M. Okamoto

N. Nakajima

W.X. Wang

National Institute for Fusion Science (NIFS-Repository)

§25. of DKPS Approach to Neoclassical Transport Calculation Wang,W.X., Nakajima,N., Okamoto,M. A particle simulation program 8{DKPS, solv-ing drift kinetic equations by bf method, has been developed to study new collisional transport phe-nomena in reversed shear core plasma and H-mode edge plasma by taking into account finite banana width dynamics, strong radial electric field with large radial gradient, non-standard orbit topology near magnetic axis and etc. The kinetic equations being solved are aft1 +vii· \1ft- C(ft,Jo) = -vd · \1 fo + C(fo, h), (1) aft1 +(vli+vd)·\1 h - C(ft,Jo) = -vd·\1 Jo+C(fo,Jt). (2) In a little more detail, simulation particles (mark-ers) are pushed along guiding center trajectories subject to random velocity changes which account for test particle Coulomb collisions; the source terms in the right side of the equations, arising from the linearization or accounting for collisional conservation laws, are modeled via weight method; the relevant transport quantities are computed from the dyna1nics of simulation particles. Two versions ·of the code are designed, corresponding to different drift orbit being followed. One is fol-lowing the zeroth order drift orbit (corresponding to solving Eq.(1)) in toroidal coordinate; another is following the full nonlinear drift orbit ( corre-sponding to solving Eq.(2)) in flux coordinate us-ing a Ha1niltonian guiding center motion formal-ism. In latter case, we can take into account finite banana width effects which may become substan-tial in present tokamak operation. Moreover, the utilize of Hamiltonian formalism in flux coordinate allows us to treat three-dimensional problems eas-ily. Equation (1) is solved on a single magnetic surface and Eq.(2) is solved in whole poloidal cross section. The 8 f method for neoclassical trans-port calculation has two advantages: 1. low noise and 2. thermodynamic "forces", such as VT and \lp driving the plasma transport, being control-lable. An Improved like-particle model accurately conserving particle, momentum and energy is im-plemented and a general and accurate weighting sche1ne is employed in 8 fDKPS so as to upgrade its performance. To benchmark and test the code, a serious of simulation were carried out using an analytical MHD equilibrium. The test and bench-marking includes: 1. Electron neoclassical trans-port due to e-i collisions; The simulation results of particle flux, energy flux and bootstrap current in whole collisionality regime are in good agreement with the neoclassical theory. 2. Ion particle and energy fluxes and parallel velocity under zero ba-nana width limit; A shifted Maxwellian solution is recovered \JT = 0, and the energy flux driven by non-zero \JT is in good agreement with the the-ory. 3. Ion particle and energy fluxes and parallel velocity with finite banana w1dth dynamics. A so-lution with zero-particle and energy fluxes over the whole region (Fig.1) (when \ln -=1- 0 and \JT = 0) is demonstrated because of momentum and energy conservation of like-particle collisions. The inves-tigation of neoclassical transport using 8 fDKPS is currently under active progress. . 15 r 10 0 c 0 C1) ~ =----=-! p¥ti¢le! fl~x · -T ((/a-~o$Y :-· -10 20 30 40 50 60 70 80 t/ r .. 11 0.8 0 .6 -----·- ------- ------0.4 - -- --- --- -- · · ·· · -0 .2 ---- -- --- . -. -. . [ . -. . . . . . . . --. -- ~ Q 15 10 0 . . . . : enetgx fl~x · · · -r --crJa:~o:sr -~~ -. --·:. --- -: -- --~----. t- .. -5Lu.u.J.~.u....~..o.~~~.L.I..Lw..<J 0 10 20 30 40 50 60 70 80 t/ r .. 11 paral~el velocity (r/a=iO.S) : ----- -- --- - - - - ~ -- - - - ---- · ·-. ·--T --. ------;-0 20 40 60 80 100 -4 0 0.2 0.4 t/ r ii 0.6 r/a 0 .8 4 ···············1·-·············r··············i················r-····· ·· ······ Q 2 ···············j····· ···········:············· .. ·:---·············:··············· 0 ··g·-~~-~-~t~.::~.~~-~~~-i~-~&·-·-&-~-e----e-+·..U'-~~-~:1? .. l l : [ -2 ··· · ··· · ·· · ···-~·- · ·· · ·· ··· ·· ··· r-· ·· ·· · · · · · · · ·r··· · ·········l· ·· ·· ·· - · · ·· · -4 0 0.2 0 .4 0.6 r/a Fig. 1 0.8 183 

ホエf DKPS Approach to Neoclassical Transport Calculation

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ホエf DKPS Approach to Neoclassical Transport Calculation

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