Biernat, H. K.

Erkaev, N. V.

Langmayr, D.

Mühlbacher, S.

Rucker, H. O.

Semenov, V. S.

Shaidurov, V. A.

Vogl, D. F.

Elektronisches Publikationsportal der Ãsterreichischen Akademie der Wissenschaften

Field-aligned Electric Field in the Io Flux Tube as a Result of a Pressure Pulse near Io

Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschaften

FIELD–ALIGNED ELECTRIC FIELD IN THE IOFLUX TUBE AS A RESULT OF A PRESSUREPULSE NEAR IOD. Langmayr∗†, N. V. Erkaev‡, V. S. Semenov§, V. A. Shaidurov‡,H. K. Biernat∗†¶, H. O. Rucker∗†, D. F. Vogl∗, and S. Mu¨hlbachler∗†AbstractPressure pulses produced near Io by volcanic outbursts or created in the courseof torus plasma flow around Io, eventually generate slow shocks accompanied by asupersonic flow behind the shock. It is known that a supersonic flow produces afield–aligned electric field [Serizava and Sato, 1984]. It is a fact that if the massvelocity of ions is much bigger than the thermal velocity (supersonic flow), then themost part of the ions must have small pitch angles, whereas the electrons, for whichthe thermal velocity is much larger, should not be noticeably disturbed. As a result,the mirror points of the streaming protons and electrons are located at differentpositions along the Io flux tube leading to a charge separation and the occurrenceof a field–aligned electric field. The method of Serizava and Sato modified for the Ioflux tube with its very special types of ions has been used to calculate the potentialdifference, which can be as large as several kV for sufficiently strong pressure pulses.IntroductionThe interaction of Io with the magnetosphere of Jupiter has been, and continues to be, asubject of intense interest in space plasma physics. In most descriptions of the Io inter-action, the motion of Io through the corotating magnetosphere results in the generationof Alfve`n waves propagating away from Io into the magnetospheric plasma [Neubauer,1980]. However, we concentrate on a mechanism connected with the slow mode actingalong the Io flux tube. A possible generation of a slow mode wave at the position of Io isgiven by Io’s high volcanic activity, or by the plasma flow past Io [Linker et al., 1991]. The∗Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, A–8042 Graz, Austria†Institute for Geophysics, Astrophysics and Meteorology, University of Graz, Universita¨tsplatz 5,A–8010 Graz, Austria‡Institute of Computational Modelling, Russian Academy of Sciences, Krasnoyarsk 660036, Russia§Institute of Physics, State University of St. Petersburg, St. Petergof 198904, Russia¶Institute for Theoretical Physics, University of Graz, Universita¨tsplatz 5, A–8010 Graz, Austria2 D. Langmayr et al.Figure 1: Sketch of the geometry and basic assumptions applied to the stated problem.slow mode waves are converted into slow shocks accompanied by an accelerated plasmaflow. Following these slow shocks towards Jupiter, reveals that the flow velocity increasestowards Jupiter along the magnetic tube up to values of the initial Alfve`n velocity at Io.The reason for this enhancement stems from the narrowing of the flux tube together withthe increase in the amount of the Jovian magnetic field. Due to this strong plasma flow,the different plasma contributions, i.e., electrons and ions, mirror at different points andthus, a charge separation develops along the magnetic field, which in turn leads to thegeneration of an electric potential difference. The aim of the present paper is to estimatethis potential drop, thereby applying well–known methods of kinetic theory following themethod of Serizava and Sato [1984].The main idea of how the potential difference is calculated is sketched in Figure 1. As astarting point, we take the plasma flow to be directed along the magnetic field towardsJupiter. At the location of this plasma flow, namely at the source point, we assume quasi–neutrality, i.e., ne,0 =∑ni,p,0, where ne, ni, p, and 0 denote electron particle number, ionparticle number, species of ions, and quantities at the source point, respectively. As a nextstep, we assume that all plasma contributions have the same bulk velocity, V0. From thesetwo basic assumptions, we directly conclude that at the source point the electron flux, Fe,0,has to be equal to the sum of the respective ion fluxes, Fi,p,0. Assuming that there is nocurrent present and, in addition, mass conservation along the magnetic flux tube, yieldsthat the reflected electron flux is equal to flux carried by the reflected ion populations.This equality allows one to obtain the electric potential difference as a function of thedistance, s, measured along the flux tube.Field–aligned electric fields 3Basic equationsAt the source point we assume the particles to be distributed according to a so–calledparallel beam distribution function given asf(v‖,j, v2⊥,j) =njT⊥,jT12‖,j(mj2pi) 32exp(−mjv2⊥,j2T⊥,j)[exp(− mj2T‖,j(v‖,j − V0)2)− exp(− mj2T‖,j(v‖,j + V0)2)], (1)where n,m, v, and T refer to particle number, mass, microscopic velocity, and temperaturein energy units, respectively. Subscript j denotes the particle species and subscripts ‖and ⊥ characterize the components of the relevant quantities parallel and normal withrespect to the magnetic field, which we approximate by using a dipole configuration.In order to calculate the reflected flux we apply the concept of moments of thedistribution function. Since we are interested in the reflected contribution, the integralover the microscopic velocities is taken over a particular region in the respective velocityspace. These regions are determined by the conservation of energy and the conservationof magnetic momentum. Combining these two conservation relations allows us to obtainthe following expression for the particles parallel velocityv2‖,j = v2‖0,j −(√1 + 3 sin2 λcos6 λ− 1)v2⊥0,j −2 qjmjΦ. (2)Here, Φ denotes the electric potential difference, which is initially zero, q refers to thecharge, and λ corresponds to the magnetic latitude. At the particles mirror points theirparallel velocity component vanishes. Thus, the right–hand side of equation (2) determinesa curve in the velocity space, which separates the reflecting contribution from the passing.The shape of the curve in the electron and ion velocity space is shown in Figure 2. As anext step, we derive the explicit expressions for the reflected fluxes, Fs , by calculatingthe first moment of the distribution function over the relevant regions. The result is asfollowsFe = n0,eV0 (γ − 1)T⊥,e(T‖,e + (γ − 1)T⊥,e)32exp(−me2V 20(γ − 1)T⊥,e + T‖,e −qeΦ(γ − 1)T⊥,e), (3)Fi = n0,iV0[1V0√2pimiT32‖,iT‖,i + (γ − 1)T⊥,i(exp (−x21)− exp (−x22))+12(Erf [x1] + Erf [x2]) +12((γ − 1)T⊥,i(γ − 1)T⊥,i + T‖,i) 32exp(−mi2V 20(γ − 1)T⊥,i + T‖,i +qiΦ(γ − 1)T⊥,i)(2− Erf [x3]− Erf [x4])], (4)4 D. Langmayr et al.vpvnfifi,0reflectedpassingvpvnfefe,0reflectedpassingFigure 2: Sketch of the electron and ion velocity space with the respective distribution functionand separation curve.withx1 =√mi2T‖,i(√qiΦmi+ V0), (5)x2 =√mi2T‖,i(√qiΦmi− V0), (6)x3 =((γ − 1)T⊥,i + T‖,i(γ − 1)T⊥,iT‖,i) 12(qiΦ)12 +mi2(γ − 1)T⊥,iT‖,i((γ − 1)T⊥,i + T‖,i)12V0, (7)x4 =((γ − 1)T⊥,i + T‖,i(γ − 1)T⊥,iT‖,i) 12(qiΦ)12 −mi2(γ − 1)T⊥,iT‖,i((γ − 1)T⊥,i + T‖,i)12V0, (8)where γ denotes the ratio of the magnetic field normalized to the magnetic field at thesource point and Erf [x] is the error function. Due to the equality of the reflected particlefluxes, i.e.,Fe =∑Fi,p, (9)the electric potential can be calculated as a function of the distance along the flux tube.SolutionIn order to simulate the conditions in the Io flux tube, we assume the plasma stream tocontain hot anisotropic ions (S+ and O+) with T⊥,i = 5 T‖,i = 200 eV, and isotropicelectrons with Tn,e = Tp,e = 150 eV [Mei et al., 1995]. We assume the source point tobe located