Kinetic Scale Slow Solar Wind Turbulence in the Inner Heliosphere: Co-existence of Kinetic Alfvén Waves and Alfvén Ion Cyclotron Waves
S. Y. Huang, J. Zhang, F. Sahraoui, J. S. He, Z. G. Yuan, N. Andrés, L. Z. Hadid, X. H. Deng, K. Jiang, L. Yu, Q. Y. Xiong, Y. Y. Wei, S. B. Xu, S. D. Bale, J. C. Kasper
KKinetic Scale Slow Solar Wind Turbulence in the Inner Heliosphere: Co-existence ofKinetic Alfvén Waves and Alfvén Ion Cyclotron Waves
S. Y. Huang , J. Zhang , F. Sahraoui , J. S. He , Z. G. Yuan , N. Andrés , L. Z. Hadid , X. H.Deng , K. Jiang , L. Yu , Q. Y. Xiong , Y. Y. Wei , S. B. Xu , S. D. Bale , and J. C. Kasper School of Electronic Information, Wuhan University, Wuhan, 430072, China Laboratoire de Physique des Plasmas, CNRS-Ecole Polytechnique-Sorbonne Université-Univ, Paris-Saclay-Observatoire deParis-Meudon, Palaiseau, F-91128, France School of Earth and Space Sciences, Peking University, Beijing, 100871, China Instituto de Astronomía y Física del Espacio, CONICET-UBA, Ciudad Universitaria, 1428, Buenos Aires, Argentina Departamento de Física, Facultad de Ciencias Exactas y Naturales, UBA, Ciudad Universitaria, 1428, Buenos Aires, Argentina Insititute of Space Science and Technology, Nanchang University, Nanchang, 330031 , China Space Sciences Laboratory and Physics Department, University of California, Berkeley, CA 94720-7450, USA Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Abstract
The nature of the plasma wave modes around the ion kinetic scales in highly Alfvénic slowsolar wind turbulence is investigated using data from the NASA’s Parker Solar Probe taken inthe inner heliosphere, at 0.18 Astronomical Unit (AU) from the sun. The joint distribution ofthe normalized reduced magnetic helicity σ m ( θ RB , τ ) is obtained, where θ RB is the anglebetween the local mean magnetic field and the radial direction and τ is the temporal scale.Two populations around ion scales are identified: the first population has σ m ( θ RB , τ ) <0 forfrequencies (in the spacecraft frame) ranging from 2.1 to 26 Hz for 60º < θ RB < 130º,corresponding to kinetic Alfvén waves (KAWs), and the second population has σ m ( θ RB , τ ) >0in the frequency range [1.4, 4.9] Hz for θ RB > 150º, corresponding to Alfvén ion CyclotronWaves (ACWs). This demonstrates for the first time the co-existence of KAWs and ACWs inthe slow solar wind in the inner heliosphere, which contrasts with previous observations in theslow solar wind at 1 AU. This discrepancy between 0.18 and 1 AU could be explained, eitherby i) a dissipation of ACWs via cyclotron resonance during their outward journey, or by ii)the high Alfvénicity of the slow solar wind at 0.18AU that may be favorable for the excitationof ACWs. . Introduction Turbulence is thought to contribute significantly to particle heating in various spaceastrophysical plasmas (e.g., Tu & Marsch, 1995; Bruno & Carbone, 2013; Goldstein et al.,2015; Huang et al., 2017b; Andrés et al., 2019; Sahraoui et al., 2020).
