Advanced Composition Explorer - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, A07108, doi:10.1029/2004JA010569, 2005

Signatures of Alfve´ n-cyclotron wave-ion scattering: Advanced Composition Explorer (ACE) solar wind observations S. Peter Gary Los Alamos National Laboratory, Los Alamos, New Mexico, USA

Charles W. Smith Space Science Center, University of New Hampshire, Durham, New Hampshire, USA

Ruth M. Skoug Los Alamos National Laboratory, Los Alamos, New Mexico, USA Received 29 April 2004; revised 18 April 2005; accepted 2 May 2005; published 29 July 2005.

[1] Theory and simulations predict that Alfveń-cyclotron fluctuations of sufficiently short

wavelengths and at propagation approximately parallel or antiparallel to the background magnetic field Bo in collisionless plasmas scatter ions so as to increase their energies in the directions perpendicular to Bo. Linear Vlasov theory for a homogeneous, isotropic plasma of electrons, protons, and alpha particles predicts that alpha particle cyclotron resonance properties and ion cyclotron damping of such fluctuations are sensitive functions of the alpha/proton relative velocity. If a strong ion resonance corresponds to strong ion pitch-angle scattering, linear theory implies observable signatures in the anisotropies of solar wind alphas and protons. Statistical analyses of proton and alpha particle anisotropies measured in the solar wind near 1 AU by the plasma and magnetic field instruments on the Advanced Composition Explorer (ACE) spacecraft are reported which are largely consistent with such signatures. Citation: Gary, S. P., C. W. Smith, and R. M. Skoug (2005), Signatures of Alfveń-cyclotron wave-ion scattering: Advanced Composition Explorer (ACE) solar wind observations, J. Geophys. Res., 110, A07108, doi:10.1029/2004JA010569.

1. Introduction [2] Explaining the high temperatures of the solar corona (typically several hundred eV) remains a challenge for solar and space plasma scientists. Any such explanation must describe coronal hole observations from the SOHO spacecraft, which show that heavy ions in the solar corona are much hotter than coronal protons, and are strongly anisotropic in the sense of T?i Tki (Here ? and k denote directions relative to the background magnetic field). Hollweg and Isenberg [2002] have provided a thorough review of these observations, and a detailed argument as to why the dissipation of Alfveń-cyclotron fluctuations is likely to be an important contributor to that heating. [3] The ion-cyclotron heating scenario is as follows: Large-amplitude, low-frequency (that is, well below the proton cyclotron frequency), nonresonant Alfveń waves are generated at the base of, and probably throughout [Cranmer, 2000, 2001], the corona, as well as in the solar wind [Roberts et al., 1992; Smith et al., 2001]. As these fluctuations propagate upward along open field lines away from the Sun and the coronal plasma becomes collisionless, the decreasing magnetic field leads to wave-particle interactions at cyclotron resonances of ions of successively larger charge-to-mass ratios; this is the ‘‘frequency sweeping’’ Copyright 2005 by the American Geophysical Union. 0148-0227/05/2004JA010569

scenario. An alternative picture is that magnetic fluctuation energy may arise at resonant wave numbers via excitation of electromagnetic ion/ion instabilities [e.g., Gary et al., 2000], a process which may operate even in homogeneous plasmas. However the fluctuation energy reaches the resonances, Alfveń-cyclotron fluctuations at k Bo = 0 heat ions predominately in the directions perpendicular to Bo [Marsch et al., 1982c; Tam and Chang, 1999; Hollweg, 2000; Vocks and Marsch, 2001]. As the corona expands into the solar wind, the magnetic mirror force accelerates these anisotropic ions to yield the high speeds of the fast solar wind. [4] The solar corona is observed only by remote sensing, so that information about plasma and magnetic field conditions near the Sun is limited. In contrast there are many spacecraft which make in situ measurements of the solar wind, providing a rich source of information about plasma and magnetic field conditions in that medium, especially near 1 AU. Although the energy densities of particles and fields in the corona are many orders of magnitude greater than those in the solar wind near Earth, the two regions are directly connected. So many basic plasma processes act in both regions; by studying the signatures of fundamental plasma processes which act relatively weakly in the solar wind we can gain insight into how these same processes act more vigorously in the corona. [5] Observations of large-amplitude, outward propagating Alfveń fluctuations throughout the solar wind [Belcher and Davis, 1971] suggest that ion heating by Alfveń-cyclotron

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GARY ET AL.: SIGNATURES OF ALFVEŃ-CYCLOTRON WAVE-ION SCATTERING

waves should take place in the interplanetary medium, so that ion signatures of this process should be evident in measurements from interplanetary spacecraft. Solar wind in situ observations near 1 AU show that, particularly in the fast wind, the core of the proton velocity distribution often bears a T?/Tk > 1 anisotropy [e.g., Bame et al., 1975; Marsch et al., 1982b; Feldman et al., 1996; Neugebauer et al., 2001]. The global adiabatic response of ions flowing outward in the decreasing magnetic field of the solar wind inside about 2 AU is to develop the opposite anisotropy, so measurements of T?p/Tkp > 1 have been interpreted as indicators of local scattering by Alfveńcyclotron fluctuations [e.g., Marsch et al., 2004]. Marsch and Tu [2001] and Tu and Marsch [2002] showed proton velocity distributions measured from the Helios spacecraft between 0.3 and 0.5 AU that strongly suggest the signature of proton pitch-angle scattering by Alfveń-like fluctuations. A major purpose of this manuscript is to describe our search for such signatures in proton and alpha particle observations from the ACE spacecraft in the solar wind near 1 AU. [6] Models of Alfveń-cyclotron fluctuation heating of heavy ions in coronal and solar wind plasmas may be categorized as analytic-based kinetic theories, fluid model computations, and particle simulations. Models in the first two categories have been reviewed exhaustively by Hollweg and Isenberg [2002]. [7] Kinetic analytic models are based on the assumption that the velocity distributions of the scattered ions undergo strong departures from bi-Maxwellian forms. Such models which include both protons and alphas or heavier ions have been developed by Tam and Chang [1999], Hollweg [1999, 2000], Cranmer [2001], Vocks and Marsch [2001], Vocks and Marsch [2002], and Vocks [2002]. Calculations using each of these models yield preferential perpendicular heating of the heavy ions as compared to that of the protons. These kinetic models may be relevant to the very low-b plasmas of the solar corona and the solar wind relatively close to the Sun [Tu and Marsch, 2002]. However, our interest here is in the intermediate-to-high b plasmas near 1 AU, where ion velocity distributions are observed to be Maxwellian-like and where, we believe, such kinetic models are less appropriate. [8] Fluid-like models assume that the velocity distributions of the scattered ions remain bi-Maxwellian, so that the ion properties may be represented as velocity moments of such distributions, that is, as densities, flow speeds, and temperatures. Analytically based fluid models of the corona and/or solar wind which describe both protons and alphas include those by Marsch et al. [1982c], Isenberg and Hollweg [1983], McKenzie [1994], Hu and Habbal [1999], Cranmer [2000], Tu and Marsch [2001a, 2001b], and Gary et al. [2001b]. [9] Most kinetic and fluid models are based on the frequency sweeping scenario. However, these models differ as to how and whether protons may be heated by this process. The coronal models of Cranmer [2000, 2001] suggest that heavy ions absorb almost all of the upward propagating Alfveń wave power, and the model of Vocks and Marsch [2001, 2002] and Vocks [2002] makes this explicit, yielding very little heating for either the alphas or the protons in the collisionless corona.

