At the time of the substorm expansion phase, an activity of auroral current loop which connects the ionosphere and magnetosphere is enhanced. The carrier of the upward field-aligned current is mainly magnetospheric hot electrons. The coupling between these hot electrons and ionospheric cold ions causes the development of ion- acoustic wave instability and subsequent nonlinear electrostatic potential drop formation. Auroral particles are thought to be accelerated along the magnetic field line by many such small electrostatic potential drops, called ``weak double layers". It is known that a field-aligned upflowing ion beam exists in the auroral particle acceleration region. This upflowing ion beam is hotter than the stationary ions of the ionospheric origin. We have not included such component in our past simulation models, but, in this study, we include this component in our initial conditions of the present study. We found that a major difference between the present model and our past model is the life time of ion hole, that is, the ion hole exists longer in a new system where the ion beam is assumed. Initially, ion holes are formed in the phase space of the cold ions, then they move into the phase space of the hot ions. We carried our runs by changing the density ratio of the hot component to that of the cold component, and drift velocities of the hot electrons as well as hot ions. The size of potential drop depends on those parameters especially on the density of the cold ionospheric ions. The potential drop is small, when the population of cold ions are low, because the charge separation formed by an ion hole is affected by the density of cold ions. If the drift velocity of hot ions exceeds a threshold condition, other type of weak double layer is formed, which is caused by the ion acoustic wave of slow beam mode. This suggests that the weak double layer causes an acceleration of ion beam, and new type of double layers are formed in higher altitudes through the mechanism as discussed above, which works positively to form the auroral particle acceleration region.
Numbers of numerical simulations of auroral particle acceleration process have been performed in the last 20 years. Auroral particles are thought to be accelerated along the magnetic field line by many small electrostatic potential drops, called ``weak double layers", which are distributed along the magnetic field line in the auroral zone. The field-aligned current excites the electrostatic ion-acoustic waves, and the weak double layers are formed as a result of nonlinear development of the ion-acoustic waves. Thus, particle electrostatic codes are suitably adopted in studying such an instability due to velocity space nonequilibrium. Those simulations are usually one-dimensional, since it has an advantage that we can put many grids along the magnetic field line and many particles in each grid. A potential drop of the weak double layer was observed with a localized density depletion in the background plasma ions. This fact is consistent with simulation results that the weak double layer is an ion hole in the ion phase space. The growth and movement of ion holes are synchronized with the behavior of weak double layers [Barnes, 1985; Tetreault, 1991]. Ion holes were formed in the stationary ion, but the upflowing ion is usually observed in the auroral acceleration region [Koskinen,1990]. Effects of this component must be studied. Gray et al.[1991] studied this hot upflowing ion by numerical simulation, but electrons were stationary which did not compose the field- aligned current. In our study, upward field-aligned current consists of both shifted Maxwellian electrons and upflowing ions.
We performed two types of numerical simulation, two component model and three component models. Both of simulations were studied with aperiodic one dimensional electrostatic particle code.
The two component model includes hot shifted Maxwellian electron which carries upward field-aligned current, and stationary cold ion. We set the value of ion to electron temperature ratio as well as the electron drift velocity to cause the ion acoustic instability.
The difference between this model and aforementioned ``two component" model is the presence of an upflowing ion beam component. A field- aligned upflowing ion beam is commonly observed in the auroral particle acceleration region by satellite, but the existence of such a component was not taken into account in the two component model. In the three component model, we assumed hot electrons, cold ions, and hot ions which represent upflowing ion of our initial conditions.
We present eleven cases of simulation, run01 and run02 are the two component model, the others (run03 $\sim $run11) are the three component model. Parameters for those eleven cases are shown as follows.
