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Charging of the Spherical Grain in Cloud

Charging of the Spherical Grain in Cloud. Kinetic equation. Electric field E=e(-Z+4 p (n i -n e )r’ 2 dr’)/r 2 j =Edr’. r. r p. L. r. Electron density n e =n 0 exp( j/T e ). Electron current on grain J= r p 2 n 0 (8eT e /(  m e )) 1/2 exp( (r p ) /T e ). Numeric cell. Conditions

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Charging of the Spherical Grain in Cloud

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  1. Charging of the Spherical Grain in Cloud

  2. Kinetic equation

  3. Electric field E=e(-Z+4p(ni-ne)r’2dr’)/r2 j=Edr’ r rp L r Electron density ne=n0exp(j/Te) Electron current on grain J=rp2n0(8eTe/(me))1/2exp((rp)/Te)

  4. Numeric cell Conditions Ni=const ( ionisation rate in cell is equal to ion current on the grain ) E(L)=0 ( neutrality of cell ) Diffuse elastic reflection of ions from cell boundary L rp

  5. Dimensionless parameters rp=rp/Di ng0=ng0Di Z=ZDi =/Te L=L/Di where Di=4/3L3Tg/(e2Ni0) ~ ~ ~ ~ ~

  6. r Simple estimations Influence of collisions on ion current on single small spherical grain li>>rDi>>rpj(rp)/Ti (rp/r)2(1-(j(r)-j(rp))/Ti)= exp(j(r)/Ti) |j(r)|<<|j(rp)|, |j(rp)|/Ti>>1 j(r)=j(rp)rp/r, |j(rp)|/j(r)2 exp(|j(r)|/Ti) r  rpj(rp)/Ti/ln(-j(rp)/Ti) Icoll (2r/ li )pr2vth i(1- j(r)/Ti)ni  (rp/li)2prp2vth ini(|j(rp)|/Ti/ln(-j(rp)/Ti))3(1+ln(- j(rp)/Ti)) Icoll/IOML  (rp/li) (|j(rp)|/Ti )2/(ln(-j(rp)/Ti))3(1+ln(- j(rp)/Ti))

  7. j(rp) Te 1 2 lDi/li 0.1 0.5 0.02 0.004 Te/Ti=100; 200 rp/li

  8. Charging in cloud collisionless case simplest approach Ii=Ii0(<ni>), Ie=Ie0(ne) (-j(rp)/Te)(1+P)(Teme/Timi)1/2=exp(j(rp)/Te) where P=Znd/ne

  9. Z/Z(P=0) rp/lDi li/ lDi=50 P=Znd/ne

  10. Z/Z(P=0) rp/lDi li/ lDi=10

  11. Z/Z(P=0) rp/lDi li/ lDi=0.5 P=Znd/ne

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