Transcript ppt

‫חלקיק טעון‬
‫בשדה‬
‫אלקטרומגנטי‬
1D electric field
Constant electric field
Potential electric field
Constant magnetic field
NR
Constant perpendicular fields
Change frame
Drifts (NR)
Gradient drift
B  Vd  B   Vd B
2
Curvature drift
Drift currents:
rg

B || zˆ
 g
ˆ
B : B0 y
ŷ
x̂
r   B  mv c  dB cos g
eB
dy
At y=0, for any given particle we have:
mv c

ˆ 
rg  y
cos g
eB
2

j d  e  f y g c , g v  g d g
y g c , g0is the
where :
 
 v  B mv c
rg 

cos g
g B
eB

v  g   v cos g xˆ
Assume to lowest order f is independent of g, and dependent just on y.
2

df  mv c
j d  e  v  f 0  
cos  g xˆ d g
dy  eB
0 
2
2
mv c df
2
 e 
cos  g d g
eB dy
0
 emv c df
 mv c df


2eB dy
2 B dy
2

2

f  y g c ,  g  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.
2

df  mv c
j d  e  v  f 0  
cos  g xˆ d g
dy  eB
0 
2
mv2 c df
 e 
cos 2  g d g
eB dy
0
 emv2 c df
 mv2 c df


2eB dy
2 B dy
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 polarization
b) circular polarization
2. Van Allen belt currents
3. Curvature drift in pulsars
4. Gyroradii of cosmic rays near Earth