Experiment description
The WADIS sounding rocket project lead by the Leibniz Institute of
Atmospheric Physics (IAP) in Kühlungsborn, Germany, with contributions
from Austria, Sweden, the USA and Norway comprised two field campaigns
conducted from the Andøya Space Center (ACS) in northern Norway
(69∘ N, 16∘ E). The second campaign was conducted in March
2015 and the instrumented sounding rocket was launched on
5 March, at 01:44:00 UT, when MLT thermal
structure and circulation regime were in a pure winter state. The name WADIS
stands for “Wave propagation and dissipation in the middle atmosphere:
Energy budget and distribution of trace constituents”. The main goal of the
mission was to study propagation of gravity waves (GWs) from their sources in
the troposphere to their level of dissipation in the MLT and quantification
of their contribution to the energy budget of the MLT. For an overview of the
WADIS project and its main mission the reader is referred to
.
The WADIS payloads were equipped with instruments to measure temperature and
density of the neutral atmosphere, neutral air turbulence and densities of
all plasma species, including positive ions, electrons and charged MSPs. A
unique feature of the WADIS experiment was that both neutral atmospheric and
plasma densities were measured simultaneously in the same volume during
upleg-facing ram. This allows us to make a reliable estimate of some MSP properties
derived and discussed in this work. Moreover, the mesosphere was also
monitored by ground-based instruments, in particular the Middle Atmosphere
Alomar Radar System (MAARSY) . MAARSY observed
no echoes during the day of the rocket launch.
Payload instrumentation
WADIS 2 payload configuration with its instruments (corresponding
institution abbreviation): CONE (IAP), FIPEX/PHLUX (IRS), two PDs (IAP) and
two photometers (MISU) on the forward deck (FWD) and a wave propagation
experiment/Faraday antennas, PIP (both TUG), LP (ERAU) and CONE on the aft
deck (AFT).
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Figure shows the WADIS payload with the instrumentation.
Both the front and rear decks of the payload were equipped with identical
CONE (COmbined sensor for Neutrals and Electrons) instruments to
measure turbulence, neutral air temperature and density, and electron density
with very high spatial resolution on the order of approximately centimeters
. These measurements allow investigation of small-scale
structures in both species (neutrals and electrons) at spatial scales from
several kilometers down to tens of centimeters along the rocket trajectory.
CONE combines an ionization gauge with a fixed biased probe for electron
density measurements. For a detailed description of the CONE instrument the
reader is referred to and .
The positive ion probe (PIP) mounted on the rear deck of the WADIS payload
and operated by University of Technology in Graz (TUG) yields measurements of
ion densities with spatial resolution down to meter scales see,
e.g.,.
Both the electron probe of the CONE instrument and PIP are electrostatic
probes, meaning that they are fixed biased at +3 and -6 V relative to
rocket skin potential. The payload is charged until the sum of currents onto
the payload surface is zero. The equilibrium potential is the floating
potential of the surrounding plasma and is usually on the order of -2 V
. Therefore, the measured currents are proportional to
the local density of the respective plasma species. It is assumed that the
payload potential changes slowly compared to changes in ionospheric densities
along the rocket path. Since the payload potential is the reference to all
electrostatic probes, the probes yield relative density measurements. Moreover, the
impact of changing payload potential onto particle detection is small since
it scales with particle kinetic energy. The change in the payload potential
is usually on the order of a couple of volts, whereas the particles greater
∼ 0.7 nm have larger kinetic energies of 10 to hundreds of electron
volts . A change in payload potential by 2 V
increases the critical detectable radius due to electrostatic barrier by only
approximately 0.2 nm, i.e., from 0.6 to 0.8 nm.
The wave propagation experiment (also often referred to as Faraday) operated
by TUG yields absolute electron density measurements but with a limited
height resolution of ≈ 1 km
e.g.,. This technique is independent of
the payload potential and is used, for example, for normalization of the relative
density measurements by electrostatic probes
e.g.,.
The two IAP particle detectors (PD 1 and PD 2) symmetrically mounted off the
symmetry axis on the front deck of the payload yield measurements of heavy
charged particles with altitude resolution on the scale of meters. The front deck
was exposed to the atmosphere after the nose cone ejection at 52 s after
lift-off at an altitude of 63 km. In the next section we describe the PD
in more detail.
Particle detector
The particle detector (PD) is a Faraday cup first applied for rocket-borne
aerosol measurements in the MLT by and repeatedly used by
other studies
e.g.,. It consists of
an electrode shielded from the ambient plasma by two grids and placed in a
metal cup. A detailed description of the instrument can be found in
. The grids of the WADIS-PD were biased at +6.2 and
-6.2 V for the outer and inner grid, respectively. Therefore, they
repelled positive ions and electrons, respectively. The grids had identical
transparencies of 0.74, which means that, without considering aerodynamic
and electrostatic barriers, a maximum of 55 % (0.742) of the incident
particles were able to penetrate to the inner electrode. The electrode and
both grids were connected to sensitive linear electrometers. Thus, the inner
electrode yielded measurements of the net charge density of the heavy
species. The measurement range for the inner electrode was from 4 pA to
20 nA. All currents were sampled with 16 bit resolution at 1 kHz.
The measured current is proportional to the rocket velocity and the charge
number density of the dust. For a typical rocket velocity of
∼ 1000 m s-1 this yields a theoretical altitude resolution of
1 m. Charged particles hitting the PD electrode deposit their charge, which
is measured as a current. This resulting current is clearly the sum of
positive and negative charges.
Data reduction
Following the MSP charge density,
NdZd, can be derived as
NdZd=Ise⋅vR⋅As⋅(1-σ)2,
where Is is the current measured by the sensor's electrode,
e is the elementary
charge, vR is the rocket velocity, As= 19.75 cm2 is the sensor electrode's area and (1-σ)=0.74
is the transparency of a grid. Note that this simplified expression does not
account for secondary charging effects inside the instrument
e.g.,. Direct electron secondary
emission does not play a role at velocities of ≤ 1000 m s-1
. The main charging effect for lower
velocities (≤ 1000 m s-1) is thought to have its origin from
particles impacting on a surface at a relatively large incident angle
relative to the surface zenith and carry away electrons or ions leaving the
surface. However, we neglect this effect since the majority of particle
trajectories are at a right angle to the surface of the electrode as well as
to the grids whose wires are rectangular since coning angle of the WADIS-2
flight did not exceed 3∘. The inner grid was also connected to an
electrometer to enable the assessment of secondary charging effects. However,
these measurement (not shown here) appeared to be very noisy with no
prominent signature
indicating the influence of the secondary effects on the prime measurements.
