The objective of this study is to understand the acceleration processes that lead to outflow and escape of ionospheric ions from Mars. Observations show that accelerated dayside and flank ionospheric ions move slowly antisunward along the direction of the external/magnetosheath flow. At high altitudes, in the central tail, ions are further accelerated, up to keV energies. However, the primary acceleration process gives velocities in the 5–15 km/s range. Two acceleration processes, capable of generating a tailward stream of low-energy ions are feasible: Mass-loaded ion pickup, and wave acceleration. We demonstrate that wave acceleration is quite adequate to generate the ion outflow characterized by density modulations in the ULF range (3–20 mHz). The waves, of magnetosheath origin, penetrate into the Martian magnetosphere, down to low (pericenter) altitudes. A close relationship is found between solar wind dynamic pressure, ULF wave activity, and mass-loaded wave acceleration of ionospheric ions. Species-dependent differences in outflow velocity are consistent with an altitude dependent mass-loaded ion acceleration process.
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 Solar EUV and solar wind forcing have a strong influence on the ionosphere and atmosphere of the weakly magnetized planet Mars. Our present understanding of the implications of solar forcing, derived from space probes such as Phobos-2, Mars Global Surveyor (MGS), and Mars Express (MEX), is that a combination of solar EUV- and solar wind forcing leads to ionization, acceleration, and escape of planetary plasma.
 Intrinsic or induced magnetic fields play an important role for the planetary plasma environment. A magnetic field may shield off plasma, but also promote plasma acceleration. The large erosion rate initiating on the dayside of Mars [e.g., Lundin et al., 2008a] suggests less effective magnetic shielding on Mars. We demonstrate that magnetic shielding is unable to stop intense magnetosheath ULF waves from penetrating into the ionosphere. These waves constitute a viable energy source capable of energizing ionospheric ions to escape velocities.
 Several authors, such as Wang and Nielsen , Espley et al. , Brain et al.  and Brain , have reported on plasma waves near Mars. Wang and Nielsen  interpreted their observations as hydrodynamic waves in the topside ionosphere of Mars. Winningham et al.  and Gunell et al.  have also reported on ion and electron wavelike modulations at Mars. Waves are expected to be important for the ion energization and outflow of ionospheric plasma at Mars [Ergun et al., 2006]. The access, propagation and implications of ULF/Alfvén waves in a planetary environment have been extensively studied in the Earth's magnetosphere. Chaston et al.  demonstrated that Alfvén waves produced in the magnetosheath leads to plasma acceleration on dayside/cusp auroral magnetic field lines. Magnetosheath MHD waves may also propagate over the polar region and into the nightside/tail of the Earth's magnetosphere, the magnetosphere acting like a focusing lens for waves as described by Papadopoulos et al. .
 In this study we analyze ion and electron data from the ASPERA-3 experiment with focus on wave acceleration of ionospheric ions. A wavelet analysis of electron and ion time-series data enables us to map the distribution of wave activity in the Martian plasma environment, and to attribute wave activity with ion acceleration.
2. Observations of Planetary Ion Energization and Outflow
 We use data from the ASPERA electron (ELS) and the ion mass analyzer IMA) experiments on the ESA Mars Express (MEX) spacecraft. The ELS instrument measures electrons in the energy range 0.001–20 keV with high-energy resolution (ΔE/E = 0.08). The IMA imager measures ion species simultaneously with limited mass resolution (m/q = 1, 2, 4, 16, 32, 44) in the energy range 0.001–20 keV/q. A full description of the ASPERA-3 experiment is contained by Barabash et al. .
 Using IMA data with 12s time resolution we can determine ion fluctuations in the ULF frequency range. The 1s fast sweep mode with ELS, enables wave analysis to higher frequencies. We apply a wavelet analysis technique (scalogram) to the ion and electron data. Combining IMA and ELS wavelet spectra the relation between wave-activity (ion and electron oscillations) and the acceleration of ionospheric ions can be studied.
Figure 1 display ion, electron and wavelet data from a Noon-Midnight pass on June 19, 2007. Orbit parameters are given in Mars Sun Oriented (MSO) coordinates. The power of the wavelet oscillations is given in arbitrary units, denoted magnitude (W(f,t)). All wavelet spectra were determined from time series of counts accumulated for each energy sweep (12 s for ions and 1 s for electrons), as illustrated by the 1 s electron count time series in Figure 1. Since it is difficult to distinguish between spatial and temporal variations with a moving spacecraft, it is reasonable to assume that the wavelet spectra contain some features arising from large-scale spatial features. For MEX, moving with velocities 2–4 km/s, and taking into account the Nyquist frequency, spatial variations are expected to dominate below 1 mHz (≈6000–12000 km). However, localized resonances, and other features in the data (Figure 2), implies predominantly temporal effects above ≈3 mHz.