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[10] Several different hybrid simulations have addressed the interplay between an imposed spectrum of Alfveńcyclotron fluctuations and ion velocity distributions in plasmas with heavy ions as minority species. Liewer et al. [2001] imposed spectra of unidirectional fluctuations, whereas the simulations of Ofman et al. [2002] and Xie et al. [2004] applied fluctuations propagating both parallel and antiparallel to Bo. In all three papers the relative heating is a function of the assumed power spectrum, but for all simulations in which the fluctuations are driven below the helium cyclotron frequency the heavy ions gain substantially more perpendicular temperature than do the protons, in agreement with the analytic models cited above. Furthermore, all computations described in these papers show that changes in the heavy-ion/proton relative speeds are very small compared to vA, the Alfveń speed. [11] The sign of the heavy-ion/proton relative speed with respect to the phase speed wr/kk of Alfveń-cyclotron fluctuations is a critical parameter in determining the associated wave-particle interactions. If a heavy-ion/proton relative speed is negative, the heavy ions are strongly resonant with Alfveń-cyclotron fluctuations and preferentially absorb their energy, whereas if that relative speed is positive and sufficiently large, that ion species becomes nonresonant and has a weak wave-particle interaction [Dusenbery and Hollweg, 1981; Isenberg and Hollweg, 1983; Gomberoff et al., 1996; Li and Habbal, 1999; Gary et al., 2001b]. We use this property in our search for signatures of Alfveń-cyclotron fluctuation scattering of alphas in the solar wind. [12] Section 2 describes our linear Vlasov theory study of magnetic fluctuation damping, with emphasis on Alfveńcyclotron fluctuations. Although solar wind fluctuations at long wavelengths are of large amplitude and in general require fully nonlinear analysis, at the relatively short wavelengths (kkc/wp > 0.1) of interest to us here magnetic fluctuations are observed to be considerably weaker, that is, jdBj2/B2o 1. So for purposes of calculating damping rates linear theory should be a valid approximation. Section 3 summarizes previous solar wind alpha observations which bear on our results, and sections 4 and 5 describe the fundamentals and the details of our data analysis. Section 6 states our conclusions. [13] Throughout this manuscript we denote electrons with the subscript e, protons by p, and alpha particles (hereafter ‘‘alphas’’) by a. Other symbols used here are defined in Appendix A. In particular, the alpha/proton relative flow velocity is vap voa vop.

2. Linear Theory [14] This section describes our use of linear Vlasov theory to determine the parameter regimes of importance for alpha cyclotron damping of Alfveń-cyclotron fluctuations at k Bo = 0 in a plasma with electrons, protons, and alphas as a minority ion species. Isotropic Maxwellian velocity distributions are assumed for each species; the alphas may have a nonzero velocity relative to the protons along Bo but the total current is zero and all calculations are done in the zero momentum frame. Unless stated otherwise, we use the following dimensionless parameters: mp/me = 1836, ma/mp = 4, vA/c = 104, ea/ep = 2, ~bkp = 0.10, na/ne =

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Figure 1. Linear theory results at k Bo = 0: (a) The real part of the frequency and damping rate and (b) the proton and alpha cyclotron resonance factors of the alpha-cyclotron branch of Alfveń-cyclotron fluctuations in a homogeneous, collisionless electron-proton-alpha plasma as functions of the parallel wave number. The solid lines represent fluctuations in an electron-proton plasma with bp = 0.10. The dashed lines and line of open circles represent fluctuations in an electron-proton-alpha plasma with ~bp = 0.10, na/ne = 0.02, Te/Tp = 1.0, and Ta/Tp = 4.0. All species are isotropic and vap = 0. 0.02, Te/Tp = 1.0 and Ta/Tp = 4.0. The applications described in subsequent sections are to solar wind observations near 1 AU, so that in the calculations which follow we use relatively large values of ~bkp appropriate for the interplanetary medium, rather than the very low bp values of the solar corona. [15] The linear Vlasov dispersion equation for electromagnetic fluctuations propagating in a collisionless, homogeneous plasma has been derived many times in the literature. For propagation at k Bo = 0 this dispersion equation is w2 k 2 c2 þ k 2 c2

X

Sj ðk; wÞ ¼ 0

j

where the sum is over each charged particle species j. If the velocity distribution of each species or component j is a flowing bi-Maxwellian, the conductivity is [Gary, 1993] 3 2 Z 0 z

2 w j T?j j 5 þ 1 Sj kk ; w ¼ 2 2 4zj Z z

j 2 Tkj kk c

where Z(z) is the plasma dispersion function and the variables are as defined in Appendix A.

