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The ionization efficiency of aluminum and iron at meteoric velocities
Planetary and Space Science xxx (2017) 1–6
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The ionization efficiency of aluminum and iron at meteoric velocities Michael DeLuca a, b, c, *, Tobin Munsat c, d, Evan Thomas c, d, Zoltan Sternovsky a, b, c a
Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO, USA Smead Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO, USA c Institute for Modeling Plasma, Atmospheres, and Cosmic Dust, University of Colorado, Boulder, CO, USA d Department of Physics, University of Colorado, Boulder, CO, USA b
A R T I C L E I N F O
A B S T R A C T
Keywords: Meteors Ionization efficiency Aluminum Iron Laboratory experiments
The ionization efficiency of aluminum was measured in the laboratory over an extended velocity range of 10.8–73.4 km/s and compared to available models. The measurements were made by shooting submicron-sized aluminum dust particles into an air chamber using the University of Colorado's dust accelerator facility. The ionization efficiency, β, is calculated from the total charge generated in the chamber during the complete ablation of particles of known mass. An array of photomultiplier tubes observed the light production by a subset of particles in the chamber to confirm that a moderate deceleration of the ablating particles occurred at low velocities. This information allows the interpretation of the β measurements to be extended to velocities <20 km/s, with the understanding that the low-velocity β measurements are lower limits. Updated β measurements for iron particles are also reported over an extended velocity range compared to previously published data: 10.5–87.3 km/s. The measurements are fit to functions for the ionization efficiency across the entire velocity range, and a semiempirical function is presented which matches the shape of the measured β curves for aluminum and iron at both high and low velocities.
1. Introduction The Earth collides with billions of micrometeoroids as it orbits the Sun (Janches et al., 2009). The incoming particle flux poses a risk to spacecraft and injects metals into Earth's mesosphere. The particles enter Earth's atmosphere as meteors traveling at geocentric speeds in the range 11–72 km/s (Baggaley, 2002). Estimates of the meteoric mass input flux range from 5–100 metric tons per day (Plane et al., 2015), mostly in the form of small particles whose distribution peaks around 1–10 μg (Williams and Murad, 2002). These particles originate mainly from asteroids and comets, and they provide a continuous source of exotic elements in the atmosphere. Among other things, meteoric elements lead to the formation of metal layers in the atmosphere, are involved in the formation of noctilucent clouds, and provide a source of bio-available iron to the oceans (Plane, 2012). Radars are sensitive to the meteor phenomena and offer the means to constrain the total meteoric mass input and velocity distribution, as they cover the mass range that provides the bulk of the input (Plane, 2012). High Power and Large Aperture (HPLA) radars, such as the sensitive 430 MHz radar at the Arecibo Observatory in Puerto Rico, detect the ball
of ionization that forms around a meteor as it enters the atmosphere, known as a head echo. Under current models, meteoroids entering the atmosphere will heat up and slow down due to collisions with air molecules, melt, and ablate through evaporation (Hood and Horanyi, 1991; Kalashnikova et al., 2000; Vondrak et al., 2008). Sputtering may also play a role, and different constituents of the particle can evaporate at different points along the meteor's path through the process of differential ablation (Vondrak et al., 2008; Janches et al., 2009). Ablated atoms will then collide with background gas molecules and ionization may occur, leading to the formation of free electrons, which are visible to radars (Baggaley, 2002). The ionization efficiency, β, is the average number of electrons that will be produced per ablated atom, and is a function of the meteor's velocity and the species involved in the collision (Bronshten, 1983; Jones, 1997). β is used to determine the detectability of different meteoroid populations and the mass of the particle from the strength of the radar signal (Close et al., 2005; Janches et al., 2014). One of the difficulties in using radars to determine meteor mass and detectability, however, lies in the challenge of finding accurate β values, which have been determined experimentally only for a few species and/or over a limited velocity range. The semi-empirical functional form for β often
* Corresponding author. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO, USA. E-mail address: [email protected] (M. DeLuca). https://doi.org/10.1016/j.pss.2017.11.003 Received 30 June 2017; Received in revised form 11 September 2017; Accepted 1 November 2017 Available online xxxx 0032-0633/© 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: DeLuca, M., et al., The ionization efficiency of aluminum and iron at meteoric velocities, Planetary and Space Science (2017), https://doi.org/10.1016/j.pss.2017.11.003
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particles are smaller than typical meteoroids, but the relevant physics for the simulated meteors and real meteors is the same because the simulated meteors in the experiment are in a free molecular flow regime, just like most real meteors. Therefore, the experimental results should scale to the analysis of typical meteors. Recently, the facility has been upgraded with a set of PMT detectors that allow the ablating particles to be monitored optically, which allows their velocities to be inferred (Thomas et al., 2017). 4 PMTs, each with 16 channels, detect the light the particles produce as they travel through the chamber. Narrow slits placed between each PMT and the chamber's windows map each of the 64 PMT channels to a 6.4 mm long portion of the 41 cm long ablation chamber. Taking into account the width of the spatial bins and the finite width of the slit, the uncertainty in position on each PMT channel observation is about ±0.38 cm. Due to limited high-speed data acquisition capabilities, only 29 out of the 64 PMT channels were monitored (distributed evenly along the path). The particle's motion in the chamber can be tracked assuming that the photons a given PMT channel observes are emitted by the particle when it is located in the field of view the PMT channel observes. The PMT data indicates that this assumption is valid.
used for interpreting meteor radar data comes from Jones (1997). To explain the lack of radar observations of low-velocity meteors which are predicted by astronomical models (Nesvorný et al., 2010), it has been proposed that β values might be up to two orders of magnitude smaller than predicted by Jones (1997) near the low end of the velocities of interest (Janches et al., 2014, 2015). This would mean that the meteors are present but not easily detected due to diminishing ionization. To study meteor ablation under laboratory conditions, a dust accelerator and ablation chamber facility is operated at the University of Colorado (Thomas et al., 2017). The University of Colorado's ablation facility measures the charge production of ablating particles. Complementary studies are undertaken at the University of Leeds using the Meteoric Ablation Simulator, which measures the ablation rates of metals (Bones et al., 2016; G omez Martín et al., 2017). At the University of Colorado, iron and aluminum have been studied to shed light on the physics of meteor ablation and ionization using simple compositions. More realistic and complex meteor compositions (e.g., olivine) will be studied in future experiments. β values have been determined for iron particles impacting various gases including N2, CO2, He, and air. The ionization efficiency measurements confirmed earlier results by Jones (1997) for velocities >20 km/s (Thomas et al., 2016). The analysis by Thomas et al. (2016) was restricted to velocities >20 km/s as numerical modeling of the ablation process indicated that low-speed particles, i.e. 10–20 km/s, could slow down significantly when encountering air drag in the experiment, thereby biasing the β measurements in the regime where the ionization efficiency changes rapidly with velocity. The goal of the ionization efficiency experiments is to get unbiased β measurements as a function purely of velocity, so that these results will be widely applicable to a range of meteoroids with different deceleration profiles. The deceleration of a meteoroid will vary depending on its size, shape, composition, velocity, and the air density (Vondrak et al., 2008). Recently, the experimental setup used for the β measurements has been upgraded to include optical observations of the ablating particle using photomultiplier tubes (PMTs). The new experimental results indicate that the slowdown of simulated meteors in the experiment is moderate and a lower limit on the β values can be placed for velocities below 20 km/s. This paper presents the results from the laboratory investigation of the ablation of aluminum particles along with the extension of the β values for iron to lower velocities.
