Table Of ContentAstronomy & Astrophysics manuscript no. AA˙2005˙4229 (cid:13)c ESO 2008
February 5, 2008
Comment on ”PIC simulations of circularly polarised Alfv´en
wave phase mixing: A new mechanism for electron acceleration
in collisionless plasmas” by Tsiklauri et al.
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F. Mottez , V. G´enot , and P. Louarn
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J 1 Centre d’´etudedes EnvironnementsTerrestre et Plan´etaires, 10-12 Av.de l’Europe, 78140 V´elizy, France;
Now at LUTH,Observatoire de Paris, 5 place Jules Janssen, 92195 Meudon, France.
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2 Centre d’EtudeSpatiale des Rayonnements,9 Av.Colonel Roche, 31400 Toulouse, France.
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1 Received September20, 2005; accepted November18, 2005
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6 ABSTRACT
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Tsiklauri et al. recently published a theoretical model of electron acceleration by Alfv´en waves in a nonuniform collisionless
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plasmas. We compare their work with a series of results published earlier by an another team, of which Tsiklauri et al. were
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probably unaware. Weshow that thesetwo series of works, apparently conductedindependently,lead to thesame conclusions.
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This reinforces thetheoretical consistency of the model.
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Key words. Sun: oscillations – Sun: Corona – Sun: solar wind – Physical data and processes: Plasma – Physical data and
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processes: Acceleration of particles
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s Two recent papers published by Tsiklauri et al. G´enot et al. investigated the acceleration of electrons
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(2005b,a), based on kinetic numerical simulations, show in the Earth’s aurora. Following in-situ exploration by
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v amechanismofastrophysicalrelevancethatcouldexplain satellites, the well-constrained observations make this re-
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X the acceleration of electrons in a magnetized collisionless gion appropriate for the testing of theoretical models.
plasma. G´enot et al. chose a plasma with a high magnetic field,
r
a given by a ratio of the electron cyclotron to the electron
The idea is the following : Alfv´en waves (AW) are of- plasma period ω /ω =4, as in the Earth auroral zone.
ce pe
ten observed or inferred in astrophysical plasmas ; it has Because plasma cavities are observed in connexion with
been theoretically demonstrated that they could be the electron acceleration and plasma turbulence, the gradi-
sourceofplasmaacceleration.Inparallelpropagation(i.e. ents delimit a density depletion. Tsiklauri et al. (2005a)
with a wave vector aligned with the local magnetic field) refer to electron acceleration in solar open coronal struc-
anAWcarriesnoparallelelectricfield,andthereforecan- tures, the magnetic field is weaker ω /ω = 1 and they
ce pe
not accelerate particles in that direction. However when consider a density bump (expected, for instance, at the
the wave is structured in the perpendicular direction, i.e. boundary of a coronal loop).
whenk⊥ 6=0andsufficientlylarge,theAWacquiresasig-
nificantparallelelectricfieldcomponent.ObliqueAWcan
form when an initially parallel AW propagates in regions Do the two works explore fundamentaly different
with perpendicular Alfven velocity (or density)gradients. regimes ? Goertz (1984), using the Maxwell-Vlasov equa-
Such a situation leads to a distortion of the wavefronts: tions, performed a linear study of the oblique AW prop-
smallperpendicular lengthscalesareformedandfinallya agation. He showed that the value of the parallel electric
parallel electric field component appears. fielddependsonthedimensionlessparameterr=βmi/me
with respect to one. (β = 2µ0p/B2 is the ratio of the
Although not new as claimed by the authors, this kinetic plasma pressure to the magnetic pressure, and
mechanism is, in our opinion, interesting. In this com- m /m is the ion to electron mass ratio.) In G´enot et al.
i e
ment, the results exposed by Tsiklauri et al. (2005a) are m /m = 100, β ∼ 800−1 and r = 0.125. In Tsiklauri et
i e
briefly discussed and compared with other works on the al. m /m = 16, β ∼ 50−1 and r = 0.32. All the pub-
i e
same subject published earlier by G´enot et al. (1999); lications discussed in this comment deal with the same
G´enot et al. (2000, 2001, 2004). regime, r <1, the inertial AW regime.
