A Perturbation Theory for Strong Plasma Turbulence

Abstract

As indicated by its title, "Electron demagnetization and heating in quasi-perpendicular shocks, " the main point of our work has been to show that electrons are not magnetized while crossing the bow shock. While this conclusion is implied in earlier work that is referenced in our paper and in the Schwartz reply, the vast majority of work on electron heating at shocks has been based on the assumption that shock-crossing electrons are magnetized and satisfy the first adiabatic invariant. Thus, our work offers an alternative view of electron heating at the terrestrial bow shock.The main thrust of Schwartz's comment concerns adiabatic electron behavior, which is irrelevant to our main conclusion because the electrons are not magnetized. The comment provides other interesting and useful insights. In particular, Schwartz's discussion of the difference between the adiabatic behavior of a single electron and an entire distribution clarifies misinterpretations in ours and others discussions of adiabatic behavior (response to Schwartz points 1, 2, and 4).Schwartz points out that demagnetization would inhibit the electron drift along the shock and asks what would then limit the amount of energy gained by the cross-shock potential. The behavior of demagnetized electrons in turbulence is a complex problem. The strong electric field fluctuations we observe have frequencies around the electron gyrofrequency. Some aspects of the behavior of the electrons can perhaps be explained by electron cyclotron drift waves [Muschietti and Lembège, 2013], where stochastic demagnetized electron orbits in strong turbulence can play a major role [Dupree, 1966]. The effect of cyclotron waves for scattering of electrons has been extensively studied in the past [see, e.g., Horne and Thorne, 2000; Guest, 2009, and references therein]. In such strong turbulence, it is plausible that electrons are heated equally in perpendicular and parallel directions by a fraction of the cross-shock potential (response to Schwartz point 3).Schwartz discusses the deHoffman-Teller (dHT) and Normal Incidence (NIF) frames of reference, along with his theoretical preference for the dHT frame in which the perpendicular electric field is zero. It is worth noting that experimentally, the preference for one frame over the other is less evident. Figure 2 of our paper gives the electric field components (in Figures 2e-2g) in what is described as the NIF frame in the paper but is actually in the dHT frame (due to an error in the figure sent to the journal). The dHT frame of reference was found by transforming to the frame tied to the plasma and, in which, the perpendicular electric field in the solar wind was zero, as can be verified by the zero values of the field components of Figures 2e-2g after 20 s. While the theoretical expectation in this frame is that the perpendicular electric field is also zero in the shock ramp and downstream, the experimental data does not generally behave in this manner. As shown in Figure 2, the perpendicular field in the ramp was as large as 3...

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“…However, as Berndt Müller pointed out in his talk [98], there exists an alternative mechanism that may be responsible for a small viscosity of a weakly coupled, but expanding quark-gluon plasma. This mechanism is based on the theory of particle transport in turbulent plasmas [97,99]. Such plasmas are characterized by strongly excited random field modes in certain regimes of instability, which coherently scatter the charged particles and thus reduce the rate of momentum transport.…”

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