Additionally, in Eq. () we neglect that particles that already
passed the primary shock front might move with a lower velocity than
vR when entering the Faraday cup.
Combined aerodynamic and electrostatic simulations
Due to the supersonic velocity of the sounding rocket a shock front is formed
in front of the payload. This shock wave influences the in situ measurements.
Fortunately, supersonic free-molecular flow and thus shock fronts can be well
simulated for sounding rockets e.g.,. The standard tool widely used for sounding
rockets is the direct simulations Monte Carlo (DSMC) technique developed by
. The DSMC algorithm is implemented in different simulation
packages and can be combined, for example, with the electrostatic simulations by the
ion optics simulation tool SIMION®
to obtain particle trajectories in non-vacuum
conditions.
We performed simulations in 2-D for a cross section of the forward instrument
deck of the WADIS-2 payload. Using axial symmetry we simulated just half of
the deck. To assess the particles sizes passing through the primary shock
front and reaching the PDs outer grid, i.e., the cup's inlet, four heights
within the measurement altitude range of the PD were simulated, i.e., for
70, 75, 82 and 95 km. The background atmosphere and the flight
conditions for simulations were taken from actual measurements during the
WADIS-2 flight. Results of these simulations (70, 82 and 95 km) are
demonstrated in Fig. , showing particle trajectories (solid
lines) and the density fields obtained from DSMC. Note that the PD grids and
the cups inside are not resolved in this 2-D simulation. The PD inlet (the
outer grid) is represented by a biased electrode with zero transparency.
Results of combined DSMC and electrostatic simulations for WADIS-2
payload. The black area shows one half of the WADIS-2 front deck. X axis is
along the rocket's roll axis. The position of the particle detector is
indicated with PD. Density field derived using the DSMC for 95, 82 and
70 km. White and red lines correspond to trajectories of particles with
1000 and 60 000 amu, respectively. The upstream flow is from left.
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Indicated by increased density, the main shock front is formed in front of
the CONE instrument from -0.5 to -0.4 m in the x direction with
ram factors, i.e., the ratio of undisturbed ambient density to the density inside the measurement volume, between 3.5 and 6 near the payload body. It is
apparent that, at 70 km height (Fig. c), the aerodynamics
prohibit dust measurements even for large particles with masses of
60 000 amu, which corresponds to radii of approximately 2.3 nm. It is
also seen that light particles are “blown” away from PD by the shock front
(white lines). This lower-altitude limit for Faraday cups was also found
earlier by, for example, , , and .
Note that these simulations have a probabilistic character, which implies
that number of trajectories should be calculated to get appropriate
statistics. This has been done for 4000 particles and the derived
probabilities are summarized in Fig. . The y axis in
Fig. shows probability in percent that the MSP reaches the PD.
The dashed and the dotted lines show results for 82 and 95 km height,
respectively. It is apparent by comparing those two heights that particles
reach the PD much more efficiently at 95 km than at 82 km. This is true
for all particle radii which were simulated. The difference becomes larger
for smaller radii. Particles with radii less than ∼ 0.8 nm cannot
reach the PD at 82 km, whereas 40 % of the 0.6 nm particles reach
the PD at 95 km. At 75 km altitude and lower only MSPs with radii
≳ 2.3 nm, i.e., ≳ 60 000 amu, can reach the PD, which
is beyond the plot range in Fig. .
Simulated probabilities that particles reach the PD inlet (outer
grid) as a function of mass (radius) for 82 and 95 km. The velocity and
background atmosphere correspond to WADIS-2 flight conditions. The statistics
was derived from 4000 particle trajectories keeping the statistical error
< 1 %.
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Charged particles are influenced by electrostatic forces. Therefore, the
detectable size distribution is also limited by the electrostatic potentials
at the shielding grids. If one assumes that the potential in the grids plane
is uniform, a first guess of the mass of the particles that are able to reach
the PD's electrode can be derived from the energy conservation law:
m2vR2=eU, where U is the grid bias of 6.2 V,
e is the elementary charge, vR is the rocket (particle) velocity
and m=43πϱr3 is mass of the MSP. This gives the
critical radius of the MSP due to electrostatic barrier:
r=3eU2πϱvR23,
where ϱ=2 g cm-3 is the assumed MSP mass density
.
Minimum critical radius due to electrostatic filtering
Ekin=m2v2=eU for vacuum conditions (solid black
line) and from aerodynamic simulations (black triangles). The aerodynamic
critical radius is the minimum size where the detection probability is larger
than zero. The hatchings indicate which particle size cannot be detected.
The grey shaded area marks the altitude range of the measured dust layer. The
dashed line at 82 km indicates the layer peak height.
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Figure summarizes the combined DSMC and
electrostatic simulations in terms of the critical radius as a function of
altitude. Particles of radii that cannot reach the entrance (outer grid) of
the PD due to either electrostatics or aerodynamics are indicated by the
hatched area. The grey area indicates the altitude range of the measured
negatively charged dust layer discussed in Sect. . The
horizontal line at 82 km marks the height of the charged particle layer's
peak.
The next step was to simulate the probability of particles reaching the
inside of the PD, i.e. its electrode. A more detailed 3-D DSMC described by
to obtain the background fields for
SIMION® was used.
applied the 3-D DSMC method for a complex sounding rocket instrument
resolving even small grid structures down to tens of millimeters. Simulations
in 3-D were necessary to consider the geometry of the PD grids and the
related 3-D electric field distribution. Since these calculations are
computationally expensive, only the peak height of the dust layer (82 km)
was simulated. Also, the simulation volume was limited to the cup itself plus
20 mm in front of the cup's inlet. Since the simulation volume is located
behind the primary shock front, all particles will be slower than their
initial velocity given by the rocket velocity due to collisions with air
molecules inside the shock front. The deceleration is determined by the
thickness and density of the main shock front .
PD detection efficiency (black solid line) at 82 km as a function
of particle mass (radius) by means of the product of the probabilities of
particles reaching the inlet (dashed grey line, from Fig. ) of
the PD and its electrode (dashed dotted grey line) as well as the
corresponding error bars. Note that uncertainties due to, for example, particle
structure and payload charging are not considered. The error bars therefore
only contain the statistical uncertainty of the
simulation.
