PHYS30511

Nuclear Fusion and

Astrophysical Plasmas
(Plasma Physics)
 What is plasma?
• A plasma is an ionized gas.
• Plasma is called the “fourth state of matter.”
• More than 99% of the mass of the universe is in the plasma state.
• ‘Plasma’ was coined by Tonks and Langmuir in 1929

• Examples of plasmas on Earth:

– Lightning
– Neon and Fluorescent Lights
– Laboratory Experiments (e.g. plasma acceleration)
– Nuclear fusion
• Examples of astrophysical plasmas:
– The sun and the solar wind
– Stars, interstellar medium
What is plasma?
 What is plasma?
• Levi Tonks (1897-1971) and Irving Langmuir (1881-1957, photo, 1932
Nobel Prize in Chemistry), first used the term “plasma” for a collection of
charged particles (Phys. Rev. 1929)

In plasma physics we
study ionized gases
under the influence
of electro-magnetic
fields.

• William Crookes (1832-1919) called ionized matter in a gas discharge

(Crookes-tube, photo), “4th state of matter”, (Phil. Trans 1879)
 What is plasma?
• Some examples

Catseye
Nebula
The Sun

http://bang.lanl.gov/solarsys/
http://www.stsci.edu:80/
 What is plasma?

Laboratory Experiments

Lightning

http://FusEdWeb.pppl.gov/
 What we are interested in plasma?
• Fusion Energy
– Potential source of safe, abundant energy, without climate change gases

• Astrophysics
– Understanding plasmas helps us understand stars and stellar evolution.

• Upper atmospheric dynamics

– The upper atmosphere is a plasma.

• Plasma Applications
– Plasmas can be used to build computer chips
– Plasma can clean up toxic waste
– Plasma can treat waste water and treat diseases
– Plasma can revolutionize the particle acceleration technology
– Many more…
 Contents
• Chapter 1: Introduction to fusion and astrophysical
plasmas

• Chapter 2: Basic concepts and parameters of plasma

physics

• Chapter 3: Single particle motion in non-uniform

magnetic and electric field

• Chapter 4: The magnetohydrodynamics description

 Chapter 1: Introduction
• A plasma is an ionised gas - usually ions and electrons – sometimes
called “4th state of matter”
• From Greek word πλασμα - “pliant, malleable object”
• More rigorously a plasma is a quasi-neutral gas of charged and neutral
particles which exhibits collective behaviour
• In this course, we consider only fully-ionised plasmas, mainly comprised of
protons (or deuterons) and electrons.
• More than 99% of the matter in the universe is in the plasma state
Astrophysics = Plasma Physics (approximately)
• The quest for confined thermonuclear fusion on Earth relies on using
plasmas
• Plasmas (often partially-ionised) are very widely used in industry – plasma
TV, lighting, plasma deposition and processing , medical applications etc
• Also plasma accelerators of a subject of increasing interest
• “Plasma Physics” is challenging and modern physics - experimental,
observational, theoretical and computational – collective behaviour,
complexity, nonlinearity, extreme conditions….
• Plasmas differ from gases in a number of ways – notably, plasmas interact
strongly with magnetic fields and the motion of charged particles can
generate electric and magnetic fields
• Magnetic fields are ubiquitous across the universe and often exist in
laboratory plasma devices (especially magnetically-confined fusion
plasmas)
• Main focus of this course will be to learn some basic concepts of plasma
physics and use these to understand:

– Nuclear fusion – a promising source of energy for the future – mainly

magnetically-confined fusion
– Space and astrophysical plasmas – especially the atmospheres of the Sun and
stars, the magnetosphere of the Earth, solar and stellar winds….
In studying this Fourth state of Matter we seem at length
to have within our grasp and obedient to our control the
little indivisible particles which with good warrant are
supposed to constitute the physical basis of the universe...
We have actually touched the borderland where Matter
and Force seem to merge into one another, the shadowy
realm between Known and Unknown, which for me has
always had peculiar temptations. I venture to think that
the greatest scientific problems of the future will find
their solution in this Border Land, and even beyond; here
it seems to me, lie Ultimate Realities, subtle, far-reaching,
wonderful

(Crookes, 1879)

1832-1919, England Chemist

Plasma in the universe
 Why do we need controlled fusion?
• Growing world population and increasing energy consumption - especially
in developing world
• Problems with fossil fuels (coal, gas, oil) – global warming, finite fuel
supply…
• Problems with nuclear fission power – safety, waste disposal…
• Problems with renewables – dependent on geography and weather,
unreliable…

