2001.
92. D. Loffhagen, S. Arndt, and F. Sigeneger et al., "Electron kinetics and self-consistent description of inhomogeneous and nonstationary plasmas," Contrib. Plasma Phys., vol. 45, p. 309, 2005.
93. L. D. Tsendin, "Current trends in electron kinetics of gas discharges," Plasma Sources Sci. Techol., vol. 12, p. S51, 2003.
94. D. W. Swain and S. C. Brown, "Moving striations in a low pressure Argon discharge," Phys. Fluids, vol. 14, p. 1383, 1971.
95. V. I. Kolobov and D. J. Economou, "Anomalous skin effect in gas discharge plasmas," Plasma Sources Sci. Technol., vol. 6, p. R1, 1997.
96. V. I. Kolobov, "Anomalous skin effect in bounded systems," in Electron Kinetics and Applications of Glow Discharges, U. Kortshagen and L. D. Tsendin, Eds. New York: Plenum, 1998.
97. M. M. Turner, "Collisionless electron heating in an inductively coupled discharge," Phys. Rev. Lett., vol. 71, p. 1844, 1993.
98. V. Vahedi, M. A. Lieberman, G. DiPeso, T. D. Rognlien, and D. Hewett, "Analytic model of power deposition in inductively coupled plasma sources," J. Appl. Phys., vol. 78, p. 1446, 1995.
99. R. H. Cohen and T. D. Rognlien, "Electron kinetics in radio-frequency magnetic fields of inductively coupled plasma sources," Plasma Sources Sci. Technol., vol. 5, p. 442, 1996.
100. K. C. Shaing, "Electron heating in inductively coupled discharges," Phys. Plasmas, vol. 3, p. 3300, 1996.
101. N. S. Yoon, S. S. Kim, C. S. Chang, and D. I. Choi, "One-dimensional solution for electron heating in an inductively coupled plasmas," Phys. Rev. E, vol. 54, p. 757, 1996.
102. N. S. Yoon, S. M. Hwang, and D. I. Choi, "Two-dimensional nonlocal heating theory of planar-type inductively coupled plasma discharge," Phys. Rev. E, vol. 55, p. 7536, 1997.
103. K.-I. You and N. S. Yoon, "Discharge impedance of solenoidal inductively coupled plasma discharge," Phys. Rev. E, vol. 59, p. 7074, 1999.
104. S. S. Kim, C. S. Chang, N. S. Yoon, and K.-W. Whang, "Inductively coupled plasma heating in a weakly magnetized plasma," Phys. Plasmas vol. 6, p. 2926, 1999.
105. S.-H. Seo, C.-W. Chung, J.-I. Hong, and H.-Y. Chung, "Nonlocal electron kinetics in a planar inductive helium discharge," Phys. Rev. E, vol. 62, p. 7155, 2000.
106. Y. O. Tushetsky, A. I. Smolyakov, and V. A. Godyak, Plasma Sources Sci. Technol., vol. 11, p. 203, 2002.
107. Y. M. Aliev, I. D. Kaganovich, and H. Schluter, "Quasilinear theory of collisionless electron heating in rf gas discharges," Phys. Plasmas vol. 4, p. 2413, 1997.
108. I. D. Kaganovich and O. Polomarov, "Self-consistent system of equations for a kinetic description of the low-pressure discharges accounting for the nonlocal and collisionless electron dynamics," Phys. Rev. E, vol. 68, p. 026411, 2003.
109. I. D. Kaganovich, O. V. Polomarov, and C. E. Theodosiou, "Landau damping and anomalous skin effect in low pressure gas discharges," Phys. Plasmas, vol. 11, p. 2399, 2004.
110. O. V. Polomarov, C. E. Theodosou, and I. D. Kaganovich, "Enhanced collisionless heating in a nonuniform plasma at the bounce resonance condition," Phys. Plasmas, vol. 12, p. 080704, 2005.
111. O. V. Polomarov, C. E. Theodosiou, and I. D. Kaganovich, "Effectiveness of electron-cyclotron and transmission resonant heating in inductively coupled plasmas," Phys. Plasmas, vol. 12, 2005.
112. V. I.Kolobov, D. P. Lymberopoulos, and D. J. Economou, "Electron kinetics and non-Joule heating in near-collisionless inductively coupled plasmas," Phys. Rev. E, vol. 55, p. 3408, 1997.
113. S. Rauf and M. J. Kushner, "Model of noncollisional heating in inductively coupled plasma processing sources," J. Appl. Phys., vol. 81, p. 5966, 1997.
114. M. A. Lieberman and V. A. Godyak, "From Fermi acceleration to collisionless discharge heating," IEEE Trans. Plasma Sci., vol. 26, no. 3, pp. 955-986, Jun. 1998.
115. M. Shoucri, J. P. Matte, and A. Cote, "Numerical simulation of an inductively coupled discharge using an Eulerian Vlasov code," J. Phys. D, vol. 36, p. 2083, 2003.
116. W. Liang, N. Goldsman, I. Meyergoyz, and P. Oldiges, "2-D MOSFET modeling including surface effects and impact ionization by self-consistent solution of the Boltzmann, Poisson and hole-continuity equations," IEEE Trans. Electron Devices, vol. 44, no. 2, pp. 257-267, Feb. 1997.
117. E. Bringuier, "Augmented Fokker-Planck equation for electron transport in arbitrary electric fields," J. Appl. Phys., vol. 86, p. 6847, 1999.
118. V. Latocha, L. Garrigues, P. Degond, and J. P. Boeuf, "Numerical simulation of electron transport in the channel region of a stationary plasma thruster," Plasma Sources Sci. Technol., vol. 11, p. 104, 2002.
119. M. Gutnic, M. M. Haefele, I. Paun, and E. Sonnendrucker, "Vlasov simulations on an adaptive phase-space grid," Comp. Phys. Comm., vol. 164, p. 214, 2004.
120. P. Colella, M. R. Dorr, and D. D. Wake, "Numerical solution of plasma fluid equations using locally refined grids," J. Comp. Phys., vol. 152, p.550, 1999.