A great post by the Economist on the market for Lithium, the indispensable component in most modern batteries. The price of lithium carbonate jumped 100%  to nearly $14,000 per tonne in the past few months.

Lithium is a key input for modern fusion experiments because only one of the two necessary Hydrogen isotopes is abundant on earth. Deuterium appears in trace amounts in seawater and can be extracted by electrolysis, Tritium is a different story, however.

To make Tritium we need to fire neutrons at Lithium nuclei, occasionally they fuse and quickly split apart producing Tritium. Here are the two reactions.

latex-image-2latex-image-1

Some good news, see how the Lithium 6 reaction produces energy? Well even though Lithium 6 represents only 7.6% of naturally occurring Lithium that reaction is actually the more common one. For once fusion researchers catch a break.

So commercial fusion reactors would flow Lithium through the blanket to breed Tritium. The whole happy reaction looks like this

DT fusion flow.png
The Deuterium Tritium reaction alongside Tritium breeding.

 

Fusion is competing in an open market for access to Lithium, should we worry about the price of Lithium? at what price does DT fusion become cost prohibitive?

Somewhat like relativity and quantum mechanics the numbers involved in fusion tend to baffle us. They’re often far bigger or smaller than we expect. How much Lithium and Deuterium would a 1MW power plant require?
First let’s compare a coal burning station. Let’s take coal’s specific energy to be 30MJ/Kg, then to produce 1000MW at 30% thermal efficiency we would need 111kg/sec of coal:

latex-image-1.png

or about 3.5M tonnes per year.

Now fusion. Each DT reaction gives 17.6MeV and the Tritium breeding reaction gives 4.8MeV. Assuming each DT reaction gives rise to exactly 1 Lithium reaction we have 22.4MeV for each reaction which will have used up 1 Deuterium and 1 Lithium nucleus.

I’m switching to python for these calculations (code below) the results are:

~100 kg of Deuterium per year

~340 kg of Lithium per year

~440 kg of fuel in total per year

The message here is pretty stark. Fusion uses a bafflingly small amount of fuel. That’s a grid-scale power station whose fuel could be easily carried in a small van. At today’s high price this Lithium would cost just $4,700 per year.

One more thing. How much electricity does our station produce in this time?

1GW x 1 year = 8.76B kWh.

Assuming a retail price of 10 pence / kWh that gives us £876M / year.

The cost of fusion power lies in the installation and hardware costs, the marginal cost of its output is exceptionally low. In this sense it resembles a renewable energy source.

The featured image is the emission spectrum of Lithium. Courtesy of Wikipedia.


#1 electron volt in joules
joulesPerev = float(1.6E-19)

#Reaction output is 22.4MeV
reactionEnergy = float(22.4E6)

#reaction output in joules
reactionOutput = reactionEnergy * joulesPerev

#number of reactions to produce 1MJ in 1 sec
reactions = float(1e9) / reactionOutput

#nuclei masses in kg
Mdeu = float(3.3435e-27)
Mli = float(1.1525801e-26)

totalDeu = reactions * Mdeu
totalLi = reactions * Mli

#calculate hom much we use at 30% efficiency over 1 year
totalDeu *= 60 * 60 * 24 * 365 * 100/30
totalLi *= 60 * 60 * 24 * 365 * 100/30

total = totalDeu + totalLi

print "%f kg of Deuterium per year\n%f kg of Lithium per year\n%f kg of fuel in total per year" % (totalDeu, totalLi, total)

# output:
# 98.066049 kg of Deuterium per year
# 338.055860 kg of Lithium per year
# 436.121909 kg of fuel in total per year