3. Experimental results 3.1. PMT observations The PMT observations indicate that low-speed aluminum particles experience slowdown inside the ablation chamber. Fig. 1 shows an example of light detected from a particle with an initial speed of 16.5 km/s ablating in the chamber held at a pressure of 65 mTorr. The output of each PMT channel is digitized at 40 MS/s and the pulses in the signal correspond to detected photons. There is a clear correlation between the relative time of detection and the order (or range) of the PMT channel along the ablation chamber. For this analysis, it was assumed that the photons are emitted by the ablating particle while it is in the field of view of a given channel. For PMT channels with multiple pulses, the first pulse was used to locate the particle. The slope of the line fitted to the PMT observations provides the average velocity for the particle over the spatial range for which there are PMT observations (11–28 cm into the chamber for the event in Fig. 1). The light collected by the PMT channels was sparse, usually a few photons or less. Since the PMT observations are over a limited range, a simple linear fit was used as a rough first approximation of the particle's velocity in the observed range. The linear fit in Fig. 1 is shown with a black line, and it gives a velocity of 13:8±0:3 km=s. The entry velocity of the particle is 16:5±0:5 km=s and is shown by the slope of the blue line. The PMT-observed velocity is significantly below the initial velocity, even when accounting for the uncertainty on the initial velocity. The PMT observations show that the particle is decelerating in the chamber and that this deceleration is moderate. The example shown here is typical for all other particles with high-quality PMT data, providing evidence for slowdown due to air drag inside the ablation chamber. The PMTs observed slowdown by approximately 2–3 km/s, or about 10%–20% of the initial speed, for all particles with sufficient PMT data. To assess the slowdown using PMT observations, only particles that produced sufficient amounts of light (i.e., produced clearly correlated pulses on 7 or more channels) were included in this analysis. That way, each particle's position could be determined unambiguously despite noise on the channels from dark current. There were 6 such particles observed out of 44 events where PMT data was taken. In each of the 6 cases, the linear fit to the PMT pulses is outside of the uncertainty on the initial velocity (about 3%) even when accounting for the error on the fit. It is concluded that the PMTs are observing moderate slowdown in the simulated meteors, the effect of which is to bias the β measurements. This bias deflates the measured β values as ionizing collisions on average will occur at somewhat lower values than the entrance velocity at which the β values are reported. β changes most rapidly at low velocities, so
2. Experimental setup A unique facility is operated at the University of Colorado to simulate the ablation of micrometeoroids and is described in detail by Thomas et al. (2017). Briefly, an electrostatic dust accelerator is used to generate submicron-sized particles with a wide range of velocities, about 1–100 km/s (Shu et al., 2012). The mass and velocity of each accelerator particle is measured and those particles traveling in the desired speed range are allowed to enter the ablation chamber, which is filled with the desired gas and maintained at constant pressure. Inside the ablation chamber, there is an array of 16 sensitive charge collectors that are biased to collect either the positive ions or electrons generated along the ablation path. An impact detector is mounted at the end of the ablation chamber to measure the mass of the remaining particle, if any. The pressure in the chamber is adjusted for various mass/velocity ranges of the particles to ensure full ablation. The ionization efficiency, β, is then calculated from the total generated charge and the mass of the particle. The new laboratory measurements were performed using aluminum dust particles accelerated to velocities in the 10.8–73.4 km/s range. This was the first time that aluminum had been successfully used in this accelerator facility. Based on experience with samples of other materials, a mixture of larger and smaller particles was used. By mass, the mixture was 5% 40–60 nm particles, 5% 80–100 nm particles, 45% 3–4.5 μm particles, 30% 4.7–7 μm particles, and 15% 10–14 μm particles, all measured in diameter. Scanning electron microscope images of the individual dust samples confirmed that the particles are spherical. These 2
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Fig. 1. Left: The raw data from the 29 PMT channels, stacked according to their order. Red lines indicate channels with a PMT signal, typically detecting one or a few photons. Right: The time of each PMT detection is plotted against the range inside the ablation chamber. The blue line indicates the 16.5 km/s initial velocity of the particle measured by the accelerator facility. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
measurement is shown on the velocity axis. The measurements are colorcoded based on the pressure in the ablation chamber, which was adjusted as necessary to ensure complete ablation. Slower particles required higher pressures to fully ablate inside the chamber. The aluminum β measurements reported here make use of an updated calibration of the mass measurements of the dust particles generated by the accelerator facility. The accelerator generates charged dust particles which are accelerated through a high (2–3 MV) electric potential. The initial charge of the particles is enough to accelerate them to velocities >10 km/s, but still much less than the charge produced during ablation, so the initial charge of the particle does not skew the ionization efficiency measurements. Detectors on the accelerator's beamline measure the initial charge of the particle and its velocity, from which the mass is calculated (see Shu et al. (2012) for more details). Previous measurements, including those reported by Thomas et al. (2016), overestimated the particles' masses by overestimating the particles' initial charges. The original calibration overestimated the masses by about 65%. The new calibration of the dust accelerator's beamline detectors has been completed, which also reduced the uncertainty in the dust mass to approximately 10%. The details of the new calibration procedure will be presented elsewhere in a future publication. Based on the new calibration, the β measurements by Thomas et al.
slowdown will have a more pronounced effect on the measured values of β at low speeds. It is difficult to correct for the slowdown in the β measurements as doing so would require a more detailed understanding of the ablation process. For complete ablation, as investigated in these experiments, the particle is first heated and the highest rate of mass loss occurs at the beginning after the particle's temperature is sufficiently high. Consequently, most of the charge production should occur while the particle is moving with a velocity that is close to the entry velocity, but a bias towards lower values of β will still be present. The β measurements presented below are therefore lower limits on the true β values. 3.2. β Measurements The aluminum β measurements are shown in Fig. 2. The value of β for a fully-ablated particle is calculated by dividing the total charge collected in the chamber (in units of elementary charges) by the number of aluminum atoms in the particle. Particles that did not fully ablate were discarded from this analysis. The particles’ initial velocities range from 10.8 to 73.4 km/s, covering the entire speed range over which interplanetary meteors are expected to occur. The initial velocity of each
Fig. 2. The measured β values for aluminum as a function of velocity. The data points are color-coded based on the pressure in the ablation chamber. The blue line shows the best fit to the Jones (1997) function, given by Eq. (3). The red line shows the fit to Eq. (8) with n ¼ 1:6. The dashed black line shows Eq. (3) using the parameter c predicted using the method of Janches et al. (2017). See the text for more details. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Measured β values for iron, including data below 20 km/s that were previously not considered. The blue line shows the fit to Eq. (3). The red line shows the fit to Eq. (8) with n ¼ 1:6. Compared to Thomas et al. (2016), the β values are updated based on the improved mass calibration for the accelerator facility. See the text for more details. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 3
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been in contact with air, which means that its surface is oxidized with an aluminum oxide layer up to 4 nm thick on particles greater than 10 nm in size (Suits et al., 1995; Campbell et al., 1999). For the majority of the particles used in the experiment, a 4 nm thick aluminum oxide layer would comprise 10%–30% of the particle's total volume. It is not clear whether the oxidized surface would inflate or deflate the β measurements, as this depends greatly on the form in which the compound is ablated from the particle's surface. If the compound does not dissociate when ablated, the β measurements are likely deflated as it is harder to ionize the oxide than aluminum. The effect would be most pronounced at high velocities, as high-velocity particles produced by the accelerator tend to be smaller than low-velocity particles so would have more aluminum oxide by volume (the smallest and fastest particle in the aluminum β experiment presented here had a radius of 22 nm, so would be 45% aluminum oxide by volume if it had a 4 nm thick aluminum oxide outer layer). Large low-velocity particles would be less affected. The possible presence of an aluminum oxide layer on the aluminum dust is not included in this analysis.
