Ion kinetic energy conservation and magnetic field strength constancy in multi-fluid solar wind Alfv\'enic turbulence

1.7 MB·English

by  L. Matteini

Draft version January6, 2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
ION KINETIC ENERGY CONSERVATION AND MAGNETIC FIELD STRENGTH CONSTANCY IN
MULTI-FLUID SOLAR WIND ALFVÉNIC TURBULENCE
L. Matteini1, T. S. Horbury1, F. Pantellini2, M. Velli3, and S. J. Schwartz1
(Dated: January 6, 2015)
Draft version January 6, 2015
5 Abstract
1
We investigate properties of the plasma fluid motion in the large amplitude low frequency fluctua-
0
tions of highly Alfvénic fast solar wind. We show that protons locally conserve total kinetic energy
2
when observedfrom an effective frame of reference comoving with the fluctuations. For typical prop-
n erties of the fast wind, this frame can be reasonably identified by alpha particles, which, owing to
a
their drift with respect to protons at about the Alfvén speed along the magnetic field, do not par-
J
take in the fluid low frequency fluctuations. Using their velocity to transform proton velocity into

4 the frame of Alfvénic turbulence, we demonstrate that the resulting plasma motion is characterized
by a constant absolute value of the velocity, zero electric fields, and aligned velocity and magnetic
]
field vectors as expected for unidirectional Alfvénic fluctuations in equilibrium. We propose that this
h
p constraint, via the correlation between velocity and magnetic field in Alfvénic turbulence, is at the
- origin of the observed constancy of the magnetic field: while the constant velocity corresponding to
e constant energy can be only observed in the frame of the fluctuations, the correspondingly constant
c
total magnetic field, invariant for Galilean transformations, remains the observational signature, in
a
the spacecraft frame, of the constant total energy in the Alfvén turbulence frame.
p
s
.
s 1. INTRODUCTION
c
i The solar wind constitutes a unique laboratory for
s
y plasma turbulence (Bruno & Carbone 2013). Velocity
h and magnetic field fluctuations, especially in the fast
p wind, are known to be Alfvénic (Belcher & Davis 1971;
[ Smith et al. 1995), with correlations between velocity
and magnetic field compatible with a unidirectional flux
1
of anti-sunward waves. The low frequency part of the
v
electromagnetic spectrum, referred to as the 1/f range,
2
is considered as the reservoirof energy for the turbulent
0
cascade that extends down to the small kinetic scales of
7
theplasma,whereitisdissipatedviawave-particleinter-
0
actions or other processes that are still not entirely un-
0
derstood (Leamon et al. 1999; Alexandrova et al. 2009).
.
1 The low frequency magnetic field fluctuations, δB, have
0 large amplitudes which are often of the same order as
5 the underlyingmagneticfield, B . As aconsequencethe
0
1
angle between the direction of the local magnetic field,
v: B=B0+δB,andthe radialdirection,correspondingto
i the direction of the flow, is observed to fluctuate signifi-
X
cantly.
r Despite the large excursions of the magnetic field vec-
a tor,thetotalmagneticfieldintensity B displaysamuch
| |
smaller variance and is observed to remain remarkably
Figure 1. Top 3 panels: data used in this work: proton speed
constant during highly Alfvénic periods, regardless of (top),normalcomponentofprotonvelocity(middle)andmagnetic
heliocentric distance and latitude (Bavassano & Smith field (bottom), and total magnetic field B (red, bottom panel).
1986;Smith et al.1995). Geometrically,this means that Lower 2 panels: normal (top) and radial (bottom) components of
the tip of the total magnetic field vector B moves on the proton velocity (red) and magnetic field (black), for a 8hrs
intervalselectedbetween labelsAandB.
a sphere of constant radius (Barnes 1981; Bruno et al.