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We obtained the particle velocity from the 2-D simulation by calculating the
mean velocity at x=-0.22 m (see Fig. ) from 100 particle
trajectories. This was done for each particle mass. The velocity reduction is
in the range of 30–40 % with the deceleration being larger for
smaller particles. As in the 2-D case we now can simulate particle
trajectories in 3-D and count the number of particles reaching the electrode
of the PD. The maximum percentage of particles reaching the electrode is
∼ 55 % due to the grid's mechanical transparency (Tr =0.742=0.55), which is well reproduced by the simulations (see
Fig. , dashed dotted curve “PD electrode”). The
product of the probability of particles reaching the inlet of the PD obtained
from the 2-D simulation with the probability of particles reaching the
electrode obtained from the 3-D simulation gives us the final estimated
detection efficiency of the instrument at 82 km (see
Fig. ). Note that
Fig. only shows the statistical errors derived
from the simulations and does not include the uncertainties introduced by, for example, unknown particle structure or influences of payload charging. Particles
larger than ∼ 15 000 amu can be efficiently detected, whereas
smaller particles are filtered by aerodynamics and electrostatics. The
critical radius at 82 km is ∼ 1.3 nm, which is approximately 2
times larger compared to the particle size able to reach the PD inlet
obtained the 2-D simulation shown in Fig. .
This is due to the fact that electrostatics are combined with aerodynamics
and the analysis of trajectories inside the cup behind the shielding grids.
The kinetic energy of the particles decreases due to deceleration by
collision (from 2-D) and the critical radius due to electrostatic barrier
increases (from 3-D). The results of 2-D and 3-D simulation can thus be
summarized as follows:
The 2-D simulation gives us (1) the size of particles which are transported out of the PD inflow and (2) the particle velocity in front of the PD.
From the 3-D simulation we obtain the sizes of particles which are
stopped by the shielding grids and which reach the sensor electrode.
The combination of both gives the detection efficiency of the instrument in the WADIS-2 configuration.
Measurement results
In this section we show results of the in situ measurements of MLT dusty-plasma parameters. We start with showing the raw data measured by the PDs and
describe how the MSP charge density was deduced. Then we show in situ
measurements of the background plasma densities followed by analysis of
small-scale structures. Finally, we will deduce a charged particle size
distribution from the measured parameters.
Raw PD data
The analysis of raw currents for both PDs was treated in the exact same
manner. We therefore show an example of the deduction of charge density for
PD 1. Figure shows raw
current measured by the PD 1 as a grey, noisy
profile.
Conversion from raw current to charge density exemplary for
PD 1. (a) Raw current (grey) and the interpolated trend (red). Green
is the smoothed raw current. (b) Raw current subtracted by the
interpolated trend from the upper panel. Running mean over 50 values (green)
and the maximum current per spin (red dots).
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To reduce the noise level produced by the electronics, we applied a running
mean over 50 ms. The result is shown in Fig. as a
green line. We found that a value of 50 ms gives a favorable signal-to-noise ratio. Due to their position next to the CONE instrument and off the
rocket's roll axis, the currents collected by the PDs are essentially modulated
by the spin frequency of the rocket. This modulation is due to aerodynamics
which resulted in a periodically changing shock front ahead of the PD. Since
the PDs are symmetrically mounted, this means that when one PD is in ram
position the other will be in the wake. This influence is demonstrated in
Fig. , where an altitude bin of only 1 km is shown.
The two PDs show sinusoidal spin modulation with clear anti-correlation. When
the detectors are facing the ram direction, they show maxima in the measured
currents. When the PDs are in shadow, they reveal minimum values, which
depend on orientation of the payload relative to velocity vector of the
rocket. This angle of attack was around 3∘.
From this aerodynamical reasoning we consider the maxima of the
spin-modulated currents as the most representative values for the density
measurements of the charged MSPs. Thus, to derive the charge density based on
Eq. (), we pick the local maxima per spin period from the
smoothed green profile. These values are shown in Fig. by
the red dots. Hence, the altitude resolution of the absolute density
measurements by the PDs is defined by the spin rate of 3.34 Hz, i.e., up to
∼ 300 m.
Smoothed PD currents (dashed: PD 1; dashed-dotted: PD 2) as a function
of altitude.
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Background
Figure summarizes the plasma density measurements
conducted in situ during the WADIS-2 sounding rocket flight. Density profiles
of charged MSPs obtained from the PD measurements (see Sect. )
are shown in the left panel of Fig. . The green and black
lines represent PD 1 and PD 2 measurements, respectively. It is apparent that
a pronounced negatively charged MSP layer was observed by both PDs. Altitude
range and shape of the layer is almost the same in both measurements. This
good agreement shows that the same layer was detected by independent
instruments and gives evidence of its existence. The current measured by the
PD 1 reveals a systematic offset of 1.3 relative to the PD 2 measurements due
to a lower electrometer sensitivity and the green profile is therefore scaled
by this value. The peak density of negative MSPs is -224 e cm-3
around 82 km. As shown in Fig. particle
detection becomes less efficient below ∼ 82 km. We indicate this
altitude range in the left panel of Fig. by using dashed
lines, implying that instrumental effects become more important here.
The red profile shows absolute electron density measurements derived from the
radio wave propagation technique. We recall that these measurements are not
influenced by the payload charging effects and represent the best-quality
absolute density values. The black profile in the right panel of
Fig. represents the positive ion density measurements.
This profile is normalized above 104 km by the electron density value.
Above 104 km the electron and positive ion densities agree very well, as
expected, from the quasi-neutrality of the ionospheric plasma (not shown
here). This balance between electrons and positive ions is present when other
charge carriers like negative ions or charged aerosols are absent, which is
the case above ∼ 100 km e.g.,. Below
104 km the density profiles show an increasing discrepancy, indicating that
the charge balance between electrons and positive ions is not maintained by
electrons and positive ions alone. As a support to this statement, the electron
density inferred from the positive ion density by neglecting charged MSPs and
reactions with atomic oxygen is shown by the dashed red line in
Fig. . This profile was obtained using
ne=ni+1+βαiiM2ni+,
where ni+ is the positive ion density, β is the electron
attachment rate, αii=6×10-8 cm3 s-1 is the ion–ion recombination
rate and M≃ O2 + N2 is the background neutral density
. We used a ratio β/αii=1.9×10-31, which is in agreement with earlier findings by, for example,
. This simple approach shows that without MSPs the electron density would
coincide with the positive ion density above 85 km. However, from the
measured plasma density profiles we can see that this is not the case. Thus,
the difference between the measured electron density and the one derived with
Eq. () (grey shaded area in Fig. )
above 80 km is attributed to additional electron loss due to attachment to
large particles such as MSPs e.g.,.
