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R. Rankin

Streltsov

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Comment on “Role of dispersive Alfvén waves in generating parallel electric fields along the Io-Jupiter fluxtube” by S. T. Jones and Y.-J. Su

Watt, Clare E. J.

Rankin, R.

Central Archive at the University of Reading

Comment on 'Role of dispersive Alfvén waves in generating parallel electric fields along the Io Jupiter fluxtube' by S. T. ‐Jones and Y. J. Su ‐Article Published Version Watt, C. E. J. and Rankin, R. (2009) Comment on 'Role of dispersive Alfvén waves in generating parallel electric fields along the Io Jupiter fluxtube' by S. T. Jones and Y. J. Su. ‐ ‐Journal of Geophysical Research, 114. A04212. ISSN 0148­0227 doi: https://doi.org/10.1029/2009JA014083 Available at http://centaur.reading.ac.uk/32820/ It is advisable to refer to the publisher’s version if you intend to cite from the work. Published version at: http://dx.doi.org/10.1029/2009JA014083 To link to this article DOI: http://dx.doi.org/10.1029/2009JA014083 Publisher: American Geophysical Union All outputs in CentAUR are protected by Intellectual Property Rights law, including copyright law. Copyright and IPR is retained by the creators or other copyright holders. Terms and conditions for use of this material are defined in the End User Agreement . www.reading.ac.uk/centaur CentAUR Central Archive at the University of Reading Reading’s research outputs onlineComment on ‘‘Role of dispersive Alfve´n waves in generating parallelelectric fields along the Io-Jupiter fluxtube’’ by S. T. Jonesand Y.-J. SuC. E. J. Watt1 and R. Rankin1Received 16 January 2009; accepted 16 March 2009; published 28 April 2009.Citation: Watt, C. E. J., and R. Rankin (2009), Comment on ‘‘Role of dispersive Alfve´n waves in generating parallel electric fieldsalong the Io-Jupiter fluxtube’’ by S. T. Jones and Y.-J. Su, J. Geophys. Res., 114, A04212, doi:10.1029/2009JA014083.1. Introduction[1] The authors of a recent paper [Jones and Su, 2008]have used two-fluid plasma theory [e.g., Streltsov et al.,1998] to predict the parallel electric field strength of a shearAlfve´n wave traveling through the Jovian magnetospherefrom the vicinity of Io to the Jovian ionosphere.[2] Two-fluid analyses give adequate predictions for theparallel electric field strength Ek in plasma regimes wherethe electron thermal speed vTe = (2kBTe/me)1/2 is muchlarger, or much smaller, than the Alfve´n speed vA =B0(m0r)1/2. When vTe  vA, shear Alfve´n waves can havefinite Ek when their perpendicular scale lengths arecomparable to the electron skin depth le = c/wpe, whereuponthe waves are called inertial Alfve´n waves. Conversely, whenvTe  vA, shear Alfve´n waves can have Ek when theirperpendicular scales are comparable to le (vTe/vA), and areoften known as kinetic Alfve´n waves. Analytic studiesusing full kinetic theory (either with linear approximations[Lysak, 1998] or using a fully nonlinear simulation [Wattand Rankin, 2008]) have also shown that parallel electricfields are also supported where vTe  vA, if the perpendicularscale length is comparable to the kinetic scale length.[3] If we consider a magnetic fluxtube connecting Io (at5.9RJ radial distance) with the high-latitude ionosphere atroughly 65o latitude, then the lower portion of this fluxtubehas vTe < vA and is in the inertial regime, whereas plasma inthe vicinity of Io is more likely to have vTe  vA due to thedecreasing magnetic field strength and increasing ion num-ber density in the Io torus.[4] Two-fluid analyses are inadequate in this plasmaenvironment. By portraying the kinetic and inertial correc-tions to the Alfve´n wave dispersion as ‘‘competing’’ effects,the underlying physics of Alfve´n waves with finite perpen-dicular scale lengths becomes obfuscated. In this paper, weshow the correct equation for the dispersive factor given inequation (3) of Jones and Su [2008], and we present analternate explanation for the small ratio of parallel toperpendicular electric fields predicted in the vicinity of Io.2. Kinetic Theory[5] The full derivation of the kinetic dispersion relationfor infinite plasma waves in a uniform plasma is given byLysak and Lotko [1996], along with a discussion of thenecessary assumptions and approximations required. Wewill focus on the plasma parameters given by Jones andSu [2008] for the vicinity of Io (i.e., for 6.0RJ < s < 7.9RJ,where s is the spatial parameter along the magnetic field). Inthis region, vA  c, and so the dispersion relation given byequation (5) of Lysak and Lotko [1996] is valid. The ratio ofparallel to perpendicular electric fields is given by [Lysak,1998, equation (3)]EkE?¼n2k  c2v2A1G0ðmiÞminkn?; ð1Þwhere nk = ckk/w, n? = ck?/w, and kk, k?, and w are theparallel and perpendicular wave numbers and the angularfrequency of the shear Alfve´n wave, respectively. Here, mi =k?2 ri2, ri = kBTi/(mi Wi2), and G0 (mi) is the modified Besselfunction G0 = emiI0(mi).[6] The dispersive factor of Jones and Su [2008] gives theratio between the parallel electric field and the wave scalarpotential:Y ¼ Ekikkf: ð2ÞSince E? = ik?f, we haveY ¼  k?kkEkE?; ð3Þand so the electric field ratio given in equation (2) can beused to obtain Y using kinetic theory, for comparison withthe predictions given by two-fluid theory.