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Introduction to computational plasma physics. 雷奕安 62755208 , [email protected] 课程概况. http://www.phy.pku.edu.cn/~fusion/forum/viewtopic.php?t=77 上机 成绩评定为期末大作业. Related disciplines. Computation fluid dynamics (CFD) Applied mathematics, PDE, ODE Computational algorithms

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slide2
课程概况
  • http://www.phy.pku.edu.cn/~fusion/forum/viewtopic.php?t=77
  • 上机
  • 成绩评定为期末大作业
related disciplines
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, …
contents
Contents
  • What is plasma
  • Basic properties of plasma
  • Plasma simulation challenges
  • Simulation principles
what is plasma
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
basic properties
Basic properties
  • Temperature
  • Quasi-neutrality
  • Thermal speed
  • Plasma frequency
  • Plasma period
debye length

U→0

λD

Debye length
  • System size and time
  • Debye shielding
plasma parameter
Plasma parameter
  • Strong coupling
  • Weak coupling
collision frequency
Collision frequency
  • Mean-free-path
  • Collisional plasma
  • (Collisionless)
  • Collisioning frequency
magnetized plasma
Magnetized plasma
  • Anisotropic
  • Gyroradius
  • Gyrofrequency
  • Magnetization parameter
  • Plasma beta
simulation challenges
Simulation challenges
  • Problem size: 1014 ~ 1024 particles
  • Debye sphere size: 102 ~ 106 particles
  • Time steps: 104 ~ 106
  • Point particle, computational unstable, sigularities
solution
Solution
  • No details, essence of the plasma
  • One or two dimension to reduce the size
  • No high frequency phenomenon, increase time step length
  • Reduce ND, mi / me
  • Smoothing particle charge, clouds
  • Fluidal approaches, single or double
  • Kinetic approaches, df/f
simple simulation
Simple Simulation
  • Electrostatic 1 dimensional simulation, ES1
  • Self and applied electrostatic field
  • Applied magnetic field
  • Couple with both theory and experiment, and complementing them
basic model2
Basic model
  • Field -> force -> motion -> field -> …
  • Field: Maxwell\'s equations
  • Force: Newton-Lorentz equations
  • Discretized time and space
  • Finite size particle
  • Beware of nonphysical effects
equation of motion
Equation of motion
  • vi, pi, trajectory
  • Integration method, fastest and least storage
  • Runge-Kutta
  • Leap-frog
planet problem
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

planet problem1
Planet Problem

./a.out > data

0.1

$ gnuplot

Gnuplot> plot “data” u 1:2

planet problem2
Planet Problem

./a.out > data

0.01

$ gnuplot

Gnuplot> plot “data” u 1:2

planet problem3
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

planet problem4
Planet Problem

./a.out > data

0.1

$ gnuplot

Gnuplot> plot “data” u 1:2

planet problem5
Planet Problem

./a.out > data

0.01

$ gnuplot

Gnuplot> plot “data” u 1:2

field equations
Field equations
  • Poisson’s equation
field equations1
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
particle and force weighting
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
higher order weighting
Higher order weighting
  • Quadratic or cubic splines, rounds of roughness, reduces noise, more computation
initial values
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
diagnostics
Diagnostics
  • Graphical snapshots 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
Tests
  • Compare with theory and experiment, with answer known
  • Change nonphysical initial values (NP, NG, Dt, Dx, …)
  • Simple test problems
server connection
Server connection

SshHost: 162.105.23.110, protocol: ssh2

Your username & password

Vnc connectionIn 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.)

slide44
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
Clients

Sshputty.exe

Vncviewerhttp://www.phy.pku.edu.cn/~lei/vncviewer.exe

Pscp:

http://www.phy.pku.edu.cn/~lei/pscp.exe

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