Below 80 km the results of Eq. () indicate the presence
of a large number of negative ions obtained by the difference between
inferred electron and positive ion density. However, as the approach by
does not account for destruction of negative ions by
atomic oxygen and their density is most likely overestimated.
(a) Charged MSP profiles measured by the two PDs. The
density of PD 1 (green) has been multiplied by 1.3. Dashed lines indicate the
altitude range where aerodynamic effects are likely. (b) Absolute
electron density (red) and positive ion density (black) measured by the wave
propagation experiment and PIP, respectively. The dashed red line indicates
electron density inferred from positive ion density neglecting charged MSPs
and atomic oxygen reactions. The grey shaded area marks the difference
between measured and inferred electron density.
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These measurements reveal that at 85 km there are approximately 1 order
of magnitude more positive ions than electrons. The measured charge density
of MSPs indicates that this discrepancy most likely is attributed to the
presence of heavy negatively charged MSPs, at least between 75 and
92 km. As described in Sect. , owing to technique
limitations, the PDs were only capable of measuring a fraction of the entire
population of the MSPs. Therefore, the absolute difference between ion and
electron density cannot be precisely established by the PDs. However, the
measured charge density clearly shows the presence of charged MSPs.
MSP size from small-scale structures
In this Section we utilize measurements of neutral and electron densities by
CONE to assess the mean radius of the observed aerosols. This estimate is
based on the work by , who derived mean radii of ice
particles inside a polar mesospheric summer echo (PMSE) layer. As mentioned in Sect. , the
CONE instrument consists of two parts: an electrostatic probe to measure
electron number densities and an ionization gauge to measure total density of
neutral gas. These measurements are performed with very high spatial
resolution and allow for investigation of small-scale structures in those
species.
First, modulations of both measured time series due to the rocket's spinning
motion and its harmonics were filtered using a band-stop filter. From the
filtered signal we derived the relative density fluctuations, also called
residuals, by subtracting a reference current:
rj(t)=Ij(t)-〈Ij(t)〉〈Ij(t)〉=Nj(t)-〈Nj(t)〉〈Nj(t)〉=δNj(t)〈Nj(t)〉,
where I(t) is the measured current, 〈I(t)〉 is the reference
current derived as a running mean over 2×104 data points, which
corresponds to ∼2 km height range, N is the density,
〈…〉 denotes spatial averaging and subscripts j= e, n
refer to electrons and neutrals, respectively. Then, we apply a wavelet
transform to obtain power spectra of the fluctuations
. Here we use a 12th-order Morlet
wavelet function. Figures and show
the derived residuals (left panel) and the wavelet power spectrum (right
panel) for electrons and neutrals, respectively. The wavelet power spectrum
is shown as a function of spatial scales derived as vR/f, where
vR is the rocket velocity and f is the frequency measured in
the rocket frame of reference.
It is apparent that electron density fluctuations become larger above
78 km and show well-defined structures around 79, 82 and 83 km.
Left panel: measured electron density fluctuations (residuals) of
the forward CONE EP from the upleg part of the WADIS-2 flight. Right panel:
wavelet power spectrum of the residuals. The wavelet transformation was
performed using a 12th-order Morlet wavelet.
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The same as Fig. but for neutral density.
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Noticeably, the same layers of the enhanced fluctuations are also seen in the
neutral density measurements. The advantage of these measurements is that
they were done simultaneously on the same deck-facing ram on the upleg and
therefore in the same volume, which allows assessment of the joint reaction of
neutrals and electrons to the same underlying forcing – likely neutral
air turbulence. In the next section we utilize these measured spectra to
derive the Schmidt number.
Spectral analysis
We now split the wavelet spectra shown in Figs.
and into 100 m bins and derive the corresponding global
wavelet power spectra . These one-dimensional wavelet
spectra can further be used to characterize the observed small-scale
structures quantitatively. Thus, using the spectral model technique
introduced by , and extended by , it
is possible to derive turbulence energy dissipation rate, ε, from
the measured neutral density fluctuations. It is done by fitting a spectral
model of a passive scalar tracer in a turbulent field to a measured one-dimensional power spectrum of a corresponding tracer. The derived
ε values can further be used to unambiguously obtain the Schmidt
number of other tracers involved in the same turbulent motions
. This can achieved by fitting a Sc-dependent spectral
model, for example by , in which the ε value has to
be known.
Global wavelet spectrum from 81.85 to 81.95 km of electron
density fluctuations (solid black line) and of neutral density fluctuations
(solid red line). The dashed lines shows the best fit of the theoretical
models of (green) and of
(yellow). ε was kept constant for the fit of the Driscoll and Kennedy
model to the electron density fluctuations and is obtained from the fit of
the Heisenberg model to the neutral density fluctuations. The
Driscoll and Kennedy fit yielded a Schmidt number of Sc=4.2±1.4.
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Figure demonstrates the described derivation procedure of
the Schmidt number. It shows examples of measured spectra (solid lines) at
81.9 km height alongside with the fitted model spectra (dashed lines). The
best fit of the model by to the spectrum of neutral
density fluctuation yields the energy dissipation rate of
27.22 m W kg-1. From the best fit using the model by
(D&K) to spectrum of electron density
fluctuations we derive the Schmidt number of Sc =4.2±1.4. The error
of the Schmidt number consists of the uncertainty of the least squares fit,
the statistical uncertainty of multiple fits with random fit windows and an
estimate of the uncertainty propagation of the derived ε values.
Schmidt number profile
We derive a Sc–altitude profile by applying the procedure described in the
previous section to the measured density fluctuations in
the height range 70–100 km. The results for the WADIS-2 rocket flight are
shown in the left panel of Fig. . The smallest Schmidt
numbers are not significantly larger than 1, considering the uncertainty
of Sc. Figure also shows particle radii corresponding
to the obtained Schmidt numbers. Details to the derivation of the particle sizes are given hereafter.
