Do we need breakeven to consider fusion power sources?
Posted: Tue May 27, 2014 4:16 am
I did some back of the envelope calculations.
So the fusion gain factor is
G = Q_fusion / Q_in,
G: the factor
Q_fusion: fusion power released
Q_in: input power.
In a practical power plant the setup would probably turn everything into heat and feed into a heat engine. But probably better designs possible (eg. direct conversion with decelerators?)
Both the input power and the fusion power will be turned into heat. So the total heat generated is:
Q_fusion + Q_in = Q_in*(1 + G)
The efficiencies of real heat engines (Chabal-Novikov efficiency):
eta = 1 - sqrt(T_c / T_h)
This is much smaller efficiency than of the (impossible to build) Carnot engine.
And the efficiencies of the current power plants corresponds well to this value.
So in order to make it self sustaining, we need to feed back the electric power into the device:
Q_in = eta * Q_in * (1 + G)
If we solve for G, we have:
G = (1 - eta) / eta
Or for eta, we have:
eta = 1 / (1 + G).
I don't know what was the highest gain factor confirmed. So if you have exact numbers please let me know.
On breakeven the eta required is 0.5. Which means the hot side of the heat engine should be at 1200K. Look like it's doable.
If we consider that all parts of the heat engine is made of tungsten and calculate with 3000K on the hot side, G=0.5 would be enough to be sustainable.
On the forums I read that one would need a gain factor of 5-10 to make fusion power practical... So am I missing something?
So the fusion gain factor is
G = Q_fusion / Q_in,
G: the factor
Q_fusion: fusion power released
Q_in: input power.
In a practical power plant the setup would probably turn everything into heat and feed into a heat engine. But probably better designs possible (eg. direct conversion with decelerators?)
Both the input power and the fusion power will be turned into heat. So the total heat generated is:
Q_fusion + Q_in = Q_in*(1 + G)
The efficiencies of real heat engines (Chabal-Novikov efficiency):
eta = 1 - sqrt(T_c / T_h)
This is much smaller efficiency than of the (impossible to build) Carnot engine.
And the efficiencies of the current power plants corresponds well to this value.
So in order to make it self sustaining, we need to feed back the electric power into the device:
Q_in = eta * Q_in * (1 + G)
If we solve for G, we have:
G = (1 - eta) / eta
Or for eta, we have:
eta = 1 / (1 + G).
I don't know what was the highest gain factor confirmed. So if you have exact numbers please let me know.
On breakeven the eta required is 0.5. Which means the hot side of the heat engine should be at 1200K. Look like it's doable.
If we consider that all parts of the heat engine is made of tungsten and calculate with 3000K on the hot side, G=0.5 would be enough to be sustainable.
On the forums I read that one would need a gain factor of 5-10 to make fusion power practical... So am I missing something?