In this section, the evolution characteristics of artificial plasma clouds under various release conditions were investigated, including different release altitudes (220 km and 300 km), different release masses (1 kg, 10 kg and 100 kg), different initial ionization rates (0%, 20% and 80%), and different release velocities. The ionospheric disturbances of barium and cesium were also compared.
The ambient atmospheric density, ionospheric particle density, temperature, magnetic field intensity and other initial conditions can be obtained by the atmospheric model MSIS-E-90, International Reference Ionosphere model (IRI-2016), and International Geomagnetic Reference Field model (IGRF-13). An equivalent extrapolation boundary condition is used at all boundaries. The design flow of the numerical algorithm is shown in Fig. 1, and the simulation process can be summarized as follows:
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1.
The release parameters and background ionospheric parameters are set;
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2.
The distribution of neutrals is calculated according to the neutral diffusing model (“Diffusion of neutral particles” section);
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The drift velocity is calculated according to the momentum equation (Eq. (2) in “Diffusion of charged particles” section);
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4.
The particle number density distribution can be obtained by solving the continuity equation (Eq. (1) in “Diffusion of charged particles” section);
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Steps 2–4 are repeated until the time limit is reached.
Effects of release altitude
The ambient temperature, magnetic field, and number density of neutral particles and charged particles in the ionosphere vary with altitude, so the collision frequency and diffusion coefficient vary with altitude. At low altitudes, the diffusion coefficient of barium is small due to the high concentration of atomic oxygen, molecular oxygen and other particles, and the chemical consumption of barium is high, resulting in a relatively small plasma cloud. However, if the chemical is released at a very high altitude, rapid diffusion leads to a sharp reduction in the concentration of the released substance, and the background ionospheric particles cannot be significantly affected, which is not conducive to observation. For this reason, release altitudes of 220 km and 300 km are selected in our simulation, where the diffusion velocity is moderate and the disturbing effect on the background ionosphere is obvious, which is more convenient for experimental observation.
The distribution of the density and temperature of the ambient particles, and the diffusion coefficient and damping coefficient of barium atoms, and the meridional and zonal winds obtained in Horizontal Wind Model 07 are shown in Fig. 2.
Figures 3a, 4a show the release results at 220 km and 300 km, respectively. The profile of barium ions (Figs. 3a, 4a), background oxygen ions (Figs. 3b, 4b) and electron number density (Figs. 3c, 4c) are shown in the subgraphs. Due to the binding effect of the geomagnetic field, the expansion of the plasma cloud across B is constrained. In the direction along the magnetic field, the movement of the barium ion cloud is not restricted, so the plasma cloud will be gradually tied to the magnetic field, and stretched into an elliptical structure along the direction of the magnetic field. The momentum of Ba+ and O+ are coupled together because of collision, and barium ions transfer the kinetic energy to oxygen ions, which pushes the oxygen ions to move along B, forming an oxygen ion density hole in the release center. On the other hand, the outflowing O+ slows down under the effects of the background thermal and pressure gradients, which creates two density bumps on both sides of the Ba+ cloud along B. This phenomenon is called the snowplow effect (Ma and Schunk 1991), which has been detected by a high-resolution incoherent scatter radar in the Spacelab 2 upper atmospheric modification experiment (Bernhardt et al. 1988).
Figures 3d, e, 4d, e show the number density and velocity of electrons as a function of altitude and time, respectively. Due to the high collision frequency at low altitudes, the expansion of neutral barium clouds is greatly restrained, and the plasma clouds expand more slowly, so the plasma clouds are mainly concentrated in a relatively small area. Furthermore, Figs. 3d, 4d show that the peak number density of electrons at the release center decreases more slowly at low altitudes. At a high altitude, with a lower collision frequency and higher diffusion coefficient, the expansion of neutral clouds is faster, and the plasma clouds stretch faster along the magnetic field, so the plasma clouds have a larger radius than those at low altitudes. As can be seen from Figs. 3e, 4e, when barium is released at 220 km and 300 km, the maximum diffusion velocities of electrons that can be achieved at t = 30 s are 466 m/s and 965 m/s, respectively.