(a) Schmidt number as a function of altitude obtained from
fitting the Driscoll and Kennedy theoretical model (red dots). For orientation Sc =1 is marked by the black dashed line and the transition of polarization
and hard sphere interaction by orange dashed line Sctr. The black
bars and grey shaded areas indicate the error of the Schmidt numbers (see
text for details). (b) Mean charged particle radius (r∼Sc) obtained from Schmidt numbers (green dots). The orange
dashed line indicate again the transition between polarization and hard
sphere interaction. Error bars are given in black and grey shaded areas (see
text for details).
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showed that the Schmidt number of electrons in dusty
plasma containing heavy charged aerosols can be related to the radius of
those aerosols as r=Sc/6.5 (for r in nm). This simple
relation, however, can only be applied to dust radii much larger than the mean
neutral molecule radius as in the case of mesospheric ice particles in
summer. We want to look at small radii and extend this approach. Under the
assumption that there are many more charged MSPs than electrons we may write
Sc=νDe≈νDd,forZd⋅Nd≫Ne,
where De is the electron and Dd the MSP diffusivity,
Zd=1 is the dust charge number, Nd dust number
density and Ne is the electron number density. For the smallest
particles, induced polarization in the neutral atoms dominates the interaction
between particle and neutral molecule. For larger particles a hard sphere
interaction model is appropriate. The transition between both models can be
derived by equating the collision integrals for both models and solving for
the particle transition radius yields
rtr=4.55×10-42αZa2e2ϵ0kBT14-rn,
where α=1.76×10-18 m-3 is the neutral atom
polarizability, Za is the particles charge number, e is the
elementary charge, ϵ0 is the vacuum permittivity, kB is
Boltzmann's constant and T is the temperature (assumed to be in thermal
equilibrium with the ambient gas). rn=1.8×10-10 m is
the neutral molecule radius . Note that
Eq. () only depends on temperature. A typical value for
the winter mesosphere for single charged particles and T=200 K is
rtr=0.45 nm. The diffusivity for particles with r<rtr is then given by the polarization model as
DdP=9.06×105kBTNn|Za|eϵ0παμdn,
where μdn=mdmnmd+mn is the
reduced mass with the mean molecular mass mn. The MSP mass is given by
md=4π3ϱrd3,
with the MSP radius rd and its mass density ϱ=2×103 kg m-3. Nn is the neutral air density. For
particles with rdc>rtr the diffusivity Dd
can be described by a hard sphere model :
DdH=38kBT2πμdn121Nn(rd+rn)2.
The diffusivities of both models, i.e., polarization and hard sphere, depend on the
particle size. In the polarization model the size is implicitly given by the
reduced mass μdn. By means of Eqs. (),
() and () one can derive the particle radius as
a function of Sc.
rdP=34πϱmnνScCP2-13,
where CP=9.06×105k_BTNn|Za|eϵ0παmn. For particles with radii larger than rtr
the diffusivity described by the hard sphere model is used. Inserting
Eq. () into Eq. () yields
Sc=83νNn2πmnkBT︸CH(rd+rn)21+mnmd︸reff2=CH⋅reff2,
where ν is the kinematic viscosity of air and reff is an
effective radius. Since CH can be calculated from in situ
measurements, we can derive reff for each Schmidt number via
reff=ScCH.
Schmidt number as a function of radius for the two interaction
models (hard sphere: blue; polarization: orange) and the expression found by
(dashed, black) calculated for the conditions given in
. The grey dashed line indicates the radius where the
transition between hard sphere and polarization interaction occurs.
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In the altitude range between 80 and 85 km CH is around
8 ± 0.1 nm-2, which is slightly larger than the value of
6.5 nm-2 found by . In the present work we analyze
data collected during winter conditions, whereas looked at
summer condition data. The difference can be found in temperature and
density. Figure shows Schmidt numbers calculated for the
conditions given in as a function of particle radius. The
Sc for the polarization (blue line) and hard sphere (orange line) interaction
model was derived by using Sc =νD and inserting the
respective diffusivity. The approximation found by is
shown by the dashed black line. It is apparent that the simplified relation
Sc =C(Nn,T)⋅r2 is valid only for large particles
r≳3 nm. For smaller radii the assumption that the charged particle
mean radius and mass is large compared to that of the mean neutral molecule
is not valid anymore.
However, the parameter of interest in Eq. () is the mean
charged particle radius rd, which is connected to the effective
radius by a linear relation for reff≳0.4 nm. This is
shown in Fig. , where the blue line is the functional
behavior of reff2=(rd+rn)21+mn/md, and in green a linear fit is
shown. The corresponding linear equation for rdH, in
nanometers, is
rdH=0.992⋅reff-0.154.
Using Eq. () we can calculate the mean charged particle radius
at a given height by
rdH=0.992⋅ScCH-0.154=0.992⋅3Sc8νNnkBT2πmn-0.154.
MSP radius to effective radius relation: the blue line shows the MSP
radius rd as a function of the effective radius reff.
A linear fit is shown by the green line.
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To identify whether the polarization or the hard sphere interaction is
dominant, we calculated the Schmidt number which corresponds to the
transition radius rtr. The radius can be calculated for each
height by Eq. () using the in situ-measured temperature.
The corresponding Schmidt number can thus be derived by
Sctr=νDdH,P(rtr),
where DdH,P is either the diffusivity for the hard sphere
DdH or the polarization DdP case at the transition
radius rtr. The results for Sctr and rtr
for WADIS-2 can be found in Fig. . Here the transition
Schmidt numbers and radii are shown by the orange dashed lines in the left
(Sctr) and right (rtr) panel, respectively. For
Schmidt numbers smaller than Sctr we calculated the particle
radius by means of Eq. (). For larger Schmidt numbers
Eq. () was used. The green dots show the radius of the MSPs
derived in this way. The maximum Schmidt number revealed by these
measurements was 6.6 and the minimum was 1.0, giving a mean charged
particle size from about 0.75 and 0.08 nm, respectively. The derived
Schmidt numbers or MSP radii describe an effective mean radius of the
aerosols at a given height. We will discuss the
obtained results in Sect. . It is not an issue that the entire
scope of the MSPs has to be described by a distribution function which is as yet unknown. In the next section we assess the width of an assumed
distribution function based on the simultaneous common volume in situ
measurements described above.
Particle size distribution
In the MLT research, recent works tend to describe particles size
distributions by the lognormal distribution
e.g.,.
