Fusion Message Board

In this space, visitors are invited to post any comments, questions, or skeptical observations about Philo T. Farnsworth's contributions to the field of Nuclear Fusion research.

Subject: Re: Neutron generation equation
Date: Jun 27, 1:53 pm
Poster: Larry Cress

On Jun 27, 1:53 pm, Larry Cress wrote:

>Is there an equation relating the applied voltage, current, deuterium pressure, and (possibly) geometry of the spherical fusor to the theoretical neutron flux to be expected?

An approximate calculation of the neutron generation rate can be found in Los Alamos report LAMS-1640 by James Tuck.

The neutron generation rate in neutrons/sec/cm^3 is 0.5 * n^2 * sigma_v

where n is the density of deuterium nuclei per cm^3 and is given by rho*6.023E23/A. A is the atomic mass number (A=2 for D) and rho is density in gm/cm^3. Sigma_v is Maxwellian averaged value of interaction cross section * velocity. For 40 kev sigma_v for the D-D reaction is 1.E-17 cm^3/s.

A similar equation holds for the D-T reaction: n_D * n_T * sigma_v, but now sigma_v is 7.9E-16.

These values of sigma_v hold for maxwellian distribution of particle velocities, which may not be corrrect in an electrostatically confined plasma, but calculations have shown that they are approximately correct for a more likely distribution of velocities.

The big unknown is rho, the actual density of deuterium nuclei (ions) in the central plasma. Due to electrostatic trapping of ions in the potential well, the ideal gas law will probably give only a rough estimate.

These are the kind of predictions to which experimentally measured rates of neutron production should be compared to determine whether observed neutrons are due to thermonuclear fusion or just to accelerated ions. Examination of the energy spectrum of the emerging neutrons using a plastic scintillator or proton recoil ionization chamber is also useful for answering this question.