When considering a nonuniform ionosphere, the diffusion coefficient and damping coefficient change with height, and the background density gradient also affects the ion motion. The motion of artificial ion clouds along the magnetic field and its snowplow effect on ambient oxygen ions are similar to previous simulation results in which the background ionosphere is assumed to be uniform (Gatsonis and Hastings 1991; Ma and Schunk 1991, 1993). The difference is that the asymmetric structure of the artificial ion cloud appears in the vertical direction, which can be ascribed to the asymmetry of the collision frequency and diffusion coefficient, leading to a plasma cloud with a longer top and shorter bottom. In addition, the snowplow effect of O+ is also asymmetric on both sides of the expansion cloud due to the influence of the background density gradient. Based on the results without considering the ambient wind field (not shown), the effect of the ambient wind field is not significant because the speed of the ambient neutral wind is approximately tens of meters per second, which is much smaller than the expansion velocity of the plasma cloud (on the order of kilometers per second). Qualitatively, the morphology and evolution characteristics of the artificial plasma cloud are in agreement with the observations in previous space experiments (Haerendel et al. 1967; Foppl et al. 1967; Bernhardt et al. 1987; Huba et al. 1992).
Effects of initial cloud density
In this section, we analyze the effects of different initial cloud densities on the evolution of artificial plasma clouds. Changes in release masses and initial ionization rates can both change the initial densities of the cloud.
For a fixed initial radius, different release masses mean different initial cloud densities. Qualitatively speaking, the results of ionospheric disturbances with different release amounts are similar. It can be seen from Fig. 5 that with a larger release mass, the number density of the plasma clouds will be higher, and the enhanced pressure gradient enhances the expansion kinetic energy of neutral clouds, leading to a stronger disturbance of background oxygen ions and electrons. Additionally, a large release mass causes a larger ionospheric disturbance area and a longer duration of disturbance.
In an actual release experiment, it often takes some time for the cloud to reach the initial state of our simulation (which is generally called the average collision time), so that a few barium atoms may have been ionized before the beginning of the simulation, leading to a difference between the initial number of barium atoms and the total number of barium atoms released, which is called the initial ionization rate. In addition, due to the different release techniques (thermal release, explosion release, etc.) used in the active release experiment, the ionization rates of neutral clouds at the beginning of release also vary greatly.
Figure 6 shows the simulation results with initial ionization rates of 0%, 20% and 80%. The plasma cloud consists of two parts: one part is the high-density part due to initial ionization, and this part will become longer and narrower over time, because it has little movement across the magnetic field except for the initial inertial motion (e.g., the thermal expansion after release from the canister and the velocity generated by the suborbital motion of the sounding rocket), which is soon be captured by magnetic field. Another part of the plasma cloud comes from the continual photoionization of expanding barium neutrals. At the initial stage after release, a steeper density gradient results in a faster expansion of the plasma cloud along B. As seen from Fig. 6, with the increase in the initial ionization rate, the distribution of barium ion clouds become increasingly concentrated, and the numerical dissipation brought by the numerical simulation process decreases, so the highest density of Ba+ increases, but the plasma density decreases faster. Figure 6d, e shows that the maximum Ba+ cloud densities are 7.77 × 108 cm−3, 2.02 × 108 cm−3 and 6.06 × 107 cm−3 with initial ionization rates of 0%, 20% and 80%, respectively, and the diameters of the plasma clouds with initial ionization rates of 0%, 20% and 80% are 43 km, 50 km and 57 km at t = 60 s, respectively. At the same time, the steeper density gradient makes the barium cloud stretch faster along the magnetic field, so the vertical diameter of the plasma cloud also increases rapidly, and the sheet-like structure of the plasma cloud along the magnetic field is more obvious. As time passes, the density difference of Ba+ at the release center caused by different initial ionization rates decreases.