Moreover, model calculations show that neutral MSP size distributions follow
lognormal-like distributions . With this
justification we choose the lognormal size distribution of MSPs to describe
the MLT charged dust population observed during the WADIS-2 rocket flight.
The aerosol density at a given height is then described by the following function:
f(r)=Nd-2πlnσ(r-λ)exp-12lnr-λr‾lnσ2,
where Nd- is the density of all negatively charged MSPs,
σ is the distributions width and r‾ is its mean. We added
λ as a limiting parameter, giving the lower size limit of particles
of 0.2 nm .
The entire number of dust particles at a given height can now be calculated
by integrating Eq. () over the entire population, i.e., for radii
from 0 to ∞.
Nd-=∫0∞f(r)dr
Theoretically this integral can be measured as a current of the charged
particles onto the PD electrode. In practice, the instrument measures a part
of the entire population starting at a critical radius, rc. As shown in
Sect. , for a given rocket flight, i.e., defined trajectory and
background density and temperature, rc is height dependent. The measurable
fraction of the entire distribution is described by the detection probability
function p(r) derived for particles in a mass range from 0–60 000 amu
from combined aerodynamical and electrostatic simulations in
Sect. . Thus, the measured PD charge density NPD can be
described by a product of two functions: the size distribution function
f(r) and the detection probability function p(r). This can be expressed
in terms of the measured charge number density at a given height:
NPD=∫0∞p(r)⋅f(r)dr.
In the frame of this work p(r) is a tabulated, discrete function derived
for particle radii between 0.58 and 2.28 nm (see
Table ).
The difference in measured densities of electrons and positive ions (see
Fig. ) in the height range 75–95 km can be
attributed to charged MSPs, which is in agreement with, for example,
and and shown in Sect. .
Additionally, during nighttime the majority of the MSPs are singly
negatively charged for radii less than ∼ 8 nm
e.g.,.
Thus, we can assume that the entire population of the negatively charged dust
particles, Nd-, can be derived from the difference of
densities of other plasma constituents:
Nd-=Ni+-Ne,
where Ni+ and Ne are measured densities of positive ions
and free electrons. The total number of charged particles is thus determined
by the measured electron and positive ion density. Changes in those
quantities also have an impact on the size distribution; these are
considered below.
By combining Eqs. () and () we can relate the
measured plasma densities with the parameters of the size distribution
function.
Ni+-Ne=∫0∞f(r)dr
With Eqs. () and () we now have a set of two
equations using the same size distribution function f(r) given by
Eq. (). The mean MSP radius, r‾, was derived from
independent Sc measurements in Sect. and summarized in
Fig. . The only unknown parameters is the width of the
distribution function, σ. Subsequently, we show results of the set of
equations solved numerically.
In Sect. we showed that the aerodynamics affect the MSP
density measurements below 82 km. This implies that the best-quality data to
characterize the MSP properties were measured in the range 82 to 90 km.
Therefore, we focus on this altitude range to derive the distribution
function.
First, we consider the thin layer of 100 m thickness at 82 km, where the
maximum current was measured by the PDs. The mean measured charge density
shown in Fig. reveals a value of
NPD= 224 cm-3 at 82 km height. The mean MSP radius derived from
independent Sc measurements in Sect. at this height results in
a value of r‾= 0.56 nm (see also Fig. ). The
charge difference derived from the measured densities of electrons and
positive ions shown in Fig. reveals a value of
10 000 cm-3, which is almost 2 orders of magnitude
higher than the MSP charge density measured by the PD. Substituting these
values in Eqs. (), () and () we derive
σ= 1.66. In practice, we change σ until the integral of
p(r)⋅f(r) over all r values reaches the measured peak value of
224 e cm-3 and the integral of f(r) over all r values becomes equal
to the charge difference between electrons and positive ions of
10 000 e cm-3. This difference, however, is dependent on the
uncertainty of the measurements of electron and ion density. To assess the
impact of those uncertainties on the distribution width we estimated the
uncertainty of charge difference Ne-Ni+ to be a factor of
2. Reducing Ne-Ni+ by this factor would cause an increase
in the distribution width by 0.3, i.e., to σ= 1.96, whereas
increased difference by a factor of 2 causes the width to be decreased by
0.14, i.e., to σ= 1.52. These changes are on the same order as the
uncertainty introduced by the Schmidt number.
Particle size density as a function of radius (solid lines, left-hand y axis). The blue line shows the estimated lognormal size distribution
and the green line the size distribution most likely seen as integral by the
PD at 82 km. The red dashed line indicates the fraction of the
distribution contributing to the PD current. The dashed dotted line shows the
detection probability of the PD as obtained from aerodynamic simulations
(right-hand y axis). The grey shaded areas indicate the error of the
distribution due to the uncertainty of Sc.
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Figure shows the resulting size distribution
of MSPs at 82 km height. The derived lognormal size
distribution of aerosols at 82 km is given by the blue line.
The black dashed dotted line is the particle detectors detection probability
function p(r). The measured fraction of the MSPs is indicated by the green
line. As shown above, it can be expressed as a product of the distribution
function and the detection efficiency function, f(r)⋅p(r). That is,
using these two curves (the green and the black dash-dotted) we reconstructed
the part of the distribution function shown by the red dashed line. The
uncertainty due to the error in the Schmidt number is indicated by the grey
shaded areas. The most relative variance is found for larger radii.
Our Sc analysis summarized in Fig. shows that the
observed MSP layer between 75 and 90 km may consist of several sublayers
of different sizes. Thus, considering the height range 81 to 85 km, we
derive the mean by using only Schmidt numbers larger than Sctr.
The resulting Sc is 3.3 and the corresponding radius is 0.48 nm. The
difference to the thin dust layer is within the uncertainty of the analysis.
Discussion
Aerosols play an important role in the physics of the MLT region. They can
have major impacts, for example, on the charge balance of the lower ionosphere.