(2016) for iron interacting with air have been updated. To account for the overestimate in mass, the β measurements for iron have been increased. The results are shown in Fig. 3. In the original analysis of iron β values by Thomas et al. (2016), velocities below 20 km/s were excluded due to concerns about excessive slowdown affecting the measurements, but all velocities are included here. Like the low-speed aluminum measurements, the low-speed iron measurements in Fig. 3 are lower limits. The measurement errors on the β values are calculated from the uncertainties in the collected charge and the mass determination. The mass is measured with an accuracy of about ±10%. The charge-collecting electronics in the ablation chamber are calibrated to 1% accuracy for each collector, which typically dominates the error in the charge measurement over the RMS noise of the charge sensitive amplifiers. In the worst-case scenario, the total charge is measured as the sum of all 16 collectors, adding up to ±4% uncertainty in the charge measurement. In addition, there is a 3% uncertainty in the initial velocity of the particles. The uncertainty in initial velocity translates to an error in the β value as δβ ¼ jdβðvÞ=dvjδv, where βðvÞ is given by the function with the best fit to the data (Eq. (8) in Section 5). The error bars in Figs. 2 and 3 show the total uncertainty on the measurements. There are also systematic biases (in addition to the slowdown bias) that can potentially affect the β measurements. Thomas et al. (2017) analyzed the efficiency of collecting the charge generated by the ablation process and found that the inefficiency in charge collection is small compared to the error discussed above. The inflation of β values is possible due to electron impact ionization, where the free electrons generated by ablation may generate additional electron-ion pairs as they are accelerated towards the biased charge-collecting electrodes inside the chamber. Thomas et al. (2017) analyzed this effect through numerical simulations and found that for the 90 V electrode bias potential used in the measurements here up to 30% additional charge generation is possible, depending on the pressure in the chamber. Measurement of the ionization efficiency performed over a wide range of chamber pressures (see Fig. 2) and bias potentials indicate that the effect of secondary ionization is limited and it is thus neglected in the present data analysis. Recombination between electrons and ions that form in the chamber could also introduce a bias by removing free electrons from the experiment before they are counted. However, the effect of recombination is minor, as the number density of ionized species is about 10 orders of magnitude less than the number density of neutral species. A charged particle will undergo about 10–100 collisions before being collected at the charge-collecting electrodes, so the odds of a collision between two oppositely-charged particles leading to recombination is negligible. The electron affinity of oxygen can introduce a bias by producing charged particles without producing free electrons. O2 is present in the atmosphere at a level of 21% and, as Moutinho et al. (1971) pointed out, it can enhance the ionization efficiency at low impact velocities, where it is energetically easier to generate a negative O 2 ion instead of a free electron. The ablation experiment cannot distinguish between the generation of a free electron and O 2 , although it makes a difference for radar observations. The presence of O 2 would inflate the β measurements, as the number of charges collected would not be equivalent to the number of free electrons produced. However, β measurements for iron made with the ablation chamber are similar for both N2 and air, so the effect is limited. The role of oxygen will need to be investigated in future experiments, but for the results presented in this paper it is assumed that the electron affinity of oxygen is not introducing a significant bias in the charge measurements. Oxygen can further bias the aluminum β measurements by reacting with the aluminum dust particles used in the experiment. Aluminum atoms that are ablated from the particles could chemically bond with oxygen from the background gas, but any such effect would be limited to at most a measurement bias of 21%, the fraction of oxygen in air. Ablated aluminum atoms that bond with oxygen rather than ionize will reduce the measured value of β. Furthermore, the aluminum dust sample has
4. Fits to the β measurements 4.1. Fits to the aluminum measurements The β versus velocity curves presented in Figs. 2 and 3 were fit to two functions which are commonly used to describe the ionization efficiency of meteors: a simple power law, and a function given by Jones (1997) which provides the following semi-empirical form for the primary ionization probability, i.e. the probability of ionization for a single collision between a meteor atom and an atmospheric molecule: 2
β0 ðvÞ ¼
cðv v0 Þ v0:8 : 1 þ cðv v0 Þ2 v0:8
(1)
The fitting parameter c is unique to the species of the meteoric atom and the target gas. v is the velocity of the meteoric atom and v0 is the threshold velocity below which no ionization of the meteoric atom will occur. The equation for the threshold velocity is given by Jones (1997) as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ð1 þ μÞeψ v0 ¼ μma
(2)
where μ is the ratio of the mass of a meteor atom to the mass of an average air molecule, ma is the average mass of an air molecule, e is the electron charge, and ψ is the ionization potential. v0 ¼ 9:10 km=s for aluminum interacting with air, and v0 ¼ 8:95 km=s for iron interacting with air (assuming an atmosphere that is 79% N2 and 21% O2). Jones (1997) adds a small correction to β0 to account for the possibility that ionization does not occur on the first collision and will instead occur on a subsequent collision: 2
βðvÞ ¼ β0 ðvÞ þ ð1 β0 ðvÞ Þ
ð1 þ μÞ v ∫ v0 βðv0 Þv0 dv0 : 2v2 μ
(3)
The integral correction term changes the value of β by no more than 50% over β0 for a cometary meteor (Jones, 1997). v To solve Eq. (3), a substitution of the form u ¼ ∫ v0 βðv0 Þv0 dv0 was made as described by Thomas et al. (2016), which results in the following ordinary differential equation:
du ð1 þ μÞ2 ¼ vβ0 ðvÞ þ ð1 β0 ðvÞ Þ u: dv 2vμ
(4)
Eq. (4) was solved using a fourth-order Runge-Kutta integrator for given values of c and v, and turned back into a β value using β ¼ 1v du dv. The IDL
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aluminum atom and air molecule will have a lower internal energy with less energy available for ionizing collisions. In addition to the threshold velocity, the parameter c in Eq. (1) determines the ionization efficiency of an element. The parameter c relates to the ionization and elastic collision cross sections as discussed below. The similarity in the β curves indicates that aluminum and iron have similar c parameters in Eq. (1). The measurements presented in this paper are lower limits on the true β values, especially at low velocities where the effects of slowdown are more pronounced. The effect of slowdown on β will be worst at low velocities, since those particles experience the largest slowdowns before completely ablating and the β curve is steepest at low velocities. Eq. (3) underestimates the β values at low velocities, especially when considering that the presented data are lower limits. Figs. 2 and 3 suggest that the semi-empirical form of β0 in Eq. (1) needs revision in order to provide better agreement with the data over the entire velocity range. To derive Eq. (1), Jones (1997) wrote the primary ionization as β0 ðvÞ ¼ σ i =σ t , where σ i is the ionization cross section and σ t is the total cross section, approximated as σ t ¼ σ i þ σ el where σ el is the elastic scattering cross section. For the cross sections, Jones (1997) used σ el v0:8 , citing Bronshten (1983), and σ i ðv v0 Þn following the work of Sida (1969) with a suggested value of n ¼ 2. Following this argument, and instead of fixing n ¼ 2, the suggested form for the ionization efficiency is
curvefit function was used to match Eq. (3) to the observed values of v and β by varying the value of c. Each data point in the fit was weighted by its measurement error. The best fit, for all β values across the entire measured speed range, occurs at c ¼ 3:44 105 ±0:06 105 (c given in ðs=kmÞ2:8 ). Fig. 2 shows the fit of Eq. (3) to the aluminum data across all velocities using this parameter. Note that β, and thus the parameter c, is similar for aluminum and iron. Janches et al. (2017) predicted a higher ionization efficiency for aluminum compared to iron based on aluminum's lower ionization potential. Janches et al. (2017) provide an equation to predict the parameter c for species X based on the parameter c for iron:
cðXÞ ¼ cðFeÞ
2 ψðFeÞ ψðXÞ
(5)
where ψ designates the ionization potential. The dashed black curve in Fig. 2 is βðvÞ calculated from Eq. (3) using cðAlÞ from Eq. (5). This predicted curve matches the measurements at low speeds, but overestimates β at moderate to high speeds. At speeds >20 km/s, the measured β values appear to follow a simple power law: β ¼ avb . Fitting the measured β values above 20 km/s to such a power law, with v specified in km/s, gives
βðvÞ ¼ 1:89 104 v2:07 :
(6)
cðv v0 Þ v0:8 n 1 þ cðv v0 Þ v0:8 n
The error on the coefficient is 0:28 104 , and the error on the exponent is 0:04. The power law fit is convenient for estimating β values at high velocities. As seen in Fig. 2, even though the β measurements presented here are lower limits on the true β values at low velocities, the shape of Eq. (3) is such that it still underestimates the β measurements at the lowest velocities.
