5. Nuclear Fusion

Question 1

Does fission or fusion give out more energy per kg of fuel?

Answer 1

Fusion

Question 2

Why does fusion release more energy per kg than fission?

Answer 2

The change in binding energy from one element to the next is greater for fusion than for fission (the B/A vs. A is steeper on the fusion side).

Question 3

State the starting reaction for nuclear fusion

Answer 3

Reactants: 2 hydrogen atoms
Products: 1 deuteron, 1 electron, 1 neutrino, and energy

Question 4

Why is fusion very difficult to achieve on Earth?

Answer 4

Because very high temperatures, like the temperature of the Sun, are required.

Question 5

Why are high temperatures required for fusion?

Answer 5

To overcome the Coulomb barrier.

Question 6

_________ _________ is important for fusion, meaning that the Coulomb barrier doesn’t always have to be overcome for it to occur.

Answer 6

Quantum tunnelling

Question 7

What are the two most common fuels for fusion reactions?

Answer 7

Question 8

What are the two types of fusion reactions?

Answer 8

Deuterium-deuterium (D-D) reactions
Deuterium-tritium (D-T) reactions

Question 9

What are the two possibilities for a deuterium-deuterium reaction?

Answer 9

Question 10

State the equation for a deuterium-tritium reaction

Answer 10

Question 11

Define cross-section

Answer 11

The probability for an interaction/reaction/scattering (a process) to occur per unit area.

Question 12

Give the equation for the probability of an interaction for a target with N target nuclei per unit area, A

Answer 12

P = probability of an interaction
A = area
σ = cross-sectional area of each target
N = number of target nuclei

Question 13

Do interaction cross sections have to be the same size as physical geometric areas?

Answer 13

No: they can be vastly smaller or larger

Question 14

Describe the shape of a D-T and D-D fusion reaction graph of cross section against deuteron energy

Answer 14

Question 15

Why is a D-T fusion reaction preferable over a D-D reaction?

Answer 15

Because it has a higher cross section and a higher energy release.

Question 16

Define reaction rate

Answer 16

The number of incident particle that interact with a target (with a given cross section) in unit time.

Question 17

Give the equation for the reaction rate

Answer 17

r = reaction rate
n_i = number of incident particles
σ = cross-sectional area of each target
v = velocity of a particle beam

Question 18

Give the equation for reaction rate when there are a set number of targets per unit volume

Answer 18

R = total reaction rate
n_t = number of targets
n_i = number of incident particles
σ = cross-sectional area of each target
v = velocity of a particle beam

Question 19

What is the required temperature for a deuteron energy of ~100 keV to undergo fusion?

Answer 19

T ~ 10⁹ K (as KE = 3/2kT)

Question 20

What happens to an atom at extremely high temperatures?

Answer 20

The electrons are stripped away from atoms to give a plasma (an ionised gas of electrons and nuclei).

Question 21

What are the two most common methods for achieving fusion?

Answer 21

• Inertial confinement fusion (ICF)
• Magnetic confinement fusion (MCF)

Question 22

Give the equation for the average energy release per unit volume from fusion

Answer 22

E_f = Average energy release per unit volume
R = total reaction rate
Q = energy release per fusion
t = containment time
n_1, n_2 = ion densities (of D and T)
σ = cross-sectional area of each target
v = velocity of a particle beam

Question 23

What assumption is made when calculating the average energy release per unit volume from fusion?

Answer 23

Assume n_1 = n_2 = n/2 so that the equation changes.

Question 24

State the main requirement for fusion

Answer 24

Energy input must be smaller than energy output.

Question 25

Why is the energy calculation for fusion an average?

Answer 25

Because ions have a Maxwell-Boltzmann distribution of velocities.

Question 26

Give the equation for the distribution in ion speeds

Answer 26

f(v) = velocity distribution function v = velocity m = ion mass k = Boltzmann constant T = temperature

Question 27

Give the equation for the energy input (thermal energy) of the plasma including both ions and electrons

Answer 27

E_th = thermal energy input n = number of ions k = Boltzmann constant T = temperature n_e = number of electrons

Question 28

State the Lawson Criteria

Answer 28

When E_f > E_th, fusion can occur and the Lawson Criteria holds. n = number of ions = number of electrons k = Boltzmann constant T = temperature σ = cross-sectional area of each target v = velocity of a particle beam Q = total energy release per fusion

Question 29

What is the Lawson Criteria (definition)?

Answer 29

It is the scientific break-even condition (the point at which the fusion power generated must be equal to the power needed to maintain plasma temperature).

Question 30

Why does energy need to be supplied to maintain plasma temperature in a fusion reactor?

Answer 30

Because there are always energy losses such as radiation.

Question 31

What is the ignition point in fusion?

Answer 31

The point when fusion power generated can maintain the reactor with no external energy source. It is around an order of magnitude larger than the break-even condition (or more for ICF).

Question 32

Can fusion be achieved on Earth yet?

Answer 32

No: current experiments are close but have not exceeded the Lawson criteria

Question 33

How does magnetic confinement fusion (MCF) work?

Answer 33

It works by increasing the confinement time of the plasma. The plasma is confined within specially configured magnetic field.

Question 34

Why is the magnetic field used in MCF?

Answer 34

It keeps the plasma thermally insulated from container walls so that they don't melt. This works because the plasma is charged.

Question 35

Which two magnetic field are applied to MCF?

Answer 35

- A toroidal (spiral) field: the blue field - A poloidal (axial) field: the black field The arrangement of the two fields is called a tokomak.

Question 36

Give an example of magnetic confinement fusion

Answer 36

Joint European Torus (JET)

Question 37

How does inertial confinement fusion (ICF) work?

Answer 37

It works by increasing the density of the plasma. Small pellets are caused to implode so the inner core reaches high densities/temperatures.

Question 38

Give an example of inertial confinement fusion

Answer 38

National Ignition Facility (NIF)