Conclusions

Various types of double layers

Type 1 Weak double layer
   two component model 
   three component model 
   Strong double layer resultant from type 1 weak double layer

Type 2 Weak double layer
   three component model
      moving solitary structure
      ion hole like movement




   We categorize various types of double layers into two types roughly,

a type 1 weak double layer and a type 2 weak double layer. In previous

 work, double layers are divided into two types, a strong double layer

and weak double layer. But, in our work, a strong double layer is a 

resultant of a weak double layer, then we do not adopt such categorization.

We performed three component simulation.  In this case, most proper 

classification is based on the original wave mode of weak double 

layers. The type 2 weak double layer can not form in two component model.




   A type 1 weak double layer and a type 2 weak double layer are formed

as a resultant of nonlinear growth of ion acoustic waves respectively, 

but the two modes of ion acoustic waves are different.  The one is ion

acoustic slow mode, propagating downward, the same direction of electron

 flow, and the other is ion acoustic fast mode, propagating upward.  

They are distinguished in the point of their original wave modes.



   The type 1 weak double layer consists of three charge layers, positive-

negative-positive charge.  The ion acoustic slow mode wave grows into 

solitary wave  with a negative potential bay, having positive-negative-

positive charge layers.  But, the solitary wave has not net potential jump.

A type 1 weak double layer has field-aligned potential jump, because a spatial

 structure of three charge layers is asymmetric.  The negative potential bay

acts as barrier against electrons, and electrons are reflected by this potential

barrier at both sides of solitary wave.  Because electrons stream downward 

aligned magnetic field line faster than such solitary waves, more electrons 

are reflected in the upstream region.  Positive-negative-positive triple charge

 layers change to positive-negative-relatively small positive charge layers 

forming net potential jump consisting of a potential negative bay and a 

potential jump.  



   Type 1 weak double layers make a movement like ion holes, which move downward

 initially and are accellerated to move upward by the momentum transfer from 

electrons, drawing an arc in the ion phase scape.  In our model, under upward 

ion beams, the movement of ion holes continue in ion beam region of phase space.

  


   Type 2 weak double layer is characteristic of the three component model, 

containing upward ion beam.  It is a consequence resultant of nonlinear 

growth of ion acoustic wave travelling upward, the same direction of ion beam

 flow.  In two component model, this mode is dumped by downward electron flow. 

In this case, a solitary wave flowing upward have potential clamp which acts 

potential barrier aginst upward ion beam.  Ions in the upward ion beam are reflected

 by this potential barrier, and more ions are reflected in downward region of the 

solitary wave to configure an asymetry profile of charge density.  A solitary wave has 

a net potential jump and grows to a type 2 WDL.  Type 2 WDL accelerate electrons downward

and ions upward.


   In two component model simulation, a WDL is formed by ionospheric cold ion and magnetospheric 

hot electrons.  We call this classical WDL a type 1 WDL, which has net potential jump much as 

hot electron thermal energy.  However, in three component model, this speculation must be changed.

Single WDL has not so much potential drop as thermal energy of hot electrons, because positive charge 

depletion of WDL is composed ionospheric cold ion component and the density of cold ion component is 

less in three component model than in two component model.  The size of potential well of WDL depends 

on the density of background cold ions, and the size of potential jump of a WDL is propotional to the 

size of potential well because the positive charge layers of WDL are formed by depletion of electrons 

reflected by the potential well.  In three component model, the interval between WDLs is not so wide 

as that in two component model.  Electrons are reflected by potential well specially in upward 

region, and in this region, the distribution function of electrons are modificated.  In this electron 

excess region ,which enlarges spatially during formation of potential well, an additional WDL cannot be 

formed, because this excess of electron prohibit a formation of electron deflection region.  In three 

component model, the depth of a potential well is nearly propotional to the density of cold ion.  

A large potetial well can trap fast electrons, and the large electron deflection region is formed.

As a result, the interval between WDLs are small in three component model.  Sato and Okuda[1981] shows 

an interval of WDLs is about 1000 Debye length.  In this case, the size of potential well is nearly an 

electron thermal energy, and an potential drop can trap electrons whose velocity is electron thermal velocity.  

These electrons can run hundreds of Debye length during an WDL formation.