Statistical Evidence for the Existence of Alfvénic Turbulence in Solar Coronal Loops
Jiajia Liu, Scott W. McIntosh, Ineke De Moortel, James Threlfall, Christian Bethge
aa r X i v : . [ a s t r o - ph . S R ] N ov Statistical Evidence for the Existence of Alfv´enic Turbulence in SolarCoronal Loops
Jiajia Liu , , Scott W. McIntosh , Ineke De Moortel , James Threlfall , Christian Bethge , ABSTRACT
Recent observations have demonstrated that waves which are capable of carryinglarge amounts of energy are ubiquitous throughout the solar corona. However, thequestion of how this wave energy is dissipated (on which time and length scales) andreleased into the plasma remains largely unanswered. Both analytic and numericalmodels have previously shown that Alfv´enic turbulence may play a key role not onlyin the generation of the fast solar wind, but in the heating of coronal loops. In an effortto bridge the gap between theory and observations, we expand on a recent study [DeMoortel et al., ApJL, 782:L34, 2014] by analyzing thirty-seven clearly isolated coronalloops using data from the Coronal Multi-channel Polarimeter (CoMP) instrument. Weobserve Alfv´enic perturbations with phase speeds which range from −
750 km s − and periods from −
270 s for the chosen loops. While excesses of high frequencywave-power are observed near the apex of some loops (tentatively supporting the on-set of Alfv´enic turbulence), we show that this excess depends on loop length and thewavelength of the observed oscillations. In deriving a proportional relationship be-tween the loop length/wavelength ratio and the enhanced wave power at the loop apex,and from the analysis of the line-widths associated with these loops, our findings aresupportive of the existence of Alfv´enic turbulence in coronal loops.
Subject headings:
Sun: corona — waves
1. Introduction
Recent advances in the field of ground- and space-based observations of the solar coronahave revealed the prevalence of oscillatory/wave-like phenomena across a wide range of struc- Earth and Space Science School, University of Science and Technology of China, NO. 96, JinZhai Road, Hefei,China High Altitude Observatory, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, USA. School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife, KY16 9SS, UK. Kiepenheuer Institute for Solar Physics, Freiburg, Germany
De Moortel and Nakariakov
Tomczyk et al.
McIntosh et al.
Parnell and De Moortel
Osterbrock
Parker
Suzuki and Inutsuka
Nakariakov and Verwichte
McIntosh et al.
McIntosh
De Moortel and Nakariakov
Ulmschneider and Musielak
Aschwanden et al.
Tomczyk et al.
Threlfall et al.
Morton and McLaughlin
Cirtain et al.
De Pontieu et al.
He et al.
Okamoto et al.
Antolin and Verwichte
Erd´elyi and Fedun
Van Doorsselaere et al.
De Moortel and Nakariakov
Hood et al.
Pascoe et al.
Terradas et al.
McIntosh et al.
De Moortel and Pascoe
McIntosh and De Pontieu
Goossens et al.
Pascoe et al.
Parker
Oughton et al.
Cranmer and van Ballegooijen
Verdini et al. van Ballegooijen et al.
Asgari-Targhi and van Ballegooijen
De Moortel et al. (2014), which motivated this paper,has shown the tentative evidence for the onset of Alfv´enic turbulence in a trans-equatorial coro-nal loop, by exploring the novel “excess of high-frequency FFT (Fast Fourier Transform) power”(hereafter referred as the “EHFF”) phenomenon near the loop apex.Following
De Moortel et al. (2014), we present a detailed statistical analysis of thirty-sevenclearly isolated coronal loops observed in the field-of-view (FOV) of the Coronal MultichannelPolarimeter (CoMP) instrument (
Tomczyk et al.
2. Instrument and Data
The Coronal Multi-channel Polarimeter (CoMP;
Tomczyk et al.
XIII coronal emission lines. It was deployed behind the20-cm aperture Coronal One Shot (COS) coronagraph (
Smartt et al. ⊙ at a spatial sampling of 4.5 ′′ . The data studied in thispaper are the “Dynamics 3” data which take three wavelength positions at the 10747 ˚A Fe XIII lineand cadence of 30 s. All of the data analyzed below are openly available on the CoMP webpage( ).The reduced CoMP FITS data contain four components: line peak intensity, Doppler veloc-ity, line width and the enhanced intensity. We have found forty-six isolated (without significantline-of-sight complexity) bright coronal loops sets for study that can be grossly grouped as be-longing to coronal cavities, active regions and trans-equatorial systems. We then compared theseloops observed in the CoMP enhanced line peak intensity images with those tracked through a“wave-tracking” method, which employs the wave-propagation-angle map generated by a cross-correlation method on the Doppler velocity images (
McIntosh et al.