βðvÞ ¼
(8)
where n and c are parameters that can be varied to produce a better empirical fit to the data. The integral correction term in Eq. (3) is neglected in Eq. (8) as it provides a correction of <50% over the primary ionization given by Eq. (1). Eq. (8) is limited to β < 1 because it is based on the primary ionization probability, so further theoretical work will be needed to find a functional form for the ionization efficiency that can account for all β values including β 1. β > 1 was measured multiple times for iron, but only at the highest speeds measured here which would mainly be relevant to interstellar meteors (Chau et al., 2007). Eq. (8) is therefore taken as a reasonable approximation to empirically fit the majority of the data. A value of n ¼ 1:6 in Eq. (8) was found to give a reasonable fit to both the iron and the aluminum β measurements, so that is the value of n suggested for fitting data to Eq. (8). With n fixed to 1.6, the fit of Eq. (8) to the aluminum β measurements gives c ¼ 1:60 104 ±0:03 104 (c
4.2. Fits to the modified iron measurements The β values for iron corroborate the findings based on aluminum. Thomas et al. (2016) found the parameter for iron striking air to be c ¼ 1:97 105 when fit to particles traveling over 20 km/s, which differs from the value c ¼ 3:45 105 which Jones (1997) originally calculated. However, the β values used in the study by Thomas et al. (2016) were underestimated due to calibration errors in the mass determination as discussed above. Using the updated β measurements, the parameter for iron-air interactions is now calculated to be c ¼ 3:76 105 ±0:07 105 when fitting to speeds over 20 km/s, which is closer to the value reported by Jones (1997) who fit earlier data by Slattery and Friichtenicht (1967). Extending the fit to all velocities gives c ¼ 4:07 105 ±0:07 105 , which is shown in Fig. 3 along with the corrected β values. Like aluminum, the fit to the extended iron data using Eq. (3) underestimates the value of β at low speeds. The updated power law for iron, for v > 20 km=s, is given by
The error on the coefficient is 0:31 104 , and the error on the exponent is 0:04. Note that the exponent in Eq. (7) for iron is very similar to the exponent in Eq. (6) for aluminum.
specified in ðs=kmÞ2:4 ). The fit is shown in Fig. 2. The new fit is better than the original especially at the lowest velocities reported here, and it does a better job of matching the shape of the observed β curve at both high and low velocities. For the iron data, the best fit to Eq. (8) when n ¼ 1:6 is at c ¼ 1:95 104 ±0:03 104 , as shown in Fig. 3. It is also an improvement over the fit of Eq. (3). The new fits presented here by empirically matching Eq. (8) to the data are likely to need modification, particularly if the low-velocity β values are corrected to account for slowdown bias effects. Improved modeling of the ionization, deceleration, and ablation processes, and a more comprehensive theory that can fit the measured data across all velocities, will be needed to create an improved model of the ionization efficiency.
5. Discussion
6. Summary
The aluminum β measurements are similar to the iron β measurements at all velocities, which is somewhat surprising given that aluminum has a lower ionization potential than iron (6.0 eV for aluminum, 7.9 eV for iron). We attribute part of the similarity of the β curves to the similarity of the threshold velocities for both iron and aluminum using Eq. (2): in air, v0 ¼ 9:10 km=s for aluminum and v0 ¼ 8:95 km=s for iron. Although aluminum has a lower ionization potential than iron, its lower mass also means that the system formed by a colliding
Measurements of charge production and slowdown for simulated aluminum meteors have been made using the University of Colorado's dust accelerator facility. The measurements were enabled by the facility's ablation chamber with an updated PMT observing setup. The PMT observations clearly indicate slowdown occurs when low-velocity particles enter the ablation chamber, which will bias the β measurements made at low velocities towards lower values. Despite the bias introduced by air drag, the measured β values can still be taken as lower limits on the
βðvÞ ¼ 2:49 104 v2:04 :
(7)
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detectability of aluminum in meteors. The current understanding of meteor ionization is provided by Jones (1997), but Eq. (3) underestimates the low-velocity β values for aluminum when fit across the entire velocity range, and does not match the shape of the measured β curve. A similar problem is encountered when the results are applied to updated iron measurements originally reported by Thomas et al. (2016). Eq. (8) with n ¼ 1:6 better matches the shape of the observed β curves for both iron and aluminum at both high and low velocities. Eq. (8) gives an empirical match to the measurements, but will probably need to be modified after accounting for the bias due to slowdown. Future theoretical work and modeling is needed to create improved models of meteor ablation and ionization, which will reduce the uncertainty in the meteoric mass influx rate using radar observations.
Janches, D., Dyrud, L.P., Broadley, S.L., Plane, J.M.C., 2009. First observation of micrometeoroid differential ablation in the atmosphere. Geophys. Res. Lett. 36, L06101 https://doi.org/10.1029/2009GL037389. Janches, D., Plane, J.M.C., Nesvorný, D., Feng, W., Vokrouhlický, D., Nicolls, M.J., 2014. Radar detectability studies of slow and small zodiacal dust cloud particles. I. The case of Arecibo 430 MHz meteor head echo observations. Astrophys. J. 796, 41. https:// doi.org/10:1088/0004-637X/796/1/41. Janches, D., Swarnalingam, N., Carrillo-Sanchez, J.D., G omez-Martín, J.C., Marshall, R., Nesvorný, D., Plane, J.M.C., Feng, W., Pokorný, P., 2017. Radar detectability studies of slow and small zodiacal dust cloud particles. III. The role of sodium and the head echo size on the probability of detection. Astrophys. J. 843, 1. https://doi.org/ 10.3847/1538-4357/aa775c. Janches, D., Swarnalingam, N., Plane, J.M.C., Nesvorný, D., Feng, W., Vokrouhlický, D., Nicolls, M.J., 2015. Radar detectability studies of slow and small zodiacal dust cloud particles. II. A study of three radars with different sensitivity. Astrophys. J. 807, 13. https://doi.org/10:1088/0004-637X/807/1/13. Jones, W., 1997. Theoretical and observational determinations of the ionization coefficient of meteors. Mon. Not. R. Astron. Soc. 288, 995–1003. https://doi.org/ 10.1093/mnras/288.4.995. Kalashnikova, O., Horanyi, M., Thomas, G.E., Toon, O.B., 2000. Meteoric smoke production in the atmosphere. Geophys. Res. Lett. 27, 3293–3296. https://doi.org/ 10.1029/1999GL011338. Moutinho, A.M.C., Baede, A.P.M., Los, J., 1971. Charge transfer between alkali atoms and oxygen molecules. Physica 51, 432–444. https://doi.org/10.1016/0031-8914(71) 90051-6. Nesvorný, D., Jenniskens, P., Levison, H., Bottke, W., Vokrouhlický, D., Gounelle, M., 2010. Cometary origin of the zodiacal cloud and carbonaceous micrometeorites. Implications for hot debris disks. Astrophys. J. 713, 816–836. https://doi.org/ 10.1088/004-637X/713/2/816. Plane, J.M.C., 2012. Cosmic dust in the Earth's atmosphere. Chem. Soc. Rev. 41, 6507–6518. https://doi.org/10.1039/c2cs35132c. Plane, J.M.C., Feng, W., Dawkins, E.C.M., 2015. The mesosphere and metals: chemistry and changes. Chem. Rev. 115, 4497–4541. https://doi.org/10.1021/cr500501m. Shu, A., Collette, A., Drake, K., Grün, E., Horanyi, M., Kempf, S., Mocker, A., Munsat, T., Northway, P., Srama, R., Sternovsky, Z., Thomas, E., 2012. 3 MV hypervelocity dust accelerator at the Colorado center for lunar dust and atmospheric studies. Rev. Sci. Instrum. 83, 075108 https://doi.org/10.1063/1.4732820. Sida, D.W., 1969. The production of ions and electrons by meteoritic processes. Mon. Not. R. Astron. Soc. 143, 37–47. https://doi.org/10.1093/mnras/143.1.37. Slattery, J.C., Friichtenicht, J.F., 1967. Ionization probability of iron particles at meteoric velocities. Astrophys. J. 147, 235–244. https://doi.org/10.1086/148995. Suits, B.H., Apte, P., Wilken, D.E., Siegel, R.W., 1995. NMR Study of nanophase Al/Aloxide powder and consolidated composites. Nanostruct. Mater. 6, 609–612. https:// doi.org/10.1016/0965-9773(95)00132-8. Thomas, E., Horanyi, M., Janches, D., Munsat, T., Simolka, J., Sternovsky, Z., 2016. Measurements of the ionization coefficient of simulated iron micrometeoroids. Geophys. Res. Lett. 43, 3645–3652. https://doi.org/10.1002/2016GL068854. Thomas, E., Simolka, J., DeLuca, M., Horanyi, M., Janches, D., Marshall, R., Munsat, T., Plane, J.M.C., Sternovsky, Z., 2017. Experimental setup for the laboratory investigation of micrometeoroid ablation using a dust accelerator. Rev. Sci. Instrum. 88, 034501 https://doi.org/10.1063/1.4977832. Vondrak, T., Plane, J.M.C., Broadley, S., Janches, D., 2008. A chemical model of meteoric ablation. Atmos. Chem. Phys. 8, 7015–7031. https://doi.org/10.5194/acp-8-70152008. Williams, I.P., Murad, E., 2002. Introduction. In: Murad, E., Williams, I.P. (Eds.), Meteors in the Earth's Atmosphere. Cambridge Univ. Press, Cambridge, U.K., pp. 1–11
