Dissipation and heating in solar wind turbulence: from the macro to

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Dissipation and heating
in solar wind turbulence:
from the macro to the micro
and back again
Introduction
Khurom H. Kiyani1,2 , Kareem T. Osman1 and
Cite this article: Kiyani KH, Osman KT,
Chapman SC. 2015 Dissipation and heating
in solar wind turbulence: from the macro to
the micro and back again. Phil. Trans. R. Soc. A
373: 20140155.
http://dx.doi.org/10.1098/rsta.2014.0155
Accepted: 23 February 2015
One contribution of 11 to a theme issue
‘Dissipation and heating in solar wind
turbulence’.
Subject Areas:
plasma physics, astrophysics,
solar system, geophysics
Keywords:
solar wind, turbulence,
magnetohydrodynamics, collisionless plasmas
Author for correspondence:
Khurom H. Kiyani
e-mail: [email protected]
Sandra C. Chapman1
1 Centre for Fusion, Space and Astrophysics, Department of Physics,
University of Warwick, Coventry CV4 7AL, UK
2 Laboratoire de Physique des Plasmas, École Polytechnique,
91128 Palaiseau CEDEX, France
The past decade has seen a flurry of research activity
focused on discerning the physics of kinetic scale
turbulence in high-speed astrophysical plasma flows.
By ‘kinetic’ we mean spatial scales on the order
of or, in particular, smaller than the ion inertial
length or the ion gyro-radius—the spatial scales at
which the ion and electron bulk velocities decouple
and considerable change can be seen in the ion
distribution functions. The motivation behind most
of these studies is to find the ultimate fate of the
energy cascade of plasma turbulence, and thereby
the channels by which the energy in the system is
dissipated. This brief Introduction motivates the case
for a themed issue on this topic and introduces the
topic of turbulent dissipation and heating in the solar
wind. The theme issue covers the full breadth of
studies: from theory and models, massive simulations
of these models and observational studies from the
highly rich and vast amount of data collected from
scores of heliospheric space missions since the dawn
of the space age. A synopsis of the theme issue
is provided, where a brief description of all the
contributions is discussed and how they fit together
to provide an over-arching picture on the highly
topical subject of dissipation and heating in turbulent
collisionless plasmas in general and in the solar wind
in particular.
2015 The Author(s) Published by the Royal Society. All rights reserved.
1. Motivation
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rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 373: 20140155
The physics of interplanetary space plasmas represents an archetypal non-equilibrium collective
phenomenon; interdisciplinary in scope, it brings together several branches of physics from
plasma physics and statistical mechanics to signal processing and high-performance computing.
Plasmas exhibit diverse physical phenomena which range from macroscopic scales on the size of
planetary and galactic systems where the plasma is behaving as a turbulent fluid with random
intermittent magnetic field fluctuations, the so-called ‘magneto-hydrodynamics’ (MHD); to
micro-scale kinetic physics and complex individual charged particle dynamics in electromagnetic
fields. Among the scientific observations of astrophysical plasma that are available to us, the solar
wind provides an excellent laboratory for the study of fully developed plasma turbulence. The
solar wind and the near-Earth environment are also the only in situ observationally accessible
highly turbulent plasmas [1–3] with magnetic Reynolds numbers of the order of 105 [4] at 1 AU.
In situ spacecraft observations from both field and particle instruments, show highly developed
turbulence at 1 AU. This is evidenced by a very broadband power spectral density that illustrates
the amount of energy at each scale and is one of the manifestations of the ‘turbulence energy
cascade’ [5]. In this well-known paradigm, energy from large-scale fluctuations cascades through
smaller and smaller scales until being dissipated into heat at very small scales. In neutral fluids,
such as fast flowing water in a river or pipe, this dissipation is provided by microscopic collisions
manifested macroscopically as the viscosity or stickiness of the fluid.
As in the case of many interplanetary and astrophysical plasmas, the near-earth solar wind
is extremely sparse with very low densities (around 10 particles per cubic centimetre); this
implies that collisions between particles are rare, and hence the plasma is considered collisionless.