100 km s − ), which may be a result of line-of-sight superposition effects. Forthe remaining loops we use CoMP data with less than three missing frames with at least 90 minutesof continuous observation. Any data gaps are filled by linear interpolation using the preceding andfollowing images. As in Threlfall et al. (2013), we select six points along a given coronal loop todefine an arc using spline interpolation (see for example Fig. 1B). The coordinates of the arc aresubsequently resampled to be equally spaced, where the spacing is chosen to be the CoMP pixelsize of 4.5 ′′ (3.24 Mm) for simplicity. For every position along the loop, data are also sampledalong a ∼
20 Mm perpendicular cut, again spaced by the 4.5 ′′ (3.24 Mm) CoMP resolution andhence building up a grid of perpendicular cuts centred on the arc.
3. Example: The Cavity Loops of Sept. 22 nd In this section, we present a detailed analysis of a (long) coronal loop that was part of acoronal cavity on Sept. 22 nd De Moortel et al. nd ◦ , where PA is measured in degrees fromsolar North to the apex of the loop.Let us start with the analysis of the long (green) loop. As described in Section 2, we repeat 5 – −1000 −500 0 500 1000x (arcsec)−1000−50005001000 y ( a r cs e c ) −1000 −500 0 500 1000−1000−50005001000 (A)
800 1000 1200x (arcsec)4006008001000 y ( a r cs e c )
800 1000 12004006008001000 (B)
800 1000 1200x (arcsec)4006008001000 y ( a r cs e c )
800 1000 12004006008001000
0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 (C)
Fig. 1.— (A) Full FOV observation of CoMP enhanced line peak intensity on Sept. 22 nd spline-fitting procedure of Threlfall et al. (2013) by choosing 6 spline points along the loop,shown as six green stars labeled from 0 (footpoint 1) to 5 (footpoint 2) in Fig. 1C. These splinepoints are used to generate an arc, shown in green in Fig. 1C, with the spacing along the arc equalto the CoMP resolution of 4.5 ′′ (3.24 Mm). By integrating the distance between pixels along thearc, the length of the arc is calculated to be ∼ ′′ ( ∼
420 Mm). We should point out, however,that the length of the arc does not equal the real (physical) length of the loop due to (i) projectioneffects and (ii) the fact that the spline points (0) and (5) are not located at the exact footpoints ofthe loop. To compensate for the latter effect, we add the distance from the footpoints to the solarlimb to the length of the arc, giving a total length of 452 Mm. Projection effects have not beentaken into account as it is difficult to exactly identify the corresponding object in
STEREO imagesfor a loop found at the limb of CoMP.Fig. 2A shows the time-distance plot of the CoMP Doppler velocity, along the arc highlightedin Fig. 1C by the dashed green line. A clear “herringbone” pattern of perturbations (red dashedarrows in Fig. 2A), originating from both of the loop footpoints (green dashed lines in Fig. 2A), isvisible in the time-distance diagram (similar to the example analyzed by
De Moortel et al.
