Team 81
The effect of ULF turbulence and flow chaotization
on plasma energy and mass transfer at the
magnetopause
Scientific rationale
The penetration of solar wind matter and energy inside the planetary magnetospheres is one of the major issues of magnetospheric physics. The physical mechanisms that are underlying this penetration are still not understood, even if there is some consensus that they certainly imply diffusion and, even more probably, some form of magnetic reconnection. The same physics, that we intend to elucidate, is likely to occur at many places in astrophysics and in laboratory, whenever two plasmas are converging, each of them bringing a magnetic field of different origin: ideal MHD would predict imperviousness, while a small rate of penetration of one plasma in the other can be allowed only through small scale phenomena.
The present build up in multi-spacecraft
data in the terrestrial environment, especially from the Cluster mission, in
parallel with recent pertinent insights in theory and modeling of magnetized
plasmas, makes timely the present proposal. We intend to gather in the ISSI
site, for the first time, some of the best specialists of spacecraft data
analysis (Cluster but also older missions as Interball), together with the specialists of theory and
simulation who work on the basic physical phenomena at play. This meeting is
expected to trigger pivotal progresses and a qualitative increase in our
understanding of the subject. Its results should be also important for defining
the future space
missions focused on micro scale phenomena.
As indicated in the title, the central goal of this proposal is to understand the role of waves and turbulence for creating the small scales necessary for the particle penetration through a magnetic barrier (whatever the mechanism, diffusion or reconnection). For developing this main topic, three sub-subjects can be distinguished and investigated from the data: 1) the creation of small scales by a non linear cascade from the large amount of magnetic energy which is indeed observed in the ULF range in the magnetosheath, upstream of the magnetopause; 2) the chaotization of the magnetosheath flow 3) the role of the coherent structures in these processes, especially the filamentation of Alfvén waves and their dissipation via their interaction with density gradients. Hereafter each of these three subjects is briefly presented.
ULF
turbulence and cascade toward small scales
The intense
ULF magnetic turbulence observed in the magnetosheath doubtless plays an
important role in the transfers between the solar wind and the magnetosphere
[Belmont et al., 2005]. Nevertheless, this large energy, which is mainly
observed at large scale, is not directly efficient to allow for mass and energy
transfers toward the magnetosphere since these transfers demand very short
scales, of the order of the electron ones (inertial length/ Larmor radius) whenever magnetic reconfiguration must be
implied. The guiding line of the proposed study consists in determining first
what is the nature of the main large scale fluctuations
and then how this energy cascades from large to small scales, and what are the
propagation modes mediating these transfers. It is worth noticing that the small
scales, once created, can cause reconnection phenomena and therefore plasma
transfers through the boundary when they impinge the magnetopause, without any
need of local instabilities (e.g. tearing), contrary to all the classical
scenarios proposed hitherto. The transfer from large to small scales can be due
to non linear couplings between the magnetosheath modes directly in this
upstream region [Sahraoui et al., 2003a, 2004, 2005, Walker et al., 2004] or
they can be due to the interaction of these modes with the magnetopause boundary
[Belmont and Rezeau, 2001]. Experimental tests have to be found to decide
between these different hypotheses, which can also be
complementary.
The 4-point
measurements of the Cluster mission now allows a much
better determination of the magnetosheath turbulence characteristics. The
k-filtering technique, which is a new signal processing tool that has been
designed and developed with this aim, provides a 3-D spectrum in the wave-vector
space for each temporal frequency. By this way, one is now able to determine the
magnetic energy distribution in the (w,k) space. The location of the energy maxima so
obtained can be compared with the theoretical dispersions of the LF linear modes
existing in this high beta plasma (including the non
propagating "mirror mode"). On the few cases studies made up to now, it can be
shown that 1) the Doppler shifts are of primary importance in the spectrum, and
2) the linear modes are well retrieved, which seems in favour of a “weak
turbulence” approach, the role of well organized structures being not
determining.
Such a weak
turbulence theory still remains to be developed, taking all the experimental
results into account and continuing the initial contribution of Sahraoui et al.
[2003b], who introduced the necessary canonical Hamiltonian description of
Hall-MHD. Models at least as complete as Hall-MHD are
indeed necessary since the compressibility cannot be ignored (not only shear
Alfven waves) and since the frequency limit of the
ideal MHD (frequency much less than the ion gyrofrequency) is not valid on the whole spectrum.
Nevertheless, the “kinetic equation of waves” remains to be established, and its
stationary solutions, possibly of the “Kolmogorov-Zakharov” form, remains
to be determined. Furthermore, some kinetic effects will have to be introduced
since they are at the origin of the mirror mode which is dominant in the
b>1 cases that have been observed
in the first studies, and to introduce realistic dissipation phenomena. A lack
of theory has been recognized for several years which prevents significant progresses to be made in this field;
gathering theoreticians and experimentalists in the Team should favour such
in-depth developments.
