[Paper Review] Alfvén wave phase-mixing in flows: Why over-dense, solar coronal, open magnetic field structures are cool?

D. Tsiklauri|arXiv (Cornell University)|Jul 19, 2015

Solar and Space Plasma Dynamics18 references3 citations

TL;DR

This paper proposes that co-directional plasma flows in over-dense, open magnetic field structures (OMFS) in the solar corona reduce Alfvén wave phase-mixing, thereby decreasing wave-induced heating and explaining why these structures appear cooler than their surroundings. The key result is an anti-correlation between non-thermal velocity (flow) and temperature in over-dense OMFS due to suppressed phase-mixing when flow and wave propagate in the same direction.

ABSTRACT

The motivation for this study is to include the effect of plasma flow in Alfvén 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: $C_A^\prime(x) o C_A^\prime(x)+V_0^\prime(x)$, 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.

Motivation & Objective

• To investigate how background plasma flows affect Alfvén wave damping via phase-mixing in magnetohydrodynamic (MHD) systems.
• To explain the observed cooler temperatures in over-dense solar coronal open magnetic field structures (OMFS), such as polar plumes, compared to the surrounding corona.
• To determine whether co-directional or counter-directional flows enhance or suppress phase-mixing-induced heating in inhomogeneous plasma structures.
• To provide a theoretical and simulation-based framework linking flow direction, Alfvén wave damping, and observed temperature variations in OMFS.
• To offer testable predictions for observational correlation between non-thermal velocity and temperature in solar coronal structures.

Proposed method

• Conduct 3D magnetohydrodynamic (MHD) simulations to model Alfvén wave propagation and damping in structured plasma with background flows.
• Perform analytical calculations to derive modified expressions for phase-mixing damping under the influence of flow, replacing $ C_A'(x) \to C_A'(x) + V_0'(x) $, where $ C_A $ is Alfvén speed and $ V_0 $ is flow speed, both differentiated across the magnetic field.
• Model over-dense plasma structures with uniform magnetic fields where $ C_A $ is lower than in the surrounding plasma, simulating conditions in coronal polar plumes.
• Analyze the effect of flow direction (co-directional vs. counter-directional) on wave front stretching and transverse phase-mixing efficiency.
• Use observational data from Hinode/EIS and Solar Dynamics Observatory/AIA to compare predicted flow-temperature correlations with real measurements.
• Apply the WKB approximation and non-linear wave coupling models to validate results in different plasma regimes.

Experimental results

Research questions

• RQ1 How does a background plasma flow modify the phase-mixing damping of Alfvén waves in inhomogeneous plasma?
• RQ2 Why do over-dense, open magnetic field structures in the solar corona appear cooler than the surrounding plasma?
• RQ3 Does co-directional flow reduce Alfvén wave phase-mixing and hence heating in over-dense coronal structures?
• RQ4 What is the expected correlation between non-thermal velocity (bulk flow) and temperature in over-dense OMFS if phase-mixing is the dominant heating mechanism?
• RQ5 Can the observed anti-correlation between flow speed and temperature in coronal plumes be explained by flow-modified phase-mixing?

Key findings

• Co-directional plasma flow in over-dense OMFS reduces Alfvén wave phase-mixing by counteracting transverse wave front stretching, leading to slower wave damping and reduced heating.
• The mathematical modification $ C_A'(x) \to C_A'(x) + V_0'(x) $ shows that when $ C_A' $ and $ V_0' $ have opposite signs (as in over-dense structures with co-directional flow), phase-mixing is suppressed.
• In over-dense structures with $ C_A $ lower than in the surroundings, co-directional flow results in an anti-correlation between non-thermal velocity and temperature, consistent with observations of cooler coronal plumes.
• Counter-directional flow enhances phase-mixing and thus increases heating, leading to a positive correlation between flow speed and temperature in under-dense structures.
• The model predicts that in fast solar wind streams with constant magnetic field, a positive correlation between flow speed and temperature is expected if Alfvén speed is higher inside the stream.
• Observational validation is feasible by correlating EIS/AIA measurements of non-thermal velocity and temperature in coronal structures, especially on the solar disk where Doppler shifts can distinguish flow from turbulence.