Indeed, the mean-free path (average distance between collisions) of the charged particles in
the solar wind is of the order of 1 AU. Thus, the classic viscous channel is ruled out as a
viable mechanism for dissipation. Owing to the extremely high conductivity of the solar wind,
the resistivity is also negligible; and thus joule-heating is also ruled out as a mechanism for
dissipation and heating. In the absence of these more classical macroscopic fluid channels, most
of the relevant interactions in this collisionless plasma are in the form of necessarily kinetic field–
particle interactions between the charged particles and the electromagnetic fields and currents
that they create by their collective motion. In addition to this, kinetic scale changes to the
magnetic field topology in the form of magnetic reconnection can serve to both convert the field
energy into particle energy, as well as being a possible channel of dissipation and irreversible
heating. An outstanding problem—and the central theme of this special issue—is how, in the
absence of collisional viscosity in the solar wind, the broad range of large-scale MHD turbulence
terminates at smaller scales. Understanding the nature of the dissipation processes will inform
open questions such as how the solar corona is heated and how its heliospheric extension, the
solar wind, is accelerated and heated.
The physics of solar wind turbulence is played out over a vast range of dynamical spatial
and temporal scales from the period of one (synodic) solar rotation of 27 days and spatial
correlations of mega kilometres to the smallest scales of electron gyration periods of a few
hundredths of a second and gyro-radii of a kilometre or less. To this end, we organize the
issue to some degree to match the scales of the various topics that will be discussed in
each article. This is reflected in this introduction that presents this multiscale ordering of
the subject from macroscopic to microscopic physics, and how this then feeds back to some
extent into the macroscopic structure of the near-heliosphere. However, before we move to the
synopsis of the theme issue, we briefly outline the underlying phenomenology of the turbulent
cascade of energy in space plasma flows—a phenomenology that is constantly referred to
throughout the issue. We also provide some clarification on terminology and nomenclature,
which can on occasion obfuscate the discussion to those discerning researchers outside the
topic.
2
−1.65 ± 0.01
102
1
f –1 range
transition region
trace power spectral density (nT2 Hz–1)
104
inertial range
sub-ion range
10−2
−2.73 ± 0.01
10−4
ACE MFI (58 days)
ACE MFI (51 h)
Cluster FGM + STAFF−SC (70 min)
10−6
10 −6
10−5
10−4
10−3
10−2
10−1
spacecraft frequency (Hz)
1
10
Figure 1. Typical trace power spectral density of the magnetic field fluctuations of a βi ∼ O(1) plasma in the ecliptic solar
wind at 1 AU. Dashed lines indicate ordinary least-squares fits, with the corresponding spectral exponents and their fit errors
indicated. This spectrum represents an aggregate of intervals with each smaller interval being contained within the subsequent
larger interval—hence the higher frequencies of this spectrum are not representative of the interval describing the lower
frequencies. At the largest scales is a 58 day interval [2007/01/01 00.00–2007/02/28 00.00 UT] from the MFI instrument on
board the ACE spacecraft, illustrating the large-scale forcing range (the so-called f −1 range). The inertial range is computed
from a shorter 51 h interval [2007/01/29 21.00–2007/02/01 00.00 UT] also from the same instrument. Both these datasets are at
1 Hz cadence, so they just begin to touch the beginning of the sub-ion range. The kinetic scale spectrum in the sub-ion scale
range is given by magnetometer data from the FGM and STAFF-SC instruments on the Cluster multi-spacecraft mission, from
spacecraft 4, while it was in the ambient solar wind [2007/01/30 00.10-01.10 UT] and operating in burst mode with a cadence
of 450 Hz—the two signals from both of these instruments have been merged as in [6]. The vertical dashed lines indicate the
three length scales mentioned above: λc the correlation length, ρi the ion gyro-radius and ρe the electron gyro-radius. (Online
version in colour.)
(a) Brief phenomenology of the energy cascade
We ask the reader to turn their attention to figure 1, which shows a canonical power spectral
density at 1 AU in the solar wind. We have chosen the power spectral density as it is not only the
focus of many, if not most, studies of turbulence, but also serves as a simple map to illustrate the
scales of interest in the phenomena. It is also reflective—being the Fourier transform pair—of the
two-point field correlation, another obsession of generations of turbulence researchers. Owing to
the extremely high speed of the solar wind, faster than most temporal dynamics in the system, we
can invoke the ‘Taylor frozen-in flow’ hypothesis to relate temporal scales to spatial scales (see [7]
for caveats to this). Thus, although the abscissa shows a temporal scale of spacecraft frequency,
for most of this spectrum (in the inertial range and above) it can be viewed as a proxy for spatial
scales—some of which are marked at the top of the figure. In particular, we have highlighted four
distinct regions of interest demarcated by three important length scales:
— The f −1 range. At these very small frequencies—corresponding to temporal scales over
many days—what we are actually measuring is the temporal variability of the source of
the solar wind: the Sun and its solar atmosphere. Near the top of this range, we have
the first of our important length scales: the correlation length λc . Below this scale (higher
.........................................................
