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Langmuir probe in collisionless and collisional plasma including dusty plasma

  • Sayak Bose (a1), Manjit Kaur (a1) (a2), P. K. Chattopadhyay (a1), J. Ghosh (a1), Y. C. Saxena (a1) and R. Pal (a3)...


Measurements of local plasma parameters in dusty plasma are crucial for understanding the physics issues related to such systems. The Langmuir probe, a small electrode immersed in the plasma, provides such measurements. However, designing of a Langmuir probe system in a dusty plasma environment demands special consideration. First, the probe has to be miniaturized enough so that its perturbation on the ambient dust structure is minimal. At the same time, the probe dimensions must be such that a well-defined theory exists for interpretation of its characteristics. The associated instrumentation must also support the measurement of current collected by the probe with high signal to noise ratio. The most important consideration, of course, comes from the fact that the probes are prone to dust contamination, as the dust particles tend to stick to the probe surface and alter the current collecting area in unpredictable ways. This article describes the design and operation of a Langmuir probe system that resolves these challenging issues in dusty plasma. In doing so, first, different theories that are used to interpret the probe characteristics in collisionless as well as in collisional regimes are discussed, with special emphasis on application. The critical issues associated with the current–voltage characteristics of Langmuir probe obtained in different operating regimes are discussed. Then, an algorithm for processing these characteristics efficiently in presence of ion-neutral collisions in the probe sheath is presented.