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[16] Under certain conditions the wr versus kk dispersion of left-hand polarized Alfveń-cyclotron fluctuations may split into two branches, the alpha-cyclotron branch at wr < Wa and the proton-cyclotron branch at Wa < wr < Wp [e.g., Hollweg and Isenberg, 2002, Figure 1]. We have used our linear Vlasov code to study the dispersion of both branches at k Bo = 0 as functions of several dimensionless parameters. We find that, for isotropic species with no alpha/proton relative flow, the conditions which yield such splitting include a sufficiently large value of na/ne, a sufficiently small value of Tka/Tkp, and a sufficiently small value of ~ bkp. The dispersion is also a function of the proton and alpha anisotropies [e.g., Gary et al., 1993] and the alpha/proton relative flow. [17] Figure 1 shows the real frequency and damping rate of the alpha-cyclotron branch of Alfveń-cyclotron fluctuations at parallel propagation as functions of parallel wave number for the parameters stated above. For comparison the real frequency and damping rate of the same fluctuation in a plasma with na = 0 are also illustrated. The differences between the two cases are relatively small; in particular wr is a continuous function of kk through the helium cyclotron frequency. [18] If the magnitudes of the jth species resonance factors zj and z±j (see Appendix A for definitions) are all greater than 3 for any mode, the resonant vk lies far from the thermal part of the velocity distribution fj(vk) [e.g., Gary, 1993]; then that mode is nonresonant and the corresponding wave-particle interactions are weak. However, jzjj ] 3 or jz±j j ] 3 is a necessary but not sufficient condition for resonance and strong damping by the jth species. Figure 1b shows that the magnitudes of both the proton and alpha cyclotron resonance factors for Alfveńcyclotron fluctuations decrease monotonically with increasing parallel wave number. In particular, the onset of damping at kkc/wp ’ 0.30 takes place near the wave number for which the condition jz a j = 3 is satisfied, demonstrating that this dissipation is due to the alpha cyclotron resonance. In contrast, the protons remain nonresonant until shorter wavelengths (kkc/wp ’ 0.70) [e.g., Gary and Borovsky, 2004, Figure 3], after which their cyclotron resonance dominates the damping. If, as in the frequency sweeping scenario, the source of field fluctuation energy is at long wavelengths, this figure implies that, as this energy migrates toward larger kkc/wp, it encounters the alpha cyclotron resonance first and heats that species before continuing to the proton cyclotron resonance at still shorter wavelengths. [19] Next we computed the linear theory damping rates and alpha cyclotron resonant factors of the alpha-cyclotron branch over relevant ranges of several dimensionless parameters. Figure 2 illustrates these results for four different values of vap/vA at ~bp = 0.10. As the alpha/proton relative speed increases from zero, the alpha cyclotron resonance gradually weakens and its contribution to fluctuation damping diminishes until at vap/vA = 0.50 the damping becomes almost completely due to the proton cyclotron resonance. In contrast, as vap/vA becomes negative, the Alfveń-cyclotron mode remains strongly resonant with the alphas and the alpha cyclotron damping becomes stronger, with its onset moving to successively longer wavelengths. Other linear theory calculations at ~bp = 0.50 and at na/ne = 0.05 show the same result: as vap/vA is increased from zero the alpha

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Figure 2 as follows: When the alpha/proton relative speed is sufficiently large and in the same direction as the fluctuation phase speed wr/jkkj, the alpha resonance with Alfveńcyclotron fluctuations is weak, and we expect little or no perpendicular heating of the alphas. When jvapj/vA is small, whatever its sign, and when vap is opposite in direction to wr/jkkj, whatever its magnitude, the alpha resonance with such waves is strong, and we expect strong perpendicular heating of the alphas. [22] Figure 3 shows the damping and alpha cyclotron resonance factor of the alpha-cyclotron branch for five different values of na/ne at ~bp = 0.10. As long as na/ne 1, the alphas do not make significant changes in wr(kk), and z a does not change very much as a function of the dimensionless alpha density. Thus Figure 3b shows that the alphas become resonant at sufficiently short wavelengths for all density ratios considered here. However, satisfaction of the resonance condition is not the only factor determining the alpha response to the fluctuations. Figure 3a shows, not surprisingly, that the greater the relative alpha density, the stronger the alpha cyclotron damping. The change in character of the damping rate curve between na/ne = 0.02 and 0.05 corresponds to the bifurcation of the wr versus kk dispersion curve into two branches, one at wr < Wa and one at wr > Wp.

Figure 2. Linear theory results at k Bo = 0: The (a) damping rates and (b) alpha cyclotron resonance factors of the alpha-cyclotron branch of Alfveń-cyclotron fluctuations in a homogeneous, collisionless electronproton-alpha plasma as functions of the parallel wave number. The four curves of individual symbols correspond to successively increasing values of the alpha/proton relative speed. From left to right: vap/vA = 0.20, 0, 0.20, and 0.50. The solid curve represents results for an electron-proton plasma with na = 0. Other parameters are the same as stated in the caption of Figure 1. cyclotron resonance is weakened and by vap/vA = 0.50 the damping has reverted to that of an electron-proton plasma of the equivalent bp. [20] Thus an increasingly positive alpha/proton relative speed weakens the alpha cyclotron resonance; if vap/vA and the wave amplitudes are sufficiently small, Alfveń-cyclotron waves should primarily drive an increasing T?a/Tka, but as vap/vA increases, the wave energy should go primarily into increasing T?p/Tkp. Tu and Marsch [2001a, 2001b] used this idea to develop a quasilinear theory for oxygen ion and proton heating in the solar corona. In their model, if the Alfveń fluctuation energy density is sufficiently large, the oxygen ions are accelerated, their ability to absorb fluctuation energy is reduced, and the wave energy is able to reach ion resonances at higher frequencies. [21] The results shown here are based on wr > 0, but are valid for both Bo > 0 and Bo < 0. If we consider Alfveńcyclotron fluctuations at wr < 0, linear theory (not shown here) shows that the alphas become nonresonant when vap/vA becomes sufficiently negative, and that alpha cyclotron damping becomes significant only for jvapj/vA 1 and all positive values of vap. Thus we summarize the results of

Figure 3. Linear theory results at k Bo = 0: The (a) damping rates and (b) alpha cyclotron resonance factors of the alpha-cyclotron branch of Alfveń-cyclotron fluctuations in a homogeneous, collisionless electron-proton-alpha plasma as functions of the parallel wave number. The curves correspond to different values of the dimensionless alpha density. From right to left (Figure 3a): na/ne = 0, 0.01, 0.02, 0.10, and 0.05. Other parameters are the same as stated in the caption of Figure 1.

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Figure 4. Linear theory results at k Bo = 0: The (a) damping rates and (b) alpha cyclotron resonance factors of the alpha-cyclotron branch of Alfveń-cyclotron fluctuations in a homogeneous, collisionless electron-proton-alpha plasma as functions of the parallel wave number. The curves of individual symbols correspond to Ta/Tp = 1, 4, and 8 as labeled. The solid curve represents results for an electron-proton plasma with na = 0. Other parameters are the same as stated in the caption of Figure 1. [23] Figure 4 shows the damping and alpha cyclotron resonance factor of the alpha-cyclotron branch for three different values of Ta/Tp. As the alpha temperature appears in the denominator of the alpha cyclotron resonance factor, an increasing Ta/Tp corresponds to a decreasing jz a j, implying that hotter alphas come into cyclotron resonance at smaller values of kc/wp, as illustrated in Figure 4b. This is further illustrated in Figure 4a, which suggests that sufficiently hot alphas may produce an observable shift to smaller wave numbers of the onset of the dissipation range of cyclotron resonant magnetic turbulence. [24] We have prepared plots in the same format as the three previous figures for variations in ~ bp, T?p/Tkp, and T?a/Tka. The results are not shown here, but are summarized in the following sentences. An increase in ~bp increases the effective temperature of the alphas, thereby reducing the values of jz a j at long wavelengths and pushing the onset of alpha cyclotron damping to smaller values of kc/wp. As T?p/Tkp increases, there is a gradual increase in wr at relatively short wavelengths and an associated decrease in the damping rate until the threshold of the electromagnetic proton cyclotron anisotropy instability is reached. The jz a (kk)j show no important qualitative differences between proton isotropy and instability onset. Similarly, a modest increase in T?a/Tka makes no important changes in the

