---
abstract: 'Alfv\''en wave transport in the solar wind, including non-linear spectral
  energy transfer, is studied. We present numerical solutions of wave transport using
  a diffusive flux function previously introduced for spectral energy transfer, and
  compare it with the analytical solution obtained for a convective flux function.
  The two models of cascading produce very similar behavior of a power spectrum initially
  of 1/f-form at the solar surface, provided that the cascading constants are tuned
  to produce the same spectral flux in the inertial range. We present an analytical
  expression for the power spectrum of the diffusively-cascading Alfv\''en waves
  in the solar wind derived from a solution of the wave transport equation and show
  that it compares well with the exact solutions. Our expression enables (semi) analytical
  evaluation of the cyclotron heating rate, the wave pressure gradient, and the energetic-particle
  mean free path related to the Alfv\''en waves in the corona and solar wind.'
adsnote: Provided by the SAO/NASA Astrophysics Data System
adsurl: https://ui.adsabs.harvard.edu/abs/2003A&A...407..713V
authors:
- R. Vainio
- T. Laitinen
- H. Fichtner
category: publications
date: '2003-08-01'
doi: 10.1051/0004-6361:20030914
draft: false
featured: false
journal: A&A
month: August
pages: 713-723
projects: []
publication: A&A
publication_types:
- '2'
tags:
- 'Sun: corona'
- 'Sun: particle emission'
- 'Sun: solar wind'
- Turbulence
title: 'A simple analytical expression for the power spectrum of cascading Alfv\''en
  waves in the solar wind'
type: ARTICLE
volume: '407'
year: '2003'
---