• Fossil fuels use chemical reactions

– Energy density based on molecular-bonds 0.1 – 1 eV/nucleon
• Nuclear fission and fusion use nuclear reactions
– Energy density based on nuclear binding energy – much higher (about 10
MeV/nucleon for fusion)

• Fusion is a very efficient source of energy – safe - almost unlimited fuel

supply – harmless waste product
 Energy from nuclear fusion I
• Nuclear fusion powers main-sequence stars - fusion of protons into helium
• Controlled fusion on Earth will most likely use deuterium (D or 2H) and
tritium (T or 3H) as fuels 2
1 H 1 H  2 He  n  17.6 MeV
3 4

• Fusion produces about 5 – 8 times energy/nucleon compared with fission,

about 1 million times more efficient than fossil fuel!
• Products are neutron (14.1 MeV; used to carry away energy and to breed
tritium) and alpha particle (3.5 MeV; remains confined in magnetic field –
see later)
• Fuels are:
– Deuterium from sea water (0.015% of naturally-occurring hydrogen is D)
– Tritium produced in lithium blanket surrounding a reactor by further
nuclear reactions n  6 Li  T  4 He
n  7 Li  T  4 He  n
– Hence Lithium is also a fuel (current known reserves could supply all
world energy for 6000 years)
 Energy from nuclear fusion II

•Other reactions possible (e.g. D + D and D + 3He) but these have a lower cross-
section (less probable reactions) and/or produce less energy
Ex 1.1 Calculate energy produced from 1 kg of deuterium fuel

•Fusion power output is measured by power amplification factor

Q = (fusion power)/(external heating power)
•Clearly we would at least like Q >1. “Ignition” (a self-sustaining reactor) means
Q = infinity. A practical working reactor (“burning plasma” ) needs Q > 10.
 Conditions for fusion – why plasma?
• Require high temperature to overcome electrostatic repulsion of nuclei
Derivation 1.1 Efficient DT fusion requires temperature of order 10 keV (hence
fully-ionised plasma since 1 keV >> hydrogen ionisation energy 13.6 eV)

• Require power produced by fusion to exceed power needed to heat plasma

(Q > 1)
Derivation 1.2 The Lawson criterion (condition for output power to exceed input
power)
n E  f (T )
where n is density and τE is energy confinement time; f(T) has a minimum value
of about 1020 m-3 s at around T = 10 keV
• Ex - fusion breakeven could be achieved by confining a 10 keV plasma with a
density of 1020 m-3 for 1 second
Two main routes:
• Magnetic confinement - moderate density, moderate confinement time
• Inertial confinement - very high density, very short confinement time
 Key problem for fusion

• …. Is the Coulomb barrier

 Reaction cross-sections and rates –
dependence on energy/temperature

•Reaction rate = <σv> where σ is cross-section (in m2 ) and < > denotes average
over velocity distribution
•Note D-T fusion has lowest optimal temperature and higher reaction rate
Approach to fusion conditions – Lawson criterion and Q
•Lawson criterion and
temperature
requirement often
combined into a
condition on the
“Fusion triple
product nτT
•Note T here is the
ion temperature
•Stronger condition
required for ignition
(switch off external
power) – Q = ∞
•Practical reactor
requires about Q >
10
 Magnetic confinement fusion
• A plasma cannot be maintained at fusion temperatures if it has direct contact
with any material wall → use magnetic fields to confine the plasma
Derivation 1.3 Motion of charged particle in magnetic field – gyromotion and
Larmor radius

eB mvperp
c  , rc 
m eB

• Particles can move freely along the field lines – hence bend field lines into
circles to avoid end losses → toroidal magnetic confinement devices
• The most promising magnetic confinement device at present is the tokamak
(from Russian for “toroidal magnetic chamber”). This has two magnetic field
components (reasons to be given in Chapter 2 ):
– Toroidal field (long way round the torus) generated by toroidal field coils
(solenoid bent into a circle)
– Poloidal field (short way round the torus) generated by plasma current
– The plasma current is provided by transformer action from a central solenoid
(poloidal field coils)
– Hence field lines spiral around the chamber
The tokamak

•Invented in mid
1950s by Soviet
physicists Igor
Tamm and Andrei
Sakharov
•Many tokamaks
worldwide
•Largest is Joint
European Torus
(JET)
Joint European Torus (JET) - a tokamak.
At Culham Laboratory, near Oxford
JET
How close are we to fusion?

