Introduction to computational plasma physics
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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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Introduction to computational plasma physics

Introduction to computational plasma physics

雷奕安

62755208,[email protected]


Introduction to computational plasma physics

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, …


Introduction to computational plasma physics

大规模数值模拟的特殊性


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


Plasma vs gas

Plasma vs gas


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


Debye lengths

Debye lengths


Plasma parameter

Plasma parameter

  • Strong coupling

  • Weak coupling


Weakly coupled plasmas

Weakly coupled plasmas


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 model

Basic model


Basic model1

Basic model


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


Computational cycle

Computational cycle


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


Initial values1

Initial values


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.)


Introduction to computational plasma physics

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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