−1.00 ± 0.04
3
106
re ~ 1 km
ri ~102 km
lc ~ 106 km
.........................................................
There is much that has been left out in this very brief description of the phenomenology, e.g.
the very important aspect of anisotropy [10]. However, this and other topics will be discussed in
detail in the theme issue and these contributions will be briefly discussed in the synopsis below.
4
frequencies), fluctuations have lost memory of their solar origins and are a product of the
in situ dynamics as the solar wind travels towards the Earth. Above this length scale, the
fluctuations retain memory of their solar origins and this is what comprises most of the
so-called f −1 range. A discussion of the origins of this f −1 range can be found in [8], in
this issue. The correlation length can be seen as the biggest size of the energy containing
‘eddies’ or structures in a turbulent flow and is normally defined through the two-point
field correlation tensor mentioned above. Multispacecraft measurements of this scale at
1 AU in the ecliptic solar wind [4] have yielded a figure of λc O(106 ) km which, with an
average speed of 500 km s−1 , corresponds to a spacecraft frequency of about 6 × 10−5 Hz.
— The inertial range. This is the range where the classic fluid (MHD) energy cascade
from large to small spatial scales occurs. The power spectral density of magnetic field
fluctuations at MHD scales is widely shown to be of power-law form with the now
famous and ubiquitous Kolmogorov power-law spectra with exponent value of ∼ −5/3.
Although, the value of this exponent is still debated among some researchers, much of
the phenomenology here is borrowed from neutral fluid hydrodynamics with additional
physics such as anisotropy. The dynamics within this range is considered to evolve
independently from the details of its initial conditions at larger scales, only constrained
by the rate of energy driving the system, and is also ‘unaware’ of its fate at smaller
scales—it is thus purported to be of universal form with the energy cascade progressing
in a statistically scale-invariant manner. This range is bounded at the lower end by the
correlation length λc and at the higher end by an ion spatial scale: the ion inertial length
di for βi ≤ 1, or the ion-gyro scale ρi for βi ≥ 1.
— The transition region and the sub-ion range. also known historically as the ‘dissipation range’
or in some quarters of the community as the ‘dispersion’ range [9]. This is bounded at the
lower end by the ion gyro-scale ρi and at the higher end by the electron gyro-scale ρe .
If we ignore for the moment the dynamics parallel to the mean guide magnetic field
(see [10] in this issue), this is essentially where the kinetic physics begins and is the
main topic of this theme issue. One of the earliest presentations of the spectra of this
range was shown by Denskat et al. [11] using Helios spacecraft observations—albeit, not
as detailed as figure 1 due to the scarcity of measurements. This study was followed
by many others over the last two decades based on better cadence measurements from
the ACE, WIND and Cluster spacecraft missions; the last one of which provides the
most detailed measurement of waveforms to date (see [7] in this issue). These studies all
showed the now well-documented fact that at scales around the typical length of an orbit
radius of protons/ions gyrating around a magnetic field (proton/ion gyro-scale), the
power-law spectra in the inertial range, mentioned above, break abruptly and at smaller
scales another steeper power-law [12–17] is found spanning about two decades in scales
(figure 1). At these scales the fluid picture given by MHD breaks down, and it is necessary
to take into account kinetic effects of the individual charged particles. The value of the
exponent of this second power-law is also variable and changes depending on plasma
conditions such as magnetic energy, anisotropy of the magnetic field fluctuations with
respect to the mean magnetic field and bulk plasma velocity, etc. [18–20]. The physics
of these scales, in this sub-ion range, is still unknown and is hotly debated. Current
studies anticipate a cross-over from the turbulence energy cascade, mentioned above, to
dissipative and/or dispersive processes via wave-particle resonances, and reconnecting
magnetic fields; with the associate transfer of energy from the electromagnetic fields to
the plasma particles.
