Tsiklauri et al. recently published a theoretical model of electron
acceleration by Alfv\'en waves in a nonuniform collisionless plasmas. We
compare their work with a series of results published earlier by an another
team, of which Tsiklauri et al. were probably unaware. We show that these two
series of works, apparently conducted independently, lead to the same
conclusions. This reinforces the theoretical consistency of the model.Comment: 2 pages. Accepted at "Astronomy and Astrophysics

F. Mottez

Goertz

Génot

Hasegawa

P. Louarn

Tsiklauri

V. Génot

English

arXiv

2 pages. Accepted at "Astronomy and Astrophysics".International audienceTsiklauri et al. recently published a theoretical model of electron acceleration by Alfvén waves in a nonuniform collisionless plasmas. We compare their work with a series of results published earlier by an another team, of which Tsiklauri et al. were probably unaware. We show that these two series of works, apparently conducted independently, lead to the same conclusions. This reinforces the theoretical consistency of the model

Mottez, Fabrice

Génot, Vincent

Louarn, Philippe

HAL-INSU

Comment on ’PIC simulations of circularly polarisedAlfve´n wave phase mixing: A new mechanism forelectron acceleration in collisionless plasmas’ byTsiklauri et al.Fabrice Mottez, Vincent Ge´not, Philippe LouarnTo cite this version:Fabrice Mottez, Vincent Ge´not, Philippe Louarn. Comment on ’PIC simulations of circularlypolarised Alfve´n wave phase mixing: A new mechanism for electron acceleration in collisionlessplasmas’ by Tsiklauri et al.. 2 pages. Accepted at ”Astronomy and Astrophysics”. 2006.<hal-00017333>HAL Id: hal-00017333https://hal.archives-ouvertes.fr/hal-00017333Submitted on 19 Jan 2006HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.ccsd-00017333, version 1 - 19 Jan 2006Astronomy & Astrophysics manuscript no. AA˙2005˙4229 c© ESO 2006January 19, 2006Comment on ”PIC simulations of circularly polarised Alfve´nwave phase mixing: A new mechanism for electron accelerationin collisionless plasmas” by Tsiklauri et al.F. Mottez1, V. Ge´not2, and P. Louarn21 Centre d’e´tude des Environnements Terrestre et Plane´taires, 10-12 Av. de l’Europe, 78140 Ve´lizy, France;Now at LUTH, Observatoire de Paris, 5 place Jules Janssen, 92195 Meudon, France.2 Centre d’Etude Spatiale des Rayonnements, 9 Av. Colonel Roche, 31400 Toulouse, France.Received September 20, 2005; accepted November 18, 2005ABSTRACTTsiklauri et al. recently published a theoretical model of electron acceleration by Alfve´n waves in a nonuniform collisionlessplasmas. We compare their work with a series of results published earlier by an another team, of which Tsiklauri et al. wereprobably unaware. We show that these two series of works, apparently conducted independently, lead to the same conclusions.This reinforces the theoretical consistency of the model.Key words. Sun: oscillations – Sun: Corona – Sun: solar wind – Physical data and processes: Plasma – Physical data andprocesses: Acceleration of particlesTwo recent papers published by Tsiklauri et al.