General

MCNEUT tracks ions through the given experimental geometry and calculates neutron TOF and energy spectra measured in the detector. The probability for detecting a neutron in the detector with a solid angle ∆Ω generated by fusion of a single ion with the energy E0,i is given as

Pn(E0,i, αi) = ∆Ω· Z 0 E0,i dσ dΩ(Ei, αi)·nd(x(Ei))· dx dEi · dEi. (4.11)

Here αi is the angle between the ion trajectory and the neutron (and therefore the detector), _ddσ_Ω is the differential reaction cross-section, nd(x(E)) is the local deuteron atom density at the position x(E) an ion with the energy E has in the target, and _dEdx is the derivative of the energy dependent ion range x(E).

To obtain a neutron spectrum, it is necessary to treat the above expression differentially for each energyEiin the slowing down process of the ion and calculate the neutron energy and time of flight delay for the current Ei and αi. If the ion reaches a material boundary, one has to take care of changes in stopping, and for jumps of αi due to crossing of large vacuum gaps as between the jet and the catcher target. Angular straggling at the end of the ion range is neglected, since the contribution to the neutron output is maximal at high ion energies, where straggling is still weak. Scattering in the target chamber and the detector shielding is implemented from a simulation of the actual experimental setup with MCNP [59].

Technically, the code starts ions accelerated in the laser focus according to a predefined angular and energy distribution Pang(θ, φ)·Pe(Ei), which can be either given analytically or read from a PIC code output file. Here θ is the angle of the ion trajectory with the positive laser axis and φdenotes the angle of the ion to an axis perpendicular to the polarization plane in the plane normal to the laser axis. (See Fig. 4.8.)

Figure 4.8: Definition of axes and angles in MCNEUT

For droplet or wire targets the source point can be randomly scanned over the target surface to take into account an unstable laser spot. This changesd(θ), which is the thickness of material an ion emitted at an angle θ to the laser axis travels through, and therefore has an influence on the spectral weight of ions at certain angles θ. For ions accelerated off the rear target surface, the target thickness can be set to zero; so all ions will directly proceed to the catcher without interaction in the primary target.

An ion from the first energy bin in the input spectrum is started with a direction given by a Monte-Carlo sampling of the input angular distribution. In a first step, the length of the ion’s trajectory through the target is calculated. Each ion is slowed down in equidistant energy steps ∆E along its trajectory through matter, and moves on a distance ∆x for each step as determined by the inverse of its stopping power _dEdx, as given by modified SRIM ([46]) stopping tables (see section

4.2.1 and 4.4.2). The areal density of fusion partners on its trajectory is then

given by Nd,cold = ρd·∆x. The differential (d,d)-fusion cross-section dσ/dΩ(Ei,α) tabulated by DROSG2000 ([45]) is interpolated for the current ion energy Ei and the angle between the ion direction and the detector direction α. It is multiplied with the number of cold fusion partners, Nd,cold, to yield a total fusion probability of the ion while it travels with the energy Ei. This probability is then weighted with the total number of ions in the input energy bin and added to the neutron energy bin and/or time-of-flight bin in the output file that is calculated from the reaction kinematics forαand Ei. This treatment yields a whole probability spectrum from one ion. Note that the annihilation of the neutron due to fusion is neglected, since the binary fusion event is replaced by the fusion probability. The error arising from this treatment is small, since the total fusion probability for a MeV deuteron

stopping in CD2 is of the order of 10−4. If the deuteron has sufficient energy to reach the back surface of the target, its exit energy (Eflight)is recorded and the distance to the catcher target (∆lt−c) is calculated to determine the ion time-of- flight delay ∆tionTOF. The further treatment of the ion is similar to inside the target, except that the detector solid angle is computed with the distance between detector and the location of the ion impact on the catcher, and the stopping is adjusted to the catcher material, which can be different from the target. The neutron time of flight is also computed with this new distance and includes the contribution of ∆tionTOF. This procedure is repeated with a few hundred deuterons of the same input energy bin to sample specified angular distribution, before the next energy bin is treated in the same way. The output generated by the code is a file with energy and time-of-flight neutron spectra as seen in the detector normalized to the total ion number in the input spectrum and a file of points in three dimensions which represent the locations of ions exiting the target and/or entering the catcher.