Calculation of the power level required to initiate thermonuclear fusion

Approximate Calculation

The container of the plasma reaction is assumed to be a pyrex torus with a coil wound as in a Farady coil. Radio frequency current in this winding ionises, heats and contains the plasma as described elsewhere in this web site.

The torus is assumed to be 2 cm in principle diameter and 0.75 cm in tube diameter. The volume is therefore piX0.675XpiX.375X.375=1.02 cc. Or about 1cc. If Hydrogen at Atmospheric pressure an temperature has a density of 0.07 g/l then at 3 mm Hg it will be 2.6E-4 so the mass 1cc of hydrogen is 2.6E-7 g.

To heat this to 200Million K requires an amount of energy.

Assuming constant volume (actually neither volume nor pressure will be constant and to do the calculation properly the exact cycle of changes needs to be worked out, the cycle is similar to the Kelvin cycle and is well known but it would need to be measured to know actual values) the specific heat of hydrogen is 10.09 KJ/Kg/K=10.09 J/g/K So the energy to raise by 1 K is 2.62E-5 so to raise by 200E6 is 52468 Joules. To raise the temperature by this amount in 1/100 sec (10mSec) requires 5.24 MW. To do this in 1 sec requires 52.46KW. So 52.468 Amps RMS at 1000 Volts RMS would be required OR 229V RMS at 229A RMS.

Required torus wound with 10 Turns of 400 Amp copper wire. Capacitor with 1000 Volt breakdown voltage. The inductance will be about 0.2uH and to resonate at 28Mhz requires the capacitor to be 160 pF. A trimmer to tune up after power on is also required.

This tuned circuit needs to be energised with a suitable high power RF source set to 28Mhz and at about 60KW.

Once reactions are underway the oscillations will be self sustaining and the RF power source may be disconnected and removed.

It would be a good idea to have a directional power meter to see when the power from the reaction exceeds the input power at which point the reaction will be self sustaining.

There is likely to be gamma rays and neutrons emitted. So shielding is required.

Loading to tap the power could be done with a pick-up coil wound over the winding on the toroid. Conventional diodes and inverters would change the output to mains frequency for domestic use.

Salutary anecdote of previous test

If I remember rightly I could not turn off the reaction because when turned the anode voltage to zero and switched off the EHT unit and the valve unit the reaction continued. I went to the director and told him what had happened. The army took the thing away still reacting. I am told they took it to a shielded underground bunker. I believe one of the soldiers must have disconnected the circuit but none lived to tell the tale and the apparatus is buried under feet of concrete as it is very, very radioactive. They died in minutes. The apparatus produces an intense burst a radiation if the containment is disrupted.

I believe it was later found that it could be quietly and safely die by stroking the reaction tube with a bar magnet.

Chris