M. Okamoto

N. Nakajima

W.X. Wang

National Institute for Fusion Science (NIFS-Repository)

§26. Like-particle Collision Model for ()f Particle Simulation Wang,W.X., Nakajima,N., Okamoto,M. Collisions between ions and electrons can be simply modeled by employing the large mass ra-tio approximation. Here we present a linear like-particle collision model, accurately conserving all of particle number, momentum and energy for 8 f particle simulation. Our like-particle collision n1odel reads (1) where Cb(fl) = CTP(fl) + PfM, (2) P(r, v) =A· :t (V)TP + B :t (v2)TP, pl (r, v) =A. :t (V)TP+P + B :t (v 2)TP+P, Q1 (r, v) = D :t (v0 ) p, .... d d 2 P2 =A· dt (V)TP+P+P1+Q1 +B dt (v )TP+P+P1+Q1, Q2(r, v) = D :t (v0) P+Pl +Ql' A= -6 0"_¢ VthV' B = -2 fY_ [¢- d¢]_1_, Y 2 v3 Y 2 dx VVth D(i,V) = 3~ [¢- ~~] v~h- L ¢(x) is Maxwellian integral with x = v2jvzh· The CT p (fl) is drag and diffusion part that describes the test particle (/1) collisions with Maxwellian field particles (/ M), and is readily implemented by Monte Carlo method. The P !M works for com-pensating ft(V)TP and -ft(v2)TP, the averaged mo-mentum and energy loss due to CT p. P f M and the other rest terms of Eq.(1) can be implemented by weight method in 8 f simulation. Cb repre-sents the previous collision operator[1,2]. In the implementation of Cb, there are still considerable non-vanishing Jt (V)TP+P, :ft (v2)TP+P and -ft(v0 ) p due to numerical errors, and the numerical errors may get so enlarged as to distort simulation re-sults. The compensation terms are developed to restore conservations. For example, P1 f M is in-troduced to compensate the momentum and en-ergy loss, ft(0TP+P and ft(v 2)TP+P, and Ql!M to compensate -ft(v0 ) p, the numerical particle loss due to PfM· As shown in Fig.1, the conserva-tions of all three quantities are greatly improved by using present collision operator. A shifted Maxwellian solution of ion drift kinetic equation 184 under \IT = 0, which gives zero particle and en-ergy flux, is recovered (Fig.2) owing to the utilize of the improved operator 20 ~ 1S 0 10 r 0 l i 0 : : -s . .!'~rtici_e .. ~.'!~~~--10 0 50 100 150 200 250 100 ~ ao 0 60 ~ 1-----·----·· - -- · ~ · ·····-····-·--t-· ·~······-···t··· · ·· · ·- ·-·· --:-··· ····-·-·--­0 <40 ~ .;:;. e;: 20 ·······-··---J-·- ------------·······--·;·--~~~~~~~~---·-··-----20 0 so 100 ISO 200 250 25 ~ 20 0 15 ~ 0 10 ~ ~ s en~rgy . . . .. . . .. . ~ - ~ . . -5 50 100 150 200 250 t/ r a a Fig.l The time history of three conservations 400 II 200 0 -200 -400 - 3 -Th~ory • By using C1 0 By using C10 -2 -1 . 0 vI v II t h Fig.2 The solution of ion drift kinetic equation References 1) Dimits,A.M. and Cohen,B.I., Phys. Rev. E 49 (1994) 709. 2) Lin,Z., Tang,W.M. and Lee,W.W., Phys. Plasmas 2_ (1995) 2975. 

Like-particle Collision Model for ホエf Particle Simulation

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