Shocklets and Short Large Amplitude Magnetic Structures (SLAMS) in the High Mach Foreshock of Venus

Shocklets and short large‐amplitude magnetic structures (SLAMS) are steepened magnetic fluctuations commonly found in Earth's upstream foreshock. Here we present Venus Express observations from the 26th of February 2009 establishing their existence in the steady‐state foreshock of Venus, building on a past study which found SLAMS during a substantial disturbance of the induced magnetosphere. The Venusian structures were comparable to those reported near Earth. The 2 Shocklets had magnetic compression ratios of 1.23 and 1.34 with linear polarization in the spacecraft frame. The 3 SLAMS had ratios between 3.22 and 4.03, two of which with elliptical polarization in the spacecraft frame. Statistical analysis suggests SLAMS coincide with unusually high solar wind Alfvén mach‐number at Venus (12.5, this event). Thus, while we establish Shocklets and SLAMS can form in the stable Venusian foreshock, they may be rarer than at Earth. We estimate a lower limit of their occurrence rate of ≳14%.

• Shocklets and short large-amplitude magnetic structures (SLAMS) can form in the steady-state foreshock of Venus despite the magnetosphere being 1/10th the size of Earths • The Venusian Shocklets and SLAMS had comparable magnetic signatures to those reported near Earth, but may be rarer • Analysis of the solar wind at 0.72AU suggests Shocklets and SLAMS occur during high Alfvén mach-numbers with a lower limit on occurrence rate of ≳14% 10.1029/2023GL104610 2 of 12 Scarf et al., 1970).They are often referred to as "30 s waves" (Eastwood, Balogh, et al., 2005) due to their typical period at Earth (in the spacecraft frame), which comes from the strength and cone angle of the interplanetary magnetic field (Takahashi et al., 1984).A similar field of 30 s ULF waves was discovered upstream of Venus by Greenstadt et al. (1987).They found the general morphology of the Venusian foreshock ULF wave field is similar to that at Earth despite the vastly different scale sizes of the planetary bow shocks.Statistical analysis by Shan et al. (2018) revealed their mean frequency to be 20-30 s in the spacecraft frame (similar to Earth), 2 to 3 times the local proton cyclotron period.As at Earth, foreshock ULF waves originate in the quasi-parallel region of the Venusian foreshock (Omidi et al., 2017).
ULF waves attempt to propagate upstream from the planet they are generated near but are blown back toward the bow shock by the solar wind.As they move deeper into the foreshock, they encounter higher levels of superthermal ion density.These ions modify the refractive index of the medium, causing the transverse modes to become compressive, leading to the waves steepening (Tsubouchi & Lembège, 2004;Tsurutani et al., 1987;L. B. Wilson III et al., 2009).The waves become more oblique and compressive as they penetrate deeper into the foreshock.Two foreshock phenomena which can result from this steepening of ULF waves are (a) Shocklets (Hoppe & Russell, 1981) and (b) Short large-amplitude magnetic structures (SLAMS) (Chen et al., 2021;Schwartz, 1991).
To date, the only report of SLAMS forming sunward of Earth is by Collinson, Wilson, et al. (2012), who presented a case study of 3 SLAMS upstream of the bow shock of Venus (0.72 AU).However, these were associated with a transient event in the foreshock driven by a discontinuity in the interplanetary magnetic field (possibly a Hot Flow Anomaly (Collinson, Sibeck, et al., 2014) or similar).This foreshock transient substantially perturbed the Venusian induced magnetosphere, driving the bow shock outwards from its typical location by ≈3,000 km.Thus, SLAMS have only been reported at Venus during a substantial disturbance of the foreshock and induced magnetosphere.It is unclear if they can exist in the steady-state foreshock of Venus, when the solar wind, interplanetary magnetic field, and magnetosphere are quiescent.