Original Timeseries
Leng t h A l ong A r c [ Mm ] C o M P Å I n t en s i t y [ l og µ B ] Original Timeseries FFT Power − − − − − FFT P o w e r (A)(C) (D)(B)(E) (F) Original Timeseries
Leng t h A l ong A r c [ Mm ] − − − − C o M P Å L O S V e l o c i t y [ k m / s ] Original Timeseries FFT Power
Shuffled Timeseries
Leng t h A l ong A r c [ Mm ] Shuffled Timeseries FFT Power − − − − − FFT P o w e r Fig. 2.— (A) and (C): Time-distance plots of Doppler velocity along the arc highlighted by thegreen curve in Fig. 1C, based on the original and reshuffled time series, respectively. Perturbationswith phase speed around 640 km/s are indicated by red dashed arrows in panel (A). Two greendashed horizontal lines represent the footpoints of the arc. (B) and (D): Corresponding FFT powerspectra of (A) and (C) as functions of distance and frequency. FFT power in panel (B) for theoriginal time series and (D) for the reshuffled time series. (E) and (F): Corresponding time-distanceplot of line peak intensity along the arc based on the original time series and its associated FFTpower spectrum.oped by
Tomczyk and McIntosh (2009). We cross-correlate the time series at each position alongthe arc with the timeseries at the midpoint of the arc (i.e. the apex of the loop). The peak of thecross-correlation function is then fitted with a parabola such that lag or lead time at each pointalong the arc is returned. We then fit the lag/lead times versus the distance along the loop with astraight line - the phase speed (and the associated error in the phase speed) of the propagating per-turbations are the gradient of this line. When waves are counter propagating this technique givesrise to anomalously high phase speeds (see
Tomczyk and McIntosh
Tomczyk and McIntosh (2009)to identify the phase speeds of waves moving in either direction along the loop: pro/retro-grade 7 –filtering is done by masking the positive/negative frequency halves of the k − ω diagram gener-ated from the FFT of the original time-distance plot, and then performing the inverse transform toconstruct two space time plots, one for each direction of propagation. The cross-correlation phasespeed method is applied to each to yield the (mean) phase speed of the wave on that arc, where thetwo propagation directions mostly show very similar phase speeds.By averaging the phase speeds obtained from the filtered time-distance plots employing thecross-correlation method described above, the phase speed of perturbations (waves) propagatingalong the loop is estimated at 640 ( ± ) km/s (red dashed arrows in Fig. 2A). It is substan-tially larger than the (estimated) local sound speed of a cavity ( ∼
100 km/s,
Liu et al.
Tomczyk et al.
Tomczyk and McIntosh
Threlfall et al.
De Moortel et al.
Wright and Garman
De Moortel et al. > < De Moortel et al. (2014), the wave amplitude could increase by a maximum factor of 3.4 at theloop apex, using linear superposition (a maximum factor of 2) and an e z apex / (4 H ) ≈ . gravitational 8 – > 8 min3 ~ 8 min< 3 min FootpointsFootpoint AverageApex (A) Doppler Velocity Original Timeseries (B) Doppler Velocity Shuffled Timeseries(C) Doppler Velocity Original Timeseries (D) Doppler Velocity Shuffled Timeseries m i n m i n N o r m a li z ed A v e r aged FFT P o w e r N o r m a li z ed A v e r aged FFT P o w e r − − − − − l og10 ( A v e r aged N o r m a li z ed FFT P o w e r) − − − − − l og10 ( A v e r aged N o r m a li z ed FFT P o w e r) Fig. 3.— (A) and (B): The normalized averaged FFT power at low ( < > nd Wright and Garman H = 75 Mm andthe height of the loop apex z apex = 160 Mm for this particular loop. Fig. 3A shows that the FFTpower for the LF and MF parts is about 1.36 higher at the apex than at foot points, indicating a √ . ≈ . growth in wave amplitude (as the FFT power scales as the square of the amplitude),which corresponds to a damping of up to 65 % compared to the ideal non-damping estimation (as1.17 is about 35% of 3.4, the maximum possible growth rate). On the other hand, the damping ofthe HF part is estimated to be roughly 55%, less than that of the MF and LF parts, implying thepresence of an additional effect other than the linear superposition and gravitational stratification.The results for the randomly shuffled time series (Fig. 3B) show similar growth rates for the three 9 –frequency ranges.Fig. 3C shows the logarithm of the averaged FFT power over distance as a function of fre-quency. To remove the influence of linear superposition and gravitational stratification effects,the FFT power at each position along the loop is divided by the total FFT power over the wholefrequency range at that position. The two dashed black curves show the FFT power at the twofootpoint regions (the first and last 20 points of the arc) and the solid curve is their average. Thesolid red curve is the FFT power around the apex (the middle 20 points of the arc). The FFT powerdecreases with frequency at the footpoints as well as at the apex. However, a detailed comparisonof the two solid curves reveals that the power at the apex (red curve) is less than or at