(2005b,a), based on kinetic numerical simulations, showa mechanism of astrophysical relevance that could explainthe acceleration of electrons in a magnetized collisionlessplasma.The idea is the following : Alfve´n waves (AW) are of-ten observed or inferred in astrophysical plasmas ; it hasbeen theoretically demonstrated that they could be thesource of plasma acceleration. In parallel propagation (i.e.with a wave vector aligned with the local magnetic field)an AW carries no parallel electric field, and therefore can-not accelerate particles in that direction. However whenthe wave is structured in the perpendicular direction, i.e.when k⊥ 6= 0 and sufficiently large, the AW acquires a sig-nificant parallel electric field component. Oblique AW canform when an initially parallel AW propagates in regionswith perpendicular Alfven velocity (or density) gradients.Such a situation leads to a distortion of the wavefronts:small perpendicular length scales are formed and finally aparallel electric field component appears.Although not new as claimed by the authors, thismechanism is, in our opinion, interesting. In this comment,the results exposed by Tsiklauri et al. (2005a) are brieflydiscussed and compared with other works on the samesubject published earlier by Ge´not et al. (1999); Ge´notet al. (2000, 2001, 2004).Ge´not et al. investigated the acceleration of electronsin the Earth’s aurora. Following in-situ exploration bysatellites, the well-constrained observations make this re-gion appropriate for the testing of theoretical models.Ge´not et al. chose a plasma with a high magnetic field,given by a ratio of the electron cyclotron to the electronplasma period ωce/ωpe = 4, as in the Earth auroral zone.Because plasma cavities are observed in connexion withelectron acceleration and plasma turbulence, the gradi-ents delimit a density depletion. Tsiklauri et al. (2005a)refer to electron acceleration in solar open coronal struc-tures, the magnetic field is weaker ωce/ωpe = 1 and theyconsider a density bump (expected, for instance, at theboundary of a coronal loop).Do the two works explore fundamentaly differentregimes ? Goertz (1984), using the Maxwell-Vlasov equa-tions, performed a linear study of the oblique AW prop-agation. He showed that the value of the parallel electricfield depends on the dimensionless parameter r = βmi/mewith respect to one. (β = 2µ0p/B2 is the ratio of thekinetic plasma pressure to the magnetic pressure, andmi/me is the ion to electron mass ratio.) In Ge´not et al.mi/me = 100, β ∼ 800−1 and r = 0.125. In Tsiklauri etal. mi/me = 16, β ∼ 50−1 and r = 0.32. All the pub-lications discussed in this comment deal with the sameregime, r < 1, the inertial AW regime.2 Mottez et al.: Comment on ”PIC simulations of cicrularly...”Ge´not et al. (1999) made a linear study of the wavepropagation in a transverse gradient (for r < 1), andshowed that to create a parallel electric field, the char-acteristic size of the gradient must be of the order of theelectron inertial length c/ωpe. The simulations carried outby Tsiklauri et al. and by Ge´not et al. are all in this regime;this allows for almost direct comparisons.Tsiklauri et al. (2005b) compare their results to thoseof Hasegawa & Chen (1975, 1976). Many conclusions seemto agree, and we expect that the differences (appart fromnon homogeneity, not treated by Hasegawa and Chen)are due to the parameter r that is greater than one inHasegawa & Chen (1975, 1976). When r > 1, the charac-teristic transverse length is not c/ωpe but the ion Larmorradius.The PIC simulation codes used by Ge´not et al. andTsiklauri et al. are slightly different. In Tsiklauri et al.(2005b,a), the code describes the full dynamics of the elec-trons, and requires a small time step (a run requires 8days). In Ge´not et al. (2000); Ge´not et al. (2001); Ge´notet al. (2001, 2004), the code describes the guiding centredynamics of the electrons, and if ωce/ωpe > 1, it allows forlarger time steps. A simulation typically lasts 10 hours.The initial conditions are very similar in Tsiklauri et al.