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The process of gas discharge is very complicated and experimental observations indicate that streamers in short gap under non-uniform electric fields always exhibit irregularity and self-similarity, so a dielectric breakdown model, which is the combination of the random fractal method and the traditional streamer theory, can simulate this phenomenon.In this paper, a stochastic model with the growth probability index at any point proportional to the power of the electric field is utilized to quantify the channel tortuosity, and the space charge effect is taken into account as well. The potential distribution is solved by the Poisson's equation which is calculated iteratively by finite difference method; and the box counting method is used to characterize the channel tortuosity and estimate the fractal dimensions of the discharge channels. Based on this, an idea is proposed that the analysis of the experimental results, which in turn provide the appropriate parameters for the model, can better elucidate this phenomenon.The growth probability index can always get from the previous data, but the range of the will change under different experimental condition and there will exist differences in simulation results on fractal dimensions for different , so the limitation of the previous studies is its possible lack of generalizability. In order to define the range of the growth probability index in this model, the bifurcation phenomenon of plasma channels generated by the discharge, affected by HVDC (high-voltage direct current) of short-air-gap in a needle-plate electrode, is captured by ICCD. Before estimating the fractal dimensions of discharge channels, experimental images are saved as a binarized (black and white) image, and the gray-level transformation and boundary identification algorithm will be conducted to remove the apparent thickness of the discharge channel caused by the magnitude of the flowing currents through different branches. Experimental results show that the range of fractal dimensions in the box counting method for the discharge channel is 1.40-1.55. Under the same condition that other factors remain the same but the adjusted growth probability index in this simulation model should accord with the experimental results, all the facts demonstrate that the value of must lie between 0.04 and 0.05.
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Keywords:
- fractal dimension /
- image processing /
- probability index /
- bifurcation
[1] Sun X, Wu Z Q 2001 Acta Phys. Sin. 50 2126 (in Chinese) [孙霞, 吴自勤 2001 50 2126]
[2] Huo Y L, Zhang G S, Lv S H, Yuan P 2013 Acta Phys. Sin. 62 059201 (in Chinese) [火元莲, 张广庶, 吕世华, 袁萍 2013 62 059201]
[3] Sun K Y, Zhao X Y, Zhang G L, Zang H M 2014 Acta Phys. Sin. 63 029204 (in Chinese) [孙柯岩, 赵小莹, 张功磊, 臧洪明 2014 63 029204]
[4] Jia Z D, Le B, Jiang X W 1999 High Voltage Engineering 25 1 (in Chinese) [贾志东, 乐波, 蒋雄伟 1999 高电压技术 25 1]
[5] Niemeyer L, Pietronero L, Wiesmann H J 1984 Phys. Rev. Lett. 52 12
[6] Wiesmann H J, Zeller H R 1986 J. Phys. D: Appl. Phys. 60 1770
[7] Noskov M D, Kukhta V R, Lopatin V V 1995 J. Phys. D: Appl. Phys. 28 1187
[8] Veldhuizen E M, Kemps P C M, Rutgers W R 2002 IEEE Trans. Plasma Sci. 30 162