Acknowledgements This research was supported by NASA's Heliophysics Technology and Instrument Development for Science (HTIDeS) program, Grant No. NNX15AJ96G. The development of the ablation facility was also supported by NASA's Solar System Exploration Research Virtual Institute (SSERVI): Institute for Modeling Plasma, Atmospheres, and Cosmic Dust (IMPACT), and the NSF's Aeronomy program (Atmospheric and Geospace Sciences), Award No. 1451218. References Baggaley, W., 2002. Radar observations. In: Murad, E., Williams, I.P. (Eds.), Meteors in the Earth's Atmosphere. Cambridge Univ. Press, Cambridge, UK, pp. 123–147. Bones, D.L., G omez Martín, J.C., Empson, C.J., Carrillo Sanchez, J.D., James, A.D., Conroy, T.P., Plane, J.M.C., 2016. A novel instrument to measure differential ablation of meteorite samples and proxies: the Meteoric Ablation Simulator (MASI). Rev. Sci. Instrum. 87, 094504 https://doi.org/10.1063/1.4962751. Bronshten, V.A., 1983. Physics of Meteoric Phenomena. Reidel Publishing, Dordrecht, Holland. Campbell, T., Kalia, R.K., Nakano, A., Vashishta, P., Ogata, S., Rodgers, S., 1999. Dynamics of oxidation of aluminum nanoclusters using variable charge moleculardynamics simulations on parallel computers. Phys. Rev. Lett. 82, 4866–4869. https:// doi.org/10.1103/PhysRevLett.82.4866. Chau, J., Woodman, R., Galindo, F., 2007. Sporadic meteor sources as observed by the Jicamarca high-power large-aperture VHF radar. Icarus 188, 162–174. https:// doi.org/10.1016/j.icarus.2006.11.006. Close, S., Oppenheim, M., Durand, D., Dyrud, L., 2005. A new method for determining meteoroid mass from head echo data. J. Geophys. Res. 110, A09308 https://doi.org/ 10.1029/2004JA010950. G omez Martín, J.C., Bones, D.L., Carillo-Sanchez, J.D., James, A.D., TrigoRodríguez, J.M., Fegley Jr., B., Plane, J.M.C., 2017. Novel experimental simulations of the atmospheric injection of meteoric metals. Astrophys. J. 836, 212. https:// doi.org/10.3847/1538-4357/aa5c8f. Hood, L.L., Hor anyi, M., 1991. Gas dynamic heating of chondrule precursor grains in the solar nebula. Icarus 93, 259–269. https://doi.org/10.1016/0019-1035(91)90211-B.
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The ionization efficiency of aluminum and iron at meteoric velocities Michael DeLuca a, b, c, *, Tobin Munsat c, d, Evan Thomas c, d, Zoltan Sternovsky a, b, c a
Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO, USA Smead Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO, USA c Institute for Modeling Plasma, Atmospheres, and Cosmic Dust, University of Colorado, Boulder, CO, USA d Department of Physics, University of Colorado, Boulder, CO, USA b
A R T I C L E I N F O
A B S T R A C T
Keywords: Meteors Ionization efficiency Aluminum Iron Laboratory experiments
The ionization efficiency of aluminum was measured in the laboratory over an extended velocity range of 10.8–73.4 km/s and compared to available models. The measurements were made by shooting submicron-sized aluminum dust particles into an air chamber using the University of Colorado's dust accelerator facility. The ionization efficiency, β, is calculated from the total charge generated in the chamber during the complete ablation of particles of known mass. An array of photomultiplier tubes observed the light production by a subset of particles in the chamber to confirm that a moderate deceleration of the ablating particles occurred at low velocities. This information allows the interpretation of the β measurements to be extended to velocities <20 km/s, with the understanding that the low-velocity β measurements are lower limits. Updated β measurements for iron particles are also reported over an extended velocity range compared to previously published data: 10.5–87.3 km/s. The measurements are fit to functions for the ionization efficiency across the entire velocity range, and a semiempirical function is presented which matches the shape of the measured β curves for aluminum and iron at both high and low velocities.
1. Introduction The Earth collides with billions of micrometeoroids as it orbits the Sun (Janches et al., 2009). The incoming particle flux poses a risk to spacecraft and injects metals into Earth's mesosphere. The particles enter Earth's atmosphere as meteors traveling at geocentric speeds in the range 11–72 km/s (Baggaley, 2002). Estimates of the meteoric mass input flux range from 5–100 metric tons per day (Plane et al., 2015), mostly in the form of small particles whose distribution peaks around 1–10 μg (Williams and Murad, 2002). These particles originate mainly from asteroids and comets, and they provide a continuous source of exotic elements in the atmosphere. Among other things, meteoric elements lead to the formation of metal layers in the atmosphere, are involved in the formation of noctilucent clouds, and provide a source of bio-available iron to the oceans (Plane, 2012). Radars are sensitive to the meteor phenomena and offer the means to constrain the total meteoric mass input and velocity distribution, as they cover the mass range that provides the bulk of the input (Plane, 2012). High Power and Large Aperture (HPLA) radars, such as the sensitive 430 MHz radar at the Arecibo Observatory in Puerto Rico, detect the ball
of ionization that forms around a meteor as it enters the atmosphere, known as a head echo. Under current models, meteoroids entering the atmosphere will heat up and slow down due to collisions with air molecules, melt, and ablate through evaporation (Hood and Horanyi, 1991; Kalashnikova et al., 2000; Vondrak et al., 2008). Sputtering may also play a role, and different constituents of the particle can evaporate at different points along the meteor's path through the process of differential ablation (Vondrak et al., 2008; Janches et al., 2009). Ablated atoms will then collide with background gas molecules and ionization may occur, leading to the formation of free electrons, which are visible to radars (Baggaley, 2002). The ionization efficiency, β, is the average number of electrons that will be produced per ablated atom, and is a function of the meteor's velocity and the species involved in the collision (Bronshten, 1983; Jones, 1997). β is used to determine the detectability of different meteoroid populations and the mass of the particle from the strength of the radar signal (Close et al., 2005; Janches et al., 2014). One of the difficulties in using radars to determine meteor mass and detectability, however, lies in the challenge of finding accurate β values, which have been determined experimentally only for a few species and/or over a limited velocity range. The semi-empirical functional form for β often
* Corresponding author. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO, USA. E-mail address: [email protected] (M. DeLuca). https://doi.org/10.1016/j.pss.2017.11.003 Received 30 June 2017; Received in revised form 11 September 2017; Accepted 1 November 2017 Available online xxxx 0032-0633/© 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: DeLuca, M., et al., The ionization efficiency of aluminum and iron at meteoric velocities, Planetary and Space Science (2017), https://doi.org/10.1016/j.pss.2017.11.003
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particles are smaller than typical meteoroids, but the relevant physics for the simulated meteors and real meteors is the same because the simulated meteors in the experiment are in a free molecular flow regime, just like most real meteors. Therefore, the experimental results should scale to the analysis of typical meteors. Recently, the facility has been upgraded with a set of PMT detectors that allow the ablating particles to be monitored optically, which allows their velocities to be inferred (Thomas et al., 2017). 4 PMTs, each with 16 channels, detect the light the particles produce as they travel through the chamber. Narrow slits placed between each PMT and the chamber's windows map each of the 64 PMT channels to a 6.4 mm long portion of the 41 cm long ablation chamber. Taking into account the width of the spatial bins and the finite width of the slit, the uncertainty in position on each PMT channel observation is about ±0.38 cm. Due to limited high-speed data acquisition capabilities, only 29 out of the 64 PMT channels were monitored (distributed evenly along the path). The particle's motion in the chamber can be tracked assuming that the photons a given PMT channel observes are emitted by the particle when it is located in the field of view the PMT channel observes. The PMT data indicates that this assumption is valid.
