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

[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 shear Alfvén wave traveling through the Jovian magnetosphere from the vicinity of Io to the Jovian ionosphere. [2] Two-fluid analyses give adequate predictions for the parallel electric field strength in plasma regimes where the electron thermal speed vTe = (2kBTe/me)1/2 is much larger, or much smaller, than the Alfvén speed vA = B0(μ0ρ)−1/2. When vTe ≪ vA, shear Alfvén waves can have finite when their perpendicular scale lengths are comparable to the electron skin depth λe = c/ωpe, whereupon the waves are called inertial Alfvén waves. Conversely, when vTe ≫ vA, shear Alfvén waves can have when their perpendicular scales are comparable to λe (vTe/vA), and are often known as kinetic Alfvén waves. Analytic studies using full kinetic theory (either with linear approximations [Lysak, 1998] or using a fully nonlinear simulation [Watt and Rankin, 2008]) have also shown that parallel electric fields are also supported where vTe ∼ vA, if the perpendicular scale length is comparable to the kinetic scale length. [3] If we consider a magnetic fluxtube connecting Io (at 5.9RJ radial distance) with the high-latitude ionosphere at roughly 65o latitude, then the lower portion of this fluxtube has vTe < vA and is in the inertial regime, whereas plasma in the vicinity of Io is more likely to have vTe ∼ vA due to the decreasing magnetic field strength and increasing ion number density in the Io torus. [4] Two-fluid analyses are inadequate in this plasma environment. By portraying the kinetic and inertial corrections to the Alfvén wave dispersion as “competing” effects, the underlying physics of Alfvén waves with finite perpendicular scale lengths becomes obfuscated. In this paper, we show the correct equation for the dispersive factor given in equation (3) of Jones and Su [2008], and we present an alternate explanation for the small ratio of parallel to perpendicular electric fields predicted in the vicinity of Io. [7] In this paper, Ψ is calculated using the same plasma model and perpendicular scale lengths as in the baseline model of Jones and Su [2008]. These values are used in the kinetic dispersion relation [Lysak and Lotko, 1996] to find the complex frequency ω as a function of at equally spaced points along the magnetic field. As in the work of Jones and Su [2008], we assume that the results from an idealized, uniform linear dispersion relation are valid locally, and so we ignore the plasma inhomogeneities along the field line. One (ω, ) pair is selected from the solutions of the dispersion relation at each spatial point, and then used in equation (2) to calculate /, before equation (4) is used to evaluate Ψ. Note that we have investigated a wide range of values of , and Ψ is insensitive to the selection of a particular (ω, ) pair. [8] Figure 1a shows the predictions of ∣Ψ∣ from the two-fluid analysis given by Jones and Su [2008] (solid line) and the kinetic analysis discussed in this paper (diamonds). We compare ∣Ψ∣, since equation (4) returns a complex quantity, especially where vTe >∼ vA (Figure 1b gives the ratio vTe/vA for the same model region). The two-fluid analysis predicts that the parallel electric field will disappear at s ∼ 7.2, but the full kinetic analysis reveals that is nonzero over the entire Io plasma torus (6.0 < s < 7.9). The vital difference between the two approaches is that the kinetic treatment retains the full complex relationship between and . The complex nature of / is important because the phase difference between and changes as the ratio vTe/vA is increased, with the imaginary part becoming comparable to the real part [see Watt and Rankin, 2008]. [9] The kinetic and inertial corrections to the Alfvén wave dispersion do not “cancel,” but must be treated carefully using a full kinetic analysis which retains the imaginary part of /. [10] The explanation for the small values of ∣Ψ∣, and hence the small predicted values of , in the Io torus lies in the selection of in the model of Jones and Su [2008]. Figure 2 shows the variation of λe and λevTe/vA throughout the model domain (1.0 < s < 7.9). For 6.0 < s < 7.9, both quantities are much smaller than one, indicating that the modeled perpendicular scale length of the Alfvén wave is too large to support any significant in the vicinity of Io. [11] If we were to repeat this analysis with larger values of , then the full kinetic treatment would yield larger values of Ψ, and hence , throughout the region near Io, whereas the two-fluid analysis would erroneously produce Ψ = 0 at some point close to Io [see Jones and Su, 2008, Figure 5]. Only observations of waves near Io can indicate realistic perpendicular scale sizes, but once researchers have this information, it is clear that the full kinetic treatment should be used to predict the size of the parallel electric fields due to shear Alfvén waves in this region. [12] 1. For plasma with vTe ∼ vA, a full kinetic analysis should be used to obtain more accurate predictions of parallel electric field strength due to shear Alfvén waves. [13] 2. For the model used by Jones and Su [2008], the predicted parallel electric field strength is small in the vicinity of Io not because the inertial and kinetic effects of the shear Alfvén waves are “in competition,” but because the modeled perpendicular scale length is large compared to characteristic length scales in the plasma. [14] This work was supported by the Canadian Space Agency (CSA) and the Natural Sciences and Engineering Research Council of Canada (NSERC). [15] Wolfgang Baumjohann thanks Robert Lysak for his assistance in evaluating this paper.

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