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Introduction to computational plasma physics 雷奕安 62755208 ,

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Presentation on theme: "Introduction to computational plasma physics 雷奕安 62755208 ,"— Presentation transcript:

1 Introduction to computational plasma physics 雷奕安 ,

2 课程概况 iewtopic.php?t=77 上机 成绩评定为期末大作业

3 Related disciplines Computation fluid dynamics (CFD) Applied mathematics, PDE, ODE Computational algorithms Programming language, C, Fortran Parallel programming, OpenMP, MPI Plasma physics, space, fusion, … Unix, Linux, …

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5 大规模数值模拟的特殊性 数值计算数学问题算法编程数值模拟物理问题数学模型算法编程 大规模数值模 拟 物理问题及 数学模型 相关学科研 究人员支持 超级计算机 软硬件系统

6 Contents What is plasma Basic properties of plasma Plasma simulation challenges Simulation principles

7 What is plasma Partially ionized gas, quasi-neutral Widely existed –Fire, lightning, ionosphere, polar aurora –Stars, solar wind, interplanetary (stellar, galactic) medium, accretion disc, nebula –Lamps, neon signs, ozone generator, fusion energy, electric arc, laser-material interaction Basic properties –Density, degree of ionization, temperature, conductivity, quasi-neutrality –magnetization

8 Plasma vs gas PropertyGasPlasma ConductivityVery low, insulatorVery high, conductor SpeciesUsually oneAt least two, ion, electron DistributionUsually MaxwellianUsually non-Maxwellian InteractionBinary, short rangeCollective, long range

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10 Basic properties Temperature Quasi-neutrality Thermal speed Plasma frequency Plasma period

11 Debye length System size and time Debye shielding λDλD U→0

12 Debye lengths

13 Plasma parameter Strong coupling Weak coupling

14 Weakly coupled plasmas

15 Collision frequency Mean-free-path Collisional plasma (Collisionless) Collisioning frequency

16 Magnetized plasma Anisotropic Gyroradius Gyrofrequency Magnetization parameter Plasma beta

17 Simulation challenges Problem size: ~ particles Debye sphere size: 10 2 ~ 10 6 particles Time steps: 10 4 ~ 10 6 Point particle, computational unstable, sigularities

18 Solution No details, essence of the plasma One or two dimension to reduce the size No high frequency phenomenon, increase time step length Reduce N D, m i / m e Smoothing particle charge, clouds Fluidal approaches, single or double Kinetic approaches,  f/f

19 Simple Simulation Electrostatic 1 dimensional simulation, ES1 Self and applied electrostatic field Applied magnetic field Couple with both theory and experiment, and complementing them

20 Basic model

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22 Field -> force -> motion -> field -> … Field: Maxwell's equations Force: Newton-Lorentz equations Discretized time and space Finite size particle Beware of nonphysical effects

23 Computational cycle

24 Equation of motion v i, p i, trajectory Integration method, fastest and least storage Runge-Kutta Leap-frog

25 Planet Problem x0 = 1; vx0 = 0; y0 = 0; vy0 = 1 read (*,*) dt N = 30/dt do i = 0, N+3 x1 = x0 + vx0*dt y1 = y0 + vy0*dt r = sqrt(x0*x0 + y0*y0) fx = -x0/r**3 fy = -y0/r**3 vx1 = vx0 + fx*dt vy1 = vy0 + fy*dt ! if(mod(i,N/10).eq.2) write(*,*) x0, y0, -1/r+(vx0*vx0+vy0*vy0)/2 x0 = x1; y0 = y1; vx0 = vx1; vy0 = vy1 enddo end Forward differencing

26 Planet Problem./a.out > data 0.1 $ gnuplot Gnuplot> plot “data” u 1:2

27 Planet Problem./a.out > data 0.01 $ gnuplot Gnuplot> plot “data” u 1:2

28 Planet Problem x0 = 1; vx0 = 0; y0 = 0; vy0 = 1 read (*,*) dt N = 30/dt x1 = x0 + vx0*dt y1 = y0 + vy0*dt xh0 = (x0+x1)/2; yh0 = (y0+y1)/2 do i = 0, N xh1 = xh0+vx0*dt; yh1 = yh0 + vy0*dt; r = sqrt(xh0*xh0 + yh0 *yh0 ) fx = -xh1/r**3 fy = -yh1/r**3 vx1 = vx0 + fx*dt vy1 = vy0 + fy*dt ! if(mod(i,N/100).eq.0) write(*,*) xh0, yh0, -1/r+(vx0*vx0+vy0*vy0)/2 xh0 = xh1; yh0 = yh1; vx0 = vx1; vy0 = vy1 enddo end Leap Frog

29 Planet Problem./a.out > data 0.1 $ gnuplot Gnuplot> plot “data” u 1:2

30 Planet Problem./a.out > data 0.01 $ gnuplot Gnuplot> plot “data” u 1:2

31 Field equations Poisson’s equation

32 Field equations Poisson’s equation is solvable In periodic boundary conditions, fast Fourier transform (FFT) is used, filtering the high frequency part (smoothing), is easy to calculate

33 Particle and force weighting Particle positions are continuous, but fields and charge density are not, interpolating Zero-order weighting First-order weighting, cloud-in-cell

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36 Higher order weighting Quadratic or cubic splines, rounds of roughness, reduces noise, more computation

37 Initial values Number of particles and cells Weighting method Initial distribution and perturbation The simplest case: perturbed cold plasma, with fixed ions. Warm plasma, set velocities

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40 Initial values

41 Diagnostics Graphical snapshots of the history x, v, , , E, etc. Not all t i For particle quantities, phase space, velocity space, density in velocity For grid quantities, charge density, potential, electrical field, electrostatic energy distribution in k space

42 Tests Compare with theory and experiment, with answer known Change nonphysical initial values (NP, NG,  t,  x, …) Simple test problems

43 Server connection Ssh Host: , protocol: ssh2 Your username & password Vnc connection In ssh shell: “vncserver”, input vnc passwd, remember xwindow number Tightvnc: :xx (the xwindow number) Kill vncserver: “vncserver –kill :xx” (x-win no.)

44 Xes1 Xes1 document Xgrafix already compiled in /usr/local Xes1 makefile make./xes1 -i inp/ee.inp LIBDIRS = -L/usr/local/lib -L/usr/lib -L/usr/X11R6/lib64

45 Clients Ssh putty.exe Vncviewer exe Pscp:


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