(2005a) and Ge´not et al. (1999) : a local perturbationis propagated by parallel Alfve´n waves. Tsiklauri et al.show that the AW propagation in their kinetic simulationis like in MHD. In the other works conducted by Ge´notet al. (2000); Ge´not et al. (2001); Ge´not et al. (2004), thesimulations are initialised with bi-fluid (therefore almostMHD) Alfve´n waves filling the whole simulation domain.The kink in the ion velocities, observed by Tsiklauri et al.is set initially by Ge´not et al. Such an initialization allowsone to control the direction of propagation of the wave.Ge´not et al. (2000) could show that the electron accelera-tion occurs most efficiently in the direction of propagationof the AW; the bulk velocity is translated in the directionof propagation of the wave. But some electrons are (muchless) accelerated in the reverse direction. As the Alfve´n ve-locity is, in our regime, much faster than the electron ther-mal velocity, we consider that the acceleration process isnon-resonnant (and therefore not a Landau process), evenif second-order resonance effects give more efficient accel-eration in the direction of the wave (Ge´not et al. 2001).The parallel electric field (Ge´not et al. 2000; Ge´notet al. 2001; Ge´not et al. 2004) shows a spiky structuresuperimposed on a smooth and less intense electric field.The smooth electric field is created in the linear phase ofthe AW dissipation process (Ge´not et al. 1999), as canbe seen in simulations (Ge´not et al. 2001). As this fieldexists over large distances along the magnetic field, it hasa high potential for accelerating electrons. Then, whenthe acceleration begins, many strong and localized quasi-electrostatic high amplitude spikes develop. These spikesare probably the structures seen on the Ex displayed inTsiklauri et al. (2005a). Their nature and origin have beenextensively studied (Ge´not et al. 2001, 2004). They are theconsequence of the nonlinear interaction of the beams ofaccelerated electrons and current densities with the bulkof the plasma (beam-plasma and Buneman instabilities).These spikes have the same characteristics as those ob-served near the plasma cavities by auroral satellites. Ifthis process is indeed correctly understood, they are aconsequence, and not the cause of the electron acceler-ation (Ge´not et al. 2004).As the magnetic field is lower in the simulations con-ducted by Tsiklauri et al., the Alfve´n wave velocity issmaller, closer to the electron thermal velocity, and it ispossible that resonnant effects are more important in thewave particle interaction.In spite of some minor differences of regime and mi-nor divergences in the interpretation of the simulation re-sults, the rediscovery of the acceleration process initiallyproposed by Ge´not et al. and the similarity of the mostimportant results strenghtens the theoretical relevance ofthis model.ReferencesGe´not, V., Louarn, P., & Mottez, F. 2000, J. Geophys.Res., 105, 27611Ge´not, V., Louarn, P., & Mottez, F. 2001, J. Geophys.Res., 106, 29633Ge´not, V., Louarn, P., & Mottez, F. 2004, AnnalesGeophysicae, 6, 2081Ge´not, V., Louarn, P., & Le Que´au, D. 1999, Journal ofGeophysical Research (Space Physics), 104, 22649Ge´not, V., Mottez, F., & Louarn, P. 2001, Physics andChemistry of the Earth C, 26, 219Goertz, C. K. 1984, Planetary and Space Science, 32, 1387Hasegawa, A. & Chen, L. 1975, Physical Review Letters,35, 370Hasegawa, A. & Chen, L. 1976, Physics of Fluids, 19, 1924Tsiklauri, D., Sakai, J.-I., & Saito, S. 2005a, A&A, 435,1105Tsiklauri, D., Sakai, J.-I., & Saito, S. 2005b, New Journalof Physics, 7, 79