[7] In this paper, Y is calculated using the same plasmamodel and perpendicular scale lengths as in the baselinemodel of Jones and Su [2008]. These values are used in theJOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, A04212, doi:10.1029/2009JA014083, 20091Department of Physics, University of Alberta, Edmonton, Alberta,Canada.Copyright 2009 by the American Geophysical Union.0148-0227/09/2009JA014083A04212 1 of 3kinetic dispersion relation [Lysak and Lotko, 1996] to findthe complex frequency w as a function of kk at equallyspaced points along the magnetic field. As in the work ofJones and Su [2008], we assume that the results from anidealized, uniform linear dispersion relation are validlocally, and so we ignore the plasma inhomogeneities alongthe field line. One (w, kk) pair is selected from the solutionsof the dispersion relation at each spatial point, and then usedin equation (2) to calculate Ek/E?, before equation (4) isused to evaluate Y. Note that we have investigated a widerange of values of kk, and Y is insensitive to the selection ofa particular (w, kk) pair.3. Results and Discussion[8] Figure 1a shows the predictions of jYj from the two-fluid analysis given by Jones and Su [2008] (solid line) andthe kinetic analysis discussed in this paper (diamonds). Wecompare jYj, since equation (4) returns a complex quantity,especially where vTe > vA (Figure 1b gives the ratio vTe/vAfor the same model region). The two-fluid analysis predictsthat the parallel electric field will disappear at s  7.2, butthe full kinetic analysis reveals that Ek is nonzero over theentire Io plasma torus (6.0 < s < 7.9). The vital differencebetween the two approaches is that the kinetic treatmentretains the full complex relationship between Ek and E?.The complex nature of Ek/E? is important because the phasedifference between Ek and E? changes as the ratio vTe/vA isincreased, with the imaginary part becoming comparable tothe real part [see Watt and Rankin, 2008].[9] The kinetic and inertial corrections to the Alfve´nwave dispersion do not ‘‘cancel,’’ but must be treatedcarefully using a full kinetic analysis which retains theimaginary part of Ek/E?.[10] The explanation for the small values of jYj, andhence the small predicted values of Ek, in the Io torus lies inthe selection of k? in the model of Jones and Su [2008].Figure 2 shows the variation of k?le and k?levTe/vAthroughout the model domain (1.0 < s < 7.9). For 6.0 < s <7.9, both quantities are much smaller than one, indicatingthat the modeled perpendicular scale length of the Alfve´nwave is too large to support any significant Ek in the vicinityof Io.[11] If we were to repeat this analysis with larger valuesof k?, then the full kinetic treatment would yield largervalues of Y, and hence Ek, throughout the region near Io,whereas the two-fluid analysis would erroneously produceY = 0 at some point close to Io [see Jones and Su, 2008,Figure 5]. Only observations of waves near Io can indicaterealistic perpendicular scale sizes, but once researchers havethis information, it is clear that the full kinetic treatmentshould be used to predict the size of the parallel electricfields due to shear Alfve´n waves in this region.4. Conclusions[12] 1. For plasma with vTe  vA, a full kinetic analysisshould be used to obtain more accurate predictions ofparallel electric field strength due to shear Alfve´n waves.[13] 2. For the model used by Jones and Su [2008], thepredicted parallel electric field strength is small in thevicinity of Io not because the inertial and kinetic effectsof the shear Alfve´n waves are ‘‘in competition,’’ butbecause the modeled perpendicular scale length is largecompared to characteristic length scales in the plasma.[14] Acknowledgments. This work was supported by the CanadianSpace Agency (CSA) and the Natural Sciences and Engineering ResearchCouncil of Canada (NSERC).[15] Wolfgang Baumjohann thanks Robert Lysak for his assistance inevaluating this paper.Figure 1. (a) Predictions of jYj using two-fluid theory(solid line) and kinetic theory (diamonds) for the Io torusregion. (b) Modeled vTe/vA for the same plasma region.Figure 2. The modeled perpendicular wavelength of shearAlfve´n waves over the entire Io-Jupiter fluxtube comparedto the inertial scale length le (solid line) and the kineticscale length levTe/vA (dashed line).A04212 WATT AND RANKIN: COMMENTARY2 of 3A04212ReferencesJones, S. T., and Y.-J. Su (2008), Role of dispersive Alfve´n waves ingenerating parallel electric field along the Io-Jupiter fluxtube, J. Geophys.Res., 113, A12205, doi:10.1029/2008JA013512.Lysak, R. L. (1998), The relationship between electrostatic shocks andkinetic Alfve´n waves, Geophys. Res. Lett., 25, 2089–2092.Lysak, R. L., and W. Lotko (1996), On the kinetic dispersion relation forshear Alfve´n waves, J. Geophys. Res., 101, 5085–5094.Streltsov, A. V., W. Lotko, J. R. Johnson, and C. Z. Cheng (1998), Small-scale dispersive field line resonances in the hot magnetospheric plasma,J. Geophys. Res., 103, 26,559–26,572.Watt, C. E. J., and R. Rankin (2008), DK-1D: A drift-kinetic simulation toolfor modelling the shear Alfve´n wave and its interaction with collisionlessplasma, Plasma Phys. Control. Fusion, 50, 074008.R. Rankin and C. E. J. Watt, Department of Physics, University ofAlberta, Edmonton, AB T6G 2G7, Canada. (rankin@phys.ualberta.ca;cwatt@phys.ualberta.ca)A04212 WATT AND RANKIN: COMMENTARY3 of 3A04212

Comment on 'Role of dispersive Alfvén waves in generating parallel electric fields along the Io‐Jupiter fluxtube' by S. T. Jones and Y.‐J. Su

Comment on 'Role of dispersive Alfvén waves in generating parallel electric fields along the Io‐Jupiter fluxtube' by S. T. Jones and Y.‐J. Su

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