Particle acceleration in the Venus plasma wake

A suitable view of the distribution of the velocity vectors of the H+ solar wind ions measured with the VEX spacecraft projected on a plane transverse to the wake direction is reproduced in Figure 1 to describe a vortex shape configuration. The velocity distribution is oriented in a geometry different from what would be produced by magnetic tension forces along the field lines from the Venus polar regions. Instead, flow motion is dominant to produce the vortex shape in the particle displacement.

Figure 1. Velocity vectors of the H+ ions projected on the YZ-plane compiled from the VEX measurements (From Lundin et al., GRL, 40(7), 273,  2013).

 

By collecting data from VEX orbits obtained when the spacecraft entered and exited a vortex structure between 2006 and 2013 those crossings are indicated with the segments placed in Figure 2. As a whole there is a general difference between segments located within two circles that are traced with a preference to occur farther away from Venus (located at the left side) in the 2006-2009 orbits (left circle) with respect to those in the 2010-2013 orbits (right circle). At the same time, there is a corresponding difference in the width of the segments with larger values (higher values in the vertical coordinate) for those placed in the right circle. In particular, since minimum solar cycle conditions were present during the 2009-2013 orbits there is an indication that under such conditions the position of the vortex structures occurred closer to Venus along the wake and at the same time their width becomes larger.

Figure 2. Width of vortex structures in 20 VEX orbits measured downstream from Venus. The numbers at the side of each segment represent the two last digits of the year between 2006 and 2009 prior to a solar cycle minimum (left circle) and between 2009 and 2013 during that time period (right circle) (Pérez-de-Tejada and Lundin. IntechOpen, ISBN-978-1-83969-313-7), 2021.

 Such properties are compatible with the shape of a corkscrew flow in fluid dynamics depicted in Figure 3 in which its thickness decreases with distance downstream from an object immersed in a flow.

The decrease of the overall size of vortices with distance along the Venus wake as noted in Figure 2 has important implications regarding its effects on the motion of the planetary ions that stream in the wake. Most notable is that their kinetic energy around those features depends on the scale size of vortices and if the latter become smaller with the downstream distance as produced by the expansion of the solar wind into the wake the energy released should be assimilated by particles that remain moving in the smaller size vortices. In addition, such particles have directed motion along the wake and as a result, some of that energy may contribute to enhance their speed in that direction. It is thus possible that a fraction of planetary O+ ions dragged along by the solar wind may be gradually accelerated along the Venus wake. 

The acceleration of those particles can be estimated in terms of the change that the cross section of the vortex structures experience along the wake and that as shown in Figure 4 produces an increase in their speed in both panels from ~10 km/s by ~5 10³ km altitude to ~40 km/s by ~10⁴ km.  Following the shape of a vortex structure downstream from Venus similar to that indicated in the equivalent form past an object in Figure 3 we can suggest a shape that by two planetary radii downstream from Venus the thickness of the vortex should have decreased. The outcome of that geometry is that when the thickness of the corkscrew flow decreases along the wake the speed of the particles has to be larger so that their kinetic energy density integrated over the area of the cross section is preserved.

        

Figure 3. View of a corkscrew vortex flow in fluid dynamics. Its geometry is equivalent to that expected for a vortex flow in the Venus wake. The vortex flow becomes thinner when it is detected further downstream from Venus as suggested from the data in Figure 2 (from Pérez de Tejada and, Lundin, Intech Open (ISBN-978-1-83969 -313-7), 2021. 

 

Figure 4. Speed profiles of the solar wind and ionospheric ions as a function of altitude measured in the dawn-dusk (left) and in the noon-midnight meridian (right) (from Lundin et al., ICARUS, 215, 751, 2011).

 Variations in the speed profiles with altitude measured in the dawn-dusk and in the dawn-dusk meridians across the Venus wake are compatible with those expected from the shape of the corkscrew flow in Figure 3 where larger speed values should be encountered where the cross section of the vortex structure is smaller. Thus, the data points in Figure 4 at low altitudes refer to the motion of the spacecraft through a wide vortex in a region close to Venus and at higher altitudes apply where the cross section of the vortex is smaller and hence the flow speeds are larger as it is the case by ~10⁴ km altitude.

An implication also consistent with the shape of a corkscrew flow shape in Figure 3 is the abrupt ending of the speed profile by ~ 1.5 10⁴ km altitude in both panels of Figure 4 and that is not related to any drastic change in the density profile since comparable density values were measured above and below that altitude. Instead, the abrupt ending of the speed profile at that altitude may imply the exit of the spacecraft from the corkscrew flow region along its trajectory. Measurement of planetary ion flows in the Venus near wake also suggest that they proceed under superalfvenic conditions and thus are unrelated to magnetic field effects (Pérez-de-Tejada et al., JGR, 118, doi: 10.1002/2013JA019029, 2013). At the same time the flow direction appears to be independent of the magnetic field orientation (Lundin, personal communication).