2001)andthatfluctuationscannotbe describedbysim- Webb et al. 2010). The origin of this remarkable prop-
ple planar waves (Goldstein et al. 1974; Barnes 1976; erty is still an open question. Large amplitude purely
transversewavespropagatingin one directionwith total
1The Blackett Laboratory, Imperial College London, SW7 field B =const are an exact solution of the MHD equa-
2A2ZL,EUSKIA, Observatoire de Paris, CNRS, UPMC, Université tions (e.g., Barnes & Hollweg 1974), suggesting that the
solarwindplasmaisinequilibriumwithanensemblelow
Paris-Diderot,5placeJulesJanssen,92195Meudon,France
3DepartmentofEarth,Planetary,andSpaceSciences,UCLA, frequency Alfvénic fluctuations propagating away from
California,US the sun, but how this conditionis achievedinthe turbu-
2 Matteini et al.
lentexpandingsolarwindandwhichdynamicaldriveris
leading to it are not well understood. Moreover, in the
solar wind, ion species (protons and alpha particles) are
observed to interact differently with the fluctuations, as
a function of their relative drift speed (Goldstein et al.
1996).
In this work we demonstrate, using in situ spacecraft
observations and focussing on the 3-D nature of the
lowfrequencyAlfvénicfluctuationsandthemulti-species
composition of the solar wind plasma, that the property
of constant magnetic field is related to a more funda-
mental physical property, namely the local conservation
of the ensemble particle kinetic energy in the effective
wave frame of reference.
Figure 2. Left: Proton and alpha (blue) speed as a function
of θBR, angle between the radial and the local magnetic field
B. Dashed red lineindicates the correlation discussedinthe text
2. DATAANALYSIS (Matteinietal.2014). Right: Alpha-protondriftVαpasafunction
2.1. Properties of highly Alfvénic fast streams ofθBR (top)andinunitsofthelocalAlfvénspeedVA (bottom).
can be reasonably described by the relation:
Figure 1 shows the solar wind data, measured by the
Helios spacecraftat 0.3 AU, used in this work (Helios 2,
Vp V0+A[1 cos(θBR)], (1)
1976 days 102-110, time resolution 40s). The top panel ∼ −
shows the proton speed; this includes a very high speed shown in red line, with V0 = 700 km/s and A = 160
stream (Marsch et al. 1982). The predicted Parker spi- km/s, and where V0 is the minimum of the average so-
ral angle for such conditions is 10 degrees,so that the lar wind speed over the interval, and A is the "phase"
average magnetic field should ∼be directed close to the velocity of the fluctuations. The latter is proportional
radial direction R. The second and third panels show totheAlfvénspeedVA :A=VA√rA throughtheAlfvén
the N component of the velocity and magnetic field, ratiorA,the ratiobetweenvelocityandmagneticenergy
bVoNthanthdeBraNd,iaplearnpdenBdi0c.ulTarhetoTtdhierepcltaionne ctohmatplceotnestatihnes dofeptehnediflnugctounathioenliso.cenIntrifcasdtissttarnecaem.sStiynpciecarlAlydreAcre≤ase1s,
orthogonal RTN spacecraft coordinate system used in with increasing radial distance, the deviation of A from
this work. As the spacecraftenters the fast wind stream the Alfvén speed becomes more significant for observa-
an increase in amplitude of the fluctuations is observed. tions far from the Sun, as for example it is found in the
This also corresponds to an increase of Alfvénicity, or Ulyssesdata set(cfr. Matteini et al.2014). InFig. 2 the
correlation between velocity and magnetic field fluctu- value of A is quite close to the measured Alfvén speed,
ations (Bruno et al. 1985). However, the amplitude of due tothe smalldeviationfromunity ofthe Alfvénratio
the velocity fluctuations for alphas (blue line in the sec- rA in this interval (Bruno et al. 1985).
ond panel) remains small with respect to protons. As NotethatthescalingofEq. (1)alsoprovidesanexpla-
mentioned, despite the fact that the fluctuating mag- nationfortheradialone-sidedfluctuationsonthebottom
neticfieldshowsvariationofthesameorderastheback- panel of Fig 1. Being
ground field (δB/B 1), the total magnetic field B
(redpoints in|thir|dpan∼el)remainsapproximativelycon- Vp =q(V0+δVR)2+δV⊥2 (2)
stant over the period of the oscillations. Note that over
the fast wind stream the direction of the average mag- and since δVR δV⊥ V0, at first order:
∼ ≪
netic field remains approximatively constant, while the
local instantaneous magnetic field B oscillates from 0 to Vp ∼V0+δVR. (3)
beyond 90 degrees. From Eq. (1), we then expect δVR 1 cos(θBR) and
∝ −
The two lower panels show a 10hr sub-interval, since θ roughly oscillates between [0,π/2] this leads
BR
∼
demonstrating the high level of Alfvénicity in the fast to a flatter distribution when θ 0 and spike-like
BR
∼
stream, i.e. the anti-correlation between magnetic and enhancements when θ 90.