Effects of release velocity
We also considered the evolution characteristics of released clouds with different initial release velocities. The cloud evolution results with initial velocity perpendicular to B and initial velocity parallel to B were simulated, with a velocity of 2 km/s. It should be noted that, for the release with initial velocity perpendicular to magnetic field, we take the release point located at [− 20, 0, 0] km; for the release with initial velocity parallel to magnetic field, we take the release point located at [0, 0, − 20] km.
Figure 7 shows the evolution result of a cloud released with an initial velocity perpendicular to B. The expansion of the plasma cloud along B and its snowplow effect on O+ are very similar to those of a stationary release. However, since the volume of the Ba+ cloud is larger than that in the former case, the number density of the Ba+ cloud is lower. Due to the movement of neutral barium clouds, an ionic tail will be generated behind them from photoionization in the early stage, but the Ba+ cloud still becomes a sheet-like structure eventually because the motion perpendicular to B is constrained. The Ba+ cloud decelerated rapidly in response to the magnetic field, while the neutral barium cloud was not affected by the magnetic field; thus, the barium ion cloud was slowly separated from barium neutral clouds (not shown). In addition, there are still two O+ density enhancement regions and one O+ density depletion region in the background ionosphere, and it can be seen that a small number of oxygen ions are pushed to the front of the cloud due to momentum transfer, forming O+ density enhancement regions at both sides in front of the cloud.
As shown in Fig. 8, when the neutral barium cloud is released with a velocity along B, at the early stage, the snowplow effect of the ion cloud creates an O+ density hole on the back side of the expanding Ba+ cloud and an O+ density bump at the front. Compared with the cases without injection velocity and with a release velocity perpendicular to B, this case features a much greater O+ density enhancement in front of the plasma cloud, and no density enhancement appears behind the plasma cloud. While the initial velocity of the barium neutrals is parallel to the background magnetic field and although the movement of the barium ion cloud is not affected by the j × B force, with the high concentration of background particles, the motion of the ion cloud still slows down due to collisions. At t = 20 s, the plasma cloud has moved approximately 12 km. Moreover, because of the existence of Coulomb collision between charged particles, the damping coefficient of the ion cloud is higher than that of the neutral cloud, which eventually leads to the separation of the ion cloud and neutral cloud.
Cesium release
Although the thermal ionization of cesium is prone to occur due to its low ionization potential, thermal ionization is insignificant compared to photoionization under conditions of strong sunlight, so the thermal ionization process of cesium is not discussed here. The comparison of the diffusion coefficient and damping coefficient of barium and cesium is shown in Fig. 9. The diffusion coefficient of Ba is slightly larger than that of Cs, but its damping coefficient is smaller than that of Cs.
Figure 10 shows the simulation results of Cs with the same number of molecules released. Except for the type of material released, other parameters are the same as in Fig. 3. Qualitatively speaking, the expansion characteristics of Cs+ and Ba+ and the disturbance effect on background O+ are similar. Since the diffusion coefficient of cesium is smaller, the barium cloud expands more rapidly and covers a wider area than the cesium cloud, but the ionization yield of cesium is higher than that of barium under the same release mass due to the higher photoionization rate of cesium. The cesium ion cloud is denser than the barium ion cloud, so the cesium ion cloud has a larger expansion speed, as seen from Figs. 3e, 10e. The maximum vertical velocities of electrons at t = 5 s are 289 m/s and 613 m/s, respectively. At t = 60 s, the peak number density of cesium ion clouds reaches 4.48 × 107 cm−3, which is nearly one and a half times that of barium ion clouds (3.03 × 107 cm−3) under the same conditions. In addition, the collision frequency of Cs+-O+ is greater than that of Ba+-O+, and the snowplow effect of Cs+ is stronger than that of Ba+, resulting in larger oxygen ion density holes and bumps.