In the presence of those aerosols, the number density of free electrons
during nighttime is likely reduced relative to the positive ion density since
electrons attach to those aerosols e.g.,. As a consequence there can be large
differences between the electron and positive ion density depending on the
number of electrons attached to aerosols. A large difference between
electrons and positive ions was also seen by our measurements
(Fig. ). Below 104 km the measured density profiles
show an increasing discrepancy indicating that it is necessary to account for
charged aerosols to satisfy the quasi-neutrality condition for the
ionospheric plasma in the mesopause region. The same feature has also been
observed before by, for example, and . At 85 km
there is approximately 1 order of magnitude more positive ions than
electrons. The charge densities measured with the PDs indicate that this
discrepancy can be attributed to the presence of heavy, predominately
negatively charged MSPs at least between 92 and 75 km. Note that
besides negative dust also negative ions, which were not measured in the
frame of the WADIS mission, are an important player in the charge balance in
the lower D region e.g.,. Nevertheless, negative ion density
(predominantly NO3- and O2- at night around 80 km) are thought to
rapidly decrease above 80 km during nighttime due to destruction by
atomic oxygen .
In situ measurements of O density (not shown here) on WADIS-2 show a rapid
increase above ∼ 77 km, which supports the assumption that negative
ions play only a minor role in the charge balance at those heights. Thus, the
assumption that the charge balance is dominated by free electrons, positive
ions and charged MSPs above 80 km is justified.
The charged particle density measured by the PD is approximately 2 orders
of magnitude less around 85 km than the difference between
positive ions and electrons. This can be explained by aerodynamic filtering
of measured particle densities by rocket-borne detectors. In situ
measurements of charged aerosols are influenced by the aerodynamic conditions
around the rocket body and electrostatic properties of the detecting
instrument.
However, the combined aerodynamic and electrostatic simulations in
Sect. showed that the decreasing current seen by the Faraday
cups above 82 km is not due to aerodynamic filtering. It can rather be
addressed to the decrease in MSP density with radii ≳ 1 nm.
According to our current understanding summarized by, for example,
,
neutral air turbulence in the mesosphere creates small-scale structures in
all plasma species, including charged aerosols, electrons and ions. The
heavier plasma components are collisionally dominated and behave as a passive
tracer. The electrons are electrostatically coupled to the plasma components
of the opposite charge and thereby show the same turbulent structures. The
presented measurements of electrons and neutral gas density fluctuations show
that there are structures at the same altitude range in both neutrals and
electrons. We found that the electrons were structured down to smaller scales
than the neutrals (see Fig. ), which is an indication of
the presence of heavy charged particles. In summer, when large ice particles
are present in the mesopause region, this leads to the creation of the PMSEs e.g.,. This
effect can be described by an enhanced Schmidt number Sc=νD,
i.e., the ratio of kinematic viscosity of air, ν, to diffusivity D, of
electrons. The Sc of electrons is becoming large due to their ultimate
electrostatic coupling to heavy charged aerosols whose diffusivity is
significantly reduced because of their mass. Typical values for Sc found in
PMSEs are several hundred on average and can often be several thousands
. The
same mechanism but involving MSPs was proposed to explain the PMWEs in the case when neutral turbulence is not sufficiently
large e.g.,.
The latter has not yet been confirmed by direct measurement. The MLT ice
particles in summer reveal sizes of tens of nanometers to 100 nm diameter
e.g., and consist of water ice. In winter the sizes of MSPs are significantly smaller, i.e., up to some nanometers
e.g.,. Hence, in winter Sc will be much smaller as it is
connected to the radius by Sc∼r2 and
Sect. . From our measurements we obtain Schmidt
numbers between 3 and 7, supporting the hypothesis that the effect of reducing
electron diffusivity by charged MSPs above 80 km in winter during nighttime is rather small. Using uncommon volume measurements of neutrals,
positive ions and MSPs, Schmidt numbers for winter conditions were also
derived by , showing comparably small Sc. They also
compared spectral features at large scales (>100 m) and stated that
turbulent structures are different between upleg and downleg
(∼ 50 km) and common volume measurements of charged and neutral
species are needed for a robust derivation of Sc. As reported in this
paper, with the WADIS-2 payload we were able to achieve this requirement for
the first time.
To convert the measured Schmidt number to particle radii, we followed the
work of , where two models were considered for charged
particle–neutral interaction via collisions. These models are the hard sphere
and the polarization model whereas the hard sphere model applicable to large
aerosols and the polarization model, relevant for small particles. Since we
deal with relatively small Schmidt numbers, we considered the corresponding
particle size to be in the transition region between those two models. Hence,
we looked at the relation between Sc and r at small radii considering
both models. The results show that calculated particle sizes in the
polarization interaction case are in the size range of molecules. In this
case there is no indication whether the diffusivity of electrons is dominated
by MSPs or molecular ions. We therefore conclude that for Schmidt numbers
smaller than the transition Schmidt number Sctr the derivation of
MSP radii from electron density fluctuations is not appropriate. The lower
limit of the connection between Schmidt number and aerosol size is the
transition between hard sphere and polarization interaction given by the
transition radius rtr and the corresponding Sctr. In
the case for the polar winter mesopause region we derived this limit as
rtr≈ 0.45 nm and Sctr≈ 3, respectively.
The derivation of the Schmidt number involves uncertainties which come from
different sources, which are, for example, the error of the ε derivation
and the error of the least squares fit to the measured spectra of the
electron density fluctuations. Other uncertainties such as temperature and
density measurement errors are negligible. As can be seen from
Fig. , Schmidt numbers larger than 1 do exist, even if
the errors are considered. Hence, the Sc measurements confirm the presence of
charged particles and their influence on the electron diffusivity.
The very small MSPs are formed from the material deposited by incoming
meteorites e.g.,. They are thought to
grow via homogeneous nucleation and coagulation processes which yield an
altitude-dependent size distribution e.g.,. Model
results show that the particle size increases with decreasing altitude
. The same was also shown by
in situ measurements for charged particles . Other
properties, such as charge state and composition of charged MSPs, were measured
in situ e.g., and by ground-based radar
measurement techniques . The latter is
only possible when MSPs produce secondary effects by influencing properties of
ionospheric plasma which leads to radar echoes (PMWEs). There are also active
radar experiments that heat free electrons at MLT heights by HF waves emitted
from the ground and, in parallel, examine the behavior of PMWEs in VHF band
. The
so-called heating experiments gave a strong indication that dust is involved
in the PMWE formation and that there are large charged particles on the order
of ∼ 3 nm at lower altitudes which also
substantiate the increase in the number of large particles with decreasing
altitude. This is also in agreement with the results shown in the left panel
of Fig. .