In our model, the system was set to be charge neutral, and both boundaries have equal values of electric field. We fixed this value to be zero, because it is necessary for simulation system to have net electrostatic potential drop between both boundaries. Particle boundary condition is a modified periodic condition. Particles out of one boundary are reinjected into the simulation system from the other boundary with shifted-Maxwellian velocity distribution. Drift velocity of each component is calculated by averaging velocity of the particles in one grid at the boundary. Using this boundary condition, one boundary does not affect the other boundary even if the region near the boundary contains beam- like accelerated particles.
Many weak double layers were formed and vanished successively in the two component model. This process was also observable as an ion hole movement in the ion phase space. Ion hole was formed at the same velocity to the ion sound speed initially, then it was accelerated by potential drop owing to the charge layer around the ion hole. Subsequently, the ion hole left across cold ions in the ion phase space in accordance with the disappearance of the potential drop. Ion acoustic solitary wave forming this weak double layer propagates downward and construct next weak double layer. Total potential drop was maintained by repetition of such a process. We call the weak double layer formed in this case type1 weak double layer.
As seen in the previous model, many weak double layers were formed and vanished successively in the three component model as well. However, there are two major differences between the two models. One difference is the life time of an ion hole, that is, the ion hole existed longer in this system where the ion beam was assumed than that in a system where it was absent. The other difference is the simultaneous existence of other type of weak double layer. Ion hole was formed at the same velocity to the ion sound speed of hot ion slow mode initially. We call this type of weak double layer having upward velocity initially, type2 weak double layer. The results of this model indicate that a theory of weak double layer formation incorporating the ion hole as demonstrated in the former model is also applicable to this model.
Potential structure of type1 WDL Ion phase space of type1 WDL Potential structure of type2 WDL Ion phase space of type2 WDL
It is well known that the size of potential drop of a weak double layer is comparable to temperature of electrons contributing the field aligned current, and it is consistent to the result of our two component model simulation. In three component model, the size of potential drop of weak double layer depends on the density of cold ion. The potential structure of weak double layer consists of two parts, a potential well and a potential jump. The depth of potential well is proportional to the density of cold ions. Because an ion hole of type1 weak double layer forms in the phase space of cold ion, the density depletion by an ion hole decrease with the density of cold ion, and the depth of potential well increases inversely. Net potential jump of weak double layer is proportional to the depth of potential well.
The drift velocity of hot electron affects the size of potential drop. It is consistent to the estimation based on the ion hole theory.
Nci:Nhi=4:0 potential phase space | Nci:Nhi=3:1 | Nci:Nhi=2:2 |
Nci:Nhi=1:3 | |
|---|---|---|---|---|
Vde=-0.3 | --- | run03 | run04 | run05 |
Vde=-0.4 |
run01 | run06 | run07 | run08 |
Vde=-0.6 | run02 | run09 | run10 | run11 |
Type1 weak double layer causes an acceleration of ion beam, and the ion acoustic wave of slow beam mode is excited, followed by formation of type2 weak double layer. A single weak double layer can act positively to produce more weak double layers in higher altitudes through the effect of ion beam. Under the existence of the upward hot ion beam, the size of potential drop of weak double layer is not so large as that of the two component model, when the hot ion component is absent. However, the life time of each weak double layer is long, and it causes simultaneous formation of more weak double layers alinged to the magnetic field line. Consequently, the total field-aligned potential drop is roughly equal in both models.
Gray, P. C., M. K. Hudson, W. Lotko, and R. Bergmann, Decay of Ion Beam Driven Acoustic Waves into Ion Holes, Geophys. Res. Lett., 18,1675,1991 Koskinen, H. E. J., R. Lundin, and B. Holdback, On the plasma environment of solitary waves and weak double layers, J. Geophys. Res., 95,5921,1990 Tetreault, D. J., Theory of electric fields in the auroral acceleration region, J. Geophys. Res., 96,3549,1991 Sato, T. and H.Okuda, Numerical Simulations on Ion Accoustic Double Layers J.G.R vol.86,No.A5,PAGE 3357,May 1,1981