BR
∼
velocity fluctuations. The N direction displays roughly Unliketheprotons,thespeedofalphaparticlesV (blue
α
symmetricfluctuations. Bycontrast,theRcomponentof dots) is not correlated with θ . The difference be-
BR
the fluctuations (bottom panel) is one-sided, as already tween proton and alpha speed V V is therefore a
α p
−
discussed in Gosling et al. (2009); this can be explained function of the direction of the local magnetic field and
in terms of the geometry of Alfvénic fluctuations with V V when θ 90◦. It is also worth under-
α p BR
∼ ∼
constant magnetic field (Matteini et al. 2014). lining that the such a plasma motion implies effective
Some other typical properties of the highly Alfvénic changes in the speed of the centre of mass as a func-
fastsolarwind intervalconsideredhere are illustratedin tion of θ . However the drift speed between alphas
BR
Figure 2. The left panel shows the correlation between and protons V = V V , which to a good approx-
αp α p
| − |
the protonspeed(black dots)andthe angle betweenthe imation is always aligned with the local magnetic field
radial and the local direction of the magnetic field θ (Marsch et al. 1982), does not change during Alfvénic
BR
over the interval B-D. As discussed by Matteini et al. fluctuations, and is roughly independent of θ (upper
BR
(2014)thiseffectisduetothepresenceoflargeamplitude right panel). The bottom right panel shows the value of
Alfvénic fluctuations; as a consequencethe protonspeed V normalizedtothe localAlfvénspeedoverthe period
αp
Constant V and B in Alfvénic fluctuations 3
analyzed here. V is a significant fraction of V and
αp A
the ratio is closeto 1 in the faststream,with anaverage
value V 0.85V over the period shown.
αp A
h i∼
All these properties, i.e. the fact that alphas stream
faster than protons at about the Alfvén speed and that
their drift with respect to protons does not change in
time, explain why the alpha particle speed is observed
to be uncorrelated with the angle θ : since alphas
BR
travel at approximatively the phase speed of the turbu-
lence,theydonotrespondtotheoscillationsofthemag-
netic field; alphas surf the large amplitude fluctuations
of the solar wind (Marsch et al. 1981) and their speed,
unlike the protons, is not modulated by the Alfvénic ac-
tivity (Goldstein et al. 1996). Similar behavior is ob-
served for the minor heavy ions (Berger et al. 2011;
Gershman et al.2012)whichalsostreamfasterthanpro-
tons in the fast solar wind.
2.2. Particle motion and constant magnetic field
It is worth noting that not all the characteristics of Figure 3. Top: scatterplot of the normal and radial magnetic
the solar wind summarized in Figures 1 and 2 are fully field(left)andprotonvelocity(right)components,fortheinterval
B-D in Fig 1. Red points show the preceding slow wind interval
understood. In particular, despite the fact that fluc-
as reference (before label A in Fig 1). Numbered labels indicate
tuations propagating in a single direction with a to- the corresponding anti-correlation between BR and VR. Bottom:
tal constant magnetic field magnitude are a nonlinear (left) scatterplot of normal Alfvénic components for protons and
solution to the MHD equations, so that the fluctua- alphas (blue) for the interval C-D. The red dashed line identifies
the slope corresponding to the Alfvén speed. (right) scatterplot
tions may in some sense be considered to be in equi-
of proton and alpha (blue) velocity in the plane (VN,VR) for the
librium, how this is achieved in the solar wind plasma is sameinterval asleftpanel.
still an open question. For example, though monochro-
matic Alfvénwaveswith circularpolarizationareclearly
plane (V ,V ): in the fast wind the arc-shaped excur-
an example solution with constant total magnetic field N R
sion in the magnetic field corresponds to oscillations of
(e.g., Barnes & Hollweg 1974), a collection of transverse
Alfvén waves will not satisfy B = const, unless their the velocityonananalogousarcasafunction ofVN and
phasesarecloselycorrelatedin|av|eryspecificway. More VR. It can be shown that the 3D motion of the veloc-
generallyfluctuations withamplitude |δB| modulatedin itthyevmecottoiornidoefntBifi.esNaotsephthearitc,adlusuertfaocteh,ecoAnlsfivsétnenict awnittih-
time, as in Figure 1, can not fulfill the condition of con- correlationbetweenthecomponentsofBandV,minima
stant total magnetic field:
of B (labelled as 1 and 3 in the figure) correspond to
R
B2 = B +δB2 =B2+ 2B δB + δB2 =const. (4) maximainVR,andviceversa(labelledas2inthefigure).
