Fusion reactions producing neutron emission

In a plasma of isotopes of hydrogen, a number of reactions occur that
release neutrons apart from charged fusion products. While the latter
remain confined in the plasma, the neutrons can escape and be detected.
Neutrons from
d + d -> 3He + n and
d + t -> 4He + n
reactions have, in the center of mass system and neglecting the kinetic
energy of the reactants (which is small with respect to the released energy),
a fixed value of the kinetic energy En = 2.45 MeV and 14.02 MeV,
respectively. Neutrons from

t+t->4He+2n
reactions show a continuum spectrum which extends up to
En = 9.4 MeV, due to the three-body nature of the reaction. 
Illustration of fusion reactions producing neutrons.

The probability for a single reaction to occur is determined by its cross
section.The d+t reaction has the highest cross section for typical plasma
temperatures besides the highest value of the released energy Q.
This made deuterium-tritium (DT) plasmas the choice for fusion burning
plasmas experiments on next generation tokamaks, such as the planned
Ignitor and ITER. The JET experiment has provided DT discharges during the
DT experimental campaign (DTE1) in 1997.

The neutron emission from a volume element of a burning plasma involves
the averaging of the reaction cross section over the velocity distribution
of the reactant fuel ions. Moreover, the neutron emission detected along a
particular line of sight involves the integration above the
observed plasma volume where the temperature and ion densities vary, along
the radial direction, from higher values in the plasma core to lower
values at the edges.
 
Tangential line of sight through a plasma volume.

Restricting ourselves for simplicity to a small volume of plasma in which
the plasma parameters (temperature and ion densities) can be considered
constant, the reactivity is given by the average
of the cross
section over the Maxwellian fuel ion distribution fM,  

where v1 and v2 are the reactant velocities and
vrel=v2-v1. 

Cross section for the d+d and d+t reactions.

Reactivity for the d+d and d+t reactions.

Finally, the neutron emission per unit time is given by the reaction rate
R = n1n2, where n1 and n2 are
the fuel ion densities. If the reacting nuclei are of the same species, the
factor n1n2 has to be replaced by
n12/2.

The neutron energy spectrum

Besides the reaction rate, which carries information only on the total
neutron yield from the plasma, one can consider the neutron emission
spectrum which contains much more of plasma information. The t+t
neutron emission only add a small background to the 2.5-MeV emission from
d+d reactions and the 14-MeV emission from d+t reactions which both have,
in first approximation, a Gaussian shape. The average energy (spectral
peak) is given by the neutron energy in the limit T->0 (equal to 2.45 and
14.02 MeV for DD and DT neutrons, respectively) corrected by a "peak
shift" due to the finite kinetic energy of the reactants. The shift is of
the order of a few tens of keV (e.g., 58 keV and 52 keV for DD and DT
neutrons, respectively, for T=20 keV).

Neutron energy spectrum for d+d, d+t and t+t fusion reactions.

An additional shift is expected due to the plasma toroidal rotation,
which could therefore be determined through the measurement of this
spectral feature. The broadening of the spectrum is due to the finite
velocities of the reactants, which cause Doppler effect in the observation
of the neutron energy. In first approximation, the spectral full width
at half maximum (FWHM) is proportional to the square root of the temperature.
The determination of the ion temperature by the measurement of the neutron
spectral width is the most common neutron diagnostic in fusion plasmas.

Other neutron diagnostics are feasible, relying on different spectral
features:
- The so called a knock on effect causes
a spectral scape that can be detected and used to measure

a-particle heating in the plasma from
the d+t-reactions.
- The Tritium burnup effect (tritons produced in DD-reactions causing
DT-reactions) can be quantified in the DT-spectrum.
- By knowing the ion temperature and therefore the DD and
DT reactivities, the ratio of the ion densities nd and
nt can be determined from the
intensities of the 2.5- and 14-MeV neutron emission.