2 Mottez et al.: Comment on ”PIC simulations of cicrularly...”
G´enot et al. (1999) made a linear study of the wave have been extensively studied (G´enot et al. 2001, 2004).
propagation in a transverse gradient (for r < 1), and They are the consequence of the nonlinear interaction of
showed that to create a parallel electric field, the char- the beams of accelerated electrons and current densities
acteristic size of the gradient must be of the order of the with the bulk of the plasma (beam-plasma and Buneman
electroninertiallengthc/ω .Thesimulationscarriedout instabilities). These spikes have the same characteristics
pe
byTsiklaurietal.andbyG´enotetal.areallinthisregime; as those observed near the plasma cavities by auroral
this allows for almost direct comparisons. satellites. If this process is indeed correctly understood,
Tsiklauri et al. (2005b) compare their results to those they are a consequence, and not the cause of the electron
ofHasegawa & Chen(1975,1976).Manyconclusionsseem acceleration (G´enot et al. 2004).
to agree,and we expect that the differences (appart from As the magnetic field is lower in the simulations con-
non homogeneity, not treated by Hasegawa and Chen) ducted by Tsiklauri et al., the Alfv´en wave velocity is
are due to the parameter r that is greater than one in smaller, closer to the electron thermal velocity, and it is
Hasegawa & Chen (1975, 1976). When r >1, the charac- possible that resonnant effects are more important in the
teristic transverselength is not c/ω but the ion Larmor wave particle interaction.
pe
radius. In spite of some minor differences of regime and mi-
The PIC simulation codes used by G´enot et al. and nor divergencesin the interpretationof the simulationre-
Tsiklauri et al. are slightly different. In Tsiklauri et al. sults, the rediscovery of the acceleration process initially
(2005b,a), the code describes the full dynamics of the proposed by G´enot et al. and the similarity of the most
electrons, and requires a small time step (a run re- important results strenghtens the theoretical relevance of
quires8days).InG´enot et al.(2000);G´enot et al.(2001); this model.
G´enot et al. (2001, 2004), the code describes the guiding
centre dynamics of the electrons, and if ω /ω > 1, it
ce pe References
allows for larger time steps. A simulation typically lasts
10 hours. G´enot, V., Louarn, P., & Mottez, F. 2000, J. Geophys.
The initial conditions are very similar in Res., 105, 27611
Tsiklauri et al. (2005a) and G´enot et al. (1999) : a G´enot, V., Louarn, P., & Mottez, F. 2001, J. Geophys.
localperturbationispropagatedbyparallelAlfv´enwaves. Res., 106, 29633
Tsiklauri et al. show that the AW propagation in their G´enot, V., Louarn, P., & Mottez, F. 2004, Annales
kinetic simulation is like in MHD. In the other works Geophysicae, 6, 2081
conducted by G´enot et al. (2000); G´enot et al. (2001); G´enot, V., Louarn, P., & Le Qu´eau, D. 1999, Journal of
G´enot et al. (2004), the simulations are initialised with Geophysical Research (Space Physics), 104, 22649
bi-fluid (therefore almost MHD) Alfv´en waves filling the G´enot, V., Mottez, F., & Louarn, P. 2001, Physics and
whole simulation domain. The kink in the ion velocities, Chemistry of the Earth C, 26, 219
observedby Tsiklauriet al. is set initially by G´enotet al. Goertz,C.K.1984,PlanetaryandSpaceScience,32,1387
Such an initialization allows one to control the direction Hasegawa, A. & Chen, L. 1975, Physical Review Letters,
of propagation of the wave. G´enot et al. (2000) could 35, 370
showthattheelectronaccelerationoccursmostefficiently Hasegawa,A.&Chen,L.1976,PhysicsofFluids,19,1924
in the direction of propagation of the AW; the bulk Tsiklauri, D., Sakai, J.-I., & Saito, S. 2005a, A&A, 435,
velocity is translated in the direction of propagation of 1105
the wave. But some electrons are (much less) accelerated Tsiklauri,D., Sakai,J.-I.,&Saito,S. 2005b,New Journal
in the reverse direction. As the Alfv´en velocity is, in our of Physics, 7, 79
regime, much faster than the electron thermal velocity,
weconsiderthattheaccelerationprocessisnon-resonnant
(andthereforenotaLandauprocess),evenifsecond-order
resonance effects give more efficient acceleration in the
direction of the wave (G´enot et al. 2001).
The parallel electric field (G´enot et al. 2000;
G´enot et al. 2001; G´enot et al. 2004) shows a spiky
structuresuperimposedonasmoothandlessintenseelec-
tric field. The smoothelectricfield is createdin the linear
phase of the AW dissipation process (G´enot et al. 1999),
as can be seen in simulations (G´enot et al. 2001). As this
field exists over large distances along the magnetic field,
it has a high potential for accelerating electrons. Then,
when the acceleration begins, many strong and localized
quasi-electrostatic high amplitude spikes develop. These
spikes are probably the structures seen on the E dis-
x
playedinTsiklauri et al.(2005a).Theirnatureandorigin
