חלקיק טעוןבשדה

אלקטרומגנטי

1D electric field

Constant electric field

Potential electric field

Constant magnetic field

NR

Constant perpendicular fields

Change frame

Drifts (NR)

Gradient drift

2BBB dd VV

Curvature drift

Drift currents:

yBB ˆ: 0

gdy

dB

eB

cmvBr cos

gg

g eB

cmv

B

Bvr cos

gg eB

cmvyr cosˆ

gggcgd dvyfej 2

0

, xvv gg ˆcos

ggd dxeB

cmv

dy

dffvej

2

0

0 ˆcos

gg ddy

df

eB

cmve

2

0

22

cosdy

df

B

cmv

dy

df

eB

cemv

22

22

g

rg zB ˆ||

x

y

At y=0, for any given particle we have:

where : is the Assume to lowest order f is independent of g, and dependent just

on y.

gcgyf ,

ggd dxeB

cmv

dy

dffvej

2

0

0 ˆcos

gg ddy

df

eB

cmve

2

0

22

cos

dy

df

B

cmv

dy

df

eB

cemv

22

22

is the phase space density of particles whos gyro center

is ygc and gyro phase is g.

Assume to lowest order f is independent of g, and dependent just on y.

gcgyf ,

Note that the drift current does not depend on the particle’s charge, just on their mass.

Adiabatic invariants 1

Adiabatic invariants 1I

Adiabatic invariants III

First invariant

Magnetic bottle and loss cone

Second invariant

Fermi acceleration

Third invariant

drift shell orbits

nonadiabatic examples

1. shock transition

2. inhomogeneous E

Coulomb collisions

תדירות ההתנגשויות

runaway

1. Charged particle in a planar electromagnetic wave (relativistic)a) linear polarizationb) circular polarization

2. Van Allen belt currents

3. Curvature drift in pulsars

4. Gyroradii of cosmic rays near Earth