Objectives and Overview of This Paper
The dearth of observations of Shocklets and SLAMS in the steady-state foreshock of Venus calls into question whether they can form at such small magnetospheres under quiescent upstream conditions.Given that at Venus the bow shock is an order of magnitude smaller than at Earth it is not obvious whether ULF waves will have sufficient time and space to grow nonlinear and steepen into Shocklets and SLAMS.Thus, understanding under what conditions the Venusian foreshock can intrinsically generate such structures would be important for our understanding how stellar winds interact with small bow shocks, such as those found at planets and moons with induced magnetospheres (e.g., Venus, Mars, Titan), Comets, and worlds with weak magnetic dipoles (e.g., Mercury).
Here we present a case study of in situ observations by ESA's Venus Express orbiter from the 26th of February 2009, demonstrating the existence of both Shocklets and SLAMS in the steady-state foreshock and ULF wave field of Venus.We use data from the Venus Express Magnetometer (Zhang et al., 2006) and Analyzer for Space Plasmas and Energetic Atoms (ASPERA-4) Ion Mass Analyzer (IMA) (Barabash et al., 2007) and Electron Spectrometer (ELS) (Collinson et al., 2009).
Our paper is outlined as follows.In Section 2 we give a brief review of the induced magnetosphere and foreshock of Venus.In Section 3 we describe the Venus Express instruments used in this study.In Section 4 we describe orbit №1043 and give an overview of what conditions were like in the quasi-parallel magnetosheath and foreshock.In Section 5 we describe our analysis of the 5 events (3 SLAMS and 2 Shocklet candidates).In Section 6 we describe statistical analysis of solar wind measurements by the Venus Express, finding that SLAMS and Shocklets may not be common at Venus.Finally in Section 7 we summarize our findings and conclusions.

The Venusian Induced Magnetosphere and Foreshock
Without an intrinsic magnetic dipole (Smith et al., 1965) the obstacle to the solar wind at Venus is its dense and conductive ionosphere.The advection of the interplanetary magnetic field induces electrical currents within the ionosphere.These currents generate a global system of weak and overlapping induced magnetic fields (Dubinin et al., 2013).The resulting induced magnetosphere is far weaker than at Earth and roughly an order of magnitude smaller (Bertucci et al., 2011;Futaana et al., 2017;Luhmann, 1990).The Venusian bow shock stands off only ≈1.4 Venus Radii  ( ) upstream from the center of the planet (Slavin et al., 1980) (Figure 1g), as compared to ≈15R E at Earth (Fairfield, 1971).Behind the Venusian bow shock is the Magnetosheath (sometimes called the Ionosheath), a region of shock-heated solar wind.For more information on the structure of the Venusian magnetosphere (which has been recently revised in light of new data from Parker Solar Probe), see Collinson, Ramstad, et al. (2022).

Venus Express Instrumentation
The primary instrument used in this study is the Venus Express magnetometer (MAG) (Zhang et al., 2006), which measured 3D ambient magnetic fields at cadences of up to 128 Hz.In this study, standard survey data (4s) as well 10.1029/2023GL104610 4 of 12 as high-resolution (32 Hz) data is used.This study is supported by measurements of electrons and ions by the Analyzer for Space Plasmas and Energetic Atoms (ASPERA-4) (Barabash et al., 2007;Collinson et al., 2009).ASPERA-ELS measured the energy spectra of electrons between 1 eV and 21 keV at a cadence of either 1s or 4s.This study also uses solar wind measurements by the ASPERA-4 Ion Mass Analyzer (IMA) instrument, which measured the velocity distributions of ions between 12 eV and 30 keV.ASPERA-IMA had a broad 3D field of view (90° × 360°), and the ability to separate ions by mass group (H + , He + , "Heavy ions").However, ASPERA-IMA had a very slow (192 s) measurement cadence, and as will be shown in Section 6, tended to under-estimate solar-wind densities.

Venus Express Explores the Venusian Foreshock on 26 February 2009
Figure 1g shows a map of Venus Express orbit №1043, occurring on the 26th of February 2009.Figures 1a-1f show in situ measurements from this orbit.Two time periods are shown.Figures 1a-1c shows an overview of the entire encounter with the foreshock so that the events described in this paper can be put into context.Figures 1d-1f shows a close up of 2 min 30 s of data containing Shocklets and SLAMS where we shall focus our analysis.Figures 1a and 1d show color coded timelines of each of these two periods.Magnetometer (Mag) data (Figures 1b and 1e) are presented in the Venus Solar Orbital (VSO) coordinate system, where x points toward the sun, y points back along the orbital path of the planet perpendicular to the Venus-Sun line opposite to the planet's velocity vector, and z points out of the plane of the ecliptic completing the right-hand set.The angle between the magnetic field and bow-shock normal (     , Figures 1b and 1e) was calculated by propagating the IMF field line direction at the location of Venus Express until it intersects the Slavin et al. (1980) bow shock model.The magnetic compression ratio ( ∕ 0) was calculated by subtracting the 32 Hz data from the time-averaged 1/4 Hz data (B 0 ).Data from the foreshock encounter (Figures 1a-1c) reveal there was no clear boundary delineation between the magnetosheath (maroon) and foreshock (dark blue).Large amplitude waves were observed throughout the period (Figure 1b).These waves were of approximately the same amplitude (30-40 nT) until ≈06:41, after which they generally tended to reduce in amplitude with increasing distance from the planet.We thus estimate 06:41 GMT as an approximate transition between being more in the sheath to being more in the foreshock, based also on a change in energy spectra from ASPERA-4 ELS (Figure 1c).These data are very consistent with the complex field of steepened magnetosonic waves expected in the quasi-parallel sheath and foreshock (Collinson et al., 2020;Luhmann et al., 1987;Shan et al., 2014).Thus, we conclude Venus Express transitioned between quasi-parallel magnetosheath to foreshock sometime after 06:41 GMT on the 26 of February 2009, and was thus in the right place to search for SLAMS and Shocklets.