0 0 0
| | | | | · | | | As mentioned, alpha particles do not partake in the
if they are 2D lying in the plane transverse to B0 (e.g., Alfvénic motion when they stream close to the Alfvén
Dobrowolny et al.1980). Onthecontrary,magneticfluc- speed. The bottom left panel of Fig. 3 displays the
tuations in the solar wind are observed to be 3-D (i.e., correlation between B /B and V /V , for both pro-
N N A
B0/B0 δB = δBk = 0), with the magnetic field vector tons and alphas (blue). As discussed by Goldstein et al.
· 6
moving on a sphere of constant radius. (1996), while protons show a strong correlationbetween
In this framework, in order to maintain equilibrium velocity and magnetic field fluctuations, close to the re-
between particles and fluctuating fields, thus avoiding lation expected for fluctuations that propagate at the
energy exchanges leading to damping, one condition is Alfvén speed (red dashed line), the alpha velocity has
that inthe oscillating fields the plasma conservesenergy only a weak correlation with Alfvénic magnetic fluctua-
as seen in the frame moving with the fluctuations. The tions. The transverse motion of alphas is almost negli-
conservation of total kinetic energy in the wave frame gible compared to the amplitude of the proton fluctua-
wouldthenimplythatprotonsmoveonaparticularsur- tions;asaconsequence,alphasdonottraceanarcinthe
face in phase space. (V ,V )plane(rightpanel),butratherremaininafixed
N R
We now show that such a surface exists in the solar placeinphasespace. Thepositionofalphaparticleinve-
wind and can be identified with good accuracy from ob- locity space therefore identifies to a goodapproximation
servations. Figure 3, top left panel, shows the excursion the location of the wave frame, about which the protons
ofBduringtheperiodanalyzed,forfast(black)andslow oscillate. Although it is not always possible to use al-
(red)wind,inthe(B ,B )plane. Itcanbeclearlyseen phas in this way to identify the wave frame, the frame
N R
that in the fast wind, the magnetic field oscillates on an may also be found by direct inspection of the geometry
arcofconstantradius;thisistheprojectionontheplane of the fluctuations, such as the slope of the V -B /B
N N
of the excursion of B on a sphere. The picture is less correlation,whichprovidesanindependentestimationof
clear, and the level of the fluctuations is weaker, in the the phase speed associated to the fluctuations (see for
shortintervalofslowwindprecedingthe faststream,re- example Goldstein et al. 1996, for more details). In this
portedin redforcomparison. The top rightpanelshows case,the phase speedinferredfromthe V -B /B corre-
N N
the analogous evolution of the velocity vector V in the lation is 155 km/s, thus slightly less ( 0.9V ) than
p A
∼ ∼
4 Matteini et al.
associated with the fluctuations is expected to vanish5:
E= (V B)=0, (5)
− ×
meaning also that each species i maintains its total ve-
locity V aligned with the instantaneous magnetic field,
i
i.e.:
V =α B; V = α B =const. (6)
i i i i
| | | |
Notethatsuchconditionsareexpectedfornon-dispersive
Figure 4. Schematic description of plasma motion in large am- monochromatic transverse waves with circular polar-
plitude low frequency Alfvénic fluctuations in the velocity plane ization in a multi-fluid plasma (Marsch & Verscharen
(VT,VR). Circlesidentifyprotons (yellow),alphas (blue),andthe 2011). The constant of proportionality α depends on
fluid(centreofmass)frame(black). Middleandrightpanelsshow
the case of a radially aligned and transverse local magnetic field each species’ drift with respect to the wave frame,
(redarrow), respectively. αi =V0i/B0. Here, for alphas α 0, while for pro-
∼
the mean Alfvén speed measured during this interval, tonsα∼Va/B0. Thereforeparticlesofeachspeciesmove
on a surface of constant energy as discussed previously;
V 175km/s. We note here that, remarkably, the
h Ai ∼ these conditions can be directly tested on the observa-
meanalpha-protondriftshownintheright-bottompanel
tions,transformingvelocitiesmeasuredbythespacecraft
ofFig.2isalsoclosetothisvalue( V 0.85V ),sug-
h αpi∼ A into the estimated wave frame.
