TY - JOUR
T1 - A simple formula for the wall potential in the plasma sheath
AU - Pandey, B. P.
AU - Vladimirov, S. V.
PY - 2011/6
Y1 - 2011/6
N2 - An analytical formula for the plasma wall potential in a planer sheath is presented. It is shown that there is no relative error between the analytical and numerical solutions for the large negative wall potential. Even when the wall potential is not large, the relative error is only 3%. Using this analytical formula in Child's law, we show that the sheath width, d (in the unit of Debye length, λD) is proportional to the Mach number M, i.e. d/λD=0.5 M. In the low- and high-temperature plasma experiments, the present analytical formula could be utilised to accurately estimate the sheath width.
AB - An analytical formula for the plasma wall potential in a planer sheath is presented. It is shown that there is no relative error between the analytical and numerical solutions for the large negative wall potential. Even when the wall potential is not large, the relative error is only 3%. Using this analytical formula in Child's law, we show that the sheath width, d (in the unit of Debye length, λD) is proportional to the Mach number M, i.e. d/λD=0.5 M. In the low- and high-temperature plasma experiments, the present analytical formula could be utilised to accurately estimate the sheath width.
UR - http://www.scopus.com/inward/record.url?scp=79959203831&partnerID=8YFLogxK
U2 - 10.1209/0295-5075/94/55002
DO - 10.1209/0295-5075/94/55002
M3 - Article
AN - SCOPUS:79959203831
VL - 94
SP - 1
EP - 4
JO - Europhysics Letters (Online): a letters journal exploring the frontiers of physics
JF - Europhysics Letters (Online): a letters journal exploring the frontiers of physics
SN - 1286-4854
IS - 5
M1 - 55002
ER -