Overview of Observations
A time-series of Magnetometer data are shown in Figures 1b and 1e at two cadences; at 32 Hz (black) to better resolve the details of the magnetic perturbations; and at 1/4 Hz (bright red) to more clearly see the general trends in the background field.The first three events (№1, №2, №3) are highly compressive, all with dB/B 0 > 3, consistent with SLAMS.The compression ratio of event №2 was greater than the maximum factor of four for simple compression (Gurnett & Bhattacharjee, 2005), also highly indicative of SLAMS (Schwartz et al., 1992).
The latter two events (№5 and №6) were less steep, with compression ratios between 1 < dB/B 0 ≤ 2, consistent with Shocklets.These two steepened waves were observed between two ULF waves (№4, 7).Given all four were observed at a regular cadence of 20 ± 3s consistent with the period expected from the Venusian wave field (Shan et al., 2018), this suggests that the events №5 and №6 grew as a direct result of the steepening of "30 s" ULF waves, as expected for Shocklets.

Minimum Variance Analysis of Venusian SLAMS and Shocklets
Following L. B. Wilson III et al. (2009) we performed minimum variance analysis (MVA) (Sönnerup & Scheible, 1998) on each of the 3 SLAMS and 2 Shocklets using frequency filters to determine the characteristics of each magnetic structure.Figure 2 shows a close-up of magnetometer data from each of the events.The top panel shows calibrated magnetometer data at 32 Hz in VSO coordinates (black, as per Figures 1b and 1e).The bright red line shows these data with a 0.004 → 0.5 Hz filter applied.The lower panels of Figure 2 show hodograms of these filtered subintervals of data after MVA.Table 1 accompanies Figure 2, showing the collected properties of each of the events, including the results of MVA analysis.

SLAMS:
The top three panels (A, B, C) of Figure 2 show close-ups of the three SLAMS candidates.The mean compression ratio of the SLAMS (dB/B 0 ) was 3.7 times the background field, and they had periods between ≈2 → 6 s.The first SLAMS (Event №1) was linearly polarized in the spacecraft frame.The second and third SLAMS candidates (Event №2 and №3) were elliptically polarized in the spacecraft frame, consistent with previous observations of SLAMS (Dubouloz & Scholer, 1993;Mann et al., 1994).With only a single spacecraft we cannot determine the propagation direction.Of the three SLAMS candidates, event №2 exhibited the most circular polarization with MVA eigenvalues λ mid /λ min = 352 and λ max /λ mid = 1.8.Most of the five events are associated with a train of whistler waves, consistent with either SLAMS or Shockets which act as a localized miniature bow shock.Of the SLAMS candidates, Event №3 shows the best example of a classical wave train of precursor whistlers on the upstream side, consistent with previous observations of SLAMS at Earth (L.B. Wilson et al., 2013) and Saturn (Bebesi et al., 2019).Our MVA analysis shows the three SLAMS candidates had an average angle between wave vector and the magnetic field of  ̂ ⟨ ̂⟩ ≈ 71 • .These structures are thus compressive and obliquely propagating to the ambient magnetic field consistent with previous observations of SLAMS at Earth (Chen et al., 2021;Mann et al., 1994).

Shocklets:
The bottom two panels (D, E) of Figure 2 show close-ups of the two Shocklets candidates.Both have the classical asymmetrical "saw-tooth" profile of a Shocklet, with a steeper edge on the upstream (trailing) side (Hoppe & Russell, 1981).The mean compression ratio was 1.29, and both were linearly polarized, also consistent with what is expected of Shocklets (L.B. Wilson et al., 2013).The two Shocklets had a similar  ̂ ⟨ ̂⟩ of ≈78°, which, again, is highly consistent with a fast magnetospheric mode structure such as a Shocklet.