gesting that alphas are drifting with respect to protons
Figure 5 shows the results of such a transformation
with a speed which is closer to the phase speed inferred
where the superscript w indicates velocities in the new
from the analysis of the plasma motion rather than the
(wave) frame. Panels on the lefthand side show (top)
nominal Alfvén speed. This then confirms that alphas
the proton velocity in the (Vw,Vw) plane, with V =
are essentially comoving with the fluctuations, and are ⊥ R ⊥
thus at rest with them, consistently with the fact that V2 +V2 and (bottom) the correlation between the
p N T
they do not display velocity oscillations in the bottom angle, with respect to the radial, of the instantaneous
panels of Fig. 3. magnetic field vector, θBR, and of the proton velocity,
The geometry of this dynamics is summarized by the θw . These are computed using the alpha velocity for
VR
cartoon of Figure 4. The left panel shows a schematic thecoordinatechange,overthe intervalB-DofFigure1.
representationofthe solarwindplasma: protons(yellow Note that this has the effect of removing the solar wind
circle) have a purely radial velocity ( 750 km/s) and underlying structures (Thieme et al. 1989), isolating the
alphas stream faster with respect to th∼em, along the lo- contribution of Alfvénic fluctuations. Both panels show
cal magnetic field. The mean magnetic field is assumed thatthe motionofprotonsas seeninthe new framewell
to have a small angle in the R-T plane, reproducing the satisfies Eq. (6), correspondingto a goodapproximation
Parker spiral angle at 0.3 AU. The small black circle to a motion with the proton velocity aligned with the
identifies the fluid velocity (V = NpVp+4NαVα), which instantaneousmagneticfieldandonasphereofconstant
f Np+4Nα radius,sothat Vp ,andhencetheprotonkineticenergy,
lies close to the proton frame. Oscillations of the proton | |
are constant. The radius of the constant energy sphere
velocity imposed by the low frequency Alfvénic turbu-
correspondstothealpha-protondriftspeedandisconsis-
lence cause correlated changes in the proton speed and
tent,asdiscussedpreviously,withthephasespeedofthe
magnetic field vector, while they do not change signifi-
fluctuationsthatcanbe obtainedfromthecorrelationin
cantly the alpha speed (See Figure 2). When the local
theleftbottompanelofFigure3overthewholeinterval.
magnetic field rotates towards large θBR (right panel), The middle (a) panel of Figure 5 shows in red the tem-
protons are observed to speed up (Matteini et al. 2014), poralvariationofthenewprotonspeedVw: remarkably,
and V V . When the magnetic fluctuations are such p
that Bp ∼becαomes more radial, protons decelerate a bit it remains roughly constant over the whole duration of
the highspeed stream,consistently with the variationof
and the difference between proton and alpha speeds is the total magnetic field B (shown in blue). The pro-
maximum (middle panel). | |
ton speed profile V measured in the spacecraft frame is
p
reportedforcomparisoninthe (b)panel. Thisischarac-
2.3. Plasma properties in the frame of fluctuations
terized by large scale modulation (microstreams lasting
Keeping in mind the picture of Figure 4 and what we on the order of a day (Neugebauer et al. 1995)) and by
have discussed so far, we can now conclude our analysis. Alfvénic oscillations on the minute scale. As expected,
The shape of proton velocity in phase space shown in thelatterfluctuationsarelargerinV thaninVw. Thisis
p p
Figure3suggeststhe presenceofa particularframethat further demonstratedby the middle (c) panel, reporting
corresponds to the pivot of the protonoscillation, which
thevariationsoftheprotonspeedV V ,asmeasured
p p
canbe to afirstapproximationidentifiedby the velocity −h i
both in the spacecraft(black) and the waveframe (red).
