Comment on "Drift-Wave Instability Excited by Field-Aligned Ion Flow Velocity Shear in the Absence of Electron Current

Ganguli, G.

Hatakeyama, R.

Kaneko, T.

Tsunoyama, H.

Physical Review Letters

English

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Kaneko et al. Reply

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Kaneko et al. Reply著者 金子  俊郎journal orpublication titlePhysical review lettersvolume 92number 6page range 069502-1-069502-1year 2004URL http://hdl.handle.net/10097/34865P H Y S I C A L R E V I E W L E T T E R S week ending13 FEBRUARY 2004VOLUME 92, NUMBER 6Kaneko et al. Reply: In [1] Sorasio et al. show that theexperimental results obtained in our recent Letter [2] canbe explained by using the theoretical model of Shuklaet al. [3], which demonstrates that the wave is excited bythe inverse electron Landau damping effect and by theparallel ion velocity gradient. However, it has alreadybeen shown in our Letter that the experimental data fitto a considerable extent into the theory containing theseeffects (see Fig. 5 in [2]) which is based on Eq. (A15) inthe theory of Ganguli et al. [4], and it was explicitly statedthat the experimentally obtained drift waves are drivenby the inverse electron Landau damping effect.Since the theory of Shukla et al. includes effects of adust component, ion-neutral collisions, and unperturbedE B drift, their treatment is useful for analyzing theweakly ionized dusty plasmas. In [1], however, theseeffects are neglected in order to analyze our experimentalresults in [2]. Furthermore, in the theory of Shukla et al.some essential physics necessary for clarifying our ex-perimental results is absent as described below.Equation (1) in [1] can be transformed for small k?s,or b ’ 1, as follows. 21=2 !3r!e!r  2!2a2	kzVte!e2 kzui0  A21=2 !3r!e!r  2!2r !e!r	kzVte!e2 kzui0 !r !e221=2 !3r2!r !e	kzVtir !e  kzvd!r 1;(1)where !r  !e=2	  A, A ’!e=2	2 !2a2p , vd isthe relative electron-ion drift in the ion frame, and theother notation is defined in [1,2]. Although this equationappears to be similar to Eq. (1) in our recent Letter [2],there is an important and intrinsic difference in discus-sing the effects of the Landau damping. The theory ofShukla et al. considers only the electron-wave resonantinteraction (inverse electron Landau damping) and ne-glects the ion-wave resonant interaction (ion Landaudamping). We agree with Sorasio et al. in the Commentthat the ion Landau damping is insignificant for largej!r=kzVtij (typically >5), which corresponds to 2 >25 in our experimental condition. In this large 2 regime,the theory of Shukla et al. becomes consistent with oursand is applicable to the experiment. For 2 < 25, how-069502-1 0031-9007=04=92(6)=069502(1)$22.50 ever, the ion Landau damping has appreciable influenceon the growth rate. The growth rate sharply decreases at2 ’ 20 as shown in Fig. 5 of [2], which can only beexplained by increment of the ion Landau damping effectwith a decrease in 2. On the other hand, because of theabsence of the ion Landau damping term in Eq. (1) of [1],the theoretical growth rate described in Fig. 1 of [1] isvery broad in the region of the smaller 2 and is positiveeven for 2 < 10 where the drift-wave instability in ourexperiment is entirely damped by the ion Landau damp-ing. Thus, the instability growth is overestimated in themodel of Shukla et al.It is to be noted that we assume the direction of therelative electron-ion drift is positive in the ion frame in[2]. In this sense, the !r solution in [1] and the !rsolution in [2] seem to have the same meaning andpossibility of yielding the positive growth rate.For Vie > 0 in the notation in [2], namely, 2 > 0,A is larger than !e=2, and, thus, the absolute value ofthe phase velocity of the wave in the ion framej!r=kjj!e=2	  A=kj	 always increases with anincrease in 2, which leads to the reduction of ionLandau damping and the destabilization of the wave bythe inverse electron Landau damping.Finally, we emphasize that the competition between theion Landau damping and the inverse electron Landaudamping is essential to the mechanism of destabilizationand stabilization of the drift wave with increasing shearstrength as described in our Letter.T. Kaneko,1,* H. Tsunoyama,1 R. Hatakeyama,1 andG. Ganguli21Department of Electronic EngineeringTohoku UniversitySendai 980-8579, Japan2Plasma Physics DivisionNaval Research LaboratoryWashington, D.C. 20375, USAReceived 27 August 2003; published 12 February 2004DOI: 10.1103/PhysRevLett.92.069502PACS numbers: 52.35.Kt, 52.35.Qz200*Electronic address: kaneko@ecei.tohoku.ac.jp[1] G. Sorasio, P. K. Shukla, and L. Stenflo, precedingComment, Phys. Rev. Lett. 92, 069501 (2004).[2] T. Kaneko, H. Tsunoyama, and R. Hatakeyama, Phys.Rev. Lett. 90, 125001 (2003).[3] P. K. Shukla, G. Sorasio, and L. Stenflo, Phys. Rev. E66, 067401 (2002).[4] G. Ganguli et al., J. Geophys. Res. 99, 8873 (1994).4 The American Physical Society 069502-1

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