1、Introduction to computational plasma physics,雷奕安 62755208，,课程概况,http:/ 上机 成绩评定为期末大作业,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, Lin
2、ux, ,大规模数值模拟的特殊性,Contents,What is plasma Basic properties of plasma Plasma simulation challenges Simulation principles,What is plasma,Partially ionized gas, quasi-neutral Widely existed Fire, lightning, ionosphere, polar aurora Stars, solar wind, interplanetary (stellar, galactic) medium, accretion
3、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,Plasma vs gas,Basic properties,Temperature Quasi-neutrality Thermal speedPlasma frequency
4、Plasma period,Debye length,System size and timeDebye shielding,Debye lengths,Plasma parameter,Strong couplingWeak coupling,Weakly coupled plasmas,Collision frequency,Mean-free-path Collisional plasma (Collisionless) Collisioning frequency,Magnetized plasma,Anisotropic Gyroradius Gyrofrequency Magnet
5、ization parameterPlasma beta,Simulation challenges,Problem size: 1014 1024 particles Debye sphere size: 102 106 particles Time steps: 104 106 Point particle, computational unstable, sigularities,Solution,No details, essence of the plasma One or two dimension to reduce the size No high frequency phen
6、omenon, increase time step length Reduce ND, mi / me Smoothing particle charge, clouds Fluidal approaches, single or double Kinetic approaches, df/f,Simple Simulation,Electrostatic 1 dimensional simulation, ES1 Self and applied electrostatic field Applied magnetic field Couple with both theory and e
7、xperiment, and complementing them,Basic model,Basic model,Basic model,Field - force - motion - field - Field: Maxwells equations Force: Newton-Lorentz equations Discretized time and space Finite size particle Beware of nonphysical effects,Computational cycle,Equation of motion,vi, pi, trajectory Int
8、egration method, fastest and least storage Runge-Kutta Leap-frog,Planet Problem,x0 = 1; vx0 = 0; y0 = 0; vy0 = 1 read (*,*) dt N = 30/dtdo i = 0, N+3x1 = x0 + vx0*dty1 = y0 + vy0*dtr = sqrt(x0*x0 + y0*y0)fx = -x0/r*3fy = -y0/r*3vx1 = vx0 + fx*dtvy1 = vy0 + fy*dt! if(mod(i,N/10).eq.2)write(*,*) x0, y
9、0, -1/r+(vx0*vx0+vy0*vy0)/2x0 = x1; y0 = y1; vx0 = vx1; vy0 = vy1 enddo end,Forward differencing,Planet Problem,./a.out data 0.1 $ gnuplot Gnuplot plot “data” u 1:2,Planet Problem,./a.out data 0.01 $ gnuplot Gnuplot plot “data” u 1:2,Planet Problem,x0 = 1; vx0 = 0; y0 = 0; vy0 = 1 read (*,*) dt N =
10、30/dtx1 = x0 + vx0*dt y1 = y0 + vy0*dt xh0 = (x0+x1)/2; yh0 = (y0+y1)/2 do i = 0, Nxh1 = xh0+vx0*dt; yh1 = yh0 + vy0*dt;r = sqrt(xh0*xh0 + yh0 *yh0 )fx = -xh1/r*3fy = -yh1/r*3vx1 = vx0 + fx*dtvy1 = vy0 + fy*dt ! if(mod(i,N/100).eq.0)write(*,*) xh0, yh0, -1/r+(vx0*vx0+vy0*vy0)/2xh0 = xh1; yh0 = yh1;
11、vx0 = vx1; vy0 = vy1 enddo end,Leap Frog,Planet Problem,./a.out data 0.1 $ gnuplot Gnuplot plot “data” u 1:2,Planet Problem,./a.out data 0.01 $ gnuplot Gnuplot plot “data” u 1:2,Field equations,Poissons equation,Field equations,Poissons equation is solvable In periodic boundary conditions, fast Four
12、ier transform (FFT) is used, filtering the high frequency part (smoothing), is easy to calculate,Particle and force weighting,Particle positions are continuous, but fields and charge density are not, interpolatingZero-order weightingFirst-order weighting, cloud-in-cell,Higher order weighting,Quadrat
13、ic or cubic splines, rounds of roughness, reduces noise, more computation,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,Initial values,Diagnostics,Graphical sna
14、pshots of the history x, v, r, f, E, etc. Not all ti For particle quantities, phase space, velocity space, density in velocity For grid quantities, charge density, potential, electrical field, electrostatic energy distribution in k space,Tests,Compare with theory and experiment, with answer known Ch
15、ange nonphysical initial values (NP, NG, Dt, Dx, ) Simple test problems,Server connection,Ssh Host: 162.105.23.110, protocol: ssh2 Your username & password Vnc connection In ssh shell: “vncserver”, input vnc passwd, remember xwindow number Tightvnc: 162.105.23.110:xx (the xwindow number) Kill vncserver: “vncserver kill :xx” (x-win no.),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,Clients,Ssh putty.exe Vncviewer http:/ Pscp: http:/