From the
experimental point of view, three mains goals should be pursued: 1) reach a
statistical view of the large scale modes in the magnetosheath, to go beyond the
few existing case studies which have evidenced mirror modes; 2) investigate as
much as possible the cascade of energy and determine on which modes it is
transferred to short wavelengths (in the limit of the 100 km wavelength which is
the minimum spacecraft separation of Cluster) and the corresponding scaling law;
3) experimentally compare the preceding “body cascade” with the “surface
cascade” which corresponds to the interaction of the magnetosheath waves with
the magnetopause density gradient.
Plasma
jetting and flow chaotization
The
experimental investigation of case studies has highlighted the fundamental role
of a nonlinear decay of the flow disturbances into jets in the high latitude MP.
In this region, the cusp vicinity, where the plasma beta is high, the flow
disturbances appear to produce both accelerated jets -till magnetosonic (MS) speed-, and decelerated Alfvenic flows (Savin et al.,
2004, 2005). The jets carry the flow momentum downstream, while the plasma
remaining in the outer boundary layer gets decelerated by the way. The dynamic
pressure in the jets is extremely large in comparison with the magnetic pressure
in the nearby MP, which makes unlikely that they can have a reconnection origin.
But this implies conversely that they can substantially influence the MP shape
and stability, possibly favoring afterwards a driven reconnection
mechanism.
The
nonlinear cascades upstream of the MP are synchronized by waves of a few mHz, which exhibit 3-wave phase
coupling both with the incident MS fluctuations and with the leading MS-jet. The
acceleration of the MS- jets is consistent with a Fermi-type mechanism, in which
electric wave-trains, generated in the process of 3-wave interaction of the
incident and reflected waves, play the role of moving 'walls' in the MSH
bulk-flow frame. Estimates of the jet scales from the respective bicoherence maximum, treated in terms of the nonlinear Cherenkov resonance, conforms to 2-3 reflections of the jet
from the 'wall' before reaching the energy of 'wall' potential barrier and its
overcoming. Quantitative agreement of the acceleration of a particular
In the
direct plasma-plasma interaction, the Turbulent Boundary Layer (TBL) can be
viewed as the effective “obstacle” for the external flow. As described above,
the small scale non linear dynamics in this layer decelerates the incident flow,
so being equivalent to some “effective collisions”, and transfers the momentum
to an accelerated flow downstream, along the MP. These effective collisions due
to small-scale transverse electric fields in the extended turbulent zones are a
promising alternative in place of the usual parallel electric fields invoked in
the macro-reconnection scenarios.
We
propose to extend the existing studies by setting significant statistics and
including in the theoretical estimates the scales, comparable with ion gyroradius, on which the approximation of the inertial drift
fails. In the high beta regions, the proposed Fermi-type acceleration should
indeed operate only in the presence of small-scale electric potentials (~ ion
gyroradius), which can reflect the 'resonant' ions.
Both the presence of small scales and plasma interactions with such fields would
be addressed quantitatively in the proposed Project.
The role
of the jets on the weak magnetic field MP is also to be investigated further. We
propose to study well fitted cases from Cluster data and possibly to return to
retrospective analysis of the data from previous missions as well. We also would
like to check the suggestion that the supersonic jets result from a Laval-nozzle
effect.
Savin et al.(2005)
suggested that the electric wave packets at the outer border of the boundary
layer can be self-consistently produced in the course of inertial plasma drift
in the non-uniform electric field. Nevertheless, it occurs that a gradient drift
could give the same effect and we intend to check whether scenarios elaborated
for the auroral context (Genot et al., 2004) could be applied as well at the MP.
In this case, it should have a valuable consequence: the
electron-scale currents inferred from measurements (Savin et al., 1998, Moser et al., 2003) aren’t a feature of
any ‘diffusion region’ as supposed in the classical
macro-reconnection scenarios, but instead they are the necessary link in the
energy cascade from the large scale waves, well-detected at MP (Alfven and/or fast magnetosonic),
towards small scales. We propose a simple way to distinguish between ‘diffusion
regions’ and regular MP/TBL sub-structures: the latter should be seen in wide
regions along MP and inside the most intensive TBL, in contrast to the localized
‘diffusion region’, and they shouldn’t be necessarily
the locus of conversion of electromagnetic energy into the particle
one.
Finally,
we would like to outline that the intrinsically non-stationary and non-uniform
plasma jetting and related wave cascades, which we plan to explore, could be a
fundamental plasma property, which may constitute an alternative to the laminar
streamlining of a plasma around an obstacle: Savin et
al. [2004, 2005] suggested that the super-Alfvenic
flow at high latitudes can be meta-stable when magnetic stress balance cannot be
fulfilled. We hope to be in position to check this maser-like approach inside
our interdisciplinary Team.