[9] Kupershtokh A L, Charalambakos V, Agoris D 2001 J. Phys. D: Appl. Phys. 34 936
[10] Hallac A, Georghiou G E, Metaxas A C 2005 IEEE Trans. Plasma Sci. 33 266
[11] Qing X, Anton Y N, Xin P L 2011 IEEE Trans. Plasma Sci. 39 2094
[12] Luque A, Ebert U 2012 J. Comput Phys. 231 904
[13] Dulan A, Upul S A, Marcus B B, Vernon C 2015 J. Electrostat. 73 33
[14] Ren S P, Chi J P, Zhuang H C 1998 Chinese Journal of Space Science 18 363 (in Chinese) [任顺平, 迟建平, 庄洪春 1998 空间科学学报 18 363]
[15] Gu T, Yan P, Zhang S C 2006 High Voltage Engineering 32 1 (in Chinese) [谷探, 严萍, 张适昌 2006 高电压技术 32 1]
[16] Hong C 2007 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese) [洪川 2007 博士学位论文 (重庆: 重庆大学)]
[17] He H X, He J J, Qian G J 2008 High Voltage Engineering 34 2047 [贺恒鑫, 何俊佳, 钱冠军 2008 高电压技术 34 2047]
[18] Gallimberti I, Bacchiega G, Bondiou C A 2002 C. R. Physique 3 1335
[19] Dulan A, Upul S 2008 J. Natl Sci Found SR. 36 137
[20] Niemeyer L, Ullrich L, Wiegart N 1989 IEEE Trans. Electr Insul. 24 309
[21] Wang J T, Yang J M 2013 Complex Systems and Complexity Science 0 1 (in Chinese) [王江涛, 杨建梅 2013 复杂系统与复杂性科学 0 1]
[22] Canny J 1986 IEEE Trans. Pattern Anal. 8 679
[23] Nobuyuki O 1979 IEEE SMC Society 9 62
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[1] Sun X, Wu Z Q 2001 Acta Phys. Sin. 50 2126 (in Chinese) [孙霞, 吴自勤 2001 50 2126]
[2] Huo Y L, Zhang G S, Lv S H, Yuan P 2013 Acta Phys. Sin. 62 059201 (in Chinese) [火元莲, 张广庶, 吕世华, 袁萍 2013 62 059201]
[3] Sun K Y, Zhao X Y, Zhang G L, Zang H M 2014 Acta Phys. Sin. 63 029204 (in Chinese) [孙柯岩, 赵小莹, 张功磊, 臧洪明 2014 63 029204]
[4] Jia Z D, Le B, Jiang X W 1999 High Voltage Engineering 25 1 (in Chinese) [贾志东, 乐波, 蒋雄伟 1999 高电压技术 25 1]
[5] Niemeyer L, Pietronero L, Wiesmann H J 1984 Phys. Rev. Lett. 52 12
[6] Wiesmann H J, Zeller H R 1986 J. Phys. D: Appl. Phys. 60 1770
[7] Noskov M D, Kukhta V R, Lopatin V V 1995 J. Phys. D: Appl. Phys. 28 1187
[8] Veldhuizen E M, Kemps P C M, Rutgers W R 2002 IEEE Trans. Plasma Sci. 30 162
[9] Kupershtokh A L, Charalambakos V, Agoris D 2001 J. Phys. D: Appl. Phys. 34 936
[10] Hallac A, Georghiou G E, Metaxas A C 2005 IEEE Trans. Plasma Sci. 33 266
[11] Qing X, Anton Y N, Xin P L 2011 IEEE Trans. Plasma Sci. 39 2094
[12] Luque A, Ebert U 2012 J. Comput Phys. 231 904
[13] Dulan A, Upul S A, Marcus B B, Vernon C 2015 J. Electrostat. 73 33
[14] Ren S P, Chi J P, Zhuang H C 1998 Chinese Journal of Space Science 18 363 (in Chinese) [任顺平, 迟建平, 庄洪春 1998 空间科学学报 18 363]
[15] Gu T, Yan P, Zhang S C 2006 High Voltage Engineering 32 1 (in Chinese) [谷探, 严萍, 张适昌 2006 高电压技术 32 1]
[16] Hong C 2007 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese) [洪川 2007 博士学位论文 (重庆: 重庆大学)]
[17] He H X, He J J, Qian G J 2008 High Voltage Engineering 34 2047 [贺恒鑫, 何俊佳, 钱冠军 2008 高电压技术 34 2047]
[18] Gallimberti I, Bacchiega G, Bondiou C A 2002 C. R. Physique 3 1335
[19] Dulan A, Upul S 2008 J. Natl Sci Found SR. 36 137
[20] Niemeyer L, Ullrich L, Wiegart N 1989 IEEE Trans. Electr Insul. 24 309
[21] Wang J T, Yang J M 2013 Complex Systems and Complexity Science 0 1 (in Chinese) [王江涛, 杨建梅 2013 复杂系统与复杂性科学 0 1]
[22] Canny J 1986 IEEE Trans. Pattern Anal. 8 679
[23] Nobuyuki O 1979 IEEE SMC Society 9 62
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