Nuclear Fusion

Question 1

What is the easiest fusion to ignite?

Answer 1

D + T -> He + n

Question 2

What is the aim of fusion? (which reactions)

Answer 2

D + T -> He + n, and then n + Li -> T + He

Question 3

What do we need for D to fuse with T?

Answer 3

Must overcome coulomb barrier by heating up D and T up to ~ 10^8 K.

Question 4

What is the equation for the energy per particle?

Answer 4

3/2kbT, where kb is the boltzmann constant and T is the temperature

Question 5

What is the equation for the total energy density?

Answer 5

W = 23/2kbTn = 3kbT*n

Question 6

What does the D+T plasma lose energy through?

Answer 6

Through conduction, radiation at power loss rate P(L)

Question 7

What is the equation for the power loss rate P(L)?

Answer 7

P(L) = W/τ(E) = 3kbT*n/τ(E), where τ(E) is the energy confinement time

Question 8

What is the equation for the number of collisions per unit time?

Answer 8

f = 1/4 * n^2*, where σ is the fusion cross section and v is the relative velocity of D and T

Question 9

What is the equation for the energy per unit time?

Answer 9

P(H) = f*E(a) = 1/4 * n^2**E(a)

Question 10

What is the relation between P(L) and P(H) and how can we use this? What is this called?

Answer 10

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

Question 11

What condition needs to be satisfied for igniting fusion?

Answer 11

nTτ(E) >= 3*10^28 Ksm^-3

Question 12

What is magnetic confinement fusion?

Answer 12

To aim for a plasma with a pressure ~ 1 atm, we need τ(E) ~ 3 seconds.

Question 13

What path does a charged particle move in and why?

Answer 13

A helix in a uniform B-field due to the Lorentz force F = qVXB

Question 14

What is the equation for the Larmor radius?

Answer 14

r(L) = mV/qB

Question 15

What is the equation for V(T), the thermal velocity?

Answer 15

V(T) = (kb*T/m)^1/2

Question 16

What is the best way to transport the fusion particles efficiently?

Answer 16

Put them into a torus with a B-field so they can travel in a circle.

Question 17

What is plasma heating?

Answer 17

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.

Question 18

What are some stats for the Joint European Torus?

Answer 18

B~ 3.5T
I ~ 3MA
T ~ 10 million K

Question 19

What is the international thermonuclear experimental reactor?

Answer 19

-To be built by 2025
-Generate 500 MW fusion power in 8 minutes pulses
Q-factor = 10

Question 20

What is inertial confinement fusion limited by?

Answer 20

The inertia of D-T

Question 21

For a sphere D-T assembled at 10^8 K, what is the equation for the velocity of expansion?

Answer 21

V(T) ~ (kbT/m)^1/2 ~ 610^5 ms^-1

Question 22

What do we assume about the stopping point of the reaction?

Answer 22

Stops when the volume of the D-T sphere doubles.

Question 23

What is the equation for the time of the reaction if we assume it stops when the volume of the D-T sphere doubles?

Answer 23

τ(E) ~ R/(4*V(T))

Question 24

How much energy does one reaction release in ICF?

Answer 24

~ 17 MeV

Question 25

How much energy would 0.3g of fuel release?

Answer 25

100 GJ

Question 26

What is the equation for the burnt fraction of D-T, Ф?

Answer 26

Ф = ρR/(ρR + 60(kg/m^2))

Question 27

What is the equation for the mass of fuel?

Answer 27

M = 4πR^3ρ/3 = 4π(Rρ)^3/3ρ^2

Question 28

How can we use the mass of fueld equation to find the density of the fuel?

Answer 28

Rearrange for ρ^2: ρ^2 = 4π(Rρ)^3/3M, so ρ~310^5 kgm^-3

Question 29

How can we use a plastic shell in the D-T reaction?

Answer 29

Use lasers to heat the plastic shell so it expands, but then the reverse reaction compresses the D+T

Question 30

What is Rayleigh-Taylor instability?

Answer 30

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.

Question 31

What is an indirect laser drive?

Answer 31

• Use hollow gold cylinder, and send laser into Au
• X-ray radiation
• This radiation is more uniform than direct laser drive