used for interpreting meteor radar data comes from Jones (1997). To explain the lack of radar observations of low-velocity meteors which are predicted by astronomical models (Nesvorný et al., 2010), it has been proposed that β values might be up to two orders of magnitude smaller than predicted by Jones (1997) near the low end of the velocities of interest (Janches et al., 2014, 2015). This would mean that the meteors are present but not easily detected due to diminishing ionization. To study meteor ablation under laboratory conditions, a dust accelerator and ablation chamber facility is operated at the University of Colorado (Thomas et al., 2017). The University of Colorado's ablation facility measures the charge production of ablating particles. Complementary studies are undertaken at the University of Leeds using the Meteoric Ablation Simulator, which measures the ablation rates of metals (Bones et al., 2016; G omez Martín et al., 2017). At the University of Colorado, iron and aluminum have been studied to shed light on the physics of meteor ablation and ionization using simple compositions. More realistic and complex meteor compositions (e.g., olivine) will be studied in future experiments. β values have been determined for iron particles impacting various gases including N2, CO2, He, and air. The ionization efficiency measurements confirmed earlier results by Jones (1997) for velocities >20 km/s (Thomas et al., 2016). The analysis by Thomas et al. (2016) was restricted to velocities >20 km/s as numerical modeling of the ablation process indicated that low-speed particles, i.e. 10–20 km/s, could slow down significantly when encountering air drag in the experiment, thereby biasing the β measurements in the regime where the ionization efficiency changes rapidly with velocity. The goal of the ionization efficiency experiments is to get unbiased β measurements as a function purely of velocity, so that these results will be widely applicable to a range of meteoroids with different deceleration profiles. The deceleration of a meteoroid will vary depending on its size, shape, composition, velocity, and the air density (Vondrak et al., 2008). Recently, the experimental setup used for the β measurements has been upgraded to include optical observations of the ablating particle using photomultiplier tubes (PMTs). The new experimental results indicate that the slowdown of simulated meteors in the experiment is moderate and a lower limit on the β values can be placed for velocities below 20 km/s. This paper presents the results from the laboratory investigation of the ablation of aluminum particles along with the extension of the β values for iron to lower velocities.
3. Experimental results 3.1. PMT observations The PMT observations indicate that low-speed aluminum particles experience slowdown inside the ablation chamber. Fig. 1 shows an example of light detected from a particle with an initial speed of 16.5 km/s ablating in the chamber held at a pressure of 65 mTorr. The output of each PMT channel is digitized at 40 MS/s and the pulses in the signal correspond to detected photons. There is a clear correlation between the relative time of detection and the order (or range) of the PMT channel along the ablation chamber. For this analysis, it was assumed that the photons are emitted by the ablating particle while it is in the field of view of a given channel. For PMT channels with multiple pulses, the first pulse was used to locate the particle. The slope of the line fitted to the PMT observations provides the average velocity for the particle over the spatial range for which there are PMT observations (11–28 cm into the chamber for the event in Fig. 1). The light collected by the PMT channels was sparse, usually a few photons or less. Since the PMT observations are over a limited range, a simple linear fit was used as a rough first approximation of the particle's velocity in the observed range. The linear fit in Fig. 1 is shown with a black line, and it gives a velocity of 13:8±0:3 km=s. The entry velocity of the particle is 16:5±0:5 km=s and is shown by the slope of the blue line. The PMT-observed velocity is significantly below the initial velocity, even when accounting for the uncertainty on the initial velocity. The PMT observations show that the particle is decelerating in the chamber and that this deceleration is moderate. The example shown here is typical for all other particles with high-quality PMT data, providing evidence for slowdown due to air drag inside the ablation chamber. The PMTs observed slowdown by approximately 2–3 km/s, or about 10%–20% of the initial speed, for all particles with sufficient PMT data. To assess the slowdown using PMT observations, only particles that produced sufficient amounts of light (i.e., produced clearly correlated pulses on 7 or more channels) were included in this analysis. That way, each particle's position could be determined unambiguously despite noise on the channels from dark current. There were 6 such particles observed out of 44 events where PMT data was taken. In each of the 6 cases, the linear fit to the PMT pulses is outside of the uncertainty on the initial velocity (about 3%) even when accounting for the error on the fit. It is concluded that the PMTs are observing moderate slowdown in the simulated meteors, the effect of which is to bias the β measurements. This bias deflates the measured β values as ionizing collisions on average will occur at somewhat lower values than the entrance velocity at which the β values are reported. β changes most rapidly at low velocities, so
2. Experimental setup A unique facility is operated at the University of Colorado to simulate the ablation of micrometeoroids and is described in detail by Thomas et al. (2017). Briefly, an electrostatic dust accelerator is used to generate submicron-sized particles with a wide range of velocities, about 1–100 km/s (Shu et al., 2012). The mass and velocity of each accelerator particle is measured and those particles traveling in the desired speed range are allowed to enter the ablation chamber, which is filled with the desired gas and maintained at constant pressure. Inside the ablation chamber, there is an array of 16 sensitive charge collectors that are biased to collect either the positive ions or electrons generated along the ablation path. An impact detector is mounted at the end of the ablation chamber to measure the mass of the remaining particle, if any. The pressure in the chamber is adjusted for various mass/velocity ranges of the particles to ensure full ablation. The ionization efficiency, β, is then calculated from the total generated charge and the mass of the particle. The new laboratory measurements were performed using aluminum dust particles accelerated to velocities in the 10.8–73.4 km/s range. This was the first time that aluminum had been successfully used in this accelerator facility. Based on experience with samples of other materials, a mixture of larger and smaller particles was used. By mass, the mixture was 5% 40–60 nm particles, 5% 80–100 nm particles, 45% 3–4.5 μm particles, 30% 4.7–7 μm particles, and 15% 10–14 μm particles, all measured in diameter. Scanning electron microscope images of the individual dust samples confirmed that the particles are spherical. These 2
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Fig. 1. Left: The raw data from the 29 PMT channels, stacked according to their order. Red lines indicate channels with a PMT signal, typically detecting one or a few photons. Right: The time of each PMT detection is plotted against the range inside the ablation chamber. The blue line indicates the 16.5 km/s initial velocity of the particle measured by the accelerator facility. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
measurement is shown on the velocity axis. The measurements are colorcoded based on the pressure in the ablation chamber, which was adjusted as necessary to ensure complete ablation. Slower particles required higher pressures to fully ablate inside the chamber. The aluminum β measurements reported here make use of an updated calibration of the mass measurements of the dust particles generated by the accelerator facility. The accelerator generates charged dust particles which are accelerated through a high (2–3 MV) electric potential. The initial charge of the particles is enough to accelerate them to velocities >10 km/s, but still much less than the charge produced during ablation, so the initial charge of the particle does not skew the ionization efficiency measurements. Detectors on the accelerator's beamline measure the initial charge of the particle and its velocity, from which the mass is calculated (see Shu et al. (2012) for more details). Previous measurements, including those reported by Thomas et al. (2016), overestimated the particles' masses by overestimating the particles' initial charges. The original calibration overestimated the masses by about 65%. The new calibration of the dust accelerator's beamline detectors has been completed, which also reduced the uncertainty in the dust mass to approximately 10%. The details of the new calibration procedure will be presented elsewhere in a future publication. Based on the new calibration, the β measurements by Thomas et al.
slowdown will have a more pronounced effect on the measured values of β at low speeds. It is difficult to correct for the slowdown in the β measurements as doing so would require a more detailed understanding of the ablation process. For complete ablation, as investigated in these experiments, the particle is first heated and the highest rate of mass loss occurs at the beginning after the particle's temperature is sufficiently high. Consequently, most of the charge production should occur while the particle is moving with a velocity that is close to the entry velocity, but a bias towards lower values of β will still be present. The β measurements presented below are therefore lower limits on the true β values. 3.2. β Measurements The aluminum β measurements are shown in Fig. 2. The value of β for a fully-ablated particle is calculated by dividing the total charge collected in the chamber (in units of elementary charges) by the number of aluminum atoms in the particle. Particles that did not fully ablate were discarded from this analysis. The particles’ initial velocities range from 10.8 to 73.4 km/s, covering the entire speed range over which interplanetary meteors are expected to occur. The initial velocity of each
Fig. 2. The measured β values for aluminum as a function of velocity. The data points are color-coded based on the pressure in the ablation chamber. The blue line shows the best fit to the Jones (1997) function, given by Eq. (3). The red line shows the fit to Eq. (8) with n ¼ 1:6. The dashed black line shows Eq. (3) using the parameter c predicted using the method of Janches et al. (2017). See the text for more details. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. Measured β values for iron, including data below 20 km/s that were previously not considered. The blue line shows the fit to Eq. (3). The red line shows the fit to Eq. (8) with n ¼ 1:6. Compared to Thomas et al. (2016), the β values are updated based on the improved mass calibration for the accelerator facility. See the text for more details. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 3
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been in contact with air, which means that its surface is oxidized with an aluminum oxide layer up to 4 nm thick on particles greater than 10 nm in size (Suits et al., 1995; Campbell et al., 1999). For the majority of the particles used in the experiment, a 4 nm thick aluminum oxide layer would comprise 10%–30% of the particle's total volume. It is not clear whether the oxidized surface would inflate or deflate the β measurements, as this depends greatly on the form in which the compound is ablated from the particle's surface. If the compound does not dissociate when ablated, the β measurements are likely deflated as it is harder to ionize the oxide than aluminum. The effect would be most pronounced at high velocities, as high-velocity particles produced by the accelerator tend to be smaller than low-velocity particles so would have more aluminum oxide by volume (the smallest and fastest particle in the aluminum β experiment presented here had a radius of 22 nm, so would be 45% aluminum oxide by volume if it had a 4 nm thick aluminum oxide outer layer). Large low-velocity particles would be less affected. The possible presence of an aluminum oxide layer on the aluminum dust is not included in this analysis.