•Note progress from

older devices to JET and
JT60U
• The “next step” ITER
is being built
•This diagram also
shows how well
confinement time can
be predicted from a
combination of device
parameters (size,
shape, magnetic field,
etc.) using semi-
empirical scaling laws
Progress towards Lawson criterion
First power from DT
fusion reactions – JET
tokamak (1997)

See Case Study 1 “JET tokamak on the

eve of DT operation”
Horton, Europhysics News 47/5-6,
2016, p. 25–27
Coming soon - ITER

Basic facts:

•Tokamak similar to JET

•Europe, Japan, Canada, China,
USA, Korea, India, Russia
•Being built in Cadarache,
France (though behind
schedule and over budget!)
•Expect Q about 10 (input 50
MW, output 500 MW)
•1988, project initiated
•2018-2025, assembly and
integration
•2025, commissioning starts
•2035, start of deuterium-
tritium operation
•€5b->€13b
A Fusion Powerplant

•After ITER will come DEMO

(demonstration power plant)
and IFMIF (materials test
facility)
•Lithium blanket captures
energetic neutrons from the
fusion process - boils water in
a heat exchanger to produce
steam to drive a generator -
Lithium and neutron react to
produce Tritium
 Inertial Confinement Fusion (ICF)
• Fuel is quickly heated and compressed before it has time to escape – using
lasers
• A series of pulses or “mini-explosions” with the fuel starting as a small
solid pellet or capsule (few mm diameter)
Derivation 1.4 Lawson criterion and optimal temperature for ICF
• Use lasers to heat surface intensely so that it ablates – expanding hot
gases apply strong forces to remaining capsule, causing it to compress and
heat
• Requires very high power lasers e.g.
– NOVA - Lawrence Livermore Lab, 1984 – 10 laser beams,; 105 J for 10-9 s.
– OMEGA – Uni of Rochester, 1995
– NIF (National Ignition Facility) - LLNL, ignition experiments started 2010
• Direct drive – lasers directly focussed on capsule
• Indirect drive – capsule supported inside small metal cylinder (few cm) –
a hohlraum. The laser beams are focused through holes into hohlraum –
surface is evaporated forming dense metal plasma – X-rays are created
which bounce within cavity
 Ablation of outer layer
Laser heating leading to compression of Core reaches
Thermonuclear
of outer layer capsule fusion
burn
ignition
conditions
Ablated material

Laser energy

Inwardly
transported energy
(purple arrows)
 Direct drive (enlarged scale) and
indirect drive

NIF target capsule

LIFE – schematic inertial fusion power plant
 Plasmas and magnetic fields in the heliosphere I
“In a nutshell”
The Sun (and similar stars):
Interior –
Core - hot, very dense plasma T ≈ 16 million K at centre, n ≈ 1032 m-3
Outer layers – magnetic field generated by “dynamo” due to convective and
other motions.
Atmosphere -
Photosphere - T ≈ 6000 K at centre, n ≈ 1023 m-3. Weakly-ionised plasma.
“Patchy” magnetic field concentrated into isolated intense tubes of
magnetic flux. Largest concentrations of magnetic flux (≈ 0.3 T) seen as
sunspots.
Chromosphere – highly structured. Temperature rising with height while
density falls
Corona - hot, low-density outer atmosphere. T ≈ 1 -2 million K, n ≈ 1014-15
m-3. Permeated by strong magnetic field. Seen from Earth at total eclipse
but best observed from space in X-rays and EUV (since predominant
emission from hot plasma is at these wavelengths).
 Plasmas and magnetic fields in the heliosphere II
• The Sun’s magnetic field varies on a (roughly) 11 year cycle – this is
directly evident in variations in numbers of sunspots. The coronal
magnetic field is much stronger and more structured at Solar Maximum,
and is much brighter in X-rays.
• Interaction of solar magnetic field with plasma is cause of much activity –
notably solar flares and coronal mass ejections
• Corona is constantly expanding into space as the Solar Wind

Solar wind and inner heliosphere:

• The solar wind is a supersonic flow of plasma at about 500 km s-1
• At 1 au, T ≈ 105 K, n ≈ 5 X 106 m-3.
• The solar wind has a magnetic field frozen to the plasma with spiral field
lines in ecliptic plane. B ≈ 5nT at 1 au.
 Plasmas and magnetic fields in the heliosphere III
Planetary magnetospheres:
• The Earth (and many other planets) are protected from Solar Wind plasma
and high energy particles from the Sun by its magnetic field. This forms a
cavity in the solar wind called the Magnetosphere – bounded by the
magnetopause. The Magnetosphere interacts with the Solar Wind in
many ways. Upstream of the Earth, the Solar Wind is slowed down to
subsonic speeds by the Bow Shock
• Closer to the Earth is the Ionosphere – the boundary layer between the
neutral atmosphere and the plasma magnetosphere. This consists of
weakly-ionised plasma, with ionisation by solar UV