Observations of Associated Plasma Perturbations by the Electron Spectrometer (ASPERA-4 ELS)
A feature of compressive magnetosonic structures such as SLAMS and Shocklets is that they act like a local quasi perpendicular shock, locally perturbing the solar wind, and increasing both |B| and plasma density (Behlke et al., 2003;Collinson et al., 2018;Dubouloz & Scholer, 1993;Mann et al., 1994).However, the previous study of SLAMS at Venus by Collinson, Wilson, et al. (2012) were unable to examine the plasma perturbations anticipated from SLAMS.Figures 1c and 1f show measurements of superthermal electron flux from ASPERA-4 ELS, with a time/energy spectrogram on top and line-plot of total integrated superthermal electron flux at the bottom.Electron flux remained fairly constant during the two ULF waves (event №4 and №7).However electron flux was enhanced in phase with |B| at all 3 SLAMS and both Shocklets, consistent with such steepened magnetosonic structures.

How Common Are SLAMS and Shocklets at Venus?
SLAMS have now been reported at Venus on two days: 11 April 2009 (Collinson, Wilson, et al., 2012) and26 February 2009 (this study).A thorough statistical determination of the occurrence rate would require more than 2 events.However, following Collinson, Sibeck, et al. (2014) and Collinson, Fedorov, et al. (2014), we can put a lower limit on their occurrence rate through investigation of whether the conditions in the solar wind upstream of Venus were unusual on these 2 days.Specifically, we examine the solar wind Alfvén Mach number (M A ), which is thought to be a general requirement for SLAMS formation at Earth (M A ≥ 4) to reflect ions at the bow shock and set up the ion-ion beam instabilities that lead to ULF wave formation (Thomsen et al., 1993) from which SLAMS form.
Figure 3 shows histograms of the upstream conditions at Venus from the entire 2006-2014 Venus Express mission (black).The data are further divided into two types: "slow" solar wind (with bulk velocities <500 km s −1 ) and   COLLINSON ET AL.
Before we discuss M A during SLAMS observation, we note that our analysis reveals that ASPERA-4 IMA substantially underestimated solar wind n i .As shown in Figure 3b, the mean solar wind n i reported by ASPERA-4 IMA at 0.72 AU was 2.2 cm −3 , and the mode was 3.8 cm −3 , much lower than the expected value of ≈12 cm −3 (Köhnlein, 1996).We posit several potential contributing factors to this: (a) All "top hat" analyzers (such as ASPERA-4 IMA) can struggle to accurately measure the absolute densities of quasi-monoenergetic plasma beams such as the solar wind.(b) The field of view of ASPERA-4 IMA was frequently obscured by a thruster; (c) ASPERA-IMA was designed to measure diffuse low energy oxygen ions escaping down the Martian and Venusian magnetotails, and would thus sometimes saturate in the high-flux beam of the solar wind.
Assuming that the mean density was in reality closer to the expected value of ≈12 cm −3 and that this error is a linear systematic bias, then we can multiply the n i measured by ASPERA-4 IMA by ≈×3.1 to make a rough estimate of the actual density  (  *

𝑖𝑖
) . As per Equation 1, this suggests ASPERA-4 IMA also underestimated the Alfvén Mach number by a factor of ≈×1.77.However, we caution that given the multiple possible contributing factors to the underestimation of solar wind density by ASPERA-IMA (particularly detector saturation), the true bias is unlikely to be this linear and simple.
With this caveat, we find that M A was unusually high on 26 February 2009, with a mean of 7.10 (measured), in the top 14% of the distribution of all measurements of M A by the Venus Express (Figure 3e), and with an actual value possibly closer to   *  ≈ 12.5 .Likewise, when we computed M A for 11 April 2009 (e.g., conditions during the Collinson, Wilson, et al. (2012) SLAMS case study) we find a similarly high mach number of 7.17, which is in the top 12% of the distribution of all measurements of M A by the Venus Express (Figure 3e), with an estimated actual value of   *  ≈ 12.7 .To investigate whether this apparent dependence on SLAMS/Shocklet formation on high M A is significant, we ran a one-way analysis of the variance (ANOVA) test on the following two data sets: (a) Solar wind M A on the 2 days where SLAMS have so far been identified; (b) M A from the entire mission (Figure 3e).The probability of measuring such high M A on both days by random chance (The "P-value") is 1.2 × 10 −4 , that is, very small.We thus show that M A on these 2 days were statistical outliers at Venus.This suggests that solar wind Alfvén mach number is likely important for SLAMS (and Shocklet) formation at Venus.This is generally in-line with what is expected from Earth where SLAMS and Shocklets tend to be associated with a higher M A (Burgess & Scholer, 2013).However, these observations may suggest that the M A apparently required for their formation at Venus may be exceptionally high for 0.72AU (upper limit of   *  ≲ 12.5 ), corresponding to a lower limit on occurrence rate of ≳14% of the time.This strongly motivates further statistical analysis to more thoroughly establish their occurrence rate at Venus, and their dependence on solar wind Alfvén mach number.