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Adhikary, N. C., Bailung, H., Pal, A. R., Chutia, J. & Nakamura, Y. 2007 Observation of sheath modification in laboratory dusty plasma. Phys. Plasmas 14 (10), 103705.
Allen, J. E. 1992 Probe theory – the orbital motion approach. Phys. Scr. 45 (5), 497503.
Allen, J. E., Boyd, R. L. F. & Reynolds, P. 1957 The collection of positive ions by a probe immersed in a plasma. Proc. Phys. Soc. B 70 (3), 297304.
Basu, J. & Sen, C. 1973 Sheath thickness for a cylindrical or spherical probe placed in a plasma. Japan. J. Appl. Phys. 12 (7), 10811082.
Bernstein, I. B. & Rabinowitz, I. N. 1959 Theory of electrostatic probes in a low-density plasma. Phys. Fluids 2 (2), 112121.
Bilik, N., Anthony, R., Merritt, B. A., Aydil, E. S. & Kortshagen, U. R. 2015 Langmuir probe measurements of electron energy probability functions in dusty plasmas. J. Phys. D: Appl. Phys. 48 (10), 105204.
Bohm, D. 1949 The Characteristics of Electrical Discharges in Magnetic Fields. McGraw-Hill.
Brookshier, W. K. 1969 Noise signal pickup in coaxial cables. Nucl. Instrum. Meth. 70 (1), 110.
Bryant, P. M. 2008 Theory of cylindrical Langmuir probes in weakly ionized, non-thermal, stationary and moderately collisional plasmas. Plasma Sources Sci. Technol. 18 (1), 014013.
Chen, F. F. 1965a Electric Probes. chap. 4, Academic.
Chen, F. F. 1965b Numerical computations for ion probe characteristics in a collisionless plasma. J. Nucl. Energy C 7 (1), 4767.
Chen, F. F. 1965c Saturation ion currents to Langmuir probes. J. Appl. Phys. 36 (3), 675678.
Chen, F. F. 2001 Langmuir probe analysis for high density plasmas. Phys. Plasmas 8 (6), 30293041.
Choi, I., Chung, C. W. & Youn Moon, S. 2013 Electron density and electron temperature measurement in a bi-Maxwellian electron distribution using a derivative method of Langmuir probes. Phys. Plasmas 20 (8), 083508.
Chou, Y. S., Talbot, L. & Willis, D. R. 1966 Kinetic theory of a spherical electrostatic probe in a stationary plasma. Phys. Fluids 9 (11), 21502167.
Chudáček, O., Kudrna, P., Glosik, J., Šícha, M. & Tichỳ, M. 1995 Langmuir probe determination of charged particle number density in a flowing afterglow plasma. Contrib. Plasma Phys. 35 (6), 503516.
Chung, T. H. 2014 Modeling a planar sheath in dust-containing plasmas. Phys. Plasmas 21 (1), 013701.
Cohen, I. M. 1967 Asymptotic theory of ellipsoidal electrostatic probes in a slightly ionized, collision-dominated gas. AIAA J. 5 (1), 6369.
David, P., S̃ícha, M., Tichý, M., Kopiczynski, T. & Zakrzewski, Z. 1990 The use of Langmuir probe methods for plasma diagnostic in middle pressure discharges. Contrib. Plasma Phys. 30 (2), 167184.
Dunn, M. G. & Lordi, J. A. 1969 Measurement of electron temperature and number density in shock-tunnel flows. i-development of free-molecular Langmuir probes. AIAA J. 7 (8), 14581465.
Fortov, V. E. & Morfill, G. E. 2009 Complex and Dusty Plasmas: From Laboratory to Space. Taylor & Francis.
Fouial, N., Tahraoui, A. & Annou, R. 2016 Bohm criterion in dusty plasmas with two species of positive ions and non-thermal electrons. Phys. Plasmas 23 (11), 113702.
Ghim, K. Y. C. & Hershkowitz, N. 2009 Improved double planar probe data analysis technique. Rev. Sci. Instrum. 80 (3), 033502.
Godyak, V. A, Meytlis, V. P. & Strauss, H. R. 1995 Tonks-Langmuir problem for a bi-Maxwellian plasma. IEEE Trans. Plasma Sci. 23 (4), 728734.
Goertz, I., Greiner, F. & Piel, A. 2011 Effects of charge depletion in dusty plasmas. Phys. Plasmas 18 (1), 013703.
Goree, J. 1994 Charging of particles in a plasma. Plasma Sources Sci. Technol. 3 (3), 400406.
Graf, K. A. & De Leeuw, J. H. 1967 Comparison of Langmuir probe and microwave diagnostic techniques. J. Appl. Phys. 38 (11), 44664472.
Hayashi, N. 2001 Observation of submicron dust particles trapped in a diffused region of a low pressure radio frequency plasma. Phys. Plasmas 8 (6), 30513057.
Iza, F. & Lee, J. K. 2006 Particle-in-cell simulations of planar and cylindrical Langmuir probes: floating potential and ion saturation current. J. Vac. Sci. Technol. A 24 (4), 13661372.
Jakubowski, A. K. 1972 Effect of angle of incidence on the response of cylindrical electrostatic probes at supersonic speeds. AIAA J. 10 (8), 988995.
Kagan, Y. M. & Perel, V. I. 1964 Probe methods in plasma research. Sov. Phys. Uspekhi 6 (6), 767793.
Karamcheti, A. & Steinbrüchel, C. 1999 Parametrization of Laframboises results for spherical and cylindrical Langmuir probes. J. Vac. Sci. Technol. A 17 (5), 30513056.
Kaur, M., Bose, S., Chattopadhyay, P. K., Ghosh, J. & Saxena, Y. C. 2016 Complex plasma experimental device–a test bed for studying dust vortices and other collective phenomena. Pramana 87 (6), 89.
Kaur, M., Bose, S., Chattopadhyay, P. K., Sharma, D., Ghosh, J. & Saxena, Y. C. 2015a Observation of dust torus with poloidal rotation in direct current glow discharge plasma. Phys. Plasmas 22 (3), 033703.
Kaur, M., Bose, S., Chattopadhyay, P. K., Sharma, D., Ghosh, J., Saxena, Y. C. & Thomas, E. 2015b Generation of multiple toroidal dust vortices by a non-monotonic density gradient in a direct current glow discharge plasma. Phys. Plasmas 22 (9), 093702.