at s = 6 Rj, which is just slightly more than one Jupiter radius above theField–aligned electric fields 5Figure 3: Profiles of the electric potential as a function of s for different initial velocities. TheAlfve`n velocity at the position of Io is VA0 = 250 km/s.planets surface. The obtained potential drop as a function of s is shown in Figure 3,where we model two plasma flows of different strength. The main result of this study isthat the strength of the potential drop is directly proportional to the flow energy of theions. Thus, a fast plasma flow leads to a strong potential (see Figure 3). Additionally,the rather heavy ions along the Io flux tube contribute to a strong potential difference.ConclusionsIn this paper we tried to emphasize the importance and application of slow mode waveswith regard to the interaction of Io and Jupiter. The slow mode waves can be exciteddue to the Io volcanism or are created in the course of plasma flow around the satellite.The slow waves develop into slow shocks, which are propagating along the Io flux tubeaccompanied by a strong plasma flow behind the shock. This strong plasma flow leadsto an electric potential difference along the magnetic field, which can reach values ofabout 1 kV. As the precipitating electrons pass the developed potential drop, they pickthe potential drop’s energy and are effectively accelerated. Thus, the slow mode wavescenario seems to contribute to the explanation of the excitation of aurora on Jupiterand the Jovian decameter radio emission [Wu, 1988] together with the generally acceptedAlfve`n wings model [Neubauer, 1980].Acknowledgements: Part of this work was done while N. V. E. and V. V. S. were on aresearch visit to Graz. This work is supported by the INTAS–ESA projects 99–01277,by the Austrian “Fonds zur Fo¨rderung der wissenschaftlichen Forschung” under projectsP12761–TPH and P13804–TPH, by grant No 98–05–65290 and No 01–05–64954 from6 D. Langmayr et al.the Russian Foundation of Basic Research, by grant No 97–0–13.0–71 from the RussianMinistry of Education, and from the Russian Ministry of Higher Education. Furthersupport is due to grant No 01–05–02003 from the Russian Foundation of Basic Research,by project I.4/2001 from “O¨sterreichischer Akademischer Austauschdienst”, and by theAustrian Academy of Sciences, “Verwaltungsstelle fu¨r Auslandsbeziehungen”.ReferencesLinker, J. A., M. G. Kivelson, and R. J. Walker, A three–dimensional MHD simulationof plasma flow past Io, J. Geophys. Res., 96, No. A12, 21037–21053, 1991.Mei, Y., R. M. Thorne, and F. Bagenal, Analytic model for the density distribution inthe Io plasma torus, J. Geophys. Res., 100, No. A2, 1823–1828, 1995.Neubauer, F. M., Nonlinear standing Alfve`n wave current system at Io: Theory, J. Geo-phys. Res., 85, 1171, 1980.Serizava, Y., and T. Sato, Generation of large scale potential difference by currentlessplasma jets along the mirror field, Geophys. Res. Lett., 11, No. 6, 595–598, 1984.Wu, C. S., Cyclotron maser instability and its applications, in Planetary Radio EmissionsII, edited by H. O. Rucker, S. J. Bauer, and B. M. Pedersen, Austrian Academy ofScience Press, Vienna, 399–406, 1988.

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Field-aligned Electric Field in the Io Flux Tube as a Result of a Pressure Pulse near Io

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Elektronisches Publikationsportal der Ãsterreichischen Akademie der Wissenschaften

Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschaften

Field-aligned Electric Field in the Io Flux Tube as a Result of a Pressure Pulse near Io

Abstract

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Elektronisches Publikationsportal der Ãsterreichischen Akademie der Wissenschaften

Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschaften

Elektronisches Publikationsportal der Ãsterreichischen Akademie der Wissenschaften