Cyclotron resonance in coronal holes: 2. A two‐proton description

115

104

Abstract. The preferential heating and acceleration of O +s ions, as observed by Ultraviolet Coronagraph Spectrometer (UVCS) on Solar and HeliosphericObservatory (SOHO) [Kohlet al., 1998] in the solar coronal holes have been interpreted and modeled by invoking wave-particle cyclotron resonance [Cranmer et al., 1999a[Cranmer et al., , 1999b. However, in the model of Cranmer et al. [1999a, 1999b] and in other subsequent models the assumption of a rigid slope of the wave spectrum was made in calculating the wave energy absoftion by the different ion species. In the present paper it is shown that a self-consistent treatment of the wave damping and absorption is necessary and leads to substantially different results. On the basis of quasi-linear theory, the interaction between the ions and the ion-cyclotron waves [Marsch et al., 1982a;Marsch, 1998] is studied. The total energy conservation equation, including the kinetic energy of the resonant particles and the wave energy, is derived and discussed in detail. The spectral evolution equation for cyclotron waves, when being controlled by the wave growth/damping rate and WKB effects, is solved self-consistently together with the full set of anisotropic multifluid equations for the ions including the cyclotron-resonance wave heating and acceleration rates. From the numerical results we reach the following conclusions: (1) It is physically questionable to use a spectrum with a fixed spectral slope near the cyclotron resonance when one calculates the partition of wave energy among the different ionic species and the kinetic degrees of freedom parallel and perpendicular to the magnetic field. This assumption neglects the important effects of wave absorption and the concurrent reshaping of the wave spectrum, and thus leads in the dissipation domain to extremely low amplitudes of the waves and to difficulties in supplying enough energy to balance the wave absorption at the cyclotron resonances. (2) If the spectrum is allowed to evolve self-consistently and concurrently with the particles' heating and acceleration through wave absorption, such a high perpendiculax temperature and corresponding large temperature anisotropy as observed by UVCS do not occur or cannot be maintained. We conclude that the UVCS oxygen ion observations have not yet been explained satisfactorily by the cyclotron-resonance theory.

Section: 2mentioning

confidence: 99%

On cyclotron wave heating and acceleration of solar wind ions in the outer corona

Tu¹,

Marsch²

2001

115

104

“…The right-hand side of (2) represents the usual expression for quasi-linear pitch angle diffusion with diffusion coefficient D(#). As in paper 1, we do not include the nonresonant wave pressure force resulting from a gradient in the lowfrequency Alfv6n wave intensity, since this force is much smaller than the others in the corona [Hollweg, 1999c[Hollweg, , 2000. Since the sunward and antisunward halves of the proton distribution resonate with different sets of waves, we apply the kinetic shell formalism to each half separately.…”

Section: F(r) Gms E E(r) (3) 2 Rnmentioning

confidence: 99%

“…Cranmer et al [1997] and Hollweg [1999aHollweg [ , 1999b] investigated the single-particle response to resonant and nonresonant forces in the corona. Hollweg [ 1999cHollweg [ , 2000 considered the consequences of restricting the interaction to outward propagating waves and sunward protons with a two-beam representation of the proton distribution, where only the slower beam was allowed to interact with the waves. These models have provided considerable insight, but this technique cannot be extended indefinitely.…”

mentioning

confidence: 99%

“…The dissipated spectral energy is not replaced in these models, and this aspect has been criticized by Cranmer [2000Cranmer [ , 2001 as being therefore unable to provide the necessary large-scale heating of the protons. In contrast, the "cascade" models [Hollweg, 1986[Hollweg, , 1999c[Hollweg, , 2000Hollweg and Johnson, 1988;Isenberg, 1990;Li et al, 1999aLi et al, , 1999bHu et al, , 2000 hypothesize a turbulent cascade which continually provides wave energy to the ions at a turbulent rate specified by background correlation length scales or turbulent wave properties (see also Matthaeus et al [ 1999] and Dmitruk et al [2001] for some new ideas in this area). The kinetic shell models are closest to the cascade type in that they also hypothesize a continual replenishment of the wave energy in the dissipation range.…”

mentioning

confidence: 99%

See 1 more Smart Citation

The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 2. Inward and outward propagating waves

