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تسجيل مستخدم جديدParallel electric field amplification by phase-mixing of Alfven waves
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Previous numerical studies have identified phase mixing of low-frequency Alfven waves as a mean of parallel electric field amplification and acceleration of electrons in a collisionless plasma. Theoretical explanations are given of how this produces an amplification of the parallel electric field, and as a consequence, also leads to enhanced collisionless damping of the wave by energy transfer to the electrons. Our results are based on the properties of the Alfven waves in a warm plasma which are obtained from drift-kinetic theory, in particular, the rate of their electron Landau damping. Phase mixing in a collisionless low-$beta$ plasma proceeds in a manner very similar to the visco-resistive case, except for the fact that electron Landau damping is the primary energy dissipation channel. The time and length scales involved are evaluated. We also focus on the evolution of the parallel electric field and calculate its maximum value in the course of its amplification.
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Context: This paper investigates the effectiveness of phase mixing as a coronal heating mechanism. A key quantity is the wave damping rate, $gamma$, defined as the ratio of the heating rate to the wave energy. Aims: We investigate whether or not la
minar phase-mixed Alfven waves can have a large enough value of $gamma$ to heat the corona. We also investigate the degree to which the $gamma$ of standing Alfven waves which have reached steady-state can be approximated with a relatively simple equation. Further foci of this study are the cause of the reduction of $gamma$ in response to leakage of waves out of a loop, the quantity of this reduction, and how increasing the number of excited harmonics affects $gamma$. Results: We find that at observed frequencies $gamma$ is too small to heat the corona by approximately three orders of magnitude. Therefore, we believe that laminar phase mixing is not a viable stand-alone heating mechanism for coronal loops. We show that $gamma$ is largest at resonance. We find our simple equation provides a good estimate for the damping rate (within approximately 10% accuracy) for resonant field lines. However, away from resonance, the equation provides a poor estimate, predicting $gamma$ to be orders of magnitude too large. We find that leakage acts to reduce $gamma$ but plays a negligible role if $gamma$ is of the order required to heat the corona. If the wave energy follows a power spectrum with slope -5/3 then $gamma$ grows logarithmically with the number of excited harmonics. If the number of excited harmonics is increased by much more than 100, then the heating is mainly caused by gradients that are parallel to the field rather than perpendicular to it. Therefore, in this case, the system is not heated mainly by phase mixing.
The motivation for this study is to include the effect of plasma flow in Alfven wave (AW) damping via phase mixing and to explore the observational implications. Our magnetohydrodynamic (MHD) simulations and analytical calculations show that, when a
background flow is present, mathematical expressions for the AW damping via phase mixing are modified by the following substitution: $C_A^prime(x) to C_A^prime(x)+V_0^prime(x)$, where $C_A$ and $V_0$ are AW phase and the flow speeds, and the prime denotes a derivative in the direction across the background magnetic field. In uniform magnetic fields and over-dense plasma structures, where $C_A$ is smaller than in the surrounding plasma, the flow, which is confined to the structure and going in the same direction as the AW, reduces the effect of phase-mixing, because on the edges of the structure $C_A^prime$ and $V_0^prime$ have opposite signs. Thus, the wave damps by means of slower phase-mixing compared to the case without the flow. This is the result of the co-directional flow that reduces the wave front stretching in the transverse direction. We apply our findings to addressing the question why over-dense solar coronal open magnetic field structures (OMFS) are cooler than the background plasma. Observations show that the over-dense OMFS (e.g. solar coronal polar plumes) are cooler than surrounding plasma and that, in these structures, Doppler line-broadening is consistent with bulk plasma motions, such as AW. If over-dense solar coronal OMFS are heated by AW damping via phase-mixing, we show that, co-directional with AW, plasma flow in them reduces the phase-mixing induced-heating, thus providing an explanation of why they appear cooler than the background.
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