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Test Charge Response of a Dusty Plasma with Grain Size Distribution and Charging Dynamics
KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
2006 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

This doctoral thesis reports analytical and numerical results for the electrostatic response of a dusty plasma to a moving test charge. Two important physical aspects of dusty plasmas, namely grain size distribution and grain charging dynamics were taken into account. In the first case, a dusty plasma in thermal equilibrium and with a distribution of grain sizes is considered. A size distribution is assumed which decreases exponentially with the grain mass for large sizes and gives a simple smooth reduction for small sizes. The electrostatic response to a slowly moving test charge, using a second order approximation is found and the effects of collisions are also investigated. It turns out that for this particular size distribution, there is a remarkably simple result that the resulting effective distribution for the electrostatic response is a kappa (generalized Lorentzian) distribution. In the second case, we present an analytical model for the shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging for cases both with and without the collision effects. The response potential is treated as a power series in test charge velocity. Analytical expressions for the response potential are found up to second order in test charge velocity. The first-order dynamical charging term is shown to be the consequence of the delay in the shielding due to the dynamics of the charging process. It is concluded that the dynamical charging of the grains in a dusty plasma enhances the shielding of a test charge. To clarify the physics, a separate study is made where the charging is approximated by using a time delay. The resulting potential shows the delayed shielding effect explicitly. The terms in the potential that depend on the charging dynamics involve a spatial shift given by the test charge velocity and the charging time. The wake potential of a fast moving test charge in the case of grain charging dynamics was also found. It was observed that the grain charging dynamics leads to a spatial damping and a phase shift in the potential response. Finally, combining these two physical aspects, generalized results for the electrostatic potential were found incorporating the terms from both grain size distribution and grain charging dynamics. The generalized results contain the previous work where these two effects were studied separately and which can now be found as special limiting cases. This kind of work has relevance both in space and astrophysical plasmas.

Place, publisher, year, edition, pages
Stockholm: KTH , 2006. , xviii, 65 p.
Series
Trita-EE, ISSN 1653-5146 ; 2006:045
Keyword [en]
Dusty plasmas, Complex plasmas, Grain size distribution, Grain charging dynamics, Lorentzian distribution, Kappa distribution, Test charge response, Delayed shielding, Energy loss, Drag force, Wake field.
National Category
Fusion, Plasma and Space Physics
Identifiers
URN: urn:nbn:se:kth:diva-4134ISBN: 91-7178-463-2 (print)OAI: oai:DiVA.org:kth-4134DiVA: diva2:10886
Public defence
2006-10-31, KTHB Salongen, Main Library, Osquars Backe 31, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20100920Available from: 2006-10-06 Created: 2006-10-06 Last updated: 2011-10-28Bibliographically approved
List of papers
1. Test charge response of a dusty plasma with a grain size distribution
Open this publication in new window or tab >>Test charge response of a dusty plasma with a grain size distribution
2002 (English)In: Physics Letters A, ISSN 0375-9601, Vol. 305, 79-86 p.Article in journal (Refereed) Published
Abstract [en]

The form of the grain size distribution strongly influences the linear dielectric response of a dusty plasma. For a class of size distributions there is an equivalence to a Lorentzian distribution of mono-sized particles. The electrostatic response to a slowly moving test charge, using a second order approximation, is found. The effects of collisions are investigated.

Keyword
dusty plasmas, complex plasmas, grain size distribution, Lorentzian distribution, Kappa distribution, test charge response
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-6230 (URN)10.1016/S0375-9601(02)01392-0 (DOI)000179601000012 ()
Note
QC 20100917Available from: 2006-10-06 Created: 2006-10-06 Last updated: 2010-12-20Bibliographically approved
2. Shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging
Open this publication in new window or tab >>Shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging
2003 (English)In: Physics of Plasmas, ISSN 1070-664X, Vol. 10, no 9, 3484-3491 p.Article in journal (Refereed) Published
Abstract [en]

The dynamical charging of grains in a dusty plasma enhances the shielding of test charges. Time scales for charging are determined by the ambient plasma parameters and the grain dimensions. They can be very short, approaching the ion plasma period for grain sizes of the order of an electron Debye length. For a slowly moving test charge the response potential is found as a power series in the test charge velocity. Collisional effects are included. Analytical expressions for the response potential, valid for all radial distances, are found up to second order in the test charge velocity. The first-order dynamical charging term is shown to be the consequence of the delay in the shielding due to the dynamics of the charging process. The remaining first-order terms are given by analytical expressions that yield the well known asymptotic power law forms for large distances.

Keyword
energy-loss, acoustic-wave, halleys-comet, projectiles, particles
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-6231 (URN)10.1063/1.1598433 (DOI)000184899800007 ()
Note
QC 20100917Available from: 2006-10-06 Created: 2006-10-06 Last updated: 2012-06-04Bibliographically approved
3. Delayed shielding of a test charge due to dynamical grain charging in a dusty plasma
Open this publication in new window or tab >>Delayed shielding of a test charge due to dynamical grain charging in a dusty plasma
2004 (English)In: IEEE Transactions on Plasma Science, ISSN 0093-3813, E-ISSN 1939-9375, Vol. 32, 627-631 p.Article in journal (Refereed) Published
Abstract [en]

The dynamical charging of grains in a dusty plasma modifies the plasma dielectric response function and the nature of the electrostatic wave modes. The grain charging leads to an additional shielding effect that acts in the same way as Debye shielding. Both the additional shielding and the charging rate are important in determining the response of a dusty plasma to a moving test charge. The dynamics of the charging can be approximated by using a time delay. An alternative analysis of the potential of a slowly moving test charge is performed introducing a delay operator for the grain charge response. The terms in the potential that depend on the charging dynamics involve a spatial shift given by the test charge velocity and the charging time. This gives a physical interpretation of earlier results which are identical to first order in the test charge velocity.