most equalto that of the footpoints (black curve) in the LF and MF ranges, but becomes higher in the HFrange. The ratio of the power at the apex and footpoints is about 1.01 and 0.80, in the LF and MFfrequency ranges, respectively. However, the ratio grows to about 1.81 in the HF range, implyingan ‘excess’ of HF power. The randomly shuffled time series on the other hand (Fig. 3D) shows aneven distribution of the FFT power as a function of frequency for the three different regions. Toquantify the excess HF FFT power, we define a variable “Ratio Difference” (RD) which representshow much the ratio (R) between the power at the apex and footpoints grows at the HF range withrespect to the LF and MF ranges, i.e. RD = R HF − ( R LF + R MF ) / R LF + R MF ) / × where R LF , R MF and R HF are the ratios between the power at the apex and footpoints in the low,medium and high frequency ranges, respectively. Excess high frequency power at the loop apexis characterized by positive values of the Ratio Difference (the high frequency component powerdecreases slower than the low frequency and medium frequency components when traveling alongthe loop from the footpoints to the apex) whereas a negative value of the Ratio Difference wouldindicate that the high frequency component decreases faster along the loop than the low/mediumfrequency power. The Ratio Difference (RD) value for this particular loop is about 101.56%,indicating a significant excess of high frequency power at the loop apex.In addition to the long (green) loop, we have also analyzed the two shorter loops, outlined bythe blue and yellow curves in Fig. 1C. We found similar perturbations propagating upwards alongthe loops, with typical herringbone patterns in the corresponding Doppler velocity time-distancediagrams (not shown). However, the behavior of the EHFF in these two loops is of particularinterest. Fig. 4 shows the corresponding FFT power spectra (averaged and normalized as before)as a function of frequency for these two loops. The FFT power spectrum of the medium loopshows similar behavior as for the long loop: the low-frequency FFT power at the apex is lowerthan the corresponding LF power at the footpoints, but at high frequencies, the power at the apex 10 –is higher than at the footpoints (i.e. in Fig. 4A the red line (apex) falls below the solid black line(footpoints) at low frequencies but above the black line at high frequencies). The effect is notas pronounced though as for the long loop described earlier, with an RD value of about 17.92%.However, the EHFF appears to be absent for the shortest loop (Fig. 4C). The FFT power at theapex is now approximately equal to the FFT power at the footpoints for all frequencies, leading toan RD value of -16.06%. This intriguing result of different behavior of the HF power in differentloops implies that the EHFF phenomenon is not necessarily present in all loops. All three loopsstudied in this Section are located in the same cavity and hence it is likely that they share someproperties such as their magnetic field topology (and possibly their magnetic field strength andplasma density). The most clear distinction between them is their lengths, namely 452 Mm, 304Mm and 201 Mm, respectively.
4. Statistical Analysis of 37 Coronal Loops
In the previous section we presented the detailed analysis and the comparison of three cavityloops on Sept. 22 nd V phase ” is the Alfv´enic perturbation phase speed detected in a loop using the cross-correlation method described in Sect. 3; and “WD” is the line width difference and represents howmuch the average line width increases or decreases at the apex with respect to the footpoints.The parameter λ represents the “characteristic wavelength” of the Alfv´enic perturbationspropagating in a loop and is defined as follows. We integrate the Doppler velocity FFT powerover three narrow wavelength ranges: 1.5 ± ± ± FootpointsFootpoint AverageApex (A) Medium Loop Doppler Velocity Original Timeseries (B) Medium Loop Doppler Velocity Shuffled Timeseries(C) Small Loop Doppler Velocity Original Timeseries (D) Small Loop Doppler Velocity Shuffled Timeseries m i n m i n − − − − − l og10 ( A v e r aged N o r m a li z ed FFT P o w e r) − − − − − l og10 ( A v e r aged N o r m a li z ed FFT P o w e r) − − − − − l og10 ( A v e r aged N o r m a li z ed FFT P o w e r) − − − − − l og10 ( A v e r aged N o r m a li z ed FFT P o w e r) Fig. 4.— (A) and (B): The logarithm of the averaged, normalized FFT power at the two footpoints(black dashed curves) and the apex (red solid curves) as a function of frequency for the mediumloop, based on the original and reshuffled time series data of Doppler velocity. The black solidcurve is the average of the FFT power at the two footpoints. (C) and (D): same result as panels (A)and (B) but for the short loop. The two vertical dashed lines represent periods of 3 min and 8 min,respectively.Based on the limited sample in Sect. 3 we speculated that the value of RD ratio varies withloop length. As the longest loop shows a significant excess of high frequency FFT power and theshortest loop reveals evidence of roughly equal or even higher damping at the HF part - we believethat the RD metric represents the degree by which the EHFF phenomenon increases with looplength. Plotting the tabulated results in Fig. 5A would appear to add weight to our early speculationas there appears to be a linear relationship between loop length and the Ratio Difference.Fig. 5 allows us to analyse different types of coronal loops prevalent in CoMP data: cavityloops, active region loops and trans-equatorial loops. They are represented by green asterisks,blue diamonds and red triangles, respectively. It is clear that the RD value grows with the looplength and the relationship between them appears to be linear at least within the loop length range 12 –