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alpha cyclotron resonance factor, but reduces the magnitude of the damping rate in the wave number regime where the alpha cyclotron resonance is effective. A decrease in damping due to a species corresponds to a decrease in the ability of that species to absorb energy from imposed Alfveń-cyclotron fluctuations, so an increasing ion anisotropy represents a weakening of the wave-particle interactions associated with such fluctuations. [25] We have carried out similar linear theory calculations for magnetosonic-whistler fluctuations at k Bo = 0 in an electron-proton-alpha plasma. We find, for example, that enhanced alpha cyclotron damping of these fluctuations corresponds to an increasing na/ne (as for the Alfveńcyclotron mode results of Figure 3) and to an increasingly positive vap/vA (in contrast to the Alfveń-cyclotron mode results of Figure 2). However, the most relevant results for this mode concern its dependence on ~bp. Although the magnetosonic-whistler mode at k Bo = 0 can become heavily damped at kkc/wp ’ 1 if bp 2.5 [Stawicki et al., 2001], smaller values of bp correspond to smaller maximum values of jgj/Wp. As the substantial majority of ACE observations correspond to ~bkp ] 1.0 [e.g., Gary et al., 2001a], ion cyclotron damping of magnetosonic-whistler waves is weak for most ACE observations. So we expect magnetosonic-whistler modes to drive strong proton or alpha T?/Tk > 1 anisotropies only infrequently at ACE, and the interpretation of observations developed in the following sections is based on the assumption that ion anisotropy signatures should be driven primarily by Alfveń-cyclotron fluctuations.

3. Some Previous Alpha Observations in the Solar Wind [26] This section briefly discusses previous solar wind alpha observations which bear on the results presented in subsequent sections. Aellig et al. [2001] reported observations from the WIND/SWE experiment which showed that the average value of na/np rises from a minimum of less than 0.02 around solar minimum to about 0.045 in early 2000. This paper also summarizes previous measurements of solar wind alpha densities. [27] Papers which report measurements of the alpha/ proton relative speed in the solar wind include those by Marsch et al. [1982a], Neugebauer et al. [1996], Steinberg et al. [1996] and Reisenfeld et al. [2001]. As discussed in the work of Gary et al. [2003], there is no strong evidence that the alpha/proton relative speed is either driven to a large value by local processes, or that it is constrained by enhanced fluctuations from an electromagnetic alpha/proton instability. Thus, with Gary et al. [2003], we assume that the alphas gain a high speed relative to the protons in the corona, and then are gradually decelerated toward the solar wind speed by both collisional and collisionless processes as they stream away from the Sun. So, for our discussions of ACE observations near 1 AU, we assume that vap/vA is fixed and the primary ion response to local wave-particle scattering by Alfveń-cyclotron fluctuations is the development of enhanced kinetic energies in the directions perpendicular to Bo. [28] Measurements of solar wind alphas indicate that their typical condition is T?a/Tka < 1 [Marsch et al., 1982a;

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Reisenfeld et al., 2001]. Nevertheless, the opposite anisotropy is observed to arise at times [Neugebauer et al., 2001; Reisenfeld et al., 2001; Gary et al., 2002]. Whatever the source of the T?a/Tka > 1 condition, Ulysses observations [Gary et al., 2003] show that this anisotropy is constrained by a b-dependent upper bound derived from the threshold condition of the electromagnetic helium anisotropy instability. [29] Gary et al. [2002] analyzed proton and alpha anisotropies observed from Ulysses during two intervals, one corresponding to slow solar wind and one corresponding to fast wind. Figure 2 of that paper plots the proton and alpha anisotropies as functions of jvapj/vA and Figure 3 illustrates the alpha anisotropy as a function of the proton anisotropy for both intervals. The former figure shows no clear trend of the average values of either anisotropy as a function of the alpha/proton relative speed, but that in the slow wind the largest values of both anisotropies are observed at the smallest values of jvapj/vA. The latter illustration shows that T?a/Tka and T?p/Tkp are correlated in both the slow and fast wind.

4. ACE Observations: Fundamentals of the Analysis [30] Instrumentation on the ACE spacecraft includes the Solar Wind Electron Proton Alpha Monitor (SWEPAM) [McComas et al., 1998] and the Magnetic Field Experiment (MAG) [Smith et al., 1998]. SWEPAM consists of two fully independent sensors: one for electrons and one for ions. Both instruments are based on spherical section electrostatic analyzers followed by sets of channel electron multiplier detectors. Each can make full three-dimensional measurements of the electron and ion velocity distributions with 64 s time resolution. Here we use the proton and alpha densities as well as parallel and perpendicular proton and alpha temperatures derived by integration in velocity over the ion distributions observed by SWEPAM. [31] The parallel and perpendicular temperatures are appropriate parameters only if the thermal part of the ion velocity distributions are approximately bi-Maxwellian. We have examined proton distributions observed by the SWEPAM instrument using the analysis tool which produced Plate 5 of [Tokar et al., 2000]. Our analysis of anisotropic distributions sampled from several high speed intervals shows that the beam-like component is typically much more tenuous than the core component. A detailed analysis of this tenuous component is beyond the purview of this manuscript, so we therefore assume that its presence does not strongly violate the bi-Maxwellian condition, and proceed under the assumption that the T?p and Tkp derived by integration over the measured distributions are appropriate indicators of proton temperatures. [32] We used a merged SWEPAM/MAG high resolution data set to carry out a statistical analysis of ion temperature anisotropies measured during several month-long intervals. We extracted from the SWEPAM data several fundamental parameters: the solar wind speed vsw, the solar wind proton density np, the parallel and perpendicular temperatures of both the protons and the alphas, the alpha/proton relative velocity vap, and dBrms. The dBrms are calculated from