2. Synopsis of the issue
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This special issue is topical in the sense that the authors were encouraged to be relatively
unhindered to express their views on the subject and what they think the future outlook on the
field should be. In this respect, although the separate articles and reviews have been selected
to represent a wide breadth of the field of solar wind dissipation and heating, they in no way
represent a consistent set of views. This was done intentionally to reflect the different views of the
subject within the community. The authors selected are among the leaders in the field (solar wind
turbulence and related fields such as coronal heating and kinetic instabilities), many with several
years of world-class research on the topic; some of whom are widely acknowledged as developing
the subject to where it is today with key discoveries and theories. All of the contributions have
been chosen to satisfy one or more of three criteria: the first being the author/s international
leadership and expertise in the particular facet proposed in the subject title; the second being
the quality and lucidity of the pedagogic prose in their scientific publications and lastly their
ability to deliver an article which will be topical and contain new insights from their opinions
on the subject and where future research outlook should be concentrated. The authors have also
been deliberately chosen to represent a good mix between observationalists, theorists and those
engaged in state-of-the-art computer simulations and experiments. The titles represent a mix of
topical reviews that give a pedagogic background to key facets within the subject, and targeted
articles that present new insights and results as well as opinions of the authors involved.
The theme issue starts with a review article describing some of the quintessential properties
of turbulence and their role in generating the structure that one sees in plasma turbulence.
Matthaeus et al. [8] describe how the nonlinearities in the dynamical equations of plasma
turbulence can self-consistently explain the phenomenon of intermittency and non-Gaussian
fluctuations, and the formation of various coherent structures such as current sheets, filaments
and cellularization. Their explanations rely on the elegant formalism of dynamical relaxation, and
on analogies with simpler models which retain the physics of interest. Importantly, they show
with examples from simulation and observations, as well as phenomenological discussion, how
large gradients at the boundaries of these structures can impact on dissipation, heating and
transport of charged particles.
The next article of Cranmer et al. [21] reviews the current understanding of how the solar
corona is heated and the solar wind accelerated with a focus on the role of MHD turbulence in
obtaining better insights into how these outstanding problems can be solved. They debate the
relative strengths of candidate mechanisms; in particular, between the dissipation of turbulent
fluctuations emitted from the Sun, and those lower down in the solar atmosphere which, through
the mixing effect of turbulent convection in the convection zone above the solar tachocline, causes
the mixing and resultant reconnection of magnetic fields lines in the lower corona.
A staple of turbulence studies in the solar wind are attempts to ascertain the energy transfer
rate of the turbulence cascade. The logic of this approach is simple: in the absence of dissipation
in the inertial range, any energy that is cascaded through it will eventually be dissipated at the
smaller scales—the exact process of the dissipation need not be known. The research article of
Coburn et al. [22] reviews the main tool in calculating these energy cascade rates, third-moment
theory and proceed to compare these with thermal proton heating using a very large ensemble
of 1 h field and particle data intervals from 12 years of ACE spacecraft observations. One of the
most interesting results of this study are that the measured energy cascade rates show highly
intermittent values and statistics. This was briefly touched upon in the earlier review [8] as one
of the sources of temporal intermittency in solar wind observations; borrowed from an idea for
atmospheric turbulence first proposed by Oboukhov [23].
The recognition that MHD plasmas are strongly affected by the magnetic fields that thread
through them is now a well-established fact of plasma physics. Any study which does not
realistically take this essential anisotropic feature of plasmas into account has a significant
shortcoming. Oughton et al. [10] review our current understanding of anisotropy in solar wind
plasma turbulence, both in the inertial range and, crucially, at the kinetic scales of the sub-ion
5
6
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range. Both spectral and component anisotropy are reviewed. The results show that although
component anisotropy seems to be relatively well supported by observations in both the inertial
and sub-ion ranges, with a broad agreement within the community, the jury is still out on the
resolution of this in the case of sub-ion range spectral anisotropy.
Traditionally, simulations have provided an important and occasionally indispensable tool
for the study of plasma turbulence. Although they lag behind spacecraft observations in the
sense of not possessing enough spatial resolution to obtain the several decades of an inertial
range as seen in figure 1, they provide unparalleled detail in nearly everything else, e.g. full
determination of spatio/temporal dynamics, exquisitely detailed visualization of the structures
and patterns within the flow (see front cover of this issue and [24]), etc.—much of which heavily
limits definitive conclusions from single, and even multispacecraft, observations. Advancements
in massively parallel high-performance computing have allowed one to augment the in situ
observations from spacecraft missions with what are effectively computational experimental
laboratories in the form of simulations of the various models of plasma turbulence. Until a
decade ago, a full three-dimensional picture of plasma turbulence was confined to fluid codes
such as incompressible/compressible MHD, Hall-MHD and Electron MHD codes; but now,
we are at a stage where five-dimensional (2 or 3 space + 3 or 2 velocity) and even full sixdimensional (3 space + 3 velocity) kinetic simulations [25–28] are being conducted. Although we
have already encountered such simulations earlier in the issue [8], the review by Gary [29]
provides an overview of these fully kinetic simulations and how they relate to short-wavelength
plasma turbulence.