Comment on 'PIC simulations of circularly polarised Alfvén wave phase mixing: A new mechanism for electron acceleration in collisionless plasmas' by Tsiklauri et al.

Hal-Diderot

Comment on ’PIC simulations of circularly polarised
Alfve´n wave phase mixing: A new mechanism for
electron acceleration in collisionless plasmas’ by
Tsiklauri et al.
Fabrice Mottez, Vincent Ge´not, Philippe Louarn
To cite this version:
Fabrice Mottez, Vincent Ge´not, Philippe Louarn. Comment on ’PIC simulations of circularly
polarised Alfve´n wave phase mixing: A new mechanism for electron acceleration in collisionless
plasmas’ by Tsiklauri et al.. 2 pages. Accepted at ”Astronomy and Astrophysics”. 2006.
<hal-00017333>
HAL Id: hal-00017333
https://hal.archives-ouvertes.fr/hal-00017333
Submitted on 19 Jan 2006
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destine´e au de´poˆt et a` la diffusion de documents
scientifiques de niveau recherche, publie´s ou non,
e´manant des e´tablissements d’enseignement et de
recherche franc¸ais ou e´trangers, des laboratoires
publics ou prive´s.

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Astronomy & Astrophysics manuscript no. AA˙2005˙4229 c© ESO 2006
January 19, 2006
Comment on ”PIC simulations of circularly polarised Alfve´n
wave phase mixing: A new mechanism for electron acceleration
in collisionless plasmas” by Tsiklauri et al.
F. Mottez1, V. Ge´not2, and P. Louarn2
1 Centre d’e´tude des Environnements Terrestre et Plane´taires, 10-12 Av. de l’Europe, 78140 Ve´lizy, France;
Now at LUTH, Observatoire de Paris, 5 place Jules Janssen, 92195 Meudon, France.
2 Centre d’Etude Spatiale des Rayonnements, 9 Av. Colonel Roche, 31400 Toulouse, France.
Received September 20, 2005; accepted November 18, 2005
ABSTRACT
Tsiklauri et al. recently published a theoretical model of electron acceleration by Alfve´n waves in a nonuniform collisionless
plasmas. We compare their work with a series of results published earlier by an another team, of which Tsiklauri et al. were
probably unaware. We show that these two series of works, apparently conducted independently, lead to the same conclusions.
This reinforces the theoretical consistency of the model.
Key words. Sun: oscillations – Sun: Corona – Sun: solar wind – Physical data and processes: Plasma – Physical data and
processes: Acceleration of particles
Two recent papers published by Tsiklauri et al.
(2005b,a), based on kinetic numerical simulations, show
a mechanism of astrophysical relevance that could explain
the acceleration of electrons in a magnetized collisionless
plasma.
The idea is the following : Alfve´n waves (AW) are of-
ten observed or inferred in astrophysical plasmas ; it has
been theoretically demonstrated that they could be the
source of plasma acceleration. In parallel propagation (i.e.
with a wave vector aligned with the local magnetic field)
an AW carries no parallel electric field, and therefore can-
not accelerate particles in that direction. However when
the wave is structured in the perpendicular direction, i.e.
when k⊥ 6= 0 and sufficiently large, the AW acquires a sig-
nificant parallel electric field component. Oblique AW can
form when an initially parallel AW propagates in regions
with perpendicular Alfven velocity (or density) gradients.
Such a situation leads to a distortion of the wavefronts:
small perpendicular length scales are formed and finally a
parallel electric field component appears.
Although not new as claimed by the authors, this
mechanism is, in our opinion, interesting. In this comment,
the results exposed by Tsiklauri et al. (2005a) are briefly
discussed and compared with other works on the same
subject published earlier by Ge´not et al. (1999); Ge´not
et al. (2000, 2001, 2004).
Ge´not et al. investigated the acceleration of electrons
in the Earth’s aurora. Following in-situ exploration by
satellites, the well-constrained observations make this re-
gion appropriate for the testing of theoretical models.
Ge´not et al. chose a plasma with a high magnetic field,
given by a ratio of the electron cyclotron to the electron
plasma period ωce/ωpe = 4, as in the Earth auroral zone.
Because plasma cavities are observed in connexion with
electron acceleration and plasma turbulence, the gradi-
ents delimit a density depletion. Tsiklauri et al. (2005a)
refer to electron acceleration in solar open coronal struc-
tures, the magnetic field is weaker ωce/ωpe = 1 and they
consider a density bump (expected, for instance, at the
boundary of a coronal loop).
Do the two works explore fundamentaly different
regimes ? Goertz (1984), using the Maxwell-Vlasov equa-
tions, performed a linear study of the oblique AW prop-
agation. He showed that the value of the parallel electric
field depends on the dimensionless parameter r = βmi/me
with respect to one. (β = 2µ0p/B
2 is the ratio of the
kinetic plasma pressure to the magnetic pressure, and
mi/me is the ion to electron mass ratio.) In Ge´not et al.
mi/me = 100, β ∼ 800
−1 and r = 0.125. In Tsiklauri et
al. mi/me = 16, β ∼ 50
−1 and r = 0.32. All the pub-
lications discussed in this comment deal with the same
regime, r < 1, the inertial AW regime.
2 Mottez et al.: Comment on ”PIC simulations of cicrularly...”
Ge´not et al. (1999) made a linear study of the wave
propagation in a transverse gradient (for r < 1), and