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MAG data as the RMS vector fluctuation computed every 16 s using 3 vector/s measurements. [33] To obtain T?p, Tkp, T?a, and Tka, the second velocity moments of the proton and alpha distributions were computed, diagonalized, and then rotated into a frame with one axis parallel to Bo. After this operation, most observations yielded two perpendicular ion temperatures which are similar; in our figures we include only those points such that the ratio of the larger to the smaller of these two perpendicular temperatures for each species is not bigger than 1.3. The rationale here is that, under most circumstances, we expect the ion velocity distributions to be gyrotropic, and relatively large values of this ratio indicate an inaccurate temperature calculation due, for example, to time aliasing. The SWEPAM data set used here was further examined for possible data inconsistencies. For example, another indicator of time aliasing could be a significant change in the average ion velocity during a single 64-s measurement; such measurements were removed from the data set. Occasional data points show random, inexplicable fluctuations to exceptionally large or exceptionally small values; such observations also were removed from the data considered here. A third category of observations not analyzed here corresponds to alpha parameters during times of exceptionally high proton temperatures; because SWEPAM measures ion energy-per-charge, the hot proton flux may swamp the alpha flux and render inaccurate the heavy ion measurement.

5. ACE Observations: Correlations [34] This section describes our search for statistical signatures of Alfveń-cyclotron heating of ions in ACE observations. Data from four month-long intervals were considered: January 2001, April 2001, May 2002, and December 2002. The first of these encompassed primarily slow solar wind with 300 km/s ] vsw ] 560 km/s, whereas the last three intervals each included both slow wind and two or more high speed streams [e.g., Smith et al., 2004] with 550 km/s ] vsw < 1000 km/s. Because of uncertainties in the measurement of cold electron densities, we here use np + 2na as a proxy for the total electron density ne. [35] First, we considered vsw to be the independent variable. We plotted all the data subject to the constraints stated in section 4, and did least squares fits to look for trends of average values. For all four months we found consistent positive correlations between this parameter and dBrms, Tkp, T?p, Tka, and T?a. In addition for all four months we found a consistent negative correlation between the proton density and vsw [e.g., Neugebauer and Snyder, 1966]. On the other hand, we found no consistent relationships between the solar wind speed and T?p/Tkp or T?a/Tka. For three of the intervals (January 2001, May 2002, and December 2002), we found a clear positive correlation between Tka/Tkp and vsw, in agreement with the 1 AU observations of [Marsch et al., 1982a]. However, we found no correlation between the alpha-proton temperature ratio and the solar wind speed for the April 2001 data set. Again, for January 2001, May 2002, and December 2002, there is a strong positive correlation between jvapj/vA and vsw, in agreement with Marsch et al. [1982a, Figure 11]. However,

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Figure 5. ACE observations: six quantities observed during April 2001 as functions of vsw. The data have been reduced as described in the text. Here, as in Figures 6 and 7, the colors represent the number of observations which lie within each pixel. The scales are arbitrarily chosen in each panel to convey the data trends, and range from black (no observations) through purple, blue, green, yellow, orange, and red (most observations). (a) The proton density, (b) the magnetic fluctuation amplitude, (c) the parallel proton temperature, (d) the parallel alpha temperature, (e) T?p/Tkp, and (f ) T?a/Tka. See color version of this figure at back of this issue.

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the April 2001 data set exhibited a weak negative correlation between these two quantities. [36] Figure 5, using ACE data from April 2001, illustrates some of these results. The most compelling relationships are the well-known ones between the temperatures and vsw; for example, Figure 5c illustrates the correlation between proton temperature and vsw [Strong et al., 1966; Lopez, 1987, and references therein]. [37] Second we considered dBrms as the independent variable. Many of the correlations were similar to those discussed in the previous paragraph; for all four months we found consistent positive correlations between the magnetic fluctuations parameter and vsw, Tkp, T?p, Tka, and T?a . We found no consistent relations between dBrms and the three dimensionless temperature ratios, but we did find a positive correlation between the solar wind density and dBrms. [38] Third, we considered various dimensionless quantities as independent variables. Among the various statistical plots which we prepared, the most consistent correlations we found were between ion temperature anisotropies and the dimensionless alpha/proton relative flow. Gary et al. [2002] used Ulysses observations from both a fast wind interval and a slow wind interval to illustrate proton and alpha anisotropies as functions of jvapj/vA. The purpose of that study was to seek possible signatures of electromagnetic alpha/proton instabilities; the consequences of such instabilities should be a function of the magnitude of the alpha/proton relative velocity but not of its sign, which is why Gary et al. [2002] used jvapj as the independent variable. Here, however, our concern is the consequences of scattering by a spectrum of Alfveń-cyclotron fluctuations which are likely to propagate preferentially away from the Sun; in this case (as the results of section 2 make clear) the sign of vap is important. [39] If the solar wind were a featureless entity subject only to radial expansion, wave propagation away from the Sun would always correspond to the magnetic field direction with an anti-Sunward component. However, the solar wind bears many irregularities and structures, so that the anti-Sunward direction is not always the indicator of fluctuation propagation away from the Sun [e.g., Balogh et al., 1999]. Although ACE instruments do not provide measurements clearly indicating the direction of wave propagation, there is a diagnostic indicating the local anti-Sunward direction along Bo and that is the electron heat flux. It is well established that suprathermal electrons (that is, electrons with energies ^ 100 eV) are observed near 1 AU to be narrowly beamed along the background magnetic field and that, except under special conditions such as within coronal mass ejections [Gosling et al., 1987], that beaming is unidirectional in the anti-Sunward sense. [40] We define ~vap

vap Bo Signq Bo

ð1Þ

where vap and Bo are measured vectors and (Signq) is the sign of the electron heat flux relative to Bo. This quantity is thus the alpha/proton relative speed along Bo with the same sign as that of the electron heat flux. During times when the electron heat flux is not clearly defined (as in the case of

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As with April 2001 there is a peak in the proton anisotropies near ~vap/vA = 0.5, but unlike Figure 6 there is a relatively higher peak in the proton anisotropy distribution near ~vap/vA = 0. [43] Results from our statistical plots of ion anisotropies versus ~vap/vA from the other two months of data we examined are not shown here. Observations from December 2002 display the same four properties we have noted for April 2001 and are shown by Gary et al. [2005]. ACE measurements of May 2002 show three of these properties, but exhibit a positive correlation between T?a/Tka and ~vap/vA. [44] For comparison against Ulysses observations [Gary et al., 2002, Figure 3], we plotted SWEPAM measurements of T?a/Tka versus T?p/Tkp. Unlike the Ulysses results, the alpha and proton anisotropies from ACE showed no strong correlation for either January 2001 or April 2001.