Because of thecollisionless nature of the near-Earth space plasmas (e.g., the solar wind and themagnetosheath), energy dissipation into particle heating is thought to occur via a variety ofprocesses that include resonant wave-particle interactions, e.g. Landau damping (e.g.,Sahraoui et al., 2009; Chen et al., 2019), cyclotron damping (e.g., He et al., 2015; Woodhamet al., 2018), stochastic heating (Chandran et al., 2010; Bourouaine & Chandran, 2013;Bowen et al., 2020b), and intermittent heating within coherent structures (e.g., Retinò et al.,2007;
Sundkvist et al., 2007; Wang et al., 2013; Chasapis et al., 2015; Zhang et al., 2015;Huang et al., 2017a, 2017c, 2018). Identifying the dissipation processes at work requiresunraveling the plasma wave modes dominating the cascade, in particular at the sub-ion scales.At 1 Astronomical Unit (AU), the solar wind is generally categorized according to itsvelocity: fast solar wind ( V f ≥ 500 km/s) and slow solar wind ( V f < 500 km/s). Intensiveresearch work has been dedicated to identifying the nature of the wave modes in the solarwind at 1AU. Kinetic Alfvén waves (KAWs) are characterized by a quasi-perpendicular wavevector ( k || << k ) and a right-handed polarization (e.g., Howes et al., 2010; Sahraoui et al.,2012; Zhao et al., 2013, 2016). They have been identified at kinetic scales in the fast solarwind turbulence in several studies that used in-situ data. For instance, Leamon et al. (1998)have analyzed solar wind magnetic fluctuations in the sub-ion (dissipation) range and foundthat the 2D component is consistent with KAWs propagating at large angles respect to thebackground magnetic field. Bale et al. (2005) and Sahraoui et al. (2009) have established thewave dispersion based on the electric and magnetic field spectra, and found the wavedispersion around ion scales are consistent with KAWs. A subsequent work by Sahraoui et al.(2010) provided a direct evidence of the dominance of the of KAW mode at the sub-ionscales using the multi-point measurement technique, namely the k -filtering technique, on theluster data, which allowed them to obtain the 3-dimentional dispersion relation that agreedwell with the theoretical predictions for KAWs. Chen et al. (2012) used the spectral indices ofthe magnetic field and electron density at the kinetic scales to identify the nature of solar windturbulence, and were found to be consistent with the numerical simulation results of KAWturbulence (e.g., Howes et al., 2011). He et al. (2011, 2012a 2012b, 2015) used the reduced(fluctuating) magnetic helicity (Matthaeus & Goldstein, 1982), estimated as a function of theangle BV (or RB ) between the direction of the local mean magnetic field and the solar windvelocity (or the radial direction), and showed that a major population of magnetic fluctuationsin the dissipation range has quasi-perpendicular angles (relative to the local mean magneticfield) and right-handed polarization, consistent with quasi-perpendicular KAWs. Subsequentstudies by Podesta & Gary (2011), Podesta & Tenbarge (2012), Podesta (2013), and Bruno &Telloni (2015) confirmed those findings. On the other hand, a minor component of the fast and slow solar wind turbulence was foundto be left-handed polarization and has parallel propagation. This mode is known as the Alfvénion cyclotron waves (ACWs), electromagnetic ion cyclotron (EMIC) waves or ion cyclotronwaves (ICWs). Jian et al. (2009, 2010) have shown sporadic observations of ACWs with shorttime intervals and found that the ACWs have a preference for radial field alignment. He et al.(2011, 2012a, 2015) showed the existence of ACWs in the fast solar wind when the velocityand magnetic field were quasi-aligned ( BV < 30°) (See also Telloni et al. (2019)). Recently,Bowen et al. (2020a) have used the observations from Parker Solar Probe (PSP) mission toinvestigate ion-scale electromagnetic waves in the inner heliosphere, and revealed that 30-50% of radial field intervals have parallel/anti-parallel propagation and circularly polarizedwaves. The slow solar wind has low amplitude magnetic fluctuations compared to the fast solar windat 1 AU (e.g., Dasso et al., 2005; Bruno et al., 2014). D’Amicis & Bruno (2015) have showntwo different kinds of slow solar wind: one coming from coronal streams or active regionsith low Alfvénicity, and the other one from the boundary of coronal holes with highlyAlfvénicity. Further, D'Amicis et al. (2019) observed Alfvénic slow wind at 1 AU during amaximum of the solar activity, and found it be similar to fast solar wind than to typical non-Alfvénic slow wind. Thus, they suggested that the Alfvénic slow wind and fast solar windprobably have a similar solar origin. On the other hand, it is found that, at solar maximum,34% of the slow solar wind streams ( V f < 450 km s −1 ) with quiet-sun as their source region arefeatured with high Alfvénicity (| σ c | > 0.7) (Wang et al., 2019). Accordingly, Wang et al.