(2016) for iron interacting with air have been updated. To account for the overestimate in mass, the β measurements for iron have been increased. The results are shown in Fig. 3. In the original analysis of iron β values by Thomas et al. (2016), velocities below 20 km/s were excluded due to concerns about excessive slowdown affecting the measurements, but all velocities are included here. Like the low-speed aluminum measurements, the low-speed iron measurements in Fig. 3 are lower limits. The measurement errors on the β values are calculated from the uncertainties in the collected charge and the mass determination. The mass is measured with an accuracy of about ±10%. The charge-collecting electronics in the ablation chamber are calibrated to 1% accuracy for each collector, which typically dominates the error in the charge measurement over the RMS noise of the charge sensitive amplifiers. In the worst-case scenario, the total charge is measured as the sum of all 16 collectors, adding up to ±4% uncertainty in the charge measurement. In addition, there is a 3% uncertainty in the initial velocity of the particles. The uncertainty in initial velocity translates to an error in the β value as δβ ¼ jdβðvÞ=dvjδv, where βðvÞ is given by the function with the best fit to the data (Eq. (8) in Section 5). The error bars in Figs. 2 and 3 show the total uncertainty on the measurements. There are also systematic biases (in addition to the slowdown bias) that can potentially affect the β measurements. Thomas et al. (2017) analyzed the efficiency of collecting the charge generated by the ablation process and found that the inefficiency in charge collection is small compared to the error discussed above. The inflation of β values is possible due to electron impact ionization, where the free electrons generated by ablation may generate additional electron-ion pairs as they are accelerated towards the biased charge-collecting electrodes inside the chamber. Thomas et al. (2017) analyzed this effect through numerical simulations and found that for the 90 V electrode bias potential used in the measurements here up to 30% additional charge generation is possible, depending on the pressure in the chamber. Measurement of the ionization efficiency performed over a wide range of chamber pressures (see Fig. 2) and bias potentials indicate that the effect of secondary ionization is limited and it is thus neglected in the present data analysis. Recombination between electrons and ions that form in the chamber could also introduce a bias by removing free electrons from the experiment before they are counted. However, the effect of recombination is minor, as the number density of ionized species is about 10 orders of magnitude less than the number density of neutral species. A charged particle will undergo about 10–100 collisions before being collected at the charge-collecting electrodes, so the odds of a collision between two oppositely-charged particles leading to recombination is negligible. The electron affinity of oxygen can introduce a bias by producing charged particles without producing free electrons. O2 is present in the atmosphere at a level of 21% and, as Moutinho et al. (1971) pointed out, it can enhance the ionization efficiency at low impact velocities, where it is energetically easier to generate a negative O 2 ion instead of a free electron. The ablation experiment cannot distinguish between the generation of a free electron and O 2 , although it makes a difference for radar observations. The presence of O 2 would inflate the β measurements, as the number of charges collected would not be equivalent to the number of free electrons produced. However, β measurements for iron made with the ablation chamber are similar for both N2 and air, so the effect is limited. The role of oxygen will need to be investigated in future experiments, but for the results presented in this paper it is assumed that the electron affinity of oxygen is not introducing a significant bias in the charge measurements. Oxygen can further bias the aluminum β measurements by reacting with the aluminum dust particles used in the experiment. Aluminum atoms that are ablated from the particles could chemically bond with oxygen from the background gas, but any such effect would be limited to at most a measurement bias of 21%, the fraction of oxygen in air. Ablated aluminum atoms that bond with oxygen rather than ionize will reduce the measured value of β. Furthermore, the aluminum dust sample has
4. Fits to the β measurements 4.1. Fits to the aluminum measurements The β versus velocity curves presented in Figs. 2 and 3 were fit to two functions which are commonly used to describe the ionization efficiency of meteors: a simple power law, and a function given by Jones (1997) which provides the following semi-empirical form for the primary ionization probability, i.e. the probability of ionization for a single collision between a meteor atom and an atmospheric molecule: 2
β0 ðvÞ ¼
cðv v0 Þ v0:8 : 1 þ cðv v0 Þ2 v0:8
(1)
The fitting parameter c is unique to the species of the meteoric atom and the target gas. v is the velocity of the meteoric atom and v0 is the threshold velocity below which no ionization of the meteoric atom will occur. The equation for the threshold velocity is given by Jones (1997) as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ð1 þ μÞeψ v0 ¼ μma
(2)
where μ is the ratio of the mass of a meteor atom to the mass of an average air molecule, ma is the average mass of an air molecule, e is the electron charge, and ψ is the ionization potential. v0 ¼ 9:10 km=s for aluminum interacting with air, and v0 ¼ 8:95 km=s for iron interacting with air (assuming an atmosphere that is 79% N2 and 21% O2). Jones (1997) adds a small correction to β0 to account for the possibility that ionization does not occur on the first collision and will instead occur on a subsequent collision: 2
βðvÞ ¼ β0 ðvÞ þ ð1 β0 ðvÞ Þ
ð1 þ μÞ v ∫ v0 βðv0 Þv0 dv0 : 2v2 μ
(3)
The integral correction term changes the value of β by no more than 50% over β0 for a cometary meteor (Jones, 1997). v To solve Eq. (3), a substitution of the form u ¼ ∫ v0 βðv0 Þv0 dv0 was made as described by Thomas et al. (2016), which results in the following ordinary differential equation:
du ð1 þ μÞ2 ¼ vβ0 ðvÞ þ ð1 β0 ðvÞ Þ u: dv 2vμ
(4)
Eq. (4) was solved using a fourth-order Runge-Kutta integrator for given values of c and v, and turned back into a β value using β ¼ 1v du dv. The IDL
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aluminum atom and air molecule will have a lower internal energy with less energy available for ionizing collisions. In addition to the threshold velocity, the parameter c in Eq. (1) determines the ionization efficiency of an element. The parameter c relates to the ionization and elastic collision cross sections as discussed below. The similarity in the β curves indicates that aluminum and iron have similar c parameters in Eq. (1). The measurements presented in this paper are lower limits on the true β values, especially at low velocities where the effects of slowdown are more pronounced. The effect of slowdown on β will be worst at low velocities, since those particles experience the largest slowdowns before completely ablating and the β curve is steepest at low velocities. Eq. (3) underestimates the β values at low velocities, especially when considering that the presented data are lower limits. Figs. 2 and 3 suggest that the semi-empirical form of β0 in Eq. (1) needs revision in order to provide better agreement with the data over the entire velocity range. To derive Eq. (1), Jones (1997) wrote the primary ionization as β0 ðvÞ ¼ σ i =σ t , where σ i is the ionization cross section and σ t is the total cross section, approximated as σ t ¼ σ i þ σ el where σ el is the elastic scattering cross section. For the cross sections, Jones (1997) used σ el v0:8 , citing Bronshten (1983), and σ i ðv v0 Þn following the work of Sida (1969) with a suggested value of n ¼ 2. Following this argument, and instead of fixing n ¼ 2, the suggested form for the ionization efficiency is
curvefit function was used to match Eq. (3) to the observed values of v and β by varying the value of c. Each data point in the fit was weighted by its measurement error. The best fit, for all β values across the entire measured speed range, occurs at c ¼ 3:44 105 ±0:06 105 (c given in ðs=kmÞ2:8 ). Fig. 2 shows the fit of Eq. (3) to the aluminum data across all velocities using this parameter. Note that β, and thus the parameter c, is similar for aluminum and iron. Janches et al. (2017) predicted a higher ionization efficiency for aluminum compared to iron based on aluminum's lower ionization potential. Janches et al. (2017) provide an equation to predict the parameter c for species X based on the parameter c for iron:
cðXÞ ¼ cðFeÞ
2 ψðFeÞ ψðXÞ
(5)
where ψ designates the ionization potential. The dashed black curve in Fig. 2 is βðvÞ calculated from Eq. (3) using cðAlÞ from Eq. (5). This predicted curve matches the measurements at low speeds, but overestimates β at moderate to high speeds. At speeds >20 km/s, the measured β values appear to follow a simple power law: β ¼ avb . Fitting the measured β values above 20 km/s to such a power law, with v specified in km/s, gives
βðvÞ ¼ 1:89 104 v2:07 :
(6)
cðv v0 Þ v0:8 n 1 þ cðv v0 Þ v0:8 n
The error on the coefficient is 0:28 104 , and the error on the exponent is 0:04. The power law fit is convenient for estimating β values at high velocities. As seen in Fig. 2, even though the β measurements presented here are lower limits on the true β values at low velocities, the shape of Eq. (3) is such that it still underestimates the β measurements at the lowest velocities.