showed that to create a parallel electric field, the char-
acteristic size of the gradient must be of the order of the
electron inertial length c/ωpe. The simulations carried out
by Tsiklauri et al. and by Ge´not et al. are all in this regime;
this allows for almost direct comparisons.
Tsiklauri et al. (2005b) compare their results to those
of Hasegawa & Chen (1975, 1976). Many conclusions seem
to agree, and we expect that the differences (appart from
non homogeneity, not treated by Hasegawa and Chen)
are due to the parameter r that is greater than one in
Hasegawa & Chen (1975, 1976). When r > 1, the charac-
teristic transverse length is not c/ωpe but the ion Larmor
radius.
The PIC simulation codes used by Ge´not et al. and
Tsiklauri et al. are slightly different. In Tsiklauri et al.
(2005b,a), the code describes the full dynamics of the elec-
trons, and requires a small time step (a run requires 8
days). In Ge´not et al. (2000); Ge´not et al. (2001); Ge´not
et al. (2001, 2004), the code describes the guiding centre
dynamics of the electrons, and if ωce/ωpe > 1, it allows for
larger time steps. A simulation typically lasts 10 hours.
The initial conditions are very similar in Tsiklauri et al.
(2005a) and Ge´not et al. (1999) : a local perturbation
is propagated by parallel Alfve´n waves. Tsiklauri et al.
show that the AW propagation in their kinetic simulation
is like in MHD. In the other works conducted by Ge´not
et al. (2000); Ge´not et al. (2001); Ge´not et al. (2004), the
simulations are initialised with bi-fluid (therefore almost
MHD) Alfve´n waves filling the whole simulation domain.
The kink in the ion velocities, observed by Tsiklauri et al.
is set initially by Ge´not et al. Such an initialization allows
one to control the direction of propagation of the wave.
Ge´not et al. (2000) could show that the electron accelera-
tion occurs most efficiently in the direction of propagation
of the AW; the bulk velocity is translated in the direction
of propagation of the wave. But some electrons are (much
less) accelerated in the reverse direction. As the Alfve´n ve-
locity is, in our regime, much faster than the electron ther-
mal velocity, we consider that the acceleration process is
non-resonnant (and therefore not a Landau process), even
if second-order resonance effects give more efficient accel-
eration in the direction of the wave (Ge´not et al. 2001).
The parallel electric field (Ge´not et al. 2000; Ge´not
et al. 2001; Ge´not et al. 2004) shows a spiky structure
superimposed on a smooth and less intense electric field.
The smooth electric field is created in the linear phase of
the AW dissipation process (Ge´not et al. 1999), as can
be seen in simulations (Ge´not 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 Ex displayed in
Tsiklauri et al. (2005a). Their nature and origin have been
extensively studied (Ge´not et al. 2001, 2004). They are the
consequence of the nonlinear interaction of the beams of
accelerated electrons and current densities with the bulk
of the plasma (beam-plasma and Buneman instabilities).
These spikes have the same characteristics as those ob-
served near the plasma cavities by auroral satellites. If
this process is indeed correctly understood, they are a
consequence, and not the cause of the electron acceler-
ation (Ge´not et al. 2004).
As the magnetic field is lower in the simulations con-
ducted by Tsiklauri et al., the Alfve´n wave velocity is
smaller, closer to the electron thermal velocity, and it is
possible that resonnant effects are more important in the
wave particle interaction.
In spite of some minor differences of regime and mi-
nor divergences in the interpretation of the simulation re-
sults, the rediscovery of the acceleration process initially
proposed by Ge´not et al. and the similarity of the most
important results strenghtens the theoretical relevance of
this model.
References
Ge´not, V., Louarn, P., & Mottez, F. 2000, J. Geophys.
Res., 105, 27611
Ge´not, V., Louarn, P., & Mottez, F. 2001, J. Geophys.
Res., 106, 29633
Ge´not, V., Louarn, P., & Mottez, F. 2004, Annales
Geophysicae, 6, 2081
Ge´not, V., Louarn, P., & Le Que´au, D. 1999, Journal of
Geophysical Research (Space Physics), 104, 22649
Ge´not, V., Mottez, F., & Louarn, P. 2001, Physics and
Chemistry of the Earth C, 26, 219
Goertz, C. K. 1984, Planetary and Space Science, 32, 1387
Hasegawa, A. & Chen, L. 1975, Physical Review Letters,
35, 370
Hasegawa, A. & Chen, L. 1976, Physics of Fluids, 19, 1924
Tsiklauri, D., Sakai, J.-I., & Saito, S. 2005a, A&A, 435,
1105
Tsiklauri, D., Sakai, J.-I., & Saito, S. 2005b, New Journal
of Physics, 7, 79


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Comment on “PIC simulations of circularly polarised Alfvén wave phase mixing: 
a new mechanism for electron acceleration in collisionless plasmas” by Tsiklauri et al.

Tsiklauri et al. recently published a theoretical model of electron acceleration by Alfvén waves 
in a nonuniform collisionless plasmas. We compare their work with a series of results published earlier 
by an another team, of which Tsiklauri et al. were probably unaware.
We show that these two series of works, apparently conducted independently, lead 
to the same conclusions. This reinforces the theoretical consistency of the model

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