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The finite probe size effect in fluctuation measurements; application to dusty plasmas

Part of: Diagnostics of Dust in Plasmas

Published online by Cambridge University Press:  18 March 2016

P. Tolias ,
S. Ratynskaia ,
U. de Angelis  and
E. Lazzaro
P. Tolias*
Affiliation:
Space and Plasma Physics, Royal Institute of Technology (KTH), Stockholm SE-100 44, Sweden Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Naples 80126, Italy
S. Ratynskaia
Affiliation:
Space and Plasma Physics, Royal Institute of Technology (KTH), Stockholm SE-100 44, Sweden
U. de Angelis
Affiliation:
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Naples 80126, Italy
E. Lazzaro
Affiliation:
Istituto di Fisica del Plasma, Consiglio Nazionale delle Ricerche (CNR), Milano 20125, Italy
*
†Email address for correspondence: [email protected]
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Abstract

The effect of the finite probe size in plasma fluctuation measurements is revisited for dusty plasmas, where it has been argued that dust leads to a significant low-frequency enhancement in the spectral densities of ion density fluctuations, which can constitute the physical basis of a dust diagnostic technique. Theoretical predictions for the spectral modifications are presented and the dust acoustic mode contribution is analysed. The finite probe size effect is treated within the volume average approach, which introduces geometry dependent form factors that are calculated for spherical and cylindrical probes. The volume average approach is compared with the typically employed cutoff wavenumber approximation for various dust and plasma parameters. The contribution of temperature fluctuations to the spectral density of current fluctuations is also evaluated.

Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 2 , April 2016 , 615820201
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Copyright
© Cambridge University Press 2016 

