Sonofusion Calculations

This is a preliminary page of calculations related to sonofusion. Note that the calculations have not been checked by a reliable authority. Most of this page is based upon a presentation by RI Nigmatulin and RT Lahey, although they are in no way responsible for errors made here. If you have corrections or additions, please forward them to Jeffrey Clymer.

Temperature increase of a bubble due to adiabatic compression.

Tmax/To = (dmin/do)-3(γ - 1)

To (initial temperature)
K. Room temperature is 298 K.

dmin (minimum bubble diameter)
nm. Try values in the 1-10 nm range.

do (equilibrium bubble diameter)
μm. Try values in the 3-5 μm range.

γ (Cp/Cv)
γ for an ideal polyatomic is 1.33. γ for acetone is 1.11.

Tmax
thousand K. D-D fusion starts to take place in the region of 108 (i.e., ~100 million) K.

Kinetics of fusion.

<σv> is the averaged product of the cross section and the deuterium nucleus thermal velocity. It is calculated here from an empirical relationship.

log10(<σv>) = -37.5 + 16.4 {1.0 - e-0.8(log T - 6.0) }

Temperature
million K. D-D fusion starts to take place in the region of 108 K.

log10 <σv>
m3/s. D-D fusion starts to take place above 10-26 m3/s.

The concentration of deuterium atoms is given by;

n = nD ρg NAg

nD. Number of deuterium atoms per molecule.
Acetone contains 6 deuterium atoms.

ρg. Density of the gas.
kg/m3. 1,000 kg/m3 is equivalent to 1 g/ml. Try 20,000 to 80,000.

μg. Molecular weight of the molecule
kg/kmol. Acetone has a molecular weight of 64.

and NA is Avogadro's number, 6.02 x 1026 kmol-1.

n. Number concentration of deuterium atoms.
m-3.

The neutron emission intensity is given by J = 1/2 n2 <σv>.

The number of emitted neutrons is given by N = J ΔV Δt, where V = 4/3 π r3.

nm. Try 50 nm.

Time duration
ps. Try 0.1 to 1.0 ps (10-12 s)

J. Neutron emission intensity.
neutrons/m3s

N. Number of emitted neutrons.
neutrons per bubble collapse.

Heat production

D-D fusion proceeds along two pathways.

1D2 + 1D2 --> 0n1 + 2He3

1D2 + 1D2 --> 1H1 + 1H3

Both are equally probable, and for each reaction produce about 10-12 J of heat.

The heat is calculated as,

H = NN k N . 1x10-12

where NN is the number of nuclei per pulse, k is the rate of pulses and N is the number of neutrons produced per collapse.

NN. Number of nuclei per pulse
Try 20 x 109.

k. Number of pulses per second.
Hz. Try 20 kHz.

Heat
J/s

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