of the alphas in the same phase space; such a frame is
The average V is taken over 20 minutes in order to
obviouslythe waveframe4 Inthis framethe electricfield h pi
remove the effects of larger scale structures. The fluc-
tuations of the proton speed are minimized when trans-
4 This is true because to the properties of the high stream se-
forming to the wave frame; in this frame the fluctua-
lectedandgenerallycommoninthefastwind. However,thesame
descriptionwillholdintheabsenceofaproton-alphadrift;weknow
that insuch a case alphas partake inwave motion as protons. In 5 ThisisvalidwithinidealMHDwhencontribution ofthe Hall
that situation, the wave frame will obviously not be identified by term is negligible, i.e. as long as the difference between the ion
any particular species and should be estimated through particle frameandthe electron (plasma)frameisconsidered small,acon-
Alfvénicmotion. ditionsatisfiedbythelowfrequencyfluctuationsinvestigatedhere.
Constant V and B in Alfvénic fluctuations 5
Figure 5. Leftpanels: Proton velocityintheestimatedframeofAlfvénicfluctuations; (top) velocitycomponents in(V⊥w,VRw),redline
corresponds to the condition |V|=const; (bottom) correlation between the angle of the magnetic field, θBR, and of the proton velocity,
θVwR;theredlinecorresponds toV=αB. Middlepanels: proton speedVp in(a)wave(red) and(b)spacecraft framesand(c)associated
variations; blue dots in the top panel refer the |B| for comparison. Right: (top) components of the motional electric field E= −V×B
estimatedintheplasmaandwave(red)frames. (bottom)Comparisonbetween|E|estimatedinspacecraft(blue),plasma(black)andwave
(red)frames.
tions become symmetric, removing the one-sided effect the residual electric field is minimum. It can be shown
observed in the spacecraft frame. that, within observationaluncertainties about the speed
of the wave frame, such an electric field is the minimum
2.4. Motional electric field: E= V B possible (e.g., Khrabrov & Sonnerup 1998), since trans-
Finally,letusconsidertheelectricfield−asso×ciatedwith forming to a different frame along B0 produces a larger
motional electric field, while a different transformation,
the fluctuations. Despite the 3Dnature ofthe variations
in B and V shown in Figure 3, the associated electric with a component orthogonal to B0, introduces a com-
ponent E =0.
field,inthefluidframe,isessentially2D.Thisisbecause k
6
the component parallel to the mean magnetic field, 3. CONCLUSION
Ek = (V δB) B0/B0 (7) Insummary,wehaveshownthatthemotionofprotons
− × · inlargeamplitudelowfrequencyAlfvénicfluctuationsin
essentially vanishes: since the electric field in the wave
the fast solar wind conserves kinetic energy in the wave
frame is close to zero, the Lorentz transformation back- frame. Thoughthismightseemanaturalconsequenceof
wards along the main field, connecting the solar wind
theequilibriumbetweenparticlesandfluctuationsinthe
plasma frame to the wave frame, does not change the
unidirectional Alfvén-like fluctuations propagating away
component along B0 (B E is Lorentz invariant), so from the sun, it is quite remarkable that this can be re-
·
Ek 0 also in plasma frame. Data confirm that Ek, covered, using in situ observations, in the complex and
∼
ascomputedfromEq. (5)andapproximativelyradial,is turbulent dynamics of the solar wind plasma, with fluc-
significantly smaller than the other electric field compo- tuationsoftheorderorlargerthan100km/s. Moreover,
nents, even though it is not exactly zero due to the level thishighlightstheneedforidentifying amechanismable
of uncertainties contained in the measurements. to drive and control such a condition, as well as under-
TherighttoppanelofFigure5displaystheothercom- standing whether this condition is set already close to
ponents ET and EN, computed from Eq. (5), in the the Sun or if it develops dynamically in the expanding
average solar wind (proton) frame Vp (black) and in solar wind.
