Nuclear Fusion Flashcards
What is the easiest fusion to ignite?
D + T -> He + n
What is the aim of fusion? (which reactions)
D + T -> He + n, and then n + Li -> T + He
What do we need for D to fuse with T?
Must overcome coulomb barrier by heating up D and T up to ~ 10^8 K.
What is the equation for the energy per particle?
3/2kbT, where kb is the boltzmann constant and T is the temperature
What is the equation for the total energy density?
W = 23/2kbTn = 3kbT*n
What does the D+T plasma lose energy through?
Through conduction, radiation at power loss rate P(L)
What is the equation for the power loss rate P(L)?
P(L) = W/τ(E) = 3kbT*n/τ(E), where τ(E) is the energy confinement time
What is the equation for the number of collisions per unit time?
f = 1/4 * n^2*, where σ is the fusion cross section and v is the relative velocity of D and T
What is the equation for the energy per unit time?
P(H) = f*E(a) = 1/4 * n^2**E(a)
What is the relation between P(L) and P(H) and how can we use this? What is this called?
P(H) >= P(L), so add in equations and rearrange for n*τ(E). This is the Lawson criterion, where n is the ion number density
What condition needs to be satisfied for igniting fusion?
nTτ(E) >= 3*10^28 Ksm^-3
What is magnetic confinement fusion?
To aim for a plasma with a pressure ~ 1 atm, we need τ(E) ~ 3 seconds.
What path does a charged particle move in and why?
A helix in a uniform B-field due to the Lorentz force F = qVXB
What is the equation for the Larmor radius?
r(L) = mV/qB
What is the equation for V(T), the thermal velocity?
V(T) = (kb*T/m)^1/2
What is the best way to transport the fusion particles efficiently?
Put them into a torus with a B-field so they can travel in a circle.
What is plasma heating?
Pass a current through plasma and the coils around it and increase magnetic flux through centre of torus to create emf. Plasma is now the secondary coil of a transformer.
What are some stats for the Joint European Torus?
B~ 3.5T
I ~ 3MA
T ~ 10 million K
What is the international thermonuclear experimental reactor?
-To be built by 2025
-Generate 500 MW fusion power in 8 minutes pulses
Q-factor = 10
What is inertial confinement fusion limited by?
The inertia of D-T
For a sphere D-T assembled at 10^8 K, what is the equation for the velocity of expansion?
V(T) ~ (kbT/m)^1/2 ~ 610^5 ms^-1
What do we assume about the stopping point of the reaction?
Stops when the volume of the D-T sphere doubles.
What is the equation for the time of the reaction if we assume it stops when the volume of the D-T sphere doubles?
τ(E) ~ R/(4*V(T))
How much energy does one reaction release in ICF?
~ 17 MeV
How much energy would 0.3g of fuel release?
100 GJ
What is the equation for the burnt fraction of D-T, Ф?
Ф = ρR/(ρR + 60(kg/m^2))
What is the equation for the mass of fuel?
M = 4πR^3ρ/3 = 4π(Rρ)^3/3ρ^2
How can we use the mass of fueld equation to find the density of the fuel?
Rearrange for ρ^2: ρ^2 = 4π(Rρ)^3/3M, so ρ~310^5 kgm^-3
How can we use a plastic shell in the D-T reaction?
Use lasers to heat the plastic shell so it expands, but then the reverse reaction compresses the D+T
What is Rayleigh-Taylor instability?
Acceleration inwards -> pseudo-gravity outwards, similar to heavy fluid on top of a light fluid. This instability mixes hot and cold fuels and might prevent fusion.
What is an indirect laser drive?
- Use hollow gold cylinder, and send laser into Au
- X-ray radiation
- This radiation is more uniform than direct laser drive