βðvÞ ¼
(8)
where n and c are parameters that can be varied to produce a better empirical fit to the data. The integral correction term in Eq. (3) is neglected in Eq. (8) as it provides a correction of <50% over the primary ionization given by Eq. (1). Eq. (8) is limited to β < 1 because it is based on the primary ionization probability, so further theoretical work will be needed to find a functional form for the ionization efficiency that can account for all β values including β 1. β > 1 was measured multiple times for iron, but only at the highest speeds measured here which would mainly be relevant to interstellar meteors (Chau et al., 2007). Eq. (8) is therefore taken as a reasonable approximation to empirically fit the majority of the data. A value of n ¼ 1:6 in Eq. (8) was found to give a reasonable fit to both the iron and the aluminum β measurements, so that is the value of n suggested for fitting data to Eq. (8). With n fixed to 1.6, the fit of Eq. (8) to the aluminum β measurements gives c ¼ 1:60 104 ±0:03 104 (c
4.2. Fits to the modified iron measurements The β values for iron corroborate the findings based on aluminum. Thomas et al. (2016) found the parameter for iron striking air to be c ¼ 1:97 105 when fit to particles traveling over 20 km/s, which differs from the value c ¼ 3:45 105 which Jones (1997) originally calculated. However, the β values used in the study by Thomas et al. (2016) were underestimated due to calibration errors in the mass determination as discussed above. Using the updated β measurements, the parameter for iron-air interactions is now calculated to be c ¼ 3:76 105 ±0:07 105 when fitting to speeds over 20 km/s, which is closer to the value reported by Jones (1997) who fit earlier data by Slattery and Friichtenicht (1967). Extending the fit to all velocities gives c ¼ 4:07 105 ±0:07 105 , which is shown in Fig. 3 along with the corrected β values. Like aluminum, the fit to the extended iron data using Eq. (3) underestimates the value of β at low speeds. The updated power law for iron, for v > 20 km=s, is given by
The error on the coefficient is 0:31 104 , and the error on the exponent is 0:04. Note that the exponent in Eq. (7) for iron is very similar to the exponent in Eq. (6) for aluminum.
specified in ðs=kmÞ2:4 ). The fit is shown in Fig. 2. The new fit is better than the original especially at the lowest velocities reported here, and it does a better job of matching the shape of the observed β curve at both high and low velocities. For the iron data, the best fit to Eq. (8) when n ¼ 1:6 is at c ¼ 1:95 104 ±0:03 104 , as shown in Fig. 3. It is also an improvement over the fit of Eq. (3). The new fits presented here by empirically matching Eq. (8) to the data are likely to need modification, particularly if the low-velocity β values are corrected to account for slowdown bias effects. Improved modeling of the ionization, deceleration, and ablation processes, and a more comprehensive theory that can fit the measured data across all velocities, will be needed to create an improved model of the ionization efficiency.
5. Discussion
6. Summary
The aluminum β measurements are similar to the iron β measurements at all velocities, which is somewhat surprising given that aluminum has a lower ionization potential than iron (6.0 eV for aluminum, 7.9 eV for iron). We attribute part of the similarity of the β curves to the similarity of the threshold velocities for both iron and aluminum using Eq. (2): in air, v0 ¼ 9:10 km=s for aluminum and v0 ¼ 8:95 km=s for iron. Although aluminum has a lower ionization potential than iron, its lower mass also means that the system formed by a colliding
Measurements of charge production and slowdown for simulated aluminum meteors have been made using the University of Colorado's dust accelerator facility. The measurements were enabled by the facility's ablation chamber with an updated PMT observing setup. The PMT observations clearly indicate slowdown occurs when low-velocity particles enter the ablation chamber, which will bias the β measurements made at low velocities towards lower values. Despite the bias introduced by air drag, the measured β values can still be taken as lower limits on the
βðvÞ ¼ 2:49 104 v2:04 :
(7)
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detectability of aluminum in meteors. The current understanding of meteor ionization is provided by Jones (1997), but Eq. (3) underestimates the low-velocity β values for aluminum when fit across the entire velocity range, and does not match the shape of the measured β curve. A similar problem is encountered when the results are applied to updated iron measurements originally reported by Thomas et al. (2016). Eq. (8) with n ¼ 1:6 better matches the shape of the observed β curves for both iron and aluminum at both high and low velocities. Eq. (8) gives an empirical match to the measurements, but will probably need to be modified after accounting for the bias due to slowdown. Future theoretical work and modeling is needed to create improved models of meteor ablation and ionization, which will reduce the uncertainty in the meteoric mass influx rate using radar observations.
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Acknowledgements This research was supported by NASA's Heliophysics Technology and Instrument Development for Science (HTIDeS) program, Grant No. NNX15AJ96G. The development of the ablation facility was also supported by NASA's Solar System Exploration Research Virtual Institute (SSERVI): Institute for Modeling Plasma, Atmospheres, and Cosmic Dust (IMPACT), and the NSF's Aeronomy program (Atmospheric and Geospace Sciences), Award No. 1451218. References Baggaley, W., 2002. Radar observations. In: Murad, E., Williams, I.P. (Eds.), Meteors in the Earth's Atmosphere. Cambridge Univ. Press, Cambridge, UK, pp. 123–147. Bones, D.L., G omez Martín, J.C., Empson, C.J., Carrillo Sanchez, J.D., James, A.D., Conroy, T.P., Plane, J.M.C., 2016. A novel instrument to measure differential ablation of meteorite samples and proxies: the Meteoric Ablation Simulator (MASI). Rev. Sci. Instrum. 87, 094504 https://doi.org/10.1063/1.4962751. Bronshten, V.A., 1983. Physics of Meteoric Phenomena. Reidel Publishing, Dordrecht, Holland. Campbell, T., Kalia, R.K., Nakano, A., Vashishta, P., Ogata, S., Rodgers, S., 1999. Dynamics of oxidation of aluminum nanoclusters using variable charge moleculardynamics simulations on parallel computers. Phys. Rev. Lett. 82, 4866–4869. https:// doi.org/10.1103/PhysRevLett.82.4866. Chau, J., Woodman, R., Galindo, F., 2007. Sporadic meteor sources as observed by the Jicamarca high-power large-aperture VHF radar. Icarus 188, 162–174. https:// doi.org/10.1016/j.icarus.2006.11.006. Close, S., Oppenheim, M., Durand, D., Dyrud, L., 2005. A new method for determining meteoroid mass from head echo data. J. Geophys. Res. 110, A09308 https://doi.org/ 10.1029/2004JA010950. G omez Martín, J.C., Bones, D.L., Carillo-Sanchez, J.D., James, A.D., TrigoRodríguez, J.M., Fegley Jr., B., Plane, J.M.C., 2017. Novel experimental simulations of the atmospheric injection of meteoric metals. Astrophys. J. 836, 212. https:// doi.org/10.3847/1538-4357/aa5c8f. Hood, L.L., Hor anyi, M., 1991. Gas dynamic heating of chondrule precursor grains in the solar nebula. Icarus 93, 259–269. https://doi.org/10.1016/0019-1035(91)90211-B.
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