Technical Design Report Super Fragment Separator

DRAFT
radiation shielding in the limited space of the separator. All materials should be good heat conductors.
The entrance material should be low in mass number (A) to avoid too high temperatures. This can
already be seen from the simple formula below for the temperature rise (∆T) due to a number of
particles (N) characterized by a stopping power dE/d(ρx), a beam spot area σ 2 , and a molar heat
capacity (Cmol), which for high temperatures becomes a constant defined by Avogadro's number
(NA)and Boltzmann's constant (kB).
dE / d(
ρx)
A
∆T
= N
; Cmol
= 3N
Ak
2
B
σ C
mol
for high
As dE/d(ρx) only moderately changes for different A and Z of the stopping materials, low A is
clearly preferable.
Energy deposition in different materials
Besides the beam spot size the density of the deposited energy also depends on the amount of
nuclear reactions of the primary beam. Simulations with the codes FLUKA [43,44] and PHITS
[41] were performed to study the energy deposition taking into account both nuclear and atomic
interactions and the contributions of the secondary beam. An example for 10 12 Uranium at 740
MeV/u dumped in carbon with a round Gaussian beam spot with σ = 1 cm is shown in Figure
2.4.107. In this calculation the initial energy spread was assumed to be zero. Without fragmentation
the ratio of the stopping power at the entrance and in the Bragg peak would be 6.9 [45].
However, nuclear reactions reduce this ratio to 3.1.
In Li and Be the nuclear reaction rate is higher compared to the energy-loss cross section. Therefore,
the Bragg peak would be reduced by an even larger factor. Values are listed in Table 2.4.25.
The same conclusions hold for higher initial energies.
The density of energy deposition in the bulk material can also be reduced by geometrical shaping
of the entrance of the beam catcher such that the range straggling is enhanced. In the example of
Figure 2.4.107 the ratio of the peak to entrance energy deposition has been reduced to about 1.8
with an inclined surface of a slope of 0.1.
In Table 2.4.25 the specific energy deposition and the resulting temperature and pressure rise are
compared for different materials. Lithium has the lowest mass number and therefore the temperature
rise has the lowest value. Beryllium and graphite have a rather high Debye temperature
and do not reach their full heat capacity at room temperature.
T
114