(2019) suggested that the slow solar wind streams from the quiet-Sun region, like theircounterparts from coronal hole region, can directly flow outward along the open field lines. Asimilar scenario for the origin of solar wind as emerging from quiet sun region had alreadybeen proposed by He et al. (2007). Recently, Alfvénic slow wind has also been observed inthe inner heliosphere at 0.3 AU during a minimum of solar activity using Helios data (e.g.,Stansby et al., 2019, 2020; Perrone et al., 2020). Moreover, Bale et al. (2019) havedemonstrated that the slow Alfvénic solar wind from 0.17 to 0.25 AU measured during PSPEncounter 1 emerges from a small equatorial coronal hole. Moreover, Bale et al. (2019) haveshown the co-existence of electron and ion micro-instabilities in this slow solar wind. Despite a big progress in understanding the slow solar wind physics, the nature of the wavemodes dominating the turbulence cascade is still an unsettled problem, especially in the innerheliosphere. In the present study, using the NASA’s Parker Solar Probe observations at 0.18AU, we bring new insight into this problem. Our main finding is the co-existence of kineticAlfvén waves and Alfvén ion cyclotron waves for highly Alfvénic slow solar winds.
2. Data Analysis and Results
In the present study, the solar wind proton moments were measured by Solar Wind Electron,Alpha, Proton (SWEAP) experiment on PSP with sampling frequencies between 1 Sa/cycleand 4 Sa/cycle, where 1 cycle is approximately equal to 0.873 s (Kasper et al., 2016; Case etl., 2020). The magnetic field data were measured at the sampling frequency of 256 Sa/cycle(~293 samples/sec) by the FIELDS flux-gate magnetometer (Bale et al., 2016) for theEncounter mode. All vector data are presented in the radial tangential normal (RTN)coordinate system. The normalized (fluctuating) reduced magnetic helicity ( m ) is useful to diagnose polarizationcharacteristics of solar wind turbulence (Matthaeus & Goldstein, 1982), which can be linkedto the classical wave polarization of the fluctuations (see, e.g. Howes & Quataret, 2010;Meyrand & Galtier , 2012; Klein et al., 2014). Here we used the method developed in He et al.(2011, 2015), where the m spectra are estimated as function of angle RB to account for thelocal (in time) variations of the mean magnetic field.A windowed Fourier transform is performed for the magnetic field to obtain a time-frequencydecomposition of the power spectral densities (PSD ( t , )) of the magnetic field and thenormalized reduced magnetic helicity m ( t , ) ranging from -1 to +1, where t and are themeasurement time and temporal scale, respectively. To fit the spectral densities at differenttimes and temporal scales, the time-frequency spectral indices (or slope ( t , )) can beobtained. The local mean magnetic field B ( t , ) is calculated by the Equation (22) fromPodesta (2009), then one can obtain the angle RB ( t , ) between the radial direction and thelocal mean magnetic field (ranging from 0 to 180º). Figure 1 shows the PSP spacecraft observations on 6 November 2018 in the perihelion at 0.18AU. The average plasma parameters are: | B| ~ 89 nT, the proton density n p ~ 315 cm -3 , and theproton temperature T p ~ 36 eV, yielding the Alfvén speed V A ~ 109 km/s, the proton inertiallength d i ~13 km, and the proton gyro-radius i ~ 9.7 km. One can see that the magnetic fieldis well correlated with the proton velocity (correlation coefficient > 0.82, in Figure 1a-1c),indicating highly Alfvénic fluctuations in this time interval (Kasper et al., 2019). The mean V R s about 360 km/s, which is smaller than 500 km/s, indicating that PSP encountered the slowsolar wind. B R is mostly negative (Figure 1a), implying that PSP was in an inward magneticsector. The magnetic