Physics 525 - Homework 5 Solutions
1 Strongly magnetized plasmas
The dielectric tensor for a cold plasma is
lm
0
0
P
iD
S
0
S
= iD
0
Taking the limit ce,ci pe,pi , will simplify the expressions in the dielectric tensor in the following ways:
S =1
2
D=
2
Physics 525 - Homework 1 Solutions
1
Plasma Parameters
Debye lengths for electrons and ions (protons):
0 kTe
, Di
n0 e2
De =
=
0 kTi
n0 e2
plasma parameters:
Nde =
4
4
ne 3 , Nde =
ni 3
de
di
3
3
for the plasma parameter, N = n3 is also acceptable.
plasma
Physics 525 - Homework 2 Solutions
1
Earth's Magnetic Field
The magnetic eld above the equator is of the form
B(r) = B0
3
RE
3
r
where the sign comes in because the magnetic eld points from south to
north and the magnitude has been normalized so that
B(r
Physics 525 - Exam I Solutions
1
Magnetic pumping
2
The rst adiabatic invariant = V /(2B) is conserved if B is changing slowly.
Let the initial velocty of the proton be V0 (it is given that V0 = 0).
2
2
1) Change B from 0.1T to 1T : V1 = 10V0 ;
2
2
2
2) C
Physics 525 - Homework 3 Solutions
1
Plasma frequency
Linearized equations of motion, for species = cfw_e, i
m
0
E =
v
= q E
t
ns qs , n = n0 + n
s
n
+ n0
t
v = 0
In Fourier space, these become
im v = q E
0 ik
E =
ns q s
s
i + in0 k v = 0
n
Take k (1), a
Physics 525 - Homework 7 Solutions
1 Two-stream instability
For a species moving with velocity v0 , we have the momentum evolution
equation:
m n0 [
v1
+ (v0
t
)v1 ] = q n0 E
im n0 v1 + ikv0 m n0 v1 = q n0 E
v1 =
iq
E
m ( kv0 )
The continuity equation:
n1
Physics 525 - Homework 6 Solutions
1 Recombination
The equation describing recombination is given by
n
= n2
t
Solving this dierential equation with the initial condition n(0) = n0 =
1020 m3 will yield the following equation
1
1
=
+ t
n(t)
n0
Applying the
Physics 525 - Exam III Solutions
Problem 1
a) Two kinds of waves: Electron plasma waves (Langmuir waves) and EM waves.
No ion-acoustic waves, since Te Ti .
b) Only Lagnmuir waves, since EM waves have phase velocity larger than speed
of light, and no parti
PHY 525
Exam I
March. 6, 2012
Problem 1. Magnetic Pumping
A 1-Kev proton with V=0 in a uniform magnetic field B=0.1T is accelerated as B is slowly
increased to 1T. It then makes an elastic collision with a heavy particle and changes direction so
that afte
PHY 525
Exam III
May 10, 2012
Problem 1.
Consider a uniform, isotropic, non-magnetized, fully ionized collisionless plasma with
.
a) What waves can propagate in such a plasma? (derivation of dispersion relations is not required.)
b) What waves will be aff
Physics 525 - Exam II Solutions
Problem 1
a) Use the formula
11
1.5 10
L
B(z)ne (z)dz 1.5 1011 Bne L.
(1)
0
Substituting = 0.01m, ne = 1012 cm3 , and L = 0.5m, we nd B 0.12T.
Answer: 0.12T.
b) One can measure how the rotation angle of the polarization pl
PHY 525
Exam II
April 24, 2012
Problem 1.
The plane of polarization of an electromagnetic wave with frequency
GHz, propagating
-3
along the magnetic field through a uniform plasma (
cm ), rotates by
after
traversing
m of plasma.
a) What is the strength of