Isenberg¹

2001

Abstract. We extend the kinetic shell model of the cyclotron resonant interaction between coronal hole protons and outward propagating ion cyclotron waves presented in the first paper of this series . That work showed that the resonant dissipation of outward propagating waves produced proton distributions that were unstable to the generation of inward propagating waves. Here we include the kinetic shell interaction with the inward waves, assuming that both the wave generation and wave dissipation proceed much faster than all other processes in the collisionless coronal hole. In this case, the entire proton distribution will be resonant with one set of waves or the other and is thus composed of constant-energy shells in both the sunward and antisunward regions of velocity space. The evolution of the distribution as the plasma flows away from the Sun is then described by following the motion of these shells under the action of the nonresonant forces in the coronal hole. We find that the distribution consists of a core population which circulates through velocity space and a halo which continually expands to higher energy. The halo population is shown to be essential to obtain acceleration of the bulk proton plasma through its response to the mirror force. We present an illustrative calculation of this system which assumes the waves to be dispersionless. We find for this case that the halo particles soon reach extremely high energies, leading to a continuous, rather than declining, acceleration of the plasma. We suggest that these properties are due to the dispersionless assumption and that an improved model incorporating wave dispersion may give more reasonable quantitative results.

“…Also, the electrons remain significantly cooler than all ions. This has led to a flurry of papers dedicated to the construction of solar wind models in which the cyclotron resonance plays the dominant role in determining conditions close to those observed [Marsch and Tu, 1997;Liet al, 1999;Hollweg, 1999aHollweg, , 1999b but it is hard to understand how the result could generate the high frequencies required for cyclotron resonance: reflection-generated modes have extremely low frequencies (periods close to a day for waves coming from the corona), but can have large wave numbers perpendicular to the magnetic field. In this case, damping would arise more from kinetic Alfv•n waves than the ion cyclotron resonance [Leamon eta/., 1998[Leamon eta/., , 1999.…”

Section: Introductionmentioning

confidence: 99%

Alfvén wave propagation and ion cyclotron interactions in the expanding solar wind: One‐dimensional hybrid simulations

Liewer¹,

Velli²,

Goldstein³

2001

135

Abstract. We carry out one-dimensional hybrid simulations of Alfv•n waves propagating along the magnetic field in the presence of a mean radial spherically expanding plasma outflow, representing fast solar wind streams. The equations for particle ions of multiple species and fluid electrons are solved using the Expanding Box Model, a locally Cartesian representation of motion in spherical coordinates, in a frame moving with the local average wind speed. The model gives a minimally consistent description of the effects associated with such motion on particle dynamics, e.g., the flux-conserving decrease of magnetic field intensity and consequent decrease of cyclotron frequency with increasing distance from the Sun. The cyclotron frequency decreases faster than Alfv•n wave frequency, allowing fluctuations below the cyclotron frequency at smaller distance from the Sun to come into cyclotron resonance at greater distances. The hybrid treatment yields a fully self-consistent description of the consequent cyclotron wave-particle interaction in a multi-ion plasma. We present results for cases of monochromatic circularly polarized Alfv•n waves propagating radially outward and for initially well developed Alfv•nic spectra with and without alpha particles. When both alpha particles and protons are present, the alpha particles, which come into resonance first as the wind expands, are observed to be preferentially heated and accelerated. For high beta (equal to ratio of ion pressure to magnetic field pressure) the amount of alpha particles acceleration and heating is limited by the available wave power. For low beta cases the amount of heating and acceleration is limited, not by the wave power, but by the depletion of the distribution function in the resonance region by pitch-angle scattering. The implication of these results for solar wind models is discussed.