This paper presents three-dimensional numerical simulations of thermodynamic and hydrodynamic response of it wheel shaped solid graphite production target for the super conducting fragment separator (Super-FRS) that is irradiated with a fast extracted high intensity uranium beam. These fragment separator experiments will be carried out at the future Facility for Antiprotons and Ion Research (FAIR), at Darmstadt. Previously, we reported simulation results that Weir carried out using two-dimensional computer codes which showed that one can use a solid graphite target for the Super-FRS for the highest intensity (5 x 10(11) ions per spill) of the fast extracted uranium beam. Present results, however, have shown that due to three dimensional effects the maximum intensity that can he used with Such a target is 3 x 10(11) ions per spill. A detailed comparison between two-dimensional and three-dimensional results is presented in this paper.

In case of the rectangular intensity distribution, a maximum specific energy deposition of 0.27 kJ/g is achieved in the Ni part while the corresponding temperature and pressure are 940 K and 2.6 GPa, respectively. For the Gaussian distribution, the maximum specific energy is 0.14 kJ/g, the temperature is 629 K and the pressure is 2.4 GPa. It is to be noted that the target temperature remains safely below the melting temperature of Ni (1726 K) so the target will remain in the solid state. However, the high pressure in the target launches an outgoing radial compression wave which generates stress in the material that could lead to plastific ation of certain parts of the target. In Fig. 3 we plot the von Mises parameter, M, on a length–radius plane in case of the Gaussian distribution at t = 50 ns which shows that M = 1 in the Ni region which indicates material plastification. Figure 4 presents M at t = 1 μs which shows that the plastification wave has entered into the graphite by this time. Calculations at later points in time show that the aluminum region remains in an elastic regime. These calculations indicate that although plastification occurs in the interior, the target will still remain in tact.

Previously, we reported 3D hydrodynamic simulations of interaction of a wheel shaped solid graphite Super–FRS production target with the SIS100, 1.5 GeV/u uranium beam [1]. These simulations have shown that the target will survive (retain its elastic properties) for a beam intensity of up to 3x10 ions per 50 ns long bunch if one uses a focal spot size that is characterized with σ = 4 mm. However, it is very important that the thin metallic stripper behind the production target also remains intact after the impact of the secondary beam. For this purpose, we report in the present contribution, 3D numerical simulations of the beam–stripper interaction. The stripper thickness i s assumed to be 225 mg/cm 2 and we consider three different materials, namely, Al, Cu and Nb.

Extensive numerical simulations have been carried Out to design a viable solid graphite wheel shaped production target for the Super conducting fragment separator experiments (Super-FRS) at the future Facility for Antiprotons and Ion Research (FAIR) using an intense uranium beam. In this study, generation, propagation and decay of deviatoric stress waves induced by the beam in the target. have been investigated. Maximum beam intensities that the target can tolerate using different focal spot sizes that are determined by requirements of good isotope resolution and transmission of the secondary beam through the fragment separator, have been calculated. It has been reported elsewhere that the tensile strength of graphite significantly increases with temperature. To take advantage of this effect, calculations have also been done in which the target is preheated to a higher temperature, that in practice can be achieved, for example, by irradiating the target with a defocused ion beam before the experiments are performed. We report results of a few examples using an initial temperature of 2000 K. This study has shown that employing such a configuration, one may use a solid graphite production target even for the maximum intensity of the uranium beam (5 x 10(11) ion per bunch) at the Super-FRS.

The Super-FRS experiments will use highest intensities of the heaviest projectiles, namely, 5.0 ◊ 10 11 uranium ions delivered in a 50 ns long bunch. Survival of the pro- duction target over an extended period of time during this experimental campaign carried out at a repetition rate of 1 Hz, is a very important but difficult problem. One of the requirements necessary to achieve this goal is to keep the thermally induced material stress below a critical value so that the von Mises parameter remains less than 1 which implies that the target material remains in an elastic state . In this contribution we report 2D numerical simulations of interaction of a solid graphite cylindrical target that is i rra- diated with a 1 GeV/u uranium beam along the axis. The target radius is 5 cm while the beam intensity is 10 10 ions per bunch with a bunch length of 50 ns. The main purpose of this work is to study the thermal stress generated by dif- ferent focal spot geometries. We respectively consider a circular focal spot with = 1.69 mm and an elliptic focal spot with X = 0.41 mm and Y = 4.1 mm so that the focal spot area is the same in both cases.

The LAPLAS experimental scheme (beam-target geometry) is shown in Fig. 1. It is a multi-layered target that consists of s solid cylinder of frozen hydrogen that is enclosed in a cylindrical shell of a high-Z material like Pb or Au. One face of this target is irradiated with an intense ion beam that has an annular focal spot whose dimensions are chosen in such a way that the hydrogen is not directly heated by the ion beam. Moreover a small ring shaped part of the surrounding shell is left around the hydrogen which is called ”payload”. The high pressure in the beam heated region leads to a low-entropy compression of the hydrogen. Previously [1, 2, 3] we carried out two-dimensional hydrodynamic simulations of implosion of the LAPLAS target that showed that in most of the cases, the payload shell will remain in solid state and hence will retain its elastic prope ties. Analytic work [4] has shown that elasticity will have stabilizing effect on the Rayleigh-Taylor instability of t he payload shell. In the previous simulations, elastic-plast ic effects were not included. We have now carried out threedimensional numerical simulations of the LAPLAS target implosion that also include elastic-plastic effects. Thes e calculations show that the implosion dynamics is rather insensitive to inclusion of these additional physical effect s.

This contribution presents three-dimensional numerical simulations of the LAPLAS target (N.A. Tahir et al., Nucl. Inst. Meth. A 544 (2005) 16) including elastic-plastic ef- fects. These calculations have shown that the shock dy- namics is not significantly affected by inclusion of these new physical effects which demonstrates the validity of the previous calculations.

Production and collection of antiprotons will be one of the many important experiments that will be done at the FAIR. The SIS100 will deliver a bunched proton beam with, intensity = 2 ◊ 10 11 protons, bunch length = 25 ns and particle energy = 29 GeV. The design of a production target that will survive over an extended period of time is a very important and difficult problem. Figure 1 shows the proposed target geometry which is the same as used previously in the CERN antiproton pro- duction experiments. It consists of 6 iridium cylinders, each 1 cm long and having a radius of 2 mm with a small gap of 50 µm between two neighboring pieces. This avoids bending of the target as a result of expansion due to heating. The iridium part is enclosed in a solid graphite casing that is followed by an aluminum cover. The advantage of using graphite is that it has much lower absorption cross section for antiprotons. The dimensions of the different parts of th e target are shown in the figure. The proton beam is incident at the left face of the target, the protons generate a shower of secondary particles that deposit their energy in the targ et. The energy deposition is calculated using the FLUKA code and the results are plotted in Fig. 2. The focal spot size of the beam is characterized with a = 1.5 mm in this case. The antiprotons generated in the target will be collected on the right side of the target using a magnetic horn.