Khrapak, S. A. & Morfill, G. E. 2008 An interpolation formula for the ion flux to a small particle in collisional plasmas. Phys. Plasmas 15 (11), 114503.
Kiel, R. E. 1968 Electrostatic probe theory for free molecular cylinders. AIAA J. 6 (4), 708712.
Kim, S.-H. & Merlino, R. L. 2006 Charging of dust grains in a plasma with negative ions. Phys. Plasmas 13 (5), 052118.
Kirchhoff, R. H., Peterson, E. W. & Talbots, L. 1971 An experimental study of the cylindrical Langmuir probe response in the transition regime. AIAA J. 9 (9), 16861694.
Klagge, S. & Tichỳ, M. 1985 A contribution to the assessment of the influence of collisions on the measurements with Langmuir probes in the thick sheath working regime. Czechoslovak J. Phys. B 35 (9), 9881006.
Klindworth, M., Arp, O. & Piel, A. 2007 Langmuir probe system for dusty plasmas under microgravity. Rev. Sci. Instrum. 78 (3), 033502.
Laframboise, J. G.1966 Theory of spherical and cylindrical Langmuir probes in a collisionless, Maxwellian plasma at rest. Tech. Rep. DTIC Document.
Lee, D., Severn, G., Oksuz, L. & Hershkowitz, N. 2006 Laser-induced fluorescence measurements of argon ion velocities near the sheath boundary of an argon–xenon plasma. J. Phys. D 39 (24), 5230.
Liu, J.-Y., Wang, Z.-X., Wang, X., Zhang, Q., Zou, X. & Zhang, Y. 2003 The bohm criterion for the dusty plasma sheath. Phys. Plasmas 10 (9), 35073511.
Ma, J.-X. & Yu, M. Y. 1995 Electrostatic sheath at the boundary of a dusty plasma. Phys. Plasmas 2 (4), 13431348.
Magnus, F. & Gudmundsson, J. T. 2008 Digital smoothing of the Langmuir probe I–V characteristic. Rev. Sci. Instrum. 79 (7), 073503.
Mausbach, M. 1997 Parametrization of the Laframboise theory for cylindrical Langmuir probe analysis. J. Vac. Sci. Technol. A 15 (6), 29232929.
Melzer, A.2016 Introduction to colloidal (dusty) plasmas. Lecture Notes, Ernst-Moritz-Arndt-Universität Greifswald. Available at:
Mott-Smith, H. M. & Langmuir, I. 1926 The theory of collectors in gaseous discharges. Phys. Rev. 28, 727763.
Narasimhan, G., Steinbruchel, C. et al. 2001 Analysis of Langmuir probe data: analytical parametrization, and the importance of the end effect. J. Vac. Sci. Technol. A 19 (1), 376378.
Neumann, G., Kammeyer, M. & Schneemann, B. 1995 Personal-computer-based control and evaluation of Langmuir probe characteristics. Meas. Sci. Technol. 6 (4), 391399.
Nuhn, B. & Peter, G. 1977 Comparison of classical and numerical evaluation of Langmuir probe characteristics at low plasma densities. In Phenomena in Ionized Gases, XIII International Conference, p. 97. Physical Society of the GDR.
Orfanidis, S. J. 1996 Introduction to Signal Processing. Prentice Hall.
Ott, H. W. 1976 Noise Reduction Techniques in Electronic Systems. Wiley.
Peterson, E. W. & Talbot, L. 1970 Collisionless electrostatic single-probe and double-probe measurements. AIAA J. 8 (12), 22152219.
Phelps, A. V. 1994 The application of scattering cross sections to ion flux models in discharge sheaths. J. Appl. Phys. 76 (2), 747753.
Rich, A. 1983 Shielding and guarding. Analog Dialogue 17 (1), 813.
Rousseau, A., Teboul, E. & Bchu, S. 2005 Comparison between Langmuir probe and microwave autointerferometry measurements at intermediate pressure in an argon surface wave discharge. J. Appl. Phys. 98 (8), 083306.
Savitzky, A. & Golay, M. J. E. 1964 Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36 (8), 16271639.
Schulz, G. J. & Brown, S. C. 1955 Microwave study of positive ion collection by probes. Phys. Rev. 98 (6), 16421649.
Shukla, P. K. & Mamun, A. A. 2001 Introduction to Dusty Plasma Physics. CRC.
Sonin, A. A. 1966 Free-molecule Langmuir probe and its use in flow-field studies. AIAA J. 4 (9), 15881596.
Steinbrüchel, C. 1990 A new method for analyzing Langmuir probe data and the determination of ion densities and etch yields in an etching plasma. J. Vac. Sci. Technol. A 8 (3), 16631667.
Talbot, L. & Chou, Y. S. 1969 Langmuir probe response in the transition regime. In Rarefied Gas Dynamics, vol. II, pp. 17231737. Academic.
Tichý, M., S̃ícha, M., David, P. & David, T. 1994 A collisional model of the positive ion collection by a cylindrical Langmuir probe. Contrib. Plasma Phys. 34 (1), 5968.
Trottenberg, T., Brede, B., Block, D. & Piel, A. 2003 Resonance cones in a dusty magnetized plasma. Phys. Plasmas 10 (12), 46274632.
Trunec, D., Španěl, P. & Smith, D. 1995 The influence of ion–neutral collisions in the plasma sheath on the ion current to an electrostatic probe: Monte Carlo simulation. Contrib. Plasma Phys. 35 (3), 203212.
Yaroshenko, V. V., Verheest, F., Thomas, H. M. & Morfill, G. E. 2009 The Bohm sheath criterion in strongly coupled complex plasmas. New J. Phys. 11 (7), 073013.
Yu, M. Y., Saleem, H. & Luo, H. 1992 Dusty plasma near a conducting boundary. Phys. Fluids B 4 (10), 34273431.
Zakrzewski, Z. & Kopiczynski, T. 1974 Effect of collisions on positive ion collection by a cylindrical Langmuir probe. Plasma Phys. 16 (12), 11951198.
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Langmuir probe in collisionless and collisional plasma including dusty plasma

  • Sayak Bose (a1), Manjit Kaur (a1) (a2), P. K. Chattopadhyay (a1), J. Ghosh (a1), Y. C. Saxena (a1) and R. Pal (a3)...


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