以往的粒子碼（particle code）中，包含了許多尺度的物理，在研究某一尺度之現象時，會有其他尺度現象的參雜其中。粒子迴旋動力碼將原本的小尺度高頻現象經由相位平均濾除，可用來研究低頻現象之微擾動現象。其方法是解Vlasov-Poisson equation，此方程與普通的Vlasov equation不同。前者已經對拉索夫方程做相位的平均,其特點是可除去運動方程中的粒子迴旋效應。因為已經消去了粒子迴旋的效應，所以對研究低頻之物理現象，此模擬碼將優於以往的粒子碼。且因為將此迴旋效應消除，便可利用較大之時間間隔（WH*Dt<=1）與格子點（Dx/zo(s)<=1）進行模擬，其中WH為靜電切變-艾爾文頻率（electrostatic shear-Alfven wave frequency）， 遠小於電漿頻率Wpe因此其時間間隔可擴大，縮短模擬的時間。對於低頻大尺度現象的波動，可以用此迴旋動力碼進行模擬。此文中將從新的數值方法建立迴旋動力碼，並討論迴旋動力碼與一般粒子碼不同之處，並分別就相同的個案進行粒子碼與迴旋動力碼之模擬實驗，將其結果進行比較，可以證明上述迴旋動力碼的優點。

In the past simulation, particle code consistent many scale physical phenomenon, but these are mixed. When aiming at large scale, low frequency phenomenon, it can’t be recognized from simulation result. Gyro-kinetic simulation can filtered small scale, high frequency waves by average the gyro-phase angle, so it can be used in studying the low frequency wave. The main method is to solve Vlasov-Poisson equation, which different from Vlasov equation is moved out the phase angle.
Vlasov-Poisson equation averaged the phase angle, and can vanish the gyro-effect from equation of motion. Because of eliminating the gyro-effect, the simulation can use larger time step（WH*Dt<=1）and larger grid（Dx/zo(s)<=1）,where the electrostatic shear-Alfven wave frequency WH is much smaller then the plasma frequency Wpe. Using larger time step and larger grid can reduce the total computer time.
The following is used the new numerical method to construct gyro-kinetic code, and compared its result with particle code simulation result. Its comparison shows the advantage the previous discussed.

P. J. Catto, Lineatized gyro-kinetics, Plasma Phys. 20, pp.719-722, 1978.
W. W. Lee, Gyro-kinetic approach in particle simulation, Phys. Fluids 26(2), pp.556-532, 1983.
W. W. Lee, Gyro-kinetic Particle Simulation Model, J. Comput. Phys. 72. pp.243-269, 1987.
K.T. Tsang, and C.Z. Cheng, Gyro-kinetic simulation of micro-instabilities in high temperature tokamaks, Phys, Fluids B, 3(3), 1991.
W.W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z. Lin, Shear-Alfven waves in gyro-kinetic plasmas, Phys. of plasmas 8, 2000.
W. W. Lee, J. L.V. Lewandowski, T. S. Hahm, and Z. Lin, Shear-Alfven waves ingyrokinetic plasmas, Phys. of Plasma, 8, 2001.
Gang Zhao and Liu Chen, Gyro-kinetic particle-in-cell simulation of Alfvenic ion-temperature-gradient modes in tokamsk plasma, Phys. of Plasmas, 9, 2002.
W. M. Tang, J. W. Connor, and R. J. Hanstie, Kinetic-ballooning-mode theory in general geometry, Nuclear Fusion, 20(11), 1980.
Bruce I. Cohen, Thomas A. Brengle, Davis B. Conley, And Robert P. Freis, An orbit averaged particle code, J. comput. phys., 38, pp. 45-63, 1980.
Adam J. C., Langdon A. B. , Serveniere A. G., Electron Sub-Cycling in Particle Simulation of Plasma, J. comput. phys., 47(2), pp 229-244, 1982.
Lyu, L. H., M. Q. Chen, and W. H. Tsai, A theoretical model for cross-scale simulation of collisionless plasmas in space, Proceedings of the Sixth (2001) Atmospheric Science Symposium, September 25-27, 2001, Taipei, Taiwan, R.O.C., pp. 125-130, 2001.
John M. Dawson, Particle simulation of plasma, Reviews of Modern Phys., 55(2), pp.403-447, 1983.
W. W. Lee and H. Okuda, A Simulation model for Studying Low-frequency micro-instabilities, J. Comput. Phys. 26, pp.139-152, 1978.
Daniel H. E., John A. K., C. Oberman, and W. W. Lee, Nonlinear gyro-kinetic equations, Phys. Fluids 26(12), 1983.
Charles K. Birdsall, and A. Bruce Langdon, 1985, Plasma Physics via Computer Simulation, McGraw-Hill, New York, pp. 137-138.
Francis F. Chen, 1983, Introduction to Plasma Physics and Controlled Fusion Vol. 1, Plenum Press, New York.
Henri J. Nussbaumer, 1982, Fast Fourier Transform and Convolution Algorithms, Springer-Verlag, Berlin.
E. Oran Brigham, 黎文明譯, 1974, The Fast Fourier Transform(快速傅利葉變換), Prentice-Hall, Englewood Cliffs, N.J.
David Potter,1973, Computational Physics, J. Wiley, New York.
Willian H. Press, 1992, Numerical Recipes in Fortran, Cambridge University Press, New York.
呂凌霄, 數值模擬電漿束在熱電漿的交互作用, 1983
蘇鴻仁, 二維靜磁模擬碼之建立與應用,1994
林怡君, 迴旋動力碼之建立與應用, 2001