Plasmas contain far richer physics than their incompressible fluid counterpart. Alongside the
usual acoustic waves supported by neutral gases, plasmas support a veritable zoo of plasma wave
modes and instabilities. The more physics that one includes, and the more complex the models,
the more of these waves and instabilities with their associate damping and growth rates occur
[30,31]. The review by Gary [29] also provides a short pedagogic review of both the fluid
and kinetic instabilities that can occur in collisionless plasmas due to temperature anisotropies,
and discusses how these instabilities can directly drive narrowband fluctuations in shortwavelength solar wind turbulence, thereby transferring energy from the particles to the fields.
The energy in the fields can then cascade to smaller scales via the turbulent cascade and/or
wave dispersion mechanisms. To complicate matters further, recent research [28,32] has shown
that the large gradients attributed to coherent structures [8] can in turn drive the plasma to
a state of temperature anisotropy and thus feedback into this process. This serves to not only
show the connection between research on temperature anisotropy-driven instabilities and plasma
turbulence, but also the complicated nature of the different channels available which are not
necessarily sources of dissipation but of driving the turbulence, albeit at smaller scales than the
normal correlation length drivers.
In addition to the instabilities discussed above, physics at the kinetic scales introduces
more complicated dispersive wave modes. The role that these wave modes, and their fluidscale counterparts, play in turbulence is still a subject of heated debates, with many within
the community arguing that nonlinear interaction between these waves is responsible for the
turbulence cascade observed in space and astrophysical plasmas. The topical review of Howes
[33] advocates this approach (as does the previous review [29]) and discusses how much of
what we observe in solar wind turbulence from both spacecraft observations and computer
simulations can be explained by a detailed look at the dynamics of the nonlinear interactions of
these wavemodes. Significant attention is paid to the role of Alfvén wave and kinetic Alfvén wave
interactions in mediating the cascade and for the creation of current sheets. Collisionless damping
in the form of ion and electron Landau damping is attributed to transferring energy from the fields
to the particles, with significant changes to the ion/electron distribution functions. These changes
are then smoothed out in velocity space by an entropy cascade which ultimately thermalizes this
energy via weak collisions. It is also important to state that within the community advocating
the wave-mediated turbulence cascade, there are also split opinions on what wavemodes are
primarily responsible for mediating the cascade beyond the inertial range and into sub-ion scales,
7
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with resultant splits over the exact damping and dissipation mechanisms for these wavemodes.
This sub-topic itself has been, and continues to be, an active area of research within the space and
astrophysical turbulence community.
Spacecraft field and particle instruments at cadences approaching and including ion-scales
have been available for nearly two decades now with the WIND and ACE spacecraft, and some
seminal work on kinetic scale turbulence was done using these instruments at the turn of this
century [12,34–36]. However, the past decade has seen the greatest acceleration of sub-ion scale
turbulence studies using spacecraft observations; with much impact and cross-pollination to other
areas of space physics. This has largely been driven by the unprecedented high cadence magnetic
and electric field measurements from the Cluster multispacecraft mission [37]. Goldstein et al. [7]
review the historical development and the current state of the art in these observational studies.
Moreover, they also discuss the future outlook of observational studies in the light of the recently
launched Deep Space Climate Observatory (DSCOVR) and Magnetospheric Multispacecraft
(MMS) missions, and the future Solar Orbiter and Solar Probe missions.
Until recently sub-ion scale particle instruments have been sorely lacking. Without highresolution measurements of particle moments and distribution functions, our knowledge of
kinetic scale physics is at best incomplete and at worse sorely inadequate to precisely test
between competing theories and conjectures of the physics of sub-ion scale plasma turbulence.
The Russian-led BMSW instrument (Bright Monitor of Solar Wind) on the SPECTR-R spacecraft
mission launched in mid-2011 changed this. With a plasma cadence of 33 Hz, it can provide
detailed time series of density fluctuations. The research article of Riazantseva et al. [38] details
a statistical study focusing on the intermittent properties of ion flux fluctuations in solar wind
turbulence. Similar to earlier studies of spectra from magnetic field measurements of the sub-ion
range using the ACE, WIND and Cluster missions they find a variation in the parameters that
they calculate to characterize the level of intermittency in these ion flux signals, as well as highly
non-Gaussian fluctuation probability density functions.