Trans-Equatorial Loop(A) Loop Length V.S. Ratio Difference (B) Wave Count V.S. Ratio Difference * (cid:1)(cid:2) Cavity LoopActive Region Loop
100 200 300 400 500 600 700Loop Length [Mm] − − R a t i o D i ff e r en c e [ % ] − − R a t i o D i ff e r en c e [ % ] Fig. 5.— (A) Relationship between the loop length and the Ratio Difference (RD). (B) Relation-ship between wave count and Ratio Difference. Green asterisks: cavity loops. Blue diamonds:active region loops. Red triangles: trans-equatorial loops. The colored dashed lines are calculatedfrom corresponding linear fits. The black solid line is the linear fit result for the full dataset. Thepoints in black rectangles are found to strongly bias the linear fits and hence they are excludedfrom further analysis.we study of 200 Mm to 700 Mm and RD range of -61% to 144%. The slopes of the green, blueand red dashed lines are 0.295, 0.287 and 0.152, respectively. The solid black line representsthe linear fit result of the whole dataset with a relatively high cross-correlation factor (CC) ofabout 0.7, implying a reliable proportional relationship between the loop length and RD. We notethat the linear fits can be strongly biased by the two data points enclosed in rectangles - it is notimmediately clear what is incorrect or wrong with these measurements. but we exclude them fromfurther analysis. Using a Ratio Difference of 10% as a threshold value to indicate excess highfrequency power, the overall linear fit (black line) allows us to determine a critical loop length:when a loop is longer than 318 Mm, the Alfv´enic perturbations appear to damp slower at highfrequencies when propagating from the footpoints to the apex than they do at low frequencies. Theloop studied by
De Moortel et al. (2014) has a length of ∼ M m and do indeed exhibit thisbehavior.Alfv´enic perturbations propagating along different loops could display different behavior,considering that loops may have different properties (e.g. density, magnetic field strength,
Priest ∼ ±
5. Discussion
We analyzed thirty-seven clearly isolated CoMP coronal loops. In all cases, Alfv´enic per-turbations are found propagating along coronal loops. Detailed analysis reveals that these per-turbations cause obvious variations in Doppler velocity but not in simultaneous intensity data,implying their incompressible (Alfv´enic) nature, as reported in
Tomczyk et al. (2007). The phasespeed of these perturbations ranges from 250 km/s to 750 km/s and their typical period varies from140 s to 270 s (roughly 3 -5 min) - consistent with those reported in
Tomczyk et al. (2007) and
Tomczyk and McIntosh (2009).Further, time-distance analysis of the Doppler signal in a coronal loop of Sept. 22 nd ∼
450 Mm long) revealed a herringbone pattern, indicating perturbations propagating from bothfootpoints to the apex, similar to
Tomczyk and McIntosh (2009). The bi-directional perturbationshave almost the same phase speed and they interact with each other around the apex. No obviousdownward propagating perturbations around the footpoints are found, implying that these pertur-bations damp continuously on approach to, and after passing, the loop apex.Table 1 :
Statistical results of thirty-seven coronal loops in 2013
YMD Type PA ( ◦ ) L (Mm) RD (%) V phase (km s − ) λ (Mm) WD (%)20130104 CV 313.47 396.56 -15.01 309.45 ± ± ± ± ± ± ± ± ± ± ± ± Continued On Next Page
14 –Table 1 :
Continued From Previous Page
YMD Type PA ( ◦ ) L (Mm) RD (%) V phase (km s − ) λ (Mm) WD (%)20130502 TE 89.29 494.53 77.24 577.09 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± phase : Propagating perturbationphase speed in units of kilometer per second. λ : Characteristic wave length, in units ofmegameter. WD: Line width difference (see text).FFT power analysis shows that these perturbations undergo damping when propagating fromthe footpoints to the apex across the frequency range accessible to CoMP. One possible means ofdamping these waves is through “mode coupling” - a process inherent to transverse (kink) waves 15 –propagating in a loop with an inhomogeneous boundary layer and where the (observed) wavedamping occurs due to the transfer of the wave energy from the transverse waves generated atthe loop footpoint regions into azimuthal Alfv´enic waves as they propagate along the loop (e.g., Melrose
Pascoe et al.
