Coronal loops heated by turbulence-driven Alfvén waves: A two fluid model

Abstract

Abstract. We present the results of a thorough parameter study of coronal loop models in the aim to explore the mechanism behind coronal heating. The two-fluid coronal loops described in this paper have lengths from 10 Mm to 600 Mm and consist of protons and electrons. The loops are treated with our unique, self-consistent, steady state dynamic loop model to derive the basic parameters (as introduced by Li & Habbal 2003, ApJ, 598, L125). The only heating mechanism assumed is turbulently generated Alfvén waves that carry the necessary flux from the chromosphere to energize the coronal plasma through preferential heating of the proton gas. Strong Coulomb coupling allows energy to pass efficiently from protons to electrons. We have control over the independent variables, driving scale (l) and Alfvén amplitude (ξ), which influence the dissipation and flux of these resonant waves. We find "mapping" the loop parameter response to varying l with fixed ξ a useful tool to find where certain conditions for each loop length exist. From this, we are able to pin-point where the coldest solution lies. For a loop of L = 10 Mm, the coolest loops have a maximum temperature of T = 0.75 MK. We also focus on a L = 40 Mm loop and vary both l and ξ so we can compare results with existing work. From this parameter mapping we can categorise the loop heating profiles. Our model indicates the existence of footpoint, non-uniformly and quasi-uniformly heated profiles. There is also strong evidence to suggest the same mechanism may apply to hot, SXT loops.

Coronal Loops: Observations and Modeling of Confined Plasma

“…Even more attention received the propagation of Alfvén waves in coronal loops. Hydrodynamic loop modeling showed that Alfvén waves deposit significant momentum in the plasma, and that steady state conditions with significant flows and relatively high density can be reached (O’Neill and Li, 2005 ). Analogous results were obtained independently with a different approach: considering a wind-like model to describe a long isothermal loop, Grappin et al ( 2003 , 2005 ) showed that the waves can drive pressure variations along the loop which trigger siphon flows.…”

“…Ofman et al ( 1998 ) included inhomogeneous density structure and found that a broadband wave spectrum becomes necessary for efficient resonance and that it fragments the loop into many density layers that resemble the multistrand concept. The heat deposition by the resonance of Alfvén waves in a loop was investigated by O’Neill and Li ( 2005 ). A multi-strand loop model where the heating is due to the dissipation of MHD waves was applied to explain filter-ratios along loops (Bourouaine and Marsch, 2010 , see Sections 3.3.3 , 4.2 ).…”

COOL TRANSITION REGION LOOPS OBSERVED BY THEINTERFACE REGION IMAGING SPECTROGRAPH

“…The observed siphon flow field lasts for at least 10 mins, which is consistent with the picture where these loops are heated in a steady manner by an energy source in the blueshifted footpoints (southern legs). Given that there are an infinite number of ways for prescribing the spatial heating profile, we, therefore, choose to focus on one mechanism where the heating derives from Alfvén waves (for details, see O'Neill & Li 2005). The wave energy, originally in the low-frequency Magnetohydrodynamic regime, is turbulently cascaded towards high-frequencies until proton-cyclotron resonance comes into play, whereby the energy of the turbulently generated proton-cyclotron waves are absorbed by protons.…”

“…Assuming that the Alfvén waves are generated at locations in the chromosphere where the temperature is 2 × 10 4 K, what is appealing in this mechanism is that T M , the maximum temperature a loop acquires, depends only on the looplength L and the imposed wave amplitude ξ. With ξ being constrained by SOHO/SUMER measurements (e.g., Chae et al 1998), the lowest value that T M attains depends only on L. An exhaustive parameter study (O'Neill & Li 2005) suggests that T M for a loop length of ∼ 10 4 km always exceeds 0.7 MK, which is much higher than the formation temperature of Si iv. Lowering ξ from its nominal value of 14 km/s to 10 km/s does not lower T M much.…”

Kinetic Alfvén wave instability driven by a field-aligned current in high-βplasmas

“…However, large scale AWs traveling in a homogeneous plasma do not efficiently exchange energy directly with the medium because of the mismatch between the wave scales and the microscopic kinetic scales of particles in the local medium. There have been a series of proposed mechanisms to transfer the energy of AWs to plasma particles [1][2][3][4][5][6][7][8][9][10][11]; one of them involves kinetic Alfvén waves (KAWs). KAWs are dispersive AWs with a short perpendicular wavelength comparable to microscopic kinetic scales of particles, such as the electron inertia length λ e and the ion gyroradius ρ i (or the ion-acoustic gyroradius ρ s ), but with a parallel wavelength that is longer than the ion inertial length because of their low frequencies below the ion cyclotron frequency (i.e., ω i ).…”