Alfvén wave
filamentation and dissipation
In a wide range of astrophysical media, the Alfvén waves are recognized to be of the uttermost importance, in particular for information transport, and attention has been focused on the description of their dissipation and associated phenomena. The understanding of these phenomena relies on the identification of: 1) the primary source (kinetic or magnetic energy, shears); 2) the processes at work; 3) the final effects (particle heating/acceleration, wave emission). Whereas point (1) is well identified in the dedicated literature, points (2) and (3) still needs much work. A given dissipative mechanism can produce very different results depending on the context: the particle acceleration by parallel electric fields, for instance, can disturb equilibrium distribution functions in several ways, all leading to different characteristics in the observations. A rich literature bears witness to this diversity and has to be taken into account in any comprehensive model. For the auroral region, where this topic has been mainly developed thanks to detailed in-situ data, the many experimental papers (e.g. Volwerk et al., 1996, Keiling et al., 2003, Vaivads et al., 2003) have been completed by theory and numerical simulation (e.g. Genot et al., 2004). These studies can be compared with the phenomena observed in solar atmosphere (e.g. Einaudi et al, 1997, Califano and Chiuderi, 1999, Malara et al, 2003), solar wind (Galeev and Sadovski, 1998), giant planets (e.g. Kar and Mahajan, 1986, Chust et al. 2005), interstellar medium (e.g. Lazar et al., 2003), and also in laboratory plasmas for magnetic fusion (e.g. Grishanov et al., 1999).
Dispersive Alfvén waves are commonly observed in space
plasmas, especially in the solar wind, magnetosheath (Sahraoui et al. 2003) and
auroral regions (Stasiewicz
et al. 2000). A qualitative description is provided by the Hall-magnetohydrodynamic (Hall-MHD) model for a
polytropic plasma. In this description, weakly nonlinear
quasi-monochromatic Alfvén waves propagating along an ambient magnetic field can
be subject to transverse instabilities leading to the formation of intense
magnetic filaments. This phenomenon, described as a transverse collapse within
the asymptotic approach provided by the nonlinear Schrödinger equation for the
pump envelope, was also reproduced by spectral direct numerical simulations of
the Hall-MHD system. In recent simulations, the filamentary structures appear
after a while to become strongly distorted, displaying flattening and twisting
(Dreher et al. 2005). This transition from nonlinear
waves to a hydrodynamic regime is characterized by intense current sheets and a
strong acceleration of the plasma (cf the jetting
discussed above). Kinetic effects are difficult to fully include in a nonlinear
simulation but it has been possible to show analytically that they strongly
affect the instability threshold and provide a natural saturation mechanism by
Landau damping at the scale of the ion gyro-radius (Passot and Sulem 2003). This
filamentation phenomenon could be relevant to the interpretation of recent
CLUSTER observations of current tubes in magnetosheath regions close to the bow
shock, where quasi-monochromatic Alfvén ion-cyclotron waves have been identified
(Vaisberg et al., 1984, Alexandrova et al. 2004).
Another
phenomenon could be at the origin of local enhancements of the magnetic field
intensity. It is associated with the breaking of magnetic field lines, a process
similar to wave breaking in compressible hydrodynamics. In the context of
incompressible magnetohydrodynamic flows, it results
from the appearance of zeros for the Jacobian of the
mapping that relates the usual Eulerian coordinates to
a semi-Lagrangian description of the magnetic field lines. The compressible
character of the mapping results from the fact that only the transverse motion
of fluid particles is relevant in advecting field
lines (Kuznetsov et al., 2004). In both scenarios
(Alfvén wave filamentation and magnetic field line breaking), the magnetic field
intensity is rising in the coarse of the collapse while the characteristic scale
reaches the size of the ion gyroradius at which point
the MHD equations cease to be valid and finite-gyroradius stabilization of the collapse is foreseen.
Preliminary checking of the experimental data seems to confirm this prediction
(see e.g. Savin et al., 1998, 2001). A crude estimate
of the equilibrium state if any can be done by balancing the plasma outflow from
the region with rising |B|, with the backward diffusion flow, the diffusion
coefficient being evaluated using the ion gyroradius
scale. It gives a characteristic plasma speed near the collapse region of the
order of the ion thermal speed, i.e. nearly the sound speed. Such speeds have
been reported by Savin et al. [2004, 2005] in the jets
(see above). The task of our Project is to perform careful measurements of the
relevant physical parameters in regions of intensified magnetic field.
Particular attention will be paid on the relations between the plasma jets and
Alfvén collapse in order to distinguish between the proposed generation
mechanisms. We also plan to specify the plasma and magnetic field topology of
the general approach of Kuznetsov et al.[2004] in the context of realistic configurations near the
high-latitude magnetopause.