UNIVERSITY OF SOUTHAMPTON
PHYS6004W1
SEMESTER 2 EXAMINATION 2010/11
SPACE PLASMA PHYSICS
DURATION 120 MINS
Answer all questions in Section A and two and only two
questions in Section B.
Section A carries 1/3 of the total marks for the exam paper and you
should aim to spend about 40 mins on it. Section B carries 2/3 of
the total marks for the exam paper and you should aim to spend
about 80 mins on it.
An outline marking scheme is shown in brackets to the
right of each question.
A Sheet of Physical Constants is provided with this examination
paper.
Only university approved calculators may be used.
©
Copyright 2011 University of Southampton
Number of
Pages 6
2
PHYS6004W1
Section A
A1. Explain two ways that a plasma can be formed. Using the
ionisation potential of hydrogen (Io = 13.6 eV), estimate the
temperature needed to ionise a hydrogen atom, and the
wavelength of radiation required to do likewise.
[4]
A2. If protons drifting towards Earth in the tail of the magnetosphere
experience a change in the magnetic field strength from 100 nT to
600 nT, what increase in energy would result for a 10 keV proton
with pitch angle of 30°?
[6]
A3. The tail of the Earth’s magnetosphere can be modelled as having a
homogeneous field with strength 10 nT directed towards Earth above
the equatorial plane, and equal and opposite field strength below the
same plane. Draw the field configuration and consequent ‘neutral
current sheet’ in Geocentric Solar Ecliptic (GSE) coordinates in the
XZ plane. Assume that the current sheet is 100 RE long in the X
direction. Estimate the total current in the current sheet, explaining
all assumptions.
[5]
A4. What are the two limits of behaviour of a magnetoplasma, as
described by the induction equation? Which parameters ensure that
the ‘frozen-in’ approximation is valid in most of interplanetary space
and most of Earth’s magnetosphere?
[5]
3
PHYS6004W1
Section B
B1 (a) The magnetic field strength in the Earth’s magnetic equatorial
𝑅
3
plane is given by 𝐵 = 𝐵0 � 𝐸 � where B0 = 3 × 10−5 T, RE is the
𝑟
Earth’s radius, and r is the geocentric distance. Give an
expression for the drift velocity of a particle in the equatorial
plane with a pitch angle of 90° and energy W. You may use the
result that the force due to the gradient in the magnetic field
is −µm ∇𝐵, where µm is the magnetic moment of the particle.
(b)
[7]
Evaluate the drift velocity and hence the drift period in days (the
time it takes a particle to drift around the Earth) for both a proton
and electron of 1 keV energy, at a distance of 5 RE from the
centre of the Earth. In a diagram using appropriate vectors,
indicate the direction of the drift motions of both particles in the
equatorial plane.
(c)
[7]
An electron is injected into the equatorial plane of the Earth at
5 RE with magnetic field strength as given in (a), but with pitch
angle of 45°. What is the field strength at the point where the
electron reverses direction?
[6]
TURN OVER
4
B2
(a)
PHYS6004W1
What is the plasma beta? Explain why the solar wind fills the
heliosphere with a weak magnetic field.
[4]
(b)
Derive the equation for the angle that the Interplanetary
Magnetic Field (IMF) makes with respect to the Geocentric
Solar Ecliptic (GSE) X-axis, in its average configuration (i.e.
Parker Spiral). Use two well-labelled diagrams in your
derivation, one in the GSE frame, and one in a frame rotating
with the Sun.
[6]
(c)
If the solar wind speed at Saturn is 500 km/s, what angle
does the IMF make with the X-axis near Saturn? Is the angle
greater or smaller than that near Earth? (The radius of
Saturn’s orbit rS = 9.5 AU and the solar rotation period is 25
days.)
[4]
(d)
If the solar wind has the same temperature and velocity at
Saturn as at Earth, and the plasma beta at Earth, βE = 1,
show that the plasma beta at Saturn, βS, can be given by
1
2 𝐵 2
𝐸
𝛽𝑆 = �9.5� �𝐵 �
𝑆
where BE/BS is the ratio of the magnitudes of the IMF at Earth
and Saturn.
[6]
5
PHYS6004W1
B3 (a) Give a full description of the process known as magnetic
reconnection or merging, using a well-labelled diagram to
include all the main features of the process.
[10]
(b) Explain the important implications of magnetic reconnection in
the context of the solar wind and the Earth’s magnetosphere.
With a simple diagram, demonstrate how the process can occur
at the magnetopause and in the magnetospheric tail.
[4]
(c) The voltages (or reconnection rates) at a magnetopause X-line
and a tail X-line are 120 kV and 60 kV, respectively. If the polar
cap contained a magnetic flux of 108 Wb when this reconnection
started, estimate the area of the ionospheric polar cap
30 minutes later. (The magnetic field strength in the ionosphere
is 5 × 10−5 T.)
[6]
TURN OVER
6
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B4 (a) Explain what determines (i) the stand-off distance of the nose of a
planet’s magnetosphere and (ii) the maximum radius of the tail of
the magnetosphere, in a steady state.
What factors can be
neglected in both cases and why?
[10]
(b) Give expressions for both distances (i) and (ii) in (a), using the
simplification that PSW is the solar wind pressure in each case,
and using M for the magnetic moment of the dipole field, and ФT
for the magnetic flux in the tail lobe. Explain all other constants
that are needed in your expressions.
[6]
(c) The solar wind has a number density of 5 cm−3 and a plasma
temperature of 3 × 105 K. When the interplanetary magnetic field
(IMF) has a magnitude of 5 nT, calculate the magnetospheric field
of the steady-state magnetosphere in the tail lobe at the maximum
tail radius.
[4]
END OF PAPER