in high pressure the mean free path of electrons becomes much shorter than the probe dimension. I don't understand what the relation between the Langmuir probe and the free path of electrons?
In high pressure case, mean free path of electron as well as ion reduces. There are probe theories which may even apply to high pressure plasma. In low pressure plasma, ions and electrons reach to probe via collision diffusion without any collision inside the sheath region around the probe. The fore, the current at sheath edgd is equivalent to that of at probe surface. Since this current gives the information of plasma where current reach at sheath edge is due to random motion of plasma species. So in such case, you can use the Probe theory derived based on OML theory. Now, if election or ions undergoes to collision in probe sheath region then current at probe surface will be less than that of at sheath edge. In such cases, a reduction factor or modification factor is included to ion current to get the role of collision. The value of ion current may lower or higher in case of high pressure. SO you can use probe but need to incorporate the ion current modification due to collisional effect.
There is a big issue with the secondary ionization near the probe tip while probe collects electron saturation current. It is due to more collision of electrons in sheath region while electrons drifting in sheath region of probe. This secondary plasma may perturb the probe current as well as plasma. By knowing the exact plasma potential, you can stop the probe biasing at exact plasma potential where probe collect more electron current. If you bias probe beyond the plasma potential then secondary plasma will give erroneous probe current voltage characteristic and you will get erroneous results. .
Dear Fatma, Well, in fact the theory of Langmuir probe in dense ionized gas is even more complicated than Langmuir theory in rare plasmas. Effectively, probe operates in a complicated field developed by diffusion and drift of electrons and ions. The theory in dense plasmas therefore, addresses the volume charge formation around the probe. One of possible practical solutions for Langmuir probe in such conditions is to substitute the actual radius of a (spherical or cylindrical) probe with an imaginary one which corresponds to the radius around the probe where electron and ion charges still compensate each i.e. where plasma is still quasi neutral. There are also peculiarities with respect to e.g. ion saturation current (lower in dense ionized gas than that in rare plasmas) etc. Rather good and compact description can be found in a book of Yu. Raizer. The description of this book may be found at: https://www.bookdepository.com/Gas-Discharge-Physics-Yu-P-Raizer/9783540194620. I hope, it helps. Kind regards, AL.
Electrons - tiny, go anywhere, mostly charge carriers; ions- massive, need more energy to get going places. Therefore, back to your question, smal free path fo relectrons means your probe is not able to suck them out of the plasma efficiently, you won't be able to read something on your probe.
In high pressure case, mean free path of electron as well as ion reduces. There are probe theories which may even apply to high pressure plasma. In low pressure plasma, ions and electrons reach to probe via collision diffusion without any collision inside the sheath region around the probe. The fore, the current at sheath edgd is equivalent to that of at probe surface. Since this current gives the information of plasma where current reach at sheath edge is due to random motion of plasma species. So in such case, you can use the Probe theory derived based on OML theory. Now, if election or ions undergoes to collision in probe sheath region then current at probe surface will be less than that of at sheath edge. In such cases, a reduction factor or modification factor is included to ion current to get the role of collision. The value of ion current may lower or higher in case of high pressure. SO you can use probe but need to incorporate the ion current modification due to collisional effect.
There is a big issue with the secondary ionization near the probe tip while probe collects electron saturation current. It is due to more collision of electrons in sheath region while electrons drifting in sheath region of probe. This secondary plasma may perturb the probe current as well as plasma. By knowing the exact plasma potential, you can stop the probe biasing at exact plasma potential where probe collect more electron current. If you bias probe beyond the plasma potential then secondary plasma will give erroneous probe current voltage characteristic and you will get erroneous results. .