6. Conclusions

Figure 6. ACE observations: ion anisotropies measured during April 2001 as functions of ~vap/vA. The data have been reduced as described in the text. The color scale is as described in the caption of Figure 5. (a) T?p/Tkp and (b) T?a/Tka. The dashed lines represent least squares fits to the data; the correlation coefficients are (Figure 6a) R = 0.118 and (Figure 6b) R = 0.251. See color version of this figure at back of this issue. bidirectional electron flows), the associated ion measurements have been excluded from the analysis described below. We make the plausible assumption that, when the electron heat flux is clearly monodirectional, that direction is also the direction of propagation of Alfveń-cyclotron waves, so that the observed ~vap should bear the same sign relative to anti-Sunward propagating fluctuations as does the vap used in the theory of section 2. [41] Figure 6 illustrates statistical plots of observed proton and alpha anisotropies as functions of ~vap/vA for April 2001. The dashed lines indicate least squared fits to the data in each case; there is a weak positive correlation between the proton temperature anisotropies and the dimensionless alpha/proton speed, but a weak negative correlation between the alpha temperature anisotropy and that speed. Moreover, the maximum values of the alpha anisotropy (i.e., T?a/Tka ^ 2) are clustered near ~vap/vA ’ 0, whereas the maximum values of the proton anisotropy are clustered near ~vap/vA ’ 0.5. Each of these properties are consistent with the implications of the linear theory of section 2; taken together they provide substantial evidence that Alfveńcyclotron fluctuations are heating both alphas and protons in the solar wind near 1 AU. [42] Figure 7 shows statistical plots of observed ion anisotropies as functions of ~vap/vA for January 2001. Once again the T? p/Tkp correlation is positive but weak, the T?a/Tka correlation is negative but weak, and the maximum values of the alpha anisotropies again lie at ~vap/vA ’ 0.

[45] Linear Vlasov theory predicts the conditions that, in any sufficiently homogeneous, sufficiently collisionless electron-proton-alpha plasma, Alfveń-cyclotron fluctuations at k Bo = 0 and at sufficiently short wavelengths preferentially resonate with either alphas or protons. If vap/vA ] 0, alpha cyclotron damping can be substantial, implying that alphas should be scattered in the directions perpendicular to Bo. If vap/vA ^ 0.5, alpha cyclotron damping is weak so that only proton cyclotron damping remains,

Figure 7. ACE observations: ion anisotropies measured during January 2001 as functions of ~vap/vA. The data have been reduced as described in the text. The color scale is as described in the caption of Figure 5. (a) T?p/Tkp and (b) T?a/Tka. The dashed lines represent least squares fits to the data; the correlation coefficients are (Figure 7a) R = 0.175 and (Figure 7b) R = 0.299. See color version of this figure at back of this issue.

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implying that Alfveń-cyclotron fluctuations should preferentially scatter protons into perpendicular directions. We have examined four months of statistical observations from ACE of T?p/Tkp and T?a/Tka as functions of the alpha/ proton relative speed; the correlations are uniformly weak, but almost all of the results show signatures consistent with the implications of linear theory. [46] Although the correlation coefficients of the fits in Figures 6 and 7 are small, they are statistically significant; with over 104 data points for each panel of each figure, the 95% confidence level for correlation is at R > 0.02 (see, e.g., Appendix A and Borovsky and Funsten [2003]). Nevertheless, the smallness of these coefficients indicates that the source of these correlations is sporadic and/or weak. Thus further studies, both theoretical and observational, are desirable to provide more compelling evidence that Alfveń-cyclotron fluctuations are scattering ions in the solar wind at 1 AU. However, the predictions of theory set very specific criteria which other models of other mechanisms may find difficult to emulate. For example, proton and alpha anisotropies can be reduced by scattering from electromagnetic alpha/proton instabilities, but such instabilities generally operate only at jvapj/vA > 1 and cannot explain the body of our observations which reside primarily at jvapj/vA ] 1. [47] The linear theory of section 2 addresses only damping rates; our arguments concerning the associated perpendicular scattering of ions should be quantified through hybrid computer simulations such as those of Liewer et al. [2001]. Such simulations should address not only the signatures predicted for ion cyclotron resonances at k Bo = 0, but also the signatures due to ion Landau resonances which arise at sufficiently large bp and oblique angles of propagation [Gary and Borovsky, 2004]. [48] Further observational studies testing the predicted relationships should also be carried out. These studies should not only endeavor to improve the statistics of ion anisotropies as functions of dimensionless parameters, but also should seek to discover individual events in which large ion anisotropies can be directly associated with enhanced levels of Alfveńic fluctuations. Specific examples, as well as statistical studies, are necessary to provide a full observational picture of ion cyclotron scattering in the solar wind. [49] We believe that the observations reported here and in the work of Gary et al. [2005] represent the first evidence for Alfveń-cyclotron wave-alpha interactions in the solar wind near 1 AU. Further, we believe that the detailed character of in situ plasma and magnetic field observations provide a useful basis for testing theories of wave-particle interactions, and that the resulting improvements in those theories will yield a more accurate and quantitative application of those theories to the solar corona where, presumably, these interactions are much stronger and more consistent.

Appendix A:

Definitions

[50] We use subscripts k and ? to denote directions relative to the background magnetic field Bo. The species subscripts are p for protons, a for doubly ionized helium ions, and e for electrons. For the jth species we define bk j

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8pnj kBTk j/B2o; ~bk j 8pnekBTk j/B2o = (ne/nj)bk j; the plasma frequency on the total electron density, wj q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffibased ffi 2 4pne ej =mj ; the cyclotron frequency, Wj ejBo/mjc; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the thermal speed, vj kB Tkj =mj ; and the average flow velocity voj. We define the Alfveń speed as vA pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Bo/ 4pne mp , and the alpha/proton relative flow velocity as vap voa vop. The complex frequency is w = wr + ig, thepffiffiLandau resonance factor of the jth species is zj ffi w/ 2jkkjvj, and the cyclotron pffiffiffi resonance factors of the jth species are z±j (w ± Wj)/ 2jkkjvj. [51] Acknowledgments. We acknowledge useful conversations with Joe Borovsky, Curt DeKoning, Mel Goldstein, Jack Gosling, Justin Kasper, Dan Reisenfeld, and John Steinberg. The Los Alamos portion of this work was performed under the auspices of the U.S. Department of Energy (DOE) and was supported by the DOE Office of Basic Energy Sciences, Division of Engineering and Geosciences, and the Guest Investigator and Sun-Earth Connections Theory Programs of the National Aeronautics and Space Administration. [52] Shadia Rifai Habbal thanks Paulett Liewer and another referee for their assistance in evaluating this paper.