The research article of Roytershteyn et al. [39] draws on some of the topics introduced in the
earlier reviews that discussed the generation of coherent structures [8] and the role of temperature
anisotropy-driven instabilities in small-scale plasma turbulence [29]. Through the use of massive
three-dimensional fully kinetic PIC simulations, they show the self-consistent evolution of current
sheets into pressure balanced magnetic holes at ion and electron spatial scales, aligned with the
background guide field. Interestingly, all the structures they discuss at both ion and electron scales
are associated with temperature anisotropy instabilities close to the marginal stability threshold
of the mirror instability, consistent with other findings reported in [28,32].
The other candidate process for the dissipation of magnetic energy in collisionless plasmas
is magnetic reconnection. Classically, this process occurs when the resistivity allows magnetic
field lines to diffuse through the plasma in a so-called diffusion region where the magnetic
topology is rapidly changed [40]. The resultant ‘snapping’ and ‘reconnecting’ of the magnetic field
allows the transfer of energy from the fields to the particles. The determination and measurement
of the reconnection rate is at the heart of both models and observations—the key problem being
the reconciliation of predictions with observations. As well as being very turbulent, collisionless
space plasmas are also extremely conductive indicated by very large Lundquist numbers of
the order of approximately 1020 . This implies a very low or negligible resistivity and thus a
very slow rate of magnetic reconnection as described by classical resistive-MHD. However,
many observations have now unanimously determined that the rate of magnetic reconnection
is orders of magnitude larger than that predicted by such classical theories. The development
of more fundamental theories of reconnection will inevitably need to include physics of scales
smaller than the MHD (fluid) descriptions, i.e. at kinetic scales where wave–particle interactions
become important. From both laboratory and observational studies, it has been proposed that
fast reconnection spontaneously occurs when the current layer approaches the ion gyro-radius or
ion inertial length [40–43]. As mentioned above, the interplanetary medium is highly turbulent
with an enormous separation between dissipation and large-scale fluid structures. In the case of a
solar flare, singular reconnection sites can be considered; however, in the majority of cases one has
It would be no exaggeration to state that turbulence, and its associated physical processes such
as transport, reconnection, etc., are the most fundamental processes at the heart of nonlinear
plasma dynamics. And yet these processes are the least understood. They are likely to be the
key ingredients in any description of particle acceleration and heating in astrophysics; which are
needed in order to answer the outstanding questions of coronal heating, solar wind acceleration
and the acceleration of highly energetic interstellar cosmic rays in the heliosphere.
This is an exciting time for the study of kinetic scale plasma turbulence; ripe for
discovery and for solving the problem of kinetic dissipation in turbulent astrophysical plasmas.
Recent availability of high-cadence measurements from in situ space missions, coupled with
advancements in simulating realistic kinetic scale plasma conditions, has led to a resurgence in
the study of turbulence, dissipation and heating. This has manifested in an explosion of quality
science in high impact journals, as well as fertile cross-pollination in other fields of space and
laboratory plasma research. The topic of this issue has been identified by international space
agencies as scientific questions, which should be addressed with future spacecraft missions. To
this end, the next 5 years will see data from the MMS and DSCOVR missions, as well as the
launch of Solar Orbiter and Solar Probe Plus. These will push the limit on the observations we
can undertake. At the same time, advancements are being made in simulating full kinetic scale
plasmas in three dimensions. Thus, this issue is very timely, allowing key observational and
numerical results to be consolidated, and giving leaders in the field an opportunity to frame the
main scientific questions and outlook for future research.
Acknowledgements. The guest editors would like to thank the staff at the Royal Society, and in particular the
commissioning editor Bailey Fallon for his untiring efforts to get the issue published on time—we very much
appreciated his (always) polite encouragement. We would also like to thank Nick Watkins for his suggestion
of setting up a WIKI for the issue, and Romain Meyrand for his assistance in preparing and providing one
of the images for the front cover of the special issue. Lastly, we thank all the authors of the articles for their
insightful contributions, diligence and patience in helping us prepare this theme issue. In particular, we thank
Melvyn Goldstein, William Matthaeus and Gregory Howes for proofreading and suggesting improvements
to this Introduction. The data used for the preparation of figure 1 were obtained from the open and publicly
accessible NASA Space Physics Data Facility CDAWeb and the ESA Cluster Science Archive.
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3. Outlook
8
to deal with multiple reconnection sites at many scales. The interplay between these scales and
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