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List of Figures

View Image Figure 1:
The solar wind speed as a function of latitude (in km s–1) measured by Ulysses’ SWOOPS instrument near solar minimum (left panel) and near solar maximum (right panel). The direction of the magnetic field is marked (red-outward; blue-inward). The typical composite solar images near minimum (8/17/96) and maximum (12/07/00) are shown using data from SOHO/LASCO, EIT, and Mauna Loa K-coronameter images (McComas et al., 2003).
View Image Figure 2:
Example of magnetic spectrum from the ACE database. Year/day of sample (decimal day of year in 1998) and Power Spectral Density (PSD) are shown. The top curve represents the summed power in the two components perpendicular to the mean magnetic field, and the lower curve represents the power in the parallel component. The fit functions with power exponent –1.56 ± 0.3 (upper) and –1.8 ± 0.03 (lower) are shown (see Smith et al., 2006, for further details).
View Image Figure 3:
Height dependence of the frequency-integrated velocity amplitude obtained from the solution of the linearized Alfvén wave equation driven by a spectrum of transverse photospheric fluctuations. The solution was obtained in the thin flux tube approximation by Cranmer and van Ballegooijen (2005). Solid lines give the undamped value of ⟨δV ⟩ (the dashed line is for different model parameters). The red line is √ ---- ⟨δV ⟩B = ⟨δB ⟩∕ 4π ρ for the 3 km s –1 driving amplitude case. The symbols correspond to observational constraints of the Alfvén waves amplitudes from various observations discussed by Cranmer and van Ballegooijen (2005) (reproduced by permission of the AAS).
View Image Figure 4:
The typical form of the driving spectrum of Alfvén waves used in the 3-fluid model to drive the solar wind.
View Image Figure 5:
The radial velocity in the meridional plane for a two-temperature, idealize tilted-dipole simulation with 15° tilt with respect to the rotation axis. The black curves indicate the location of the Alfvénic surface. The red regions show the location of the fast solar wind, and the blue-green show sources of the slow solar wind. Image reproduced by permission from Oran et al. (2013); copyright by AAS.
View Image Figure 6:
The result of a 2.5D MHD Alfvén wave driven fast solar wind model in a coronal hole. A snapshot of the spatial dependence of B ∕ρ1∕2 ϕ, v ϕ, v r, and ρ is shown at t = 255τA = 32.5 h. The velocities and 1∕2 B ϕ∕ρ are in units of VA = 1527 km s–1, and the density is in units of 108 cm–3. The Alfvén waves are evident in V ϕ and in 1∕2 B ϕ∕ρ. The nonlinear longitudinal waves are evident in vr and ρ that propagate in-phase (Ofman and Davila, 1998).
View Image Figure 7:
Alfvén wave driven fast solar wind obtained with 2.5D MHD model (a cut through the center of the coronal hole is shown). Vr and Vϕ solar wind velocities are shown for two Alfvén wave driving frequencies. The green curve shows the Parker’s isothermal solar wind solution (adapted from Ofman and Davila, 1998).
View Image Figure 8:
Results from 1.5D solar wind model (red lines) compared to observations (symbols and symbols with error bars). See, Suzuki and Inutsuka (2005) for the details (reproduced by permission of the AAS).
View Image Figure 9:
Results of the 3-fluid model of the Alfvén wave driven fast solar wind in a coronal hole. The Vϕ and the Vr velocity components for He++ (left panels) and protons (right panels). The velocity is in units of 1527 km s–1. The distance R is in units of R⊙, and the latitude 𝜃 is in radians (Ofman, 2004a).
View Image Figure 10:
The typical form of the magnetic fluctuations spectrum obtained with the 3-fluid model at 18 R⊙. The solid line shows a fit with 2 ω, while the dashed curve shows a fit with −5∕3 ω (adapted from Ofman, 2004a).
View Image Figure 11:
Results of the 3-fluid model: the outflow speed of protons (solid) and ions (dashed) in the coronal hole averaged over 𝜃 for the fast solar wind in a coronal hole. (a) With preferential heating of He++ ions. (b) Same as (a), but with preferential heating of O5+ as the heavy ions. (c) Solar wind produced with equal heat input per particle for protons and He++ ions. (d) Wave driven wind – no empirical heating of protons, and electrons (adapted from Ofman, 2004a).
View Image Figure 12:
The temperatures and densities of the electrons, protons, and ions obtained with 3-fluid model of the fast solar wind for the cases shown in Figure 11 (adapted from Ofman, 2004a).
View Image Figure 13:
Doppler broadening of an emission line as a result of unresolved Alfvén wave motions in the line of sight obtained with the 3-fluid model. Thermal (solid line) and simulated (dashed line) line profile at 4 R ⊙. The integration time is 1.7 h (adapted from Ofman and Davila, 2001).