Keyword
Complex plasmas, dusty plasmas, dynamical grain charging, test charge response
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-6232 (URN)10.1109/TPS.2004.828451 (DOI)000222278400018 ()2-s2.0-4344715426 (Scopus ID)
Note
QC 20100920. Title changed from "Delayed shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging".Available from: 2006-10-06 Created: 2006-10-06 Last updated: 2011-10-28Bibliographically approved
4. Energy loss of test charges in a dusty plasma in the presence of dynamical grain charging, in New Vistas in Dusty Plasmas
Open this publication in new window or tab >>Energy loss of test charges in a dusty plasma in the presence of dynamical grain charging, in New Vistas in Dusty Plasmas
2005 (English)In: New Vistas in Dusty Plasmas / [ed] Boufendi, L; Mikikian, M; Shukla, PK, 2005, Vol. 799, 490-493 p.Conference paper, Published paper (Refereed)
Abstract [en]

Thedynamical charging of dust grains is an important process andis found to enhance the shielding of a test chargepassing through a multi-component dusty plasma. In the present work,the energy loss of a test charge projectile passing througha dusty plasma in the presence of dynamical grain chargingis studied. The electric forces can be written in termsof the Maxwell stress tensor for a sphere around thetest charge. For sphere with radius tending to zero theforce is just that on the test charge. For afinite radius, forces on the plasma are also included whichmakes it possible to see how the force on thetest charge is balanced by the force on the plasma.The method fails for the zero radius but the dragforce can be found from a simple physical model. Thegeneral analytical results are presented and are compared with theprevious results.

Series
AIP CONFERENCE PROCEEDINGS, ISSN 0094-243X ; 799
Keyword
dusty plasmas, complex plasmas, test charge, drag force, energy loss, dynamical grain charging
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-6233 (URN)10.1063/1.2134672 (DOI)000234508900106 ()2-s2.0-33750357760 (Scopus ID)0-7354-0287-6 (ISBN)
Conference
4th International Conference on Physics of Dusty Plasmas. Orleans, FRANCE. JUN 13-17, 2005
Note
QC 20100920 QC 20111014Available from: 2006-10-06 Created: 2006-10-06 Last updated: 2011-10-14Bibliographically approved
5. Test charge response for a dusty plasma with both grain size distribution and dynamical charging
Open this publication in new window or tab >>Test charge response for a dusty plasma with both grain size distribution and dynamical charging
2007 (English)In: Physics of Plasmas, ISSN 1070-664X, Vol. 14, no 1, 012105- p.Article in journal (Refereed) Published
Abstract [en]

The form of the grain size distribution strongly influences the linear dielectric response of a dusty plasma. For a class of size distributions and a thermal velocity distribution, there is an equivalence to a Lorentzian distribution of monosized particles. The electrostatic response to a slowly moving test charge can then be found. Dynamical charging of grains in a dusty plasma leads to an enhanced time-dependent shielding of a test charge. Here the combined effect of both grain size distribution and dynamical grain charging on the response to a slowly moving test charge is analyzed. The dynamical charging contribution to the plasma dielectric has a complicated dependence on the parameters for the size distribution and on the charging rate. However, this dependence can be expressed in terms of known functions. Series expansions are used to derive the potential response to a slowly moving test charge. Previously known results may be recovered as special limiting cases of this investigation. The analytical expression for the plasma dielectric may be used for more general cases and is applicable to the study of electrostatic waves.

Keyword
moving test charge, energy-loss, dispersion function, projectiles, particles
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-6234 (URN)10.1063/1.2431354 (DOI)000243891800010 ()2-s2.0-34047117705 (Scopus ID)
Note
Uppdaterad från "in press" till published. QC 20100920Available from: 2006-10-06 Created: 2006-10-06 Last updated: 2010-09-20Bibliographically approved
6. Effect of grain charging dynamics on the wake potential of a moving test charge in a dusty plasma
Open this publication in new window or tab >>Effect of grain charging dynamics on the wake potential of a moving test charge in a dusty plasma
2007 (English)In: Physics of Plasmas, ISSN 1070-664X, Vol. 14, no 1, 012102- p.Article in journal (Refereed) Published
Abstract [en]

The response potential of a dusty (complex) plasma to a moving test charge strongly depends on its velocity. For a test charge moving with a velocity exceeding the dust-acoustic speed, a distinctive wake-field is produced trailing behind the test charge. Here the response to a fast moving test charge, when dispersion effects are small and the dust behaves as a cold plasma component, is considered. The effects of dynamical grain charging are included, and the cases with and without these effects are analyzed and compared. The plasma dielectric function is chosen assuming that all grains are of the same size and includes a response term for charging dynamics. The wake field potential is found either explicitly in terms of known functions or by using numerical methods for the integral expression. Maximum response is found on the wake cone with apex angle determined by the ratio between the dust acoustic velocity and the test charge velocity. The structure of the wake field stretches in the direction of the test charge velocity when this increases. The functional form of the field is given by separately changing the length scales parallel and perpendicular to the velocity. The potential on the axis gives an electric field close behind the test charge that can attract charges with the same sign. The grain charging dynamics leads to a spatial damping and a phase shift in the potential response.

Keyword
Acoustic wave velocity, Charge transfer, Damping, Dielectric properties, Electric field effects, Numerical methods, Phase shift
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-6235 (URN)10.1063/1.2423018 (DOI)000243891800007 ()2-s2.0-34047187370 (Scopus ID)
Note
QC 20100909. Uppdaterad från In press till Published (20100909)Available from: 2006-10-06 Created: 2006-10-06 Last updated: 2010-09-09Bibliographically approved

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