h i
the wave frame (red). As expected the intensity of the Note that a similar description applies also to com-
electric field is significantly smaller when computed in ponents of the plasma which have not been considered
the wave frame; in that frame E should ideally vanish, here, like secondary proton beams that are ubiquitously
while here the transverse com|po|nent of E approxima- observedin the fast solar wind (e.g., Marsch et al. 1982;
tively reduces to the amplitude of Ek. The rightbottom Matteini et al. 2013). In particular, we expect that
panelshowsacomparisonof E ascomputedindifferent beams with a drift speed which is larger than the phase
| |
frames,fortheintervalC-DinFigure1. Theelectricfield speed of the turbulent fluctuations ( V ), would oscil-
A
∼
in the spacecraft frame (blue) contains the contribution lateinanti-phasewithprotons(Goldstein et al.1996). A
of the solar wind motion; this can be removed trans- simplified view of this dynamics is shown in the cartoon
forming to the average plasma (proton) frame (black), ofFigure 6, followingFigure 4, where now the smallyel-
butstillretainingthe fluctuatingcomponentofEdueto lowcircleidentifiestheprotonbeampopulation,stream-
theAlfvénicmotionofprotons. Finally,whentransform- ing at V >V (left panel).
b A
ing to the wave frame (red), the latter is removed, and If a local fluctuation is large enough to reverse the
6 Matteini et al.
radial component of the magnetic field (right panel),
the proton core-beam structure is then reversed as
well. This sketch reproduces well the dynamics ob-
served during magnetic switchbacks in the solar wind
(Neugebauer & Goldstein2012);inparticularitexplains
howduringmagneticfieldreversalscoreandbeamspeeds
areobservedto flip andwhy the rotationis not centered
on the speed of the center of mass, but rather the speed
Figure 6. Schematic description of plasma motion in Alfvénic
of alpha particles (Vα Vp +VA), resulting then in a fluctuationsasinFigure4,fordistinctprotoncoreandbeampop-
∼
significant increase of the plasma bulk speed (see figure ulations (large and small yellow circles, respectively). Left panel
2 of Neugebauer & Goldstein 2012). shows that, since the proton beam is drifting at a speed larger
A similardescriptionwouldalsoapply to the so-called thanVA,thenitoscillatesinanti-phasewiththecore. Rightpanel
showsthatinthecaseofparticularlylargeamplitudefluctuations
electron strahl population, which carries most of the so- producingareversalofthemagneticfield,thecore-beamstructure
lar wind heat flux and follows at good approximation isalsoflippedwithrespecttothealphaparticles frame.
theorientationofthelocalmagneticfield(Feldman et al. cussions with S. Landi, A. Verdini, P. Hellinger, R.
1975). We then expect that during Alfvénic oscillations Grappin, B. Goldstein, and M. Neugebauer. The re-
electronsfromthe strahlconservetheir kinetic energyin searchleadingto these results has receivedfunding from
the wave frame of fluctuations, making a rotation in ve- the UK Science and Technology Facilities Council grant
locityspacesimilarlytotheprotonbeamofFigure6,but ST/K001051/1 and the European Commission’s Sev-
with a much larger radius, owing their large drift (typi- enthFrameworkProgramme(FP7/2007-2013)underthe
cally 1000km/s VA). Confirmation of these expec- grant agreement SHOCK (project number 284515).
∼ ≫
tations will be subject of more detailed future studies
Finally,ourfindingsalsoleadtothefollowinginterpre- REFERENCES
tationabout the relative constancy ofthe magnetic field
intensityasubiquitouslymeasuredinhighlyAlfvénicso- Alexandrova, O.,Saur, J.,Lacombe,C.,Mangeney,A.,Mitchell,
lar wind streams: as discussed, under the effects of the J.,Schwartz, S.J.,&Robert, P.2009,Phys.Rev.Lett.,103,
