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Introduction to computational plasma physicsPowerPoint Presentation

Introduction to computational plasma physics

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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
- Programming language, C, Fortran
- Parallel programming, OpenMP, MPI
- Plasma physics, space, fusion, …
- Unix, Linux, …

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 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

- Temperature
- Quasi-neutrality
- Thermal speed
- Plasma frequency
- Plasma period

Plasma parameter

- Strong coupling
- Weak coupling

Collision frequency

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

Magnetized plasma

- Anisotropic
- Gyroradius
- Gyrofrequency
- Magnetization parameter
- Plasma 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 phenomenon, 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 experiment, and complementing them

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

- vi, pi, trajectory
- Integration method, fastest and least storage
- Runge-Kutta
- Leap-frog

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 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

Field equations

- Poisson’s equation

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

Higher order weighting

- Quadratic 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

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

- Compare with theory and experiment, with answer known
- Change nonphysical initial values (NP, NG, Dt, Dx, …)
- Simple test problems

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.)

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

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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