第二章 静电模型第三节 粒子移动格式的精度 假定有一简谐运动

20

dxx

dt

其解为

0 0 0 0 0( , ) ( ) cos ( )sinx t t A t t B t t

对有限差分蛙跳格式

202

2t t t t tt

x x xx

t

0sin[ ]2 2

t t

i ttx Ae

假定

则有

可得

0

0

12

12

t

t

0时,

时, 为复数

第四节 网格 - 粒子云 - 蛙跳动力论

共振因子

1( ) , ,g gl n l n

l

k v k v

为空间网格效应, n为时间离散效应

Electrostatic Solitary Structures in 2D plasma

The observations of the Fast satellite

[Ergun et al., GRL, 1998].

Characteristics ：1. The structures have a positive potential signa

ture.

2. The parallel slicing of parallel electric field has bipolar structures.

4. The parallel slicing of perpendicular electric field has unipolar structure.

5. Debye-scale size in the parallel direction.

The stacked profiles of the electric fields from 1D PIC simulations.1D PIC simulations.

The electric field and phase-space diagram of electrons from 1D PIC simulations.1D PIC simulations.

Multi-dimensional structure[From Chen, GRL, 2003]

2D PIC simulations

Case 1:Case 1:

Electron bi-stream instability: initially two Electron bi-stream instability: initially two electron components have same density aelectron components have same density and temperaturend temperature

mi/me=1836mi/me=1836

VVbb=3.5v=3.5vthth

/ 0.5e pe

20 40 60 80 100 120

50

100

150

200

250

X

Y-0.800-0.600-0.400-0.20000.2000.4000.6000.800

Ex

pe

t=40

20 40 60 80 100 120

50

100

150

200

250

X

Y

-0.360-0.270-0.180-0.09000.0900.1800.2700.360

Ey

20 40 60 80 100 120

50

100

150

200

250

X

Y

-0.700-0.525-0.350-0.17500.1750.3500.5250.700

pe

t=120

Ex

20 40 60 80 100 120

50

100

150

200

250

X

Y

-0.350-0.262-0.175-0.08700.0870.1750.2620.350

Ey

20 40 60 80 100 120

50

100

150

200

250

X

Y-0.300-0.225-0.150-0.07500.0750.1500.2250.300

pe

t=820

Ex

20 40 60 80 100 120

50

100

150

200

250

X

Y

-0.120-0.087-0.055-0.0220.0100.0430.0750.1080.140

Ey

20 40 60 80 100 120

50

100

150

200

250

X

Y

-0.250-0.188-0.125-0.06300.0630.1250.1880.250

pe

t=2000

Ex

20 40 60 80 100 120

50

100

150

200

250

X

Y

-0.120-0.090-0.060-0.03000.0300.0600.0900.120

2D PIC simulations

Case 2:Case 2:

Electron bi-stream instability: two electroElectron bi-stream instability: two electron components have same density and temn components have same density and temperatureperature

mi/me=1836mi/me=1836

VVbb=3.5v=3.5vthth

/ 2e pe

0 45 90 135 180

X

-0.250

-0.188

-0.125

-0.063

0

0.063

0.125

0.188

0.250

-0.500

-0.375

-0.250

-0.125

0

0.125

0.250

0.375

0.500

(c) pe

t=1940

0 45 90 135 180

X

-0.420

-0.315

-0.210

-0.105

0

0.105

0.210

0.315

0.420

-0.630

-0.473

-0.315

-0.158

0

0.158

0.315

0.473

0.630

b) pe

t=900

0 45 90 135 1800

45

90

135

180

X

Y

-0.700

-0.525

-0.350

-0.175

0

0.175

0.350

0.525

0.700

0

45

90

135

180

Y

-1.00

-0.75

-0.50

-0.25

0

0.25

0.50

0.75

1.00

(a) pe

t=100

-0.50

-0.25

0.00

0.25

0.50

Ex

(a) Y=71.4D

0 45 90 135 180

X

(b) Y=84.1D

0 45 90 135 180-0.4

-0.2

0.0

0.2

0.4

Ey

X

The parallel slicing of parallel and The parallel slicing of parallel and

perpendicular electric fields atperpendicular electric fields at ..920pet

0 45 90 135 180-0.4

-0.2

0.0

0.2

0.4

Ey

Y

-2

0

2

4

The charge density and perpendicular electric field The charge density and perpendicular electric field

along the perpendicular direction in the hole atalong the perpendicular direction in the hole at ..

920pet

0 45 90 135 180-0.4

-0.2

0.0

0.2

0.4

Ey

Y

The perpendicular electric field along the The perpendicular electric field along the

perpendicular direction in the hole atperpendicular direction in the hole at different different time. The solid, dash and dot lines represent time. The solid, dash and dot lines represent , and , and

860pet 820pet 900pet