turbulence, the plasma (protons) undergo large ampli- 165003
Barnes,A.1976,J.Geophys. Res.,81,281
tude collective oscillations. In the wave frame, the asso-
—.1981,J.Geophys.Res.,86,7498
ciatedelectricfieldiszeroandparticlesmoveonasurface
Barnes,A.,&Hollweg,J.V.1974,J.Geophys.Res.,79,2302
of constant energy. This condition on particle velocity Bavassano,B.,&Smith,E.J.1986,J.Geophys. Res.,91,1706
translates, due to the high level of Alfvénicity, i.e. cor- Belcher,J.W.,&Davis,Jr.,L.1971, J.Geophys. Res.,76,3534
relationoranti-correlationofmagneticfieldandvelocity Berger, L.,Wimmer-Schweingruber, R.F.,&Gloeckler,G.2011,
Phys.Rev.Lett.,106,151103
field fluctuations, into magnetic field fluctuations with
thesamecharacteristics,leadingtoV=αB,withαcon- Bruno,R.,Bavassano, B.,&Villante,U.1985,J.Geophys. Res.,
90,4373
stantintime;itfollowsthatthetipofthetotalmagnetic Bruno,R.,&Carbone, V.2013,LivingRev.inSolarPhys.,10,2
field vector also fluctuates on a sphere. When measur- Bruno,R.,Carbone, V.,Veltri,P.,Pietropaolo, E.,&Bavassano,
ing solar wind fluctuations in the spacecraft frame, the B.2001,Planet.SpaceSci.,49,1201
Dobrowolny,M.,Mangeney, A.,&Veltri,P.1980,83,26
conditiononparticlevelocityisnotobserveddirectlybe-
Feldman,W.C.,Asbridge,J.R.,Bame,S.J.,Montgomery,
cause kinetic energy is not invariant in the transforma- M.D.,&Gary,S.P.1975,J.Geophys. Res.,80,4181
tion,leadingrathertothesolarwindspeedprofileofFig Gershman,D.J.,etal.2012, J.Geophys. Res.,117,0
1. Onthe otherhandthe magnetic field, whichis invari- Goldstein,B.E.,etal.1996,A&A,316,296
antforGalileantransformations,maintainsthesignature Goldstein,M.L.,Klimas,A.J.,&Barish,F.D.1974,inSolar
B =const, as observed. WindThree, ed.C.T.Russell,385–387
| | Gosling,J.T.,McComas,D.J.,Roberts,D.A.,&Skoug, R.M.
Notethatthe datausedinthiswork,measurementsof 2009,ApJLett.,695,L213
the fast wind at 0.3 AU, are appropriate to emphasize Khrabrov, A.V.,&Sonnerup, B.U.Ö.1998,ISSIScientific
these effects, since the amplitude ofvelocityfluctuations Reports Series,1,221
scales, according to WKB, approximatively as Leamon,R.J.,Smith,C.W.,Ness,N.F.,&Wong, H.K.1999,
J.Geophys. Res.,104,22331
δV δB/B V =R0.5 R−1 =R−0.5 (8) Marsch,E.,Rosenbauer, H.,Schwenn, R.,Muehlhaeuser, K.-H.,
∝ · A · &Denskat,K.U.1981,J.Geophys. Res.,86,9199
Marsch,E.,Schwenn, R.,Rosenbauer, H.,Muehlhaeuser, K.-H.,
andis largercloserto the Sun; howeverwe havechecked
Pilipp,W.,&Neubauer, F.M.1982,J.Geophys. Res.,87,52
that the same behavior is observed in other high speed
Marsch,E.,&Verscharen, D.2011,J.PlasmaPhys.,77,385
streams at various distances. Further confirmation of Matteini,L.,Hellinger,P.,Goldstein,B.E.,Landi,S.,Velli,M.,
our findings will be possible thanks to the forthcoming &Neugebauer, M.2013,J.Geophys. Res.,118,2771
missions, Solar Orbiter and Solar Probe Plus, that will Matteini,L.,Horbury, T.S.,Neugebauer, M.,&Goldstein,B.E.
2014,Geophys. Res.Lett.,41,259
explore the internal heliosphere. Our results also imply
Neugebauer, M.,&Goldstein,B.E.2012,inProc.ofthe
that Alfvénic turbulence could lead to an enhancement
Thirteenth International SolarWindConference, American
ofradialvelocityfluctuations,uptooroftheorderofthe Institute ofPhysicsConference Series
averagewindspeed,astheabsolutemaximumoffluctua- Neugebauer, M.,Goldstein,B.E.,McComas,D.J.,Suess,S.T.,
tionamplitudeisreachedinsideoraroundtheAlfvénra- &Balogh,A.1995,J.Geophys.Res.,100,23389
Smith,E.J.,Balogh,A.,Neugebauer, M.,&McComas,D.1995,
dius,wherethesolarwindacceleratesbeyondtheAlfvén
Geophys. Res.Lett.,22,3381
speed.
Thieme,K.M.,Schwenn, R.,&Marsch,E.1989,Adv.Space
Res.,9,127
Webb,G.M.,Hu,Q.,Dasgupta,B.,Roberts,D.A.,&Zank,
Authorsacknowledgeverystimulatingandhelpfuldis- G.P.2010,ApJ,725,2128