Summary and Discussion
In this paper we report the first observation of Shocklets at Venus, and demonstrate that SLAMS can form in the steady-state quasi-parallel Venusian foreshock, despite the magnetosphere being 1/10th smaller than at Earth.Thus we presume one would need to go to an even smaller system to determine the limit in scale-size below which such steepened foreshock structures do not have sufficient time to form.
1.Both SLAMS and Shocklet candidates were observed in the quasi-parallel foreshock, the region where they are found at Earth. 2. MVA analysis revealed that all candidates propagated obliquely to the ambient field with  ̂ ⟨. ̂⟩ between 58.6° and 89.27°, consistent with SLAMS and Shocklets (Mann et al., 1994). 3. Two events exhibited the following characteristics consistent with Shocklets.
(a) They were of classic "sawtooth" appearance with a steeper upstream (trailing) edge (Hoppe & Russell, 1981).M.A. was supported by UKRI (STFC/ EPSRC) Stephen Hawking Fellowship EP/T01735X/1.D.M.L. is grateful to the Science Technology and Facilities Council for the award of an Ernest Rutherford Fellowship (ST/R003246/1).This research was supported by the International Space Science Institute (ISSI) in Bern, through ISSI International Team project 465 "Foreshocks Across The Heliosphere: System Specific Or Universal Physical Processes?."We acknowledge and thank the front-line healthcare workers of our respective countries for their service during the COVID-19 pandemic, the beginning of which coincided with the initiation of this study.

Figure 1 .
Figure1.Venus Express field and particle observations from orbit№1043, 26th of February 2009.Panels (a-c)  show data from the period 06:35 to 06:50, the time interval marked "Encounter" in (g), covering the transition from magnetosheath to foreshock.Panels (d-f) show a zoom-in of the region of interest (06:44:00 to 06:46:30) where 3 SLAMS and 2 Shocklets candidates were encountered.Panels (a and d) show a color-coded timeline.Panels (b and e) show magnetometer (MAG) data at 32 Hz (black) and 1/4 Hz (red) cadence.From top to bottom; magnetic field magnitude (|B|) in nT; Vector (Bx, By, Bz, in VSO coordinates) in nT; the angle between the magnetic field and bow-shock normal  (   ) ; and the compression ratio of the magnetic field (dB/B 0 ).Panels (c and f) show data from ASPERA-ELS, with time/energy spectrograms on top and the total measured superthermal Differential Energy Flux (DEF) below.Panel (g) shows a map of Venus Express orbit №1043 through the induced magnetosphere of Venus in units of Venus Radii  ( = 6051.8) .

Figure 2 .
Figure 2. Close up view of the 3 SLAMS and 2 Shocklet candidates from Figures 1e-1h.Top Panels: time series showing original data and filtered between 0.002 and 0.5 Hz.Bottom Panels: Hodogram of Minimum Variance Analysis of magnetometer data filtered between 0.002 and 0.5 Hz.

Figure 3 .
Figure 3. Histograms of properties of the interplanetary magnetic field and solar wind upstream of Venus as measured by the Venus Express between 2006 and 2014.Panel A shows the strength of the IMF (|B|) from MAG. Panels B and C show solar wind proton density and velocity from ASPERA-4 IMA.Panels D and E show the Alfvén speed and Alfvén Mach Number (as measured, M A ) computed from these properties.Light yellow shading on each panel shows the conditions on 26 February 2009 (this study).Modal averages for each parameter are printed top right of each Panel, and the Mean value for each parameter is printed in the border.
Event № Classification Start (GMT) Duration (s) dB/B 0 Polarization (S/C frame)  ̂ ⟨ ̂⟩  Duration was calculated by eye from the apparent start and stop time of the magnetic signature.Polarization was determined by eye from the hodogram in Figure 2.

Table 1 Table
Showing Properties of the 5 Steepened Magnetosonic Structures Show in Fig