Currently there are many functions in the literature that describe the extent of the spark plasma channel. What is the criteria that favor or exclude certain functions.
It is actually a matter of choice and there is no specific reason for selecting a certain relation. Some consider it as depending on discharge time and some others on both discharge time and current. The one which contains these two factors (current and time) can be found in: T. Ikai, K. Hashigushi, Heat input for crater formation in EDM, In: Proc. of the 11th International Symposium for Electro Machining-ISEM XI, EPFL, Lausanne, Switzerland, 1995, 163-170. The relation which is only time dependent has been proposed by Patel et.al. in their work: M. R. Patel, M. A. Barrufet, P. T. Eubank, Theoretical models of the electrical discharge machining process. II. The anode erosion model, J. Applied Physics, 66 (9) (1989), 4104-4111.
Regards,
S. Assarzadeh
Some consider it as depending on discharge current and some others on both discharge frequency and current. Consider the time dependent with on time and off time of the spark.
Experimental data on the diameter and velocityof positive and negative streamers in air has been measured and reported in the following work.
Briels TMP, Kos J, van Veldhuizen EM, Ebert U (2006) J Phys D: Appl Phys 39(24): 5201-5210 and 41(2008) 234004
As a physicist, I naturally looked at many versions of the plasma channel formation and expansion, the typical constraints of EDM, very little work gap, very small ignition voltages and high changes of contamination and are considered not as common in a liquid dielectric. Due to the very short pulse durations just interested in something more complex initial conditions and the parallelism of the plasma channel and the gas bubble development.
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