A simple analytical expression for the power spectrum of cascading Alfvén waves in the solar wind

Vainio, Rami; Laitinen, Timo; Fichtner, H.

doi:10.1051/0004-6361:20030914

Cited by 38 publications

(46 citation statements)

References 35 publications

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“…A more thorough investigation of different temperatures between electrons and ions is made by Landi (2008) and Landi & Cranmer (2009). The model effects have been extended to both 1D and 2D (e.g., Tu & Marsch 1997;Laitinen et al 2003;Vainio et al 2003;Endeve et al 2004;Hu et al 2003aHu et al , 2003b. The 2D two-temperature model of Hu et al (2003aHu et al ( , 2003b shows good agreement with Ulysses in situ observations of protons at 1 AU.…”

Section: Introductionmentioning

confidence: 85%

A Global Two-Temperature Corona and Inner Heliosphere Model: A Comprehensive Validation Study

Jin

Manchester

Holst

et al. 2011

ApJ

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The recent solar minimum with very low activity provides us a unique opportunity for validating solar wind models. During CR2077 (2008 November 20 through December 17), the number of sunspots was near the absolute minimum of solar cycle 23. For this solar rotation, we perform a multi-spacecraft validation study for the recently developed three-dimensional, two-temperature, Alfvén-wave-driven global solar wind model (a component within the Space Weather Modeling Framework). By using in situ observations from the Solar Terrestrial Relations Observatory (STEREO) A and B, Advanced Composition Explorer (ACE), and Venus Express, we compare the observed proton state (density, temperature, and velocity) and magnetic field of the heliosphere with that predicted by the model. Near the Sun, we validate the numerical model with the electron density obtained from the solar rotational tomography of Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph C2 data in the range of 2.4 to 6 solar radii. Electron temperature and density are determined from differential emission measure tomography (DEMT) of STEREO A and B Extreme Ultraviolet Imager data in the range of 1.035 to 1.225 solar radii. The electron density and temperature derived from the Hinode/Extreme Ultraviolet Imaging Spectrometer data are also used to compare with the DEMT as well as the model output. Moreover, for the first time, we compare ionic charge states of carbon, oxygen, silicon, and iron observed in situ with the ACE/Solar Wind Ion Composition Spectrometer with those predicted by our model. The validation results suggest that most of the model outputs for CR2077 can fit the observations very well. Based on this encouraging result, we therefore expect great improvement for the future modeling of coronal mass ejections (CMEs) and CME-driven shocks.

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Section: Introductionmentioning

confidence: 85%

A Global Two-Temperature Corona and Inner Heliosphere Model: A Comprehensive Validation Study

Jin

Manchester

Holst

et al. 2011

ApJ

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“…There are more sophisticated one-dimensional treatments of the solar corona (e.g., Tu & Marsch 1997;Laitinen et al 2003;Vainio et al 2003;Suzuki 2006;Cranmer 2010) that include advanced treatment of Alfvén waves, heat conduction, and radiation. For our CME simulations, we make use of a coronal model that addresses the same physical processes in fully 3D geometry, the two-temperature coronal model developed by van der Holst et al (2010), which describes the coronal plasma as a magnetized proton-electron neutral fluid with a single velocity.…”

Section: Introductionmentioning

confidence: 99%

The Coupled Evolution of Electrons and Ions in Coronal Mass Ejection-Driven Shocks

Manchester

Holst

Tóth

et al. 2012

ApJ

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We present simulations of coronal mass ejections (CMEs) performed with a new two-temperature coronal model developed at the University of Michigan, which is able to address the coupled thermodynamics of the electron and proton populations in the context of a single fluid. This model employs heat conduction for electrons, constant adiabatic index (γ = 5/3), and includes Alfvén wave pressure to accelerate the solar wind. The Wang-Sheeley-Arge empirical model is used to determine the Alfvén wave pressure necessary to produce the observed bimodal solar wind speed. The Alfvén waves are dissipated as they propagate from the Sun and heat protons on open magnetic field lines to temperatures above 2 MK. The model is driven by empirical boundary conditions that includes GONG magnetogram data to calculate the coronal field, and STEREO/EUVI observations to specify the density and temperature at the coronal boundary by the Differential Emission Measure Tomography method. With this model, we simulate the propagation of fast CMEs and study the thermodynamics of CME-driven shocks. Since the thermal speed of the electrons greatly exceeds the speed of the CME, only protons are directly heated by the shock. Coulomb collisions low in the corona couple the protons and electrons allowing heat exchange between the two species. However, the coupling is so brief that the electrons never achieve more than 10% of the maximum temperature of the protons. We find that heat is able to conduct on open magnetic field lines and rapidly propagates ahead of the CME to form a shock precursor of hot electrons.

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“…The physical parameters for the simulations are based on model parameters by Vainio et al (2003) resembling the (slow) solar wind at a distance of 2.6 solar radii. To characterize the plasma we choose the field strength of the static background magnetic field B model 0 = 0.20 G, the plasma frequency ω model p = 6.4 · 10 7 rad s −1 and the temperature T model = 2.0 · 10 6 K according to the model.…”

Section: Simulation Setupsmentioning

confidence: 99%

“…As can be seen from the model parameters from Vainio et al (2003) and the dispersion relation for parallel propagating waves, equation (13), most electrons will resonate with waves in the dispersive regime. E.g., at a distance of 2.5 solar radii electrons with energies below 1 MeV will resonate with dispersive waves.…”

Section: Context and Outlookmentioning

confidence: 99%

Particle Scattering Off of Right-Handed Dispersive Waves

Schreiner

Kilian

Spanier

2017

ApJ

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Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfvén waves are considered for this process, although dispersive waves are also present throughout the heliosphere.We investigate resonant interaction of energetic electrons with dispersive, right-handed waves. For the interaction of particles and a single wave a variable transformation into the rest frame of the wave can be performed. Here, wellestablished analytic models derived in the framework of magnetostatic quasilinear theory (QLT) can be used as a reference to validate simulation results. However, this approach fails as soon as several dispersive waves are involved. Based on analytic solutions modeling the scattering amplitude in the magnetostatic limit, we present an approach to modify these equations for the use in the plasma frame. Thereby we aim at a description of particle scattering in the presence of several waves.A Particle-in-Cell (PiC) code is employed to study wave-particle scattering on a micro-physically correct level and to test the modified model equations. We investigate the interactions of electrons at different energies (from 1 keV to 1 MeV) and right-handed waves with various amplitudes. Differences between model and arXiv:1611.00310v1 [astro-ph.HE] 1 Nov 2016 -2 -simulation arise in the case of high amplitudes or several waves. Analyzing the trajectories of single particles we find no microscopic diffusion in the case of a single plasma wave, although a broadening of the particle distribution can be observed.

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A simple analytical expression for the power spectrum of cascading Alfvén waves in the solar wind

Cited by 38 publications

References 35 publications

A Global Two-Temperature Corona and Inner Heliosphere Model: A Comprehensive Validation Study

A Global Two-Temperature Corona and Inner Heliosphere Model: A Comprehensive Validation Study

The Coupled Evolution of Electrons and Ions in Coronal Mass Ejection-Driven Shocks

Particle Scattering Off of Right-Handed Dispersive Waves

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