Nanomedicine, Volume I: Basic Capabilities

© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

 

6.3.7.2 Nuclear Fusion

Still larger energies (up to ~1% of rest mass) are available from nuclear reactions in which light nuclei fuse to form heavier nuclei, although it appears that conventional nuclear fusion is unlikely to be practical for in vivo nanomedical applications. The deuterium-tritium (D-T) fusion reaction requires the lowest temperature to ignite -- 141 million K, which is 12.1 KeV or 1.94 x 10-15 joules per nuclei -- and achieves 0.38% mass conversion to energy:

{Eqn. 6.29}

A D-T atom pair has volume ~10-3 nm3; maximum diamondoid piston (controlled) compression at 105 atm puts 10-20 joules into this volume, too low by a factor of ~106. However, target bombardment may allow micron-scale fusion ignition. Although magnetic cyclotronic confinement of 12.1 KeV particles at B = 1 tesla requires a storage ring of radius rorbit ~ 3 cm (Section 6.3.7.1), the length of a linear particle accelerator scales as ~K.E./qE (Section 4.7.4) so a 109 volt/m electric field requires only ~12 microns to accelerate an ionized triton or deuteron to the ignition temperature.

The first major problem with the D-T reaction from a nanomedical standpoint is the dangerously high flux of 14.1 MeV fast neutrons, which in human tissue interact with hydrogen to produce deuterium plus a 2.2 MeV g-ray, and with nitrogen to produce radioactive C14 plus a 0.6 MeV proton. Neutrons, like g-rays, are highly penetrating radiation, so using the D-T reaction will require much thicker shielding (see below). One alternative is to switch to a cleaner-burning (aneutronic fusion) but slightly hotter process such as the classical Cockcroft-Walton reaction involving proton bombardment of lithium which achieves 0.23% mass conversion to energy:

{Eqn. 6.30}

(A competing neutron-emitting reaction (Li7 + p ---> Be7 + n) occurs only at incident proton energies >1.6 MeV, and radiative absorption of the proton, producing a radiated g-ray, occurs as a sharp resonance absorption at a proton bombardment energy of 440 KeV.2463) A ~109 volt/m linear accelerator ~125 microns in length can produce 125 KeV protons, and from Eqn. 6.25 a platinum shield ~18 microns thick absorbs ~100% of the 8.36 MeV a-particles produced, thermalizing the energy.

The second major problem with micron-scale fusion is its low reaction cross-section. Cross-section is a measure of the probability that a given nuclear reaction will take place. If I0 incident protons/sec provoke Ir reactions/sec in a sample of thickness x with nuclear cross-section sn barns (1 barn = 10-24 cm2) and target density Ntarget (atoms/cm3) = r NA / AW, then

{Eqn. 6.31}

To get more energy out of the fusion reaction than is put into the protons (e.g., energy breakeven), the reaction probability (Ir/I0) > (125 KeV / 16.73 MeV) ~ 0.7%. For Li7, AW = 7 and r = 0.534 gm/cm3 so Ntarget = 4.6 x 1022 atoms/cm3; with sn ~ 0.01-0.001 barns for the reaction over this energy range,662 then to achieve energy breakeven the lithium target must be at least x > 16-160 cm thick. However, the range of 125 KeV protons in lithium is only ~0.0003 cm,567 so energy breakeven cannot be achieved. As for the D-T reaction, one calculation for laser compression of D-T fuel pellets indicated that the minimum pellet diameter to achieve (explosive) ignition is ~4.2 mm and requires a total incident energy of 11.2 megajoules602 in a ~nanosecond pulse. Smaller pellets could not achieve energy breakeven.* It is estimated that the minimum dimension of a high-temperature fusion reactor may be on the order of centimeters.1023 But even if a ~1011 joule/m3 energy density can be obtained with diamondoid materials allowing the reactor core to be as small as (5 cm)3, a 2.3-cm thick Pt shield for the 14.1 MeV neutrons only reduces the incident intensity by half. Thus the smallest medically safe D-T fusion reactor is probably at least ~1 meter in diameter (e.g., to reduce incident fast neutron intensity by ~106 upon exit).

* More recent hydrodynamic simulations of a 10-micron D2O-vapor-doped D2 gas bubble compressed to 0.38 micron in 0.5 microsec using a 5-atm triangular spike superimposed on a 1-atm 27.6 KHz oscillating driving pressure produces a 2.2 KeV peak central temperature ~11 picosec before the bubble reaches minimum radius, which should be hot enough to generate at least a small number of thermonuclear D-D fusion reactions in the bubble.933

D-D fusion produces either neutrons or radioactive tritium effluent, only 34 MeV per reaction, and achieves only ~0.1% mass conversion to energy. The D-He3 reaction produces 0.39% mass conversion with H and He4 effluent (both particles charged, hence field-manipulable), but is harder to ignite (~60 KeV). There are always unavoidable neutron-producing reactions due to D-D reactions in the primary fuel and D-T reactions between the primary deuterium and the secondary tritium, although Petrie2462 noted that neutron reactions can be less than ~5% of the D-He3 reactions. He3 is also very rare on Earth. The H-B11 reaction may produce C12 and is probably exoergic, but g-rays are emitted.1006,3534

 

Last updated on 18 February 2003