5. Nuclear Fusion Flashcards
Does fission or fusion give out more energy per kg of fuel?
Fusion
Why does fusion release more energy per kg than fission?
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).
State the starting reaction for nuclear fusion
Reactants: 2 hydrogen atoms
Products: 1 deuteron, 1 electron, 1 neutrino, and energy
Why is fusion very difficult to achieve on Earth?
Because very high temperatures, like the temperature of the Sun, are required.
Why are high temperatures required for fusion?
To overcome the Coulomb barrier.
_________ _________ is important for fusion, meaning that the Coulomb barrier doesn’t always have to be overcome for it to occur.
Quantum tunnelling
What are the two most common fuels for fusion reactions?
What are the two types of fusion reactions?
Deuterium-deuterium (D-D) reactions
Deuterium-tritium (D-T) reactions
What are the two possibilities for a deuterium-deuterium reaction?
State the equation for a deuterium-tritium reaction
Define cross-section
The probability for an interaction/reaction/scattering (a process) to occur per unit area.
Give the equation for the probability of an interaction for a target with N target nuclei per unit area, A
P = probability of an interaction
A = area
σ = cross-sectional area of each target
N = number of target nuclei
Do interaction cross sections have to be the same size as physical geometric areas?
No: they can be vastly smaller or larger
Describe the shape of a D-T and D-D fusion reaction graph of cross section against deuteron energy
Why is a D-T fusion reaction preferable over a D-D reaction?
Because it has a higher cross section and a higher energy release.
Define reaction rate
The number of incident particle that interact with a target (with a given cross section) in unit time.
Give the equation for the reaction rate
r = reaction rate
n_i = number of incident particles
σ = cross-sectional area of each target
v = velocity of a particle beam
Give the equation for reaction rate when there are a set number of targets per unit volume
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
What is the required temperature for a deuteron energy of ~100 keV to undergo fusion?
T ~ 10⁹ K (as KE = 3/2kT)
What happens to an atom at extremely high temperatures?
The electrons are stripped away from atoms to give a plasma (an ionised gas of electrons and nuclei).
What are the two most common methods for achieving fusion?
- Inertial confinement fusion (ICF)
- Magnetic confinement fusion (MCF)
Give the equation for the average energy release per unit volume from fusion
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
What assumption is made when calculating the average energy release per unit volume from fusion?
Assume n_1 = n_2 = n/2 so that the equation changes.
State the main requirement for fusion
Energy input must be smaller than energy output.
Why is the energy calculation for fusion an average?
Because ions have a Maxwell-Boltzmann distribution of velocities.
Give the equation for the distribution in ion speeds
f(v) = velocity distribution function
v = velocity
m = ion mass
k = Boltzmann constant
T = temperature
Give the equation for the energy input (thermal energy) of the plasma including both ions and electrons
E_th = thermal energy input
n = number of ions
k = Boltzmann constant
T = temperature
n_e = number of electrons
State the Lawson Criteria
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
What is the Lawson Criteria (definition)?
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).
Why does energy need to be supplied to maintain plasma temperature in a fusion reactor?
Because there are always energy losses such as radiation.
What is the ignition point in fusion?
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).
Can fusion be achieved on Earth yet?
No: current experiments are close but have not exceeded the Lawson criteria
How does magnetic confinement fusion (MCF) work?
It works by increasing the confinement time of the plasma. The plasma is confined within specially configured magnetic field.
Why is the magnetic field used in MCF?
It keeps the plasma thermally insulated from container walls so that they don’t melt. This works because the plasma is charged.
Which two magnetic field are applied to MCF?
- A toroidal (spiral) field: the blue field
- A poloidal (axial) field: the black field
The arrangement of the two fields is called a tokomak.
Give an example of magnetic confinement fusion
Joint European Torus (JET)
How does inertial confinement fusion (ICF) work?
It works by increasing the density of the plasma. Small pellets are caused to implode so the inner core reaches high densities/temperatures.
Give an example of inertial confinement fusion
National Ignition Facility (NIF)
