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By analyzing the breakdown threshold obtained from effective magnitude or RMS (root mean square) of microwave field, it is pointed out that the assumption of threshold is not suitable for microwave air breakdown. Variations of effective electron temperature and breakdown threshold in microwave fields, which are studied theoretically and numerically by fluid-based plasma equations coupled with the Maxwell equations, are compared with those in static fields. It is found that the effective electron temperature varies greatly with the microwave field at high pressures (electron energy transfer frequency is much larger than microwave frequency) due to its high energy transfer frequency. This causes the microwave air breakdown threshold to be smaller than that obtained from the RMS of field at high pressures because the ionization frequency varies faster than electron energy loss at an effective electron temperature. On the other hand, the effective electron temperature variation with the microwave field is insignificant at low pressures (electron energy transfer frequency is much smaller than microwave frequency) due to the negligible electron energy loss in a microwave period. In this case, the microwave air breakdown threshold is approximately equal to that obtained from the RMS one of the field. The fit formula of microwave air breakdown threshold is obtained by numerical and theoretical analysis.
[1] Gurevich A, Borisov N, Milikh G 1997 Physics of Microwave Discharges (New York:Gordon and Breach)
[2] Oda Y, Komurasaki K, Takahashi K 2006 J. Appl. Phys. 100 113307
[3] Gurevich A V, Litvak A G, Vikharev A L, Ivanov O A, Borisov N D, Sergechev K F 2000 Physics Uspekhi 43 1103
[4] Gurevich A V 1980 Sov. Phys. Usp. 23 862
[5] Kourtzanidis K, Boeuf J P, Rogier F 2014 Phys. of Plasma. 21 123513
[6] Klein T J, Ploch C J, Recknagel C J, Remillard S K 2011 , Appl. Phys. Lett. 99 121503
[7] Foster J, Krompholz H, Neuber A 2011 Phys. of Plasma. 18 113505
[8] Raizer Y P 1991 Gas Discharge Physics (Berlin: Springer)
[9] Liang C B, Qin G R, Liang Z J 1980 Electromagnetism (Beijing: Higher Education Press) (in Chinese) [梁灿彬, 秦光戎, 梁竹健 1980 电磁学 (北京: 高等教育出版社)]
[10] Zhou Q H, Dong Z W 2013 Acta Phys. Sin. 62 205202 (in Chinese) [周前红, 董志伟 2013 62 205202]
[11] Khodataev K V 2009 Microwave breakdown threshold at low and high pressure, AIAA 2009-1410
[12] Zhou Q H, Dong Z W 2013 Acta Phys. Sin. 62 205201 (in Chinese) [周前红, 董志伟 2013 62 205201]
[13] Zhou Q H, Dong Z W 2013 Acta Phys. Sin. 62 125201 (in Chinese) [周前红, 董志伟 2013 62 125201]
[14] Hagelaar G J M, Pitchford L C 2005 Plasma Souces Sci. Technol. 14 722
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[1] Gurevich A, Borisov N, Milikh G 1997 Physics of Microwave Discharges (New York:Gordon and Breach)
[2] Oda Y, Komurasaki K, Takahashi K 2006 J. Appl. Phys. 100 113307
[3] Gurevich A V, Litvak A G, Vikharev A L, Ivanov O A, Borisov N D, Sergechev K F 2000 Physics Uspekhi 43 1103
[4] Gurevich A V 1980 Sov. Phys. Usp. 23 862
[5] Kourtzanidis K, Boeuf J P, Rogier F 2014 Phys. of Plasma. 21 123513
[6] Klein T J, Ploch C J, Recknagel C J, Remillard S K 2011 , Appl. Phys. Lett. 99 121503
[7] Foster J, Krompholz H, Neuber A 2011 Phys. of Plasma. 18 113505
[8] Raizer Y P 1991 Gas Discharge Physics (Berlin: Springer)
[9] Liang C B, Qin G R, Liang Z J 1980 Electromagnetism (Beijing: Higher Education Press) (in Chinese) [梁灿彬, 秦光戎, 梁竹健 1980 电磁学 (北京: 高等教育出版社)]
[10] Zhou Q H, Dong Z W 2013 Acta Phys. Sin. 62 205202 (in Chinese) [周前红, 董志伟 2013 62 205202]
[11] Khodataev K V 2009 Microwave breakdown threshold at low and high pressure, AIAA 2009-1410
[12] Zhou Q H, Dong Z W 2013 Acta Phys. Sin. 62 205201 (in Chinese) [周前红, 董志伟 2013 62 205201]
[13] Zhou Q H, Dong Z W 2013 Acta Phys. Sin. 62 125201 (in Chinese) [周前红, 董志伟 2013 62 125201]
[14] Hagelaar G J M, Pitchford L C 2005 Plasma Souces Sci. Technol. 14 722
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