References Aellig, M. R., A. J. Lazarus, and J. T. Steinberg (2001), The solar wind helium abundance: Variation with wind speed and the solar cycle, Geophys. Res. Lett., 28, 2767. Balogh, A., R. J. Forsyth, E. A. Lucek, T. S. Horbury, and E. J. Smith (1999), Heliospheric magnetic field polarity inversions at high heliographic latitudes, Geophys. Res. Lett., 26, 631. Bame, S. J., J. R. Asbridge, W. C. Feldman, S. P. Gary, and M. D. Montgomery (1975), Evidence for local ion heating in solar wind high speed streams, Geophys. Res. Lett., 2, 373. Belcher, J. W., and L. Davis Jr. (1971), Large-amplitude Alfveń waves in the interplanetary medium, 2, J. Geophys. Res., 76, 3534. Borovsky, J. E., and H. O. Funsten (2003), Role of solar wind turbulence in the coupling of the solar wind to the Earth’s magnetosphere, J. Geophys. Res., 108(A6), 1246, doi:10.1029/2002JA009601. Cranmer, S. R. (2000), Ion cyclotron wave dissipation in the solar corona: The summed effect of more than 2000 ion species, Astrophys. J., 532, 1197. Cranmer, S. R. (2001), Ion cyclotron diffusion of velocity distributions in the extended solar corona, J. Geophys. Res., 106, 24,937. Dusenbery, P. B., and J. V. Hollweg (1981), Ion-cyclotron heating and acceleration of solar wind minor ions, J. Geophys. Res., 86, 153. Feldman, W. C., B. L. Barraclough, J. L. Phillips, and Y.-M. Wang (1996), Constraints on high-speed solar wind structure near its coronal base: A Ulysses perspective, Astron. Astrophys., 316, 355. Gary, S. P. (1993), Theory of Space Plasma Microinstabilities, Cambridge Univ. Press, New York. Gary, S. P., and J. E. Borovsky (2004), Alfveń-cyclotron fluctuations: Linear Vlasov theory, J. Geophys. Res., 109, A06105, doi:10.1029/ 2004JA010399. Gary, S. P., M. E. McKean, and D. Winske (1993), Ion cyclotron anisotropy instabilities in the magnetosheath: Theory and simulations, J. Geophys. Res., 98, 3963. Gary, S. P., L. Yin, D. Winske, and D. B. Reisenfeld (2000), Electromagnetic alpha/proton instabilities in the solar wind, Geophys. Res. Lett., 27, 1355. Gary, S. P., R. M. Skoug, J. T. Steinberg, and C. W. Smith (2001a), Proton temperature anisotropy constraint in the solar wind: ACE observations, Geophys. Res. Lett., 28, 2759. Gary, S. P., B. E. Goldstein, and J. T. Steinberg (2001b), Helium ion acceleration and heating by Alfveń/cyclotron fluctuations in the solar wind, J. Geophys. Res., 106, 24,955. Gary, S. P., B. E. Goldstein, and M. Neugebauer (2002), Signatures of wave-ion interactions in the solar wind: Ulysses observations, J. Geophys. Res., 107(A8), 1169, doi:10.1029/2001JA000269. Gary, S. P., L. Yin, D. Winske, L. Ofman, B. E. Goldstein, and M. Neugebauer (2003), Consequences of proton and alpha anisotropies in the solar wind: Hybrid simulations, J. Geophys. Res., 108(A2), 1068, doi:10.1029/2002JA009654. Gary, S. P., R. M. Skoug, and C. W. Smith (2005), Learning about coronal heating from solar wind observations, Phys. Plasmas, 12, 056501, doi:10.1063/1.1863192.

9 of 10

A07108


Gomberoff, L., F. T. Gratton, and G. Gnavi (1996), Acceleration and heating of heavy ions by circularly polarized Alfveń waves, J. Geophys. Res., 101, 15,661. Gosling, J. T., D. N. Baker, S. J. Bame, W. C. Feldman, R. D. Zwickl, and E. J. Smith (1987), Bidirectional solar wind electron heat flux events, J. Geophys. Res., 92, 8519. Hollweg, J. V. (1999), Cyclotron resonance in coronal holes: 1. Heating and acceleration of protons, O5+, and Mg9+, J. Geophys. Res., 104, 24,781. Hollweg, J. V. (2000), Cyclotron resonance in coronal holes: 3. A fivebeam turbulence-driven model, J. Geophys. Res., 105, 15,699. Hollweg, J. V., and P. A. Isenberg (2002), Generation of the fast solar wind: A review with emphasis on the resonant cyclotron interaction, J. Geophys. Res., 107(A7), 1147, doi:10.1029/2001JA000270. Hu, Y. Q., and S. R. Habbal (1999), Resonant acceleration and heating of solar wind ions by dispersive ion cyclotron waves, J. Geophys. Res., 104, 17,045. Isenberg, P. A., and J. V. Hollweg (1983), On the preferential acceleration and heating of solar wind heavy ions, J. Geophys. Res., 88, 3923. Li, X., and S. R. Habbal (1999), Ion cyclotron waves, instabilities and solar wind heating, Sol. Phys., 190, 485. Liewer, P. C., M. Velli, and B. E. Goldstein (2001), Alfveń wave propagation and ion-cyclotron interactions in the expanding solar wind: Onedimensional hybrid simulations, J. Geophys. Res., 106, 29,261. Lopez, R. E. (1987), Solar cycle invariance in solar wind proton temperature relationships, J. Geophys. Res., 92, 11,189. Marsch, E., and C.-Y. Tu (2001), Evidence for pitch angle diffusion of solar wind protons in resonance with cyclotron waves, J. Geophys. Res., 106, 8357. Marsch, E., K.-H. Mu¨hlhaüser, H. Rosenbauer, R. Schwenn, and F. M. Neubauer (1982a), Solar wind helium ions: Observations of the Helios solar probes between 0.3 and 1 AU, J. Geophys. Res., 87, 35. Marsch, E., K.-H. Mu¨hlhaüser, R. Schwenn, H. Rosenbauer, W. Pilipp, and F. M. Neubauer (1982b), Solar wind protons: Three-dimensional velocity distributions and derived plasma parameters measured between 0.3 and 1 AU, J. Geophys. Res., 87, 52. Marsch, E., C. K. Goertz, and K. Richter (1982c), Wave heating and acceleration of solar wind ions by cyclotron resonance, J. Geophys. Res., 87, 5030. Marsch, E., X.-Z. Ao, and C.-Y. Tu (2004), On the temperature anisotropy of the core part of the proton velocity distribution function in the solar wind, J. Geophys. Res., 109, A04102, doi:10.1029/2003JA010330. McComas, D. J., S. J. Bame, P. Barker, W. C. Feldman, J. L. Phillips, P. Riley, and J. W. Griffee (1998), Solar Wind Electron Proton Alpha Monitor (SWEPAM) for the Advanced Composition Explorer, Space Sci. Rev., 86, 563. McKenzie, J. F. (1994), Interaction between Alfveń waves and a multicomponent plasma with differential ion streaming, J. Geophys. Res., 99, 4193. Neugebauer, M., and C. W. Snyder (1966), Mariner 2 observations of the solar wind: 1. Average properties, J. Geophys. Res., 71, 4469. Neugebauer, M., B. E. Goldstein, E. J. Smith, and W. C. Feldman (1996), Ulysses observations of differential alpha-proton streaming in the solar wind, J. Geophys. Res., 101, 17,047. Neugebauer, M., B. E. Goldstein, D. Winterhalter, E. J. Smith, R. J. MacDowall, and S. P. Gary (2001), Ion distributions in large magnetic holes in the fast solar wind, J. Geophys. Res., 106, 5635. Ofman, L., S. P. Gary, and A. Vinãs (2002), Resonant heating and acceleration of ions in coronal holes driven by cyclotron resonant spectra, J. Geophys. Res., 107(A12), 1461, doi:10.1029/2002JA009432.