 The wavelet spectra display a similarity between H+ and electron oscillations in the magnetosheath, characterized by narrow-banded oscillations in the frequency range 3–20 mHz superimposed on broadband noise. Similar wavelet characteristics can be found for ionospheric O+ (15.40–16.00 UT), for electrons inside the induced magnetosphere boundary (IMB), and for electrons in the magnetosheath. Intense magnetosheath and ionosphere ion and electron oscillations are persistent features in the ASPERA-3 data, the oscillations reaching down to ≈300 km altitude (MEX pericenter). O+ oscillations are also common in the central tail (≈14.10 UT), altogether indicating an omnipresent ULF wave activity in the Martian plasma environment.
 The two low energy (≈1–10 eV) ion density versus altitude plots in Figure 2, illustrates that the ionosphere as a whole is subject to ULF wave-like oscillations of H+, O+ and O2+. The low altitude oscillations could in principle be spatial, such as density anomalies over crustal magnetic regions. However, the low-altitude data in Figure 2 was over the northern polar region, characterized by weak crustal magnetic field. Moreover, plotting the data versus time display quasi-periodic oscillations over extended time periods. The oscillations as evidenced by Figure 1, therefore suggests that the waves in the magnetosheath are affecting low-altitude- as well as tail ionospheric ions, i.e., wave may penetrate into all plasma domains of the Martian magnetosphere. If so, what is the relation between magnetosheath-, and ionospheric ion oscillations/waves, and what is the energy source driving the waves? Again, lacking magnetic field and wave instruments, we may only test the oscillations against plasma kinetics.
 In Figure 3 we plot 10–20 mHz wavelet magnitude, W(f,t), in the magnetosheath/Bow-shock and the ionosphere (O+) against the magnetosheath dynamic pressure derived from the electron density and He++ flow velocity in the magnetosheath. Error bars in pressure marks the difference between inbound and outbound magnetosheath pressure, while error bars of wavelet magnitudes represent variations in the time intervals of maximum wavelet intensity/magnitude in the magnetosheath (e-), and in the ionospheric O+ outflow. Applying a power law least square fit to the data points we obtain: W = 1.0 · 1012 · P0.93 (magnetosheath, e-); W = 9.7 · 1012 · P1.1 (ionosphere, O+). The power law curve indicates a positive correlation between ULF wave intensity and solar wind dynamic pressure. We note that the average magnetosheath wave magnitude is up to ten times higher than the O+ wave magnitude.
 The question is to what extent ULF waves can contribute to the energization and escape of ionospheric ions. To analyze this, and the ion acceleration in more detail, we have studied 417 ≈3 min. averaged, simultaneously measured, H+, O+ and O2+ accelerated ion energy spectra from 60 orbits. Ion energy peaks are converted to velocity peaks. Figure 4 shows a scatter diagram of the O+ and O2+ velocity peaks, plotted versus H+ velocity peaks. A linear least-square fit is then performed, the curves forced to intercept zero. Despite considerable scattering, the diagram yet demonstrates that ions of different masses are neither accelerated to the same velocity (transverse dashed line), nor to the same energy. Noticeable is the linear increase in velocity for heavy ions versus H+. This implies partial momentum balance between ion species during acceleration, i.e., the ion velocity increase is a function of, but not directly proportional to, the ion mass. The curves in Figure 4 give the following average velocity acceleration ratios: V(O+)/V(H+) = 0.31 and V(O2+)/V(H+) = 0.22. We therefore conclude that the acceleration process:
 1. Is mass dependent, providing higher velocity for lower mass.
 2. Gives neither the same energy, nor the same velocity for ions of different mass.
 The acceleration and outflow of ionospheric ions from Mars is related with ion pickup [e.g., Luhmann and Schwingenschuh, 1990], mass-loaded ion pickup [Lundin and Dubinin, 1992], waves [Ergun et al., 2006], and ambipolar electric fields [Frahm et al., 2010]. Ion acceleration and outflow commence in the dayside ionosphere, the ions subsequently moving tailward at velocities just above escape velocity [Lundin et al., 2008a]. At low altitudes where the ionospheric number density is high, the acceleration processes is subject to mass loading. Mass loading implies an interaction between a moving plasma and dense plasma at rest. Collision-less mass-loaded ion pickup near Mars was found to be in agreement with theory [Lundin and Dubinin, 1992]. Ion and electron ULF oscillations are a pervasive feature in the Martian magnetosphere. The wavelet magnitude of the oscillations maximizes in the magnetosheath, but remains high for accelerated ions in the tail, and in the core ionosphere. Plasma oscillations indicate not only plasma perturbations by waves, but suggest also plasma acceleration. The fact that the wavelet magnitude is positively correlated with magnetosheath dynamic pressure (Figure 3) indicates that plasma pressure generates waves. Waves no doubt play a role in the acceleration and outflow of ions at Mars. The question is to what extent waves contribute to ionospheric plasma acceleration and outflow. Notice that magnetosheath dynamic pressure also correlates with the ion outflow at Mars [Lundin et al., 2008b].