field has large amplitude fluctuations compared to typical slow solarwind (e.g., Bruno et al., 2014). The PSD of the magnetic field shows a scaling close to theKolmogorov spectrum in the lowest frequency range (with some fluctuations due the limitedsmall size window used to fit the local slopes), before steepening to ~ -4 above the spectralbreak, then flattening for frequencies > 20 Hz due to reaching the noise floor of theinstrument (Figure 1d). The red and blue bars at higher frequencies are due to interferencefrom the spacecraft (reaction wheels signal). The magnetic helicity m ( t , ) is illustrated inFigure 1f. It varies randomly at low frequency, but shows a coherent pattern at highfrequencies: often positive around 3 Hz and permanently negative around 7 Hz,corresponding to the steep spectra in Figure 1d-e. The angles between the radial direction andthe local mean magnetic field direction RB is shown in Figure 1g. It is found that the angle RB varies in time over the range from 40º-180º, while it does not change much in frequency,which indicates that the large scale magnetic field dictates the behavior of the radial angle atall scales. This does not contradict the observations that the fluctuations, and thus the vectororientation, are random (i.e. noise) at f >20Hz so long as the amplitudes of the high frequencyfluctuations are much smaller compared to the static (large scale) field. Figure 2 displays the time-averaged (a) PSD of the magnetic field and (b) the magnetichelicity m as a function of the frequency. One can identify two distinct ranges from the PSD:i) a Kolmogorov-like inertial range from 0.04 Hz to ~ 1 Hz, i.e., at the MHD scales; ii) atransition range around ion scales with a steep slope (up to -4.24). The time-averaged m hasvery small negative values (close to zero) at MHD scales, consistent with previousobservations (e.g., Goldstein et al., 1994; He et al., 2011; Podesta, 2013). It is interesting that m changes its polarity at 1.4 Hz, and then become negative above 4.2 Hz. The sign change of m contrasts with previous observations of net (non-zero) right-handed polarity, which hasbeen explained by the damping of left-handed fluctuations by cyclotron resonance at ioncales while whistler or KAW waves survive and carry the turbulent cascade at smaller scales(e.g., Goldstein et al., 1994; Howes & Quataret, 2010; He et al., 2011, Podesta, 2013; Klein etal., 2014; Woodham et al., 2019). Based on the angle RB ( t , ) and the magnetic helicity m ( t , ), we constructed the jointdistribution m ( RB , ) in Figure 3a. It can be clearly seen that there are two populations in m ( RB , ): the first population has negative magnetic helicity corresponding to RB ∈ [60º130º] and frequencies ∈ [2.1, 26] Hz, the second population has positive magnetic helicitycorresponding RB ∈ [150º, 180º] and frequencies ∈ [1.4, 4.9] Hz. For an inward-orientedbackground magnetic field (namely inward magnetic sector with B R <0), a left-handedpolarized wave mode has positive magnetic helicity, while a right-handed polarized wavemode has negative magnetic helicity (e.g., He et al., 2011; Bruno & Telloni, 2015). Themagnetic fluctuations with very small or large RB (i.e., close to 0º or 180º) correspond towaves propagating quasi-parallel or quasi-anti-parallel to the mean magnetic field; while themagnetic fluctuations with the intermediate RB (i.e., close to 90º) correspond to wavespropagating quasi-perpendicular to the mean magnetic field (e.g., He et al., 2011, 2015).Therefore, the magnetic fluctuations with positive helicity at low frequency and around 180 ºcan be identified as quasi-parallel left-handed ACWs, while the magnetic fluctuations withnegative helicity at high frequency and around 90º are likely to be quasi-perpendicular right-handed KAWs. Finally, the magnetic trace power spectra and magnetic helicity m for two angular ranges,i.e., < RB < < RB < f -1.8 ). Both show a spectral break around 1.7 Hz. At higher frequencies, the PSD inthe (anti) parallel direction shows a steeper transition range with a slope close to -5, incomparison to -3.73 of in the perpendicular direction. We note a slight pump between 1.7 to4.6 Hz in the PSD for quasi (anti-) parallel direction, corresponding to the frequency rangewhere positive m is observed, which might indicate that the bump is caused by the ACWs(Figure 3c).