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Reisenfeld, D. B., S. P. Gary, J. T. Gosling, J. T. Steinberg, D. J. McComas, B. E. Goldstein, and M. Neugebauer (2001), Helium energetics in the high-latitude solar wind: Ulysses observations, J. Geophys. Res., 106, 5693. Roberts, D. A., M. L. Goldstein, W. H. Matthaeus, and S. Ghosh (1992), Velocity shear generation of solar wind turbulence, J. Geophys. Res., 97, 17,115. Smith, C. W., M. H. Acunã, L. F. Burlaga, J. L’Heureux, N. F. Ness, and J. Scheifele (1998), The ACE magnetic field experiment, Space Sci. Revs., 86, 613. Smith, C. W., W. H. Matthaeus, G. P. Zank, N. F. Ness, S. Oughton, and J. D. Richardson (2001), Heating of the low-latitude solar wind by dissipation of turbulent magnetic fluctuations, J. Geophys. Res., 106, 8253. Smith, C. W., D. J. Mullan, and N. F. Ness (2004), Further evidence of wave refraction associated with extended rarefaction events in the solar wind, J. Geophys. Res., 109, A01111, doi:10.1029/2003JA010113. Stawicki, O., S. P. Gary, and H. Li (2001), Solar wind magnetic fluctuation spectra: Dispersion versus damping, J. Geophys. Res., 106, 8273. Steinberg, J. T., A. J. Lazarus, K. W. Ogilvie, R. Lepping, and J. Byrnes (1996), Differential flow between solar wind protons and alpha particles: First WIND observations, Geophys. Res. Lett., 23, 1183. Strong, I. B., J. R. Asbridge, S. J. Bame, H. H. Heckman, and A. J. Hundhausen (1966), Measurements of proton temperatures in the solar wind, Phys. Rev. Lett., 16, 631. Tam, S. W. Y., and T. Chang (1999), Kinetic evolution and acceleration of the solar wind, Geophys. Res. Lett., 26, 3189. Tokar, R. L., S. P. Gary, J. T. Gosling, D. J. McComas, R. M. Skoug, C. W. Smith, N. F. Ness, and D. Haggerty (2000), Suprathermal ions and MHD turbulence observed upstream of an interplanetary shock by Advanced Composition Explorer, J. Geophys. Res., 105, 7521. Tu, C.-Y., and E. Marsch (2001a), On cyclotron wave heating and acceleration of solar wind ions in the outer corona, J. Geophys. Res., 106, 8233. Tu, C.-Y., and E. Marsch (2001b), Wave dissipation by ion cyclotron resonance in the solar corona, Astron. Astrophys., 368, 1071. Tu, C.-Y., and E. Marsch (2002), Anisotropy regulation and plateau formation through pitch angle diffusion of solar wind protons in resonance with cyclotron waves, J. Geophys. Res., 107(A9), 1249, doi:10.1029/2001JA000150. Vocks, C. (2002), A kinetic model for ions in the solar corona including wave-particle interactions and Coulomb collisions, Astrophys. J., 568, 1017. Vocks, C., and E. Marsch (2001), A semi-kinetic model of wave-ion interactions in the solar corona, Geophys. Res. Lett., 28, 1917. Vocks, C., and E. Marsch (2002), Kinetic results for ions in the solar corona with wave-particle interactions and coulomb collisions, Astrophys. J., 568, 1030. Xie, H., L. Ofman, and A. Vinãs (2004), Multiple ions resonant heating and acceleration by Alfveń/cyclotron fluctuations in the corona and the solar wind, J. Geophys. Res., 109, A08103, doi:10.1029/2004JA010501.

S. P. Gary and R. M. Skoug, Los Alamos National Laboratory, M.S. D466, Los Alamos, NM 87545, USA. ([email protected]; [email protected]) C. W. Smith, Space Science Center, University of New Hampshire, 39 College Road, Morse Hall, Room 207, Durham, NM 03824, USA. ([email protected])

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Figure 5. ACE observations: six quantities observed during April 2001 as functions of vsw. The data have been reduced as described in the text. Here, as in Figures 6 and 7, the colors represent the number of observations which lie within each pixel. The scales are arbitrarily chosen in each panel to convey the data trends, and range from black (no observations) through purple, blue, green, yellow, orange, and red (most observations). (a) The proton density, (b) the magnetic fluctuation amplitude, (c) the parallel proton temperature, (d) the parallel alpha temperature, (e) T?p/Tkp, and (f ) T?a/Tka.

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Figure 6. ACE observations: ion anisotropies measured during April 2001 as functions of ~vap/vA. The data have been reduced as described in the text. The color scale is as described in the caption of Figure 5. (a) T?p/Tkp and (b) T?a/Tka. The dashed lines represent least squares fits to the data; the correlation coefficients are (Figure 6a) R = 0.118 and (Figure 6b) R = 0.251.

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Figure 7. ACE observations: ion anisotropies measured during January 2001 as functions of ~vap/vA. The data have been reduced as described in the text. The color scale is as described in the caption of Figure 5. (a) T?p/Tkp and (b) T?a/Tka. The dashed lines represent least squares fits to the data; the correlation coefficients are (Figure 7a) R = 0.175 and (Figure 7b) R = 0.299.

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