Our size estimate based on the obtained Sc suggests that a large number
of very small MSPs, i.e., with r<1 nm was present around 80 km. The
existence of very small MSPs with radii less than 1 nm in the winter mesosphere
was shown by remote sensing techniques as well as in situ experiments
e.g.,. The size of
the particles is a crucial parameter in the electron diffusivity and hence in
the radar backscatter theory. The mean particle radii found in this study are
in agreement with earlier findings. However, in situ measurements to quantify
the size distribution of the MSPs are very rare and rather coarse
. By means of the mean radius obtained from the
Schmidt numbers (see Sect. ), the difference between
electron and positive ion density, and the integrated density of charged
particles down to the detection limit of the PD, we estimated the size
distribution of the charged MSPs in Sect. . The
resulting distribution shows that 99.9 % of the charged particles are
smaller than ∼ 4 nm; 90 % are smaller than ∼ 1.7 nm.
In comparison with model results of neutral MSPs, where approximately
96 % of the particles are smaller than 1 nm , we
found that there are relatively more charged particles of larger sizes than
in the modeled neutral size distribution. Hence, this confirms that smallest
particles are less likely to become charged. The influence of the estimated
uncertainty in the total charge difference between electrons and positive
ions was found to be on the order of the uncertainty introduced by the
Schmidt number derivation.
The charging rate of aerosols increases proportionally to their cross section
. As already mentioned, model calculations showed that
the number density of all MSPs decreases with size e.g.,. The size distribution of charged MSPs
f(r) is a product of the charging probability and the neutral dust size
distribution. Therefore our distribution function accounts for two processes.
The first is the increase in MSP size with decreasing height due to growth,
sedimentation and coagulation. This behavior is also apparent in our results
seen in Figs. and . The second process
accounts for the smallest particles being less likely to become charged
and hence the density of charged MSPs with small radii
decreases. Considering the location and width parameter of the size
distribution function, which is given by its mean r‾ and width
σ, we find that the particle size range is in agreement with other in situ and
remote findings yielding particle sizes in the range of 0.5 to 1.5 nm
.
Compared to size distributions obtained from the model of MSPs at 90 km,
regardless of their charge, the number of particles with 0.5 nm is on the
same order of magnitude as found in the model Fig. 2.
The derived charged particle distribution shows more particles at larger
radii than found for MSPs by models . However, as
, for example, showed, their model output is highly dependent on
less well known parameters such as coagulation rate, eddy diffusion and
meteoric input and the difference to our results are in the model
uncertainty. We assume a lognormal distribution of charged MSPs. However,
other shapes of the distribution could be possible. For instance, more than
one maximum is conceivable. This is heavily dependent on the so-called
“sticking coefficient” of electrons to the smallest MSP since there are a lot
more small than large particles above 80 km
e.g.,. The sticking coefficients are
not well known and depend on the dust material . Thus,
more size-resolving measurements of neutral and charged dust in the
mesosphere are highly needed, but further study of charging processes of
smallest aerosols is also required.
Our findings show that the dust is structured in layers of increased density
of large particles. These structures can be found in the left panel of
Fig. around 78 and 79 km as
locally increased density. Additionally, those structures can be found in
both profiles of the PD measurements, which indicates that these are not
artifacts but rather a real geophysical feature. At the same heights,
independent measurements show that there are increased Schmidt numbers, i.e.,
mean particle radii (see Fig. ). Since both those
techniques are more sensitive to larger MSPs, this clearly indicates layers of
large MSPs. That is, our measurements show that, on top of the continuous MSP
background spanning over ∼ 20 km (i.e.,
75–92 km), there are layers of larger MSPs. These layers
are of ∼ 0.3 km in extent and they are separated by
∼ 1 km. The study of the exact mechanism behind this
layering lies beyond the scope of the present work.
Conclusions
In this work we presented results of in situ measurements of MLT dusty-plasma densities, including electrons, positive ions and charged
aerosols conducted during the WADIS-2 sounding rocket campaign. Neutral air density fluctuations were also measured, allowing for robust derivation of
turbulence energy dissipation rates. A unique feature of all these
measurements is that for the first time they were done in a common
volume and with high spatial resolution.
The MSP densities were measured with a classical Faraday cup. These
measurements are known to be affected by the aerodynamics of the
sounding rocket flight as well as the electrostatic potentials of the instrument's grids. We
quantified this influence from combined electrostatic and aerodynamic
simulations and derived a height-dependent critical radius. Based on
these simulations we conclude that the measured densities of
charged MSPs reflect real size–altitude dependence above 82 km. Above
those heights the electrostatic barrier of the grid potentials limits
the size of the detectable particles. The measured MSP densities below
82 km are a product of the real density and the height-dependent
aerodynamic filtering and therefore have been analyzed considering the aerodynamic effects.
We also derived an altitude profile of Schmidt numbers from electron density fluctuations
with 100 m resolution. These Sc numbers were converted to MSP radii by applying two
different models, i.e., polarization and hard sphere model for very small and
larger MSPs, respectively. These are the first reliable in situ measurements of MSP
radii based on Sc for winter conditions. Our measurements reveal a very large number of small (r<2 nm) MSPs. These findings are in agreement with
previous studies. Therefore, we derived a transition value for Sc and r
and conclude that below this value the conversion of Sc to r is not
reliable. For the WADIS-2 flight conditions, i.e., polar winter night, these
values are Sctr=3 and rtr=0.45 nm. The derived
mean radius of the charged MSPs was r=0.56 nm in the altitude range
81.9 to 82.0 km and r=0.48 nm in the range 81–85 km. The
difference lies within the uncertainty limits of this technique.
Due to the unique constellation of instruments, all the measurements were done
in the same volume, and we were able to reliably derive an MSP size distribution
function assuming lognormal shape. The derived width in log scale of the
distribution function is 1.66 for the height range
81.9–82.0 km and 1.76 for the range
81–85 km. However, the presented technique has
inevitable uncertainties and needs to be validated by a more direct in situ
measurement of charged particle size distribution.
We also found that the thick continuous layer of charged MSPs observed by the
PD between ∼ 75 and 92 km showed inhomogeneities in
terms of enhanced charged MSP density. Those inhomogeneities coincide with
enhanced electron Schmidt numbers. Thus, the large particles with
sizes > 1 nm were stratified in layers of ∼ 1 km
thickness and lying some kilometers apart from each other. This phenomenon
might be connected to wave activity or neutral turbulence. However the exact
mechanism of this layering remains unclear and will be the subject of future
studies.