3. Discussion and Conclusions
We investigated the nature of the kinetic wave modes in the slow solar wind using data fromthe NASA’s PSP spacecraft at 0.18 AU. To the best of our knowledge, this is the first timethat co-existing of KAWs and ACWs in the slow wind in the inner heliosphere is revealed. The co-existence of KAWs and ACWs in the slow solar wind is quite similar to previousobservations in the fast solar wind at 1 AU (e.g., He et al., 2011, 2015; Podesta, 2012, 2013),but inconsistent with other observations in the slow solar wind at 1 AU (Burno & Telloni,2015) which showed the disappearance of the ion-cyclotron signature of the magnetic helicityfollowed by a more gradual disappearance (or weakness) of KAWs with the decrease of solarwind speed. Those results were later confirmed by Woodham et al. (2018). If one assumesthat the ACWs appear in the slow solar wind at 0.18 AU but disappear at 1 AU, then thatwould imply that the ACWs heat the plasma protons via cyclotron resonance during theoutbound traveling from the inner heliosphere to the outer heliosphere, until they vanish at 1AU. However, the difference between the observation of ACWs at 0.18 AU and 1AU can bedue to difference in the Alfvénicity of fluctuations: the slow solar wind in Burno and Telloni(2015) has low Alfvénic fluctuations, but in our case the slow solar wind is highly Alfvénic.Another possible explanation may come from the possible generation mechanism of theACWs: because of the existence of a drift of alpha particles with respect to the protons, theroton temperature anisotropy instability that operates when T p ⊥ / T p|| >
1 preferentiallygenerates outward propagating ion-cyclotron (Podesta & Gary, 2011; Woodham et al., 2019).This condition might be met more preferentially in the inner heliosphere than at 1AU. Afuture study based on the radial the evolution of both the proton parallel and perpendiculartemperature should help deciding between the different possible explanations. Another open question is how important are the ACWs in the overall dynamics of theturbulence cascade at the sub-ion scale. We estimated that about 50% of time the ACWs wereobserved in our (1 day) data. However, this should be balanced by the level of power that iscarried by the parallel component of the fluctuations (see Fig. 3b). The integral powerdensities of the frequency range corresponding to the positive magnetic helicity for bothKAWs and ACWs are estimated. It is found that the integral power of KAWs ( dB (KAW) ~10.98 nT ) is higher than the power of ACWs ( dB (ACW) ~ 4.52 nT , i.e., ~ 41% dB (KAW)), implying that the ACWs play non-negligible role in the slow solar wind. One of the important first results from PSP is the ubiquity of the so-called ‘switchbacks’,which are probably large Alfvén waves (Kasper et al., 2019). Although the switchback doesnot affect directly the calculation of the magnetic helicity (i.e., it has no dependence on thesign of B R –see, e.g., Eq. 1 in He et al. (2011)), it may however affect the determination of thewave polarization from the magnetic helicity, where the sign of B R enters into play (Howes etal., 2010; He et al., 2011). Therefore, if B R changes sign (or equivalently RB changes from<90° to >90° or vice versa) on short time scales corresponding to those where the change ofpolarity occurs then this may affect the results of the study. However, as can be seen in Fig.1g and discussed above, the angle RB does not change significantly in the frequency range~0.1-20 Hz in which we reported the change of polarity, but it may change on larger timescales. This observation is in agreement with those of Dudok to Wit et al. (2020) whoanalyzed a larger data set (that included our time interval) and found that switchback affectlarger scales that belong to the inertial range (or even to the 1/ f range). A similar finding iseported concerning the