Outer heliosphere:
The heliosphere forms a cavity within the InterStellar Medium. It is bounded
by the heliopause. As the solar wind reaches this boundary, it slows down
through a Termination Shock
Solar Dynamic Observatory (SDO) composite
Atmospheric Imaging Assembly

June to August 2010

 Magnetic field and emission
• how plasma in solar corona is “magnetically confined”

Magnetically confined plasma structures—on the sun and in the lab. (a) Magnetic arches in the solar
corona. The structures are axially collimated over several layers in the Sun’s atmosphere, even though
the densities of the layers vary greatly. (b) Stenson and Bellan’s experiment. Hydrogen gas is confined in
a magnetic fluxtube shortly after the tube forms. The structure is axially collimated, as in actual coronal
magnetic structures. (c) Schematic of the forces that cause collimation in a magnetic flux tube, as seen
from above the arch. In a typical dipole field, the field lines spanning the two poles would bow out, but
in the coronal structures, the existence of a magnetic field azimuthal to the main field lines generates a
jxB force that pushes plasma flow towards the less constricted regions.
These flows also transport azimuthal flux from the stronger field regions resulting in a dynamic collimation of the structure. [Credit: (a)
NASA/TRACE, (b) E. V. Stenson and P. M. Bellan [1], (c) APS/Carin Cain]
 The Sun March 8th 2011
Photosphere – SoHO MDI
Chromosphere
(SDO AIA)

Photosphere SDO HMI)

MDI

Corona
Magnetogram

Corona (SDO AIA)

Magnetogram
(SDO HMI)
The Earth’s magnetosphere
 Aurorae

Interaction of energetic
magnetospheric and solar wind
charged particles with Earth’s
neutral atmosphere
 Space Weather
• Activity on the Sun can
have a major impact
on the Earth and its
environment
– Communications
– Satellites
– Humans in space
– Power systems
• Need to understand
plasma processes
involved in space
weather in order to
predict and mitigate its
effects
 The heliosphere
showing Voyager spacecraft
September 13 2013
Confirmed that Voyager 1 has left Heliosphere
from http://www.jpl.nasa.gov/news/news.php?release=2013-278
"We have been cautious because we're dealing with one of the most important milestones in
the history of exploration," said Voyager Project Scientist Ed Stone of the California Institute
of Technology in Pasadena. "Only now do we have the data -- and the analysis -- we needed."
Basically, the team needed more data on plasma, which is ionized gas, the densest and
slowest moving of charged particles in space. .... Plasma is the most important marker that
distinguishes whether Voyager 1 is inside the solar bubble, known as the heliosphere, which
is inflated by plasma that streams outward from our sun, or in interstellar space and
surrounded by material ejected by the explosion of nearby giant stars millions of years ago.
.....
"We looked for the signs predicted by the models that use the best available data, but until
now we had no measurements of the plasma from Voyager 1," said Stone
 Plasmas and magnetic
fields across the
Magnetic field of M51 galaxy universe

•Most matter in the universe in

plasma state
•Magnetic fields in these plasmas
play an important role in many
situations
e.g.
•Stars, galaxies, clusters
•Star formation
•Stellar flares
•Pulsar magnetospheres
•Magnetars
•Active Galactic Nuclei and jets
 Chapter 1 – reading list
• Chen Chapter 1.1-1.3,1.7
• Stacey Chapter 1
(Russell, Luhmann and Strangeway Chapters 1 and 4)

• www.fusion.org.uk/introduction.aspx (introduction to fusion - basic level)

• www.plasmacoalition.org (overview of plasmas – basic level)
• fusedweb.llnl.gov (online fusion course – basic level)
• sdo.gsfc.nasa.gov (Solar Dynamic Observatory – daily images of Sun and
movies)
• http://www.windows2universe.org/spaceweather/basic_facts.html (space
weather)
• www.jet.efda.org/wp-content/uploads/jeteuropeansucess.pdf (all about JET -
highly recommended reading)
• https://www.iter.org/ (The ITER tokamak)

Case study 1: Summary of JET achievements

https://www.europhysicsnews.org/articles/epn/abs/2016/05/epn2016475-
6p25/epn2016475-6p25.html