 We continue with a theoretical analysis of ion acceleration by waves using the theory of ponderomotive wave forcing. A ponderomotive force may be described as a time-averaged force unique for oscillating fields, resulting in an exchange of wave energy and momentum to charged particles. Two ponderomotive forces are considered, the Magnetic Moment Pumping force, MMP, and the gradient/Miller force. MMP represents wave forcing of charge particles in a diverging magnetic field, while the Miller force is determined by the spatial gradient of the wave electric field. Combining MMP and the Miller force in magnetized plasma for travelling Alfvén waves at frequencies less than the gyro-frequency we obtain [Lundin and Guglielmi, 2007]
Where E is the wave electric field and B the ambient magnetic field in plasma. Notice that the MMP force is governed by the gradient of the magnetic field magnitude along z, and the Miller force is determined by the gradient (damping) of the wave electric field along z. The two field-aligned forces are complementary in the sense that MMP considers spatial gradients of B, while the Miller force is related with spatial gradients of E. Under the assumption that E changes slowly with z, we may focus on the first, MMP, term of equation (1). However, the gradient E (Miller) force may also be important for ion acceleration and outflow, especially in the subsolar region where wave E-field damping may be strong, and when the divergence of B is small. From the equation of motion and the ponderomotive potential, an expression for the velocity gain by Alfvén wave MMP forcing can be derived [Lundin and Guglielmi, 2007, equation 2.40]
The velocity gain is given by a convective term (E/B0), and the magnetic field gradient (B0/B(z)), where B0 is the initial ambient magnetic field. The magnetic field gradient (B0/B(z)) gives a small amplification of the MMP ponderomotive acceleration near Mars, while the magnitude of E provide the main, most variable, contribution to ion acceleration, as suggested from the wavelet plots in Figure 3.
 We assume that the ion acceleration commence in the dayside magnetic field pileup region. The pileup magnetic field decreases tailward, reaching a minimum in the wake and distant flanks of Mars [see, e.g., Crider et al., 2004]. Taking the average values of normalized ∣B∣ from the subsolar/pileup region to the wake/flank, one obtains B0/B(tail) ≈3. This gives an amplification of the E/B0 by a factor of 3. From Figure 3 (left) we note that W(f,t) can vary by a factor of ≈100, i.e., E may vary by a factor of ≈10 (W(f, t) ∝ E2). Upon reaching the Martian tail, cold ionospheric ions may therefore have increased their speed by up to a factor of ≈30, Notice that the MMP velocity acceleration, described by equation (2), is independent of mass. Ions should be accelerated to the same velocity regardless of mass. The fact that the ion acceleration is clearly mass dependent therefore requires some further analysis.
 Introducing mass loading per se does not imply velocity differentiation with ion mass. However, since the ionospheric plasma density decreases with increasing altitude, mass loading is most pronounced at low altitudes. The altitude of the ion source is therefore critical for how mass loading affects ion acceleration. Typical ionospheric ion density profiles at Mars show that O2+ is the most abundant species at low altitudes, O+ dominating at mid-altitudes, and H+ dominating at high altitudes [e.g., Hanson et al., 1977; Fox, 2003; Terada et al., 2009]. Mass loading has therefore the largest implication for O2+ acceleration, while H+, accelerated in a more tenuous plasma environment, is least affected. The height dependence of mass loading is therefore in qualitative agreement with the O+/H+ and O2+/H+ velocity ratios observed (Figure 4).
4. Summary and Conclusions
 We have analyzed the energy and mass distribution of accelerated ions above Mars with the objective to understand acceleration processes leading to outflow and escape of ionospheric ions. ASPERA-3 ion and electron data show that intense magnetosheath ULF (3-20 mHz) waves have access to the Martian magnetosphere, down pericenter altitudes. We find a good correlation between magnetosheath and ionosphere ULF wave activity and the solar wind dynamic pressure. Considering the correlation between O+ outflow and solar wind dynamic pressure [Lundin et al., 2008b], the magnetosheath ULF wave power (W(f, t)) is expected to also correlate with the O+ outflow rate from Mars. Ponderomotive wave forcing, whether connected with spatial or temporal gradients (equation (1)), is therefore a viable mechanism for ion acceleration and outflow. We demonstrate that, even in the non-resonant case (equation (1)), temporal MMP wave forcing in the Martian diverging induced magnetic field may enhance the cold ionospheric ion speed along the flanks and tail of Mars by up to a factor of ≈30. Further energization in the tail plasma sheet may result from a combination of focused ULF waves [Papadopoulos et al., 1993] and current sheet acceleration [Dubinin et al., 1993].
 The acceleration process for ionospheric ions is partially mass dependent, i.e., the acceleration of ions of different masses gives neither the same energy, nor the same velocity. We argue that the O+/H+ and O2+/H+ velocity ratios observed results from an altitude dependent mass loading, dominating low-altitude O2+ being subject to heavier mass loading compared to high-altitude H+.
 ASPERA-3 on ESA Mars Express is a joint effort between 15 laboratories in 10 countries. We are indebted to the national agencies, e.g., the Swedish National Space Board, CNRS in France, and NASA (contract NASW00003), for supporting ASPERA-3, and to the European Space Agency for making MEX a great success. Finally, we want to express our deep appreciation to Jan Karlsson, Pär-Ola Nilsson, Leif Kalla and Emmanuel Penou for providing software support and excellent data analysis tools.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.