cross helicity (McManus et al., 2020). The fact that we observe twowave modes with distinct polarities at high frequency, which extend over relatively broadfrequency bands are argument that would exclude a possible role of the switchbacks.A final key point that is worth discussing here is a possible ambiguity in the interpretation ofthe spectral slopes observed in Figure 3b for the (anti-)parallel and perpendicular spectra thatmight stem from the sampling direction of the fluctuation due to the flow motion (w.r.t. thespacecraft). Indeed, the critical balance (CB) conjecture predicts an anisotropic scaling of thefor Alfvénic turbulence: l || l at MHD scales and l || l at the sub-ion scales (Goldreich& Sridhar, 1994; Schekochihin et al., 2009). These scaling results in reduced spectra for themagnetic fluctuations given by: B ² k ||-2 at MHD scales and B ² k ||-5 at the sub-ion scales.Using the Taylor hypothesis and considering that θ RB ~ θ VB, the parallel spectrum of Figure 3btranslates into B ² k ||-1.8 and B ² k ||-4.93 for MHD and sub-ion scales, respectively. Thisestimation is a good accord with the CB prediction (see Horbury et al. (2008) and P odesta (2009) for a similar conclusion regarding MHD scale turbulence in the fast solar wind). Thiswould mean that the spectral features of Figure 3b can be fully explained by a simplesampling effect of Alfvénic and KAW turbulence and no need for evoking the ACWs.However, the sole presence of KAW cannot explain the change of polarity observed in m around the ion scales. A further insight can be gained by examining the range of parallelscales involved in Figure 3b-3c. The ACWs seem to be observed within the frequency range[1.4, 4.9] Hz. Using the Taylor hypothesis this translates into the scale range k || d i ∈ [0.4, 1.2],given V f ~ V R ~360 km/s and d i ~13 km. This range of scales corresponds to those where thecyclotron damping is expected to be effective (Gary & Borovsky, 2004). At these scales, theKAW turbulence is expected to have k || i <<1 at k i ~1 (Sahraoui et al., 2010). This argumentsupports the scenario of ACW to explain the polarity near k || d i ~1. n the other hand, the scaling of PSD in the perpendicular direction B k -1.56 at MHDscales and B ² k -3.73 at the sub-ion scales agree with the CB prediction at MHD scales ( k -5/3) but is steeper than that in the sub-ion scales ( k -7/3 ). This steeping might be caused by adissipation of part of the KAWs into ion heating via Landau damping as suggested inSahraoui et al. (2010) and shown in numerical simulations of Howes et al. (2011) andKobayashi et al. (2017). Note that theories and numerical simulations of incompressible Hall-MHD turbulence predicts a scaling k -11/3 for the left-handed component (ACW) and k -7/3 forright-handed component (KAW) of the turbulence (Meyrand & Galtier, 2012), although thatmodel does not capture all aspects of the ACW and KAW modes, which are inherently kineticin nature. Acknowledgement
This work was supported by the National Natural Science Foundation of China (41674161,41874191, 41925018), Young Elite Scientists Sponsorship Program by CAST(2017QNRC001), and the National Youth Talent Support Program. We thank the entire PSPteam and instrument leads for data access and support. The SWEAP and FIELDSinvestigation and this publication are supported by the PSP mission under NASA contractNNN06AA01C. PSP data is publicly available from the NASA's Space Physics Data Facility(SPDF) at https://spdf.gsfc.nasa.gov/pub/data/psp/.
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60º < RB < 130º ); (b) Magnetictrace power spectra and (c) magnetic helicity m for two angular ranges (
80º < RB < 100º inblue and RB < 180º in red). Discrete spectral features above 10 Hz is noise from thespacecraft momentum wheels. The grey curves present the origin m , and the red and bluecurves present the smoothed mm