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References

Akhiezer, A. I., Akhiezer, I. A., Polovin, R. V., Sitenko, A. G. & Stepanov, K. N. 1975a Plasma Electrodynamics, Volume 1: Linear Theory and Fluctuations. Pergamon.Google Scholar
Akhiezer, A. I., Akhiezer, I. A., Polovin, R. V., Sitenko, A. G. & Stepanov, K. N. 1975b Plasma Electrodynamics, Volume 2: Non-Linear Theory and Fluctuations. Pergamon.Google Scholar
Alpert, L., Gurevich, A. V. & Pitaevskii, L. P. 1965 Space Physics With Artificial Satellites. Consultants Bureau.Google Scholar
de Angelis, U., Capobianco, G., Marmolino, C. & Castaldo, C. 2006 Fluctuations in dusty plasmas. Plasma Phys. Control. Fusion 48, B91–B97.Google Scholar
Annaratone, B. M., Allen, M. W. & Allen, J. E. 1992 Ion currents to cylindrical Langmuir probes in rf plasmas. J. Phys. D 25, 417.CrossRefGoogle Scholar
Beall, J. M., Kim, Y. C. & Powers, E. J. 1982 Estimation of wavenumber and frequency spectra using fixed probe pairs. J. Appl. Phys. 53, 3933.Google Scholar
Delzanno, G. L. & Tang, X. Z. 2015 Comparison of dust charging between orbital-motion-limited theory and particle-in-cell simulations. Phys. Plasmas 22, 113703.CrossRefGoogle Scholar
Demidov, V. I., Ratynskaia, S. & Rypdal, K. 2002 Electric probes for plasmas: the link between theory and instrument. Rev. Sci. Instrum. 73, 340.Google Scholar
Fortov, V. E., Ivlev, A. V., Khrapak, S. A., Khrapak, A. G. & Morfill, G. E. 2005 Complex (dusty) plasmas: current status, open issues, perspectives. Phys. Rep. 421, 1.Google Scholar
Fried, B. D. & Conte, S. D. 1961 The Plasma Dispersion Function: The Hilbert transform of the Gaussian. Academic.Google Scholar
Froula, D. H., Glenzer, S. H., Luhmann, N. C. & Sheffield, J. 2011 Plasma Scattering of Electromagnetic Radiation: Theory and Measurement Techniques. Academic.Google Scholar
Geissler, K. H., Greenwald, R. A. & Calvert, W. 1972 Measurement of plasma properties from the cross spectrum of thermal density fluctuations. Phys. Fluids 15, 96.Google Scholar
Gunell, H. & Skiff, F. 2002 Electrostatic fluctuations in plasmas with distribution functions described by simple pole expansions. Phys. Plasmas 9, 2585.Google Scholar
Ichimaru, S. & Yakimenko, I. P. 1973 Transition probability approach to the theory of plasmas. Phys. Scr. 7, 198.CrossRefGoogle Scholar
Ignatov, A. M., Trigger, S. A., Maiorov, S. A. & Ebeling, W. 2002 Rotational kinetics of absorbing dust grains in neutral gas. Phys. Rev. E 65, 046413.Google Scholar
Kagan, Y. M. & Perel’, V. I. 1964 Probe methods in plasma research. Sov. Phys. Uspekhi 6, 767.Google Scholar
Klimontovich, Yu. L. 1967 The Statistical Theory of Nonequilibrium Processes in a Plasma. Pergamon.Google Scholar
Klimontovich, Yu. L. 1982 Kinetic Theory of Nonideal Gases and Nonideal Plasmas. Pergamon.Google Scholar
Li, B. & Hazeltine, R. D. 2006 Applications of noise theory to plasma fluctuations. Phys. Rev. E 73, 065402.Google ScholarPubMed
Mattingly, S. W., Berumen, J., Chu, F., Hood, R. & Skiff, F. 2013 Measurement and interpretation of the velocity space correlation of a laboratory plasma fluctuation with laser induced fluorescence. J. Instrum. 8, C11015.Google Scholar
Meyer-Vernet, N. & Perche, C. 1989 Tool kit for antennae and thermal noise near the plasma frequency. J. Geophys. Res. 94, 2405.Google Scholar
Montgomery, D. C. & Tidman, D. A. 1964 Plasma Kinetic Theory. McGraw-Hill.Google Scholar
Mott-Smith, H. M. & Langmuir, I. 1926 The theory of collectors in gaseous discharges. Phys. Rev. 28, 727.Google Scholar
Pécseli, H. L. 2015 Spectral properties of electrostatic drift wave turbulence in the laboratory and the ionosphere. Ann. Geophys. 33, 875.Google Scholar
Persson, K.-B. 1965 Brush cathode plasma-a well-behaved plasma. J. Appl. Phys. 36, 3086.Google Scholar
Rao, N. N., Shukla, P. K. & Yu, M. Y. 1990 Dust-acoustic waves in dusty plasmas. Planet. Space Sci. 38, 543.Google Scholar
Ratynskaia, S., de Angeli, M., de Angelis, U., Marmolino, C., Capobianco, G., Lontano, M., Lazzaro, E., Morfill, G. E. & Gervasini, G. 2007 Observation of the effects of dust particles on plasma fluctuation spectra. Phys. Rev. Lett. 99, 075002.CrossRefGoogle ScholarPubMed
Ratynskaia, S., de Angeli, M., Lazzaro, E., Marmolino, C., de Angelis, U., Castaldo, C., Cremona, A., Laguardia, L., Gervasini, G. & Grosso, G. 2010 Plasma fluctuation spectra as a diagnostic tool for submicron dust. Phys. Plasmas 17, 043703.CrossRefGoogle Scholar
Ratynskaia, S., de Angelis, U., Khrapak, S., Klumov, B. & Morfill, G. E. 2006 Electrostatic interaction between dust particles in weakly ionized complex plasmas. Phys. Plasmas 13, 104508.CrossRefGoogle Scholar
Ratynskaia, S., Demidov, V. I. & Rypdal, K. 2002 Measurements of anomalous particle and energy fluxes in a magnetized plasma. Phys. Rev. E 65, 066403.Google Scholar
Ratynskaia, S., Dilecce, G. & Tolias, P. 2015 BABE – a brush cathode discharge for thermal fluctuation measurements. J. Plasma Phys. 81, 345810202.Google Scholar
Rynn, N. & D’Angelo, N. 1960 Device for generating a low temperature, highly ionized cesium plasma. Rev. Sci. Instrum. 31, 1326.Google Scholar
Schram, P. P. J. M. 1991 Kinetic Theory of Gases and Plasmas. Springer.Google Scholar
Schram, P. P. J. M., Sitenko, A. G., Trigger, S. A. & Zagorodny, A. G. 2000 Statistical theory of dusty plasmas: Microscopic equations and Bogolyubov–Born–Green–Kirkwood–Yvon hierarchy. Phys. Rev. E 63, 016403.Google Scholar
Schram, P. P. J. M., Trigger, S. A. & Zagorodny, A. G. 2003 New microscopic and macroscopic variables in dusty plasmas. New J. Phys. 5, 27.Google Scholar
Tang, X. Z. & Delzanno, G. L. 2014 Orbital-motion-limited theory of dust charging and plasma response. Phys. Plasmas 21, 123708.Google Scholar
Tolias, P. 2012 Low-frequency electrostatic modes in partially ionized complex plasmas: a kinetic approach. New J. Phys. 14, 013002.Google Scholar
Tolias, P. & Ratynskaia, S. 2013 Scattering of radiation in collisionless dusty plasmas. Phys. Plasmas 20, 043706.CrossRefGoogle Scholar
Tolias, P., Ratynskaia, S. & de Angelis, U. 2010 Regimes for experimental tests of kinetic effects in dust acoustic waves. Phys. Plasmas 17, 103707.CrossRefGoogle Scholar
Tolias, P., Ratynskaia, S. & de Angelis, U. 2011 Kinetic models of partially ionized complex plasmas in the low frequency regime. Phys. Plasmas 18, 073705.Google Scholar
Tolias, P., Ratynskaia, S. & de Angelis, U. 2012 Spectra of ion density and potential fluctuations in weakly ionized plasmas in the presence of dust grains. Phys. Rev. E 85, 026408.Google Scholar
Tolias, P., Ratynskaia, S., Panarese, A., Longo, S. & de Angelis, U. 2015 Natural fluctuations in un-magnetized and magnetized plasmas. J. Plasma Phys. 81, 905810314.Google Scholar
Tsytovich, V. N. 1989 Description of collective processes and fluctuations in classical and quantum plasmas. Phys. Uspekhi 32, 911.CrossRefGoogle Scholar
Tsytovich, V. N. 1995 Lectures on Nonlinear Plasma Kinetics. Springer.Google Scholar
Tsytovich, V. N. & de Angelis, U. 1999 Kinetic theory of dusty plasmas. I. General approach. Phys. Plasmas 6, 1093.Google Scholar
Tsytovich, V. N., de Angelis, U., Ivlev, A. V. & Morfill, G. E. 2005 Kinetic theory of partially ionized complex (dusty) plasmas. Phys. Plasmas 12, 082103.Google Scholar
Williams, R. H. & Chappell, W. R. 1971 Microscopic theory of density fluctuations and diffusion in weakly ionized plasmas. Phys. Fluids 14, 591.Google Scholar
Yakimenko, I. P. & Zagorodny, A. G. 1974 Transition probabilities, correlation functions and dielectric permittivity tensors for semibounded and bounded nonequilibrium plasmas. Phys. Scr. 10, 244.Google Scholar
Zweben, S., Liewer, P. C. & Couldl, R. W. 1982 Edge plasma transport experiments in the Caltech tokamak. J. Nucl. Mater. 111, 39.Google Scholar