View Image Figure 14:
The effective temperature and the kinetic temperature for protons (solid) and ions (dashes) for wave driven fast solar wind. The effective temperature that includes the contribution of unresolved Alfvénic fluctuations is shown by thick line style, while the kinetic temperature is shown by thin line style (adapted from Ofman, 2004a).
View Image Figure 15:
The temporal evolution of the O5+ ion (top panel) and proton (lower panel) temperature anisotropy obtained with 1D hybrid model for the driven wave spectrum case (adapted from Ofman et al., 2002).
View Image Figure 16:
The velocity distribution of O5+ ions (left panel) and protons (right panel) obtained with 1D hybrid model of the driven wave spectrum. The Vx is parallel to the background magnetic field shown with the solid curve, the transverse components Vy (dashes), and Vz (dots) are shown (adapted from Ofman et al., 2002).
View Image Figure 17:
The dispersion relations obtained from 1D hybrid model in three-ion plasma (p, He++, O6+). The intensity scale shows the power of the Fourier transform of (a) transverse magnetic field fluctuations, and transverse fluid velocities of (b) protons, (c) He++, and (d) O6+ (Ofman et al., 2005).
View Image Figure 18:
Velocity amplitude ratios of VHe++∕Vp (top panel) and VO6+ ∕Vp obtained from 1D hybrid simulation dispersion relation. The ratio V ++∕V He p is shown in the top panel for kCA ∕ Ωp ≈ 0 (solid line), and for kCA ∕Ωp ≈ 0.52 (dashes). Bottom panel: same as top panel, but for the ratio VO6+∕Vp (Ofman et al., 2005).
View Image Figure 19:
Top: Temporal evolution of the parallel and perpendicular components of the ion temperatures obtained by Maneva et al. (2013) with the 1.5D hybrid model involving broadband spectra. Solid lines denote the evolution without expansion, and the dashed lines illustrate the case when solar wind expansion is considered. Bottom: Temporal evolution of the H+-He++ drift speed for this case. The dashed line shows the result with expansion.
View Image Figure 20:
The final stages of the evolution of the proton (top panels) and alpha (bottom panels) velocity distributions in the V ∥-V⊥ plane in the 1.5D hybrid model initialized with the broadband spectrum of Alfvén/cyclotron waves. The formation of the accelerated particle population is evident (adapted from Maneva et al., 2013).
View Image Figure 21:
Comparison of 1D and 2D model results. The evolution of O5+ temperature anisotropy calculated with the 1D hybrid (dashes) and 2D hybrid (solid) models show good agreement (Ofman and Viñas, 2007).
View Image Figure 22:
Results of the parametric study of He++ anisotropy relaxation obtained with 2D hybrid code by Gary et al. (2003). The parameters were nα∕ne = 0.05 with initial Te∕T∥p = 1.0, T ∥α ∕T∥p = 4.0, and isotropic protons. The crosses correspond to t = 0, the squares indicate plasma parameters at saturation of the fluctuating magnetic fields, and the dots represent later times. The dashed line indicates the best fit of the anisotropies at Ωpt = 400 (adapted from Gary et al., 2003).
View Image Figure 23:
The results of the parametric study with the 1D hybrid simulation of O5+ temperature anisotropy relaxation by Ofman et al. (2001). The scaling of the relaxed T ∕T − 1 ⊥i ∥i with the final β ∥i (full circles). The scaling of the relaxation time, trel, with the initial β∥i (circles). Both quantities scale as −0.41 β∥i. The “x”’s mark the values T⊥i∕T ∥i − 1 at t = 0. The enhanced O5+ abundance of 6 × 10–4 in this parametric study leads to shorter computation times (Ofman et al., 2001).
View Image Figure 24:
The temporal evolution of the temperature anisotropy, and the drift velocity for protons and O5+ ions. (a) Ions heated by the driven wave spectrum. (b) Ions heated by a beam with Vd = 1.5 VA (adapted from Ofman and Viñas, 2007).
View Image Figure 25:
The perpendicular velocity distribution of the O5+ ions obtained with 2D hybrid model with drift velocity Vd = 2VA (adapted from Ofman and Viñas, 2007).
View Image Figure 26:
The power spectrum of fluctuations in Bz. (a) Middle of low density region, driven waves spectrum. The dashed line is for power law fit with m = –1.66. (b) Same as (a), but in the middle of high density region. The fit is with m = –2.53. (c) Middle of low density region, the case with Vd = 2 VA. The dashed line is for power law fit with m = –1.81. (d) Same as (c), but in the middle of the high density region. The dashed line is for power law fit with m = –2.80 (from Ofman, 2010).