Hood et al.
Pascoe et al.
Pascoe et al.
Terradas et al.
Terradas et al. could explain the dif-ferent inclinations between the linear fit lines (Fig. 5A and B to cavity loops (green dashed line),active region loops (blue dashed line) and trans-equatorial loops (red dashed line). For example,as the plasma density in active and trans-equatorial regions is likely to be larger than cavities,lower inclinations would be expected. However, further investigation is required to confirm thissuggestion.Given the frequency selectivity in mode coupling, less high-frequency power would be ex-pected at the loop apex compared to lower frequencies. However, this is contrary to what theobservations and analysis of the long and medium loops show. As shown in Fig. 3, the high fre-quency FFT power at the apex of these perturbations is higher than that at the low- and medium-frequencies. Recalling that we defined the Ratio Difference as a measure of how much the highfrequency power is larger than the low/medium frequency power, one would expect the valueof RD to be always below 0 if the high-frequency part damps faster (as in the mode couplingmodel). However, this is not the case and the RD is larger than 0 for the long and medium loops.
De Moortel et al. (2014) suggested that the excess of the high-frequency power may be evidenceof the onset of turbulence (e.g., van Ballegooijen et al.
McIntosh and De Pontieu ◦ angular spacing around the Sun as the background linewidth change (“WDB”). Fig. 6 shows the relationship between the wave count and the differencebetween WD and WDB. We see that ∼
70% of the points lie above 0 (the horizontal dashed line)possibly indicating that the line broadening at the majority of the loop apexes sampled is larger thanmay be expected via waves propagating through a complex structural superposition. However, suchsuperposition likely will not change the loop lengths or wave counts, possibly indicating that thedistribution of the points in Fig. 6 could be a signature of turbulence in coronal loops.
6. Conclusion
In this paper, following the work by
De Moortel et al. (2014), we performed a detailed anal-ysis of three cavity loops observed on Sept 22 nd − propagating from the loop footpoints are found in the correspondingtime-distance diagrams without any simultaneous density variations. An excess of high frequencypower (EHFF) is found in the FFT power spectrum of the two long loops and not in that of theshortest loop. This EHFF phenomenon might be tentative evidence for the onset of Alfv´enic tur-bulence. Further statistical analysis on thirty-seven clearly isolated loops shows a relationshipbetween the loop length and the Ratio Difference (a measure of the excess high frequency at theapex), in agreement with the assumption of turbulence, as a longer traveling distance could lead tomore (non-linear) interactions between opposite-propagating wave trains. Linear fits reveal a looplength of at least about 318 Mm for the EHFF phenomenon to be present.The proportional relationship between the wave count (how many wavelengths there are alonga loop) and the Ratio Difference tends to support the presence of Alfv´enic turbulence. The criticalwave count of 3.0 for the excess high frequency (EHFF) to be present is consistent with (the onsetof) turbulence. Finally, we have explored the relationship between the wave count and the back-ground subtracted line width. The weakly proportional relationship between them again supportsthe onset of Alfv´enic turbulence in coronal loops.In this study, we have presented statistical evidence for the onset of Alfv´enic turbulence incoronal loops. However, the relatively low spatial resolution and signal-to-noise ratio of CoMP 17 –data prevent us from performing a more detailed analysis and finding more direct evidence ofturbulence in those loops. Hopefully in the future, more detailed observations using instrumentswith higher spacial resolution and signal-to-noise, combined with numerical simulations will helpimprove our understanding of coronal turbulence and any potential impact on coronal heating.Acknowledgements JL is a student visitor at HAO. JL is supported by the Chinese ScholarshipCouncil (CSC 201306340034) and also supported by Grants from NSFC 41131065, 41121003, 973Key Project 2011CB811403 and CAS Key Research Program KZZD-EW-01-4. JL also thankshis advisor in China, Dr. Yuming Wang. NCAR is sponsored by the National Science Founda-tion. CoMP data can be found at http://mlso.hao.ucar.edu/ . We acknowledge supportfrom NASA contracts NNX08BA99G, NNX11AN98G, NNM12AB40P, NNG09FA40C ( IRIS ),and NNM07AA01C (
Hinode ). The research leading to these results has also received fundingfrom the European Commission Seventh Framework Programme (FP7/ 2007-2013) under the grantagreement SOLSPANET (project No. 269299, ). REFERENCES
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