Stress in tungsten target - part II -

1. Goran Skoro Stress in tungsten target- part II -

2. Target: repetition rate = 50 Hz; beam energy = 6 GeV; beam radius = target radius; 3 x 2 ns long bunches; pulse length = 20 s (2cm x 17cm), 25 s (3cm x 20cm); energy deposition = MARS Wire: 0.5 mm diameter, 3 cm long; 800 ns long pulse, exponential rise, 100 ns rise time 3 cm diameter target 2 cm diameter target Peak current [kA] Beam power [MW] REMINDER: Isostress* lines for tungsten target and wire (operating at 2000 K) • Comment 1. Here, beam energy E = 6 GeV. • ISS baseline: E = 10 GeV. 6 GeV -> 10 GeV changes the picture? • Comment 2. Here, target length = 17 (20) cm. • Is there an optimal target length (maximal pion yield vs. minimal stress)?

3. Beam power = 4 MW; repetition rate = 50 Hz; beam radius = target radius; 3 x 2 ns long bunches; energy deposition = MARS Peak Von Mises Stress [MPa] Pulse length [s] Peak Von Mises Stress [MPa] Pulse length [s] 10 GeV 10 GeV 6 GeV 6 GeV 3x20 cm target 2x17 cm target No difference ! (practically) 6 GeV 10 GeV

4. Beam power = 4 MW; beam energy = 10 GeV; repetition rate = 50 Hz; beam radius = target radius; 3 x 2 ns long bunches; energy deposition = MARS On the first sight, longer targets look better than shorter ones. But, we are looking for the pulse lengths when we have minimal peak stresses. For such pulse lengths there is (practically) no dependence of peak stress on target length. N.B. Peak stresses for target lengths between corresponding lower and upper limits (shown on the plots) have the same behaviour. 17 cm length 30 cm length 30 cm length 20 cm length Peak Von Mises Stress [MPa] Pulse length [s] Peak Von Mises Stress [MPa] Pulse length [s] 3 cm diameter 2 cm diameter Target length (stress)

5. - Pion yield IS a determining factor for the target length. The left plot shows how we should change the target length when moving from 2cm to 3cm diameter scenario (and vice versa) in order to have the same pion yield. The right plot shows that different target dimensions (yield is the same in this case) do not change the pions spectra. At the moment, it looks that stress defines the diameter while pion yield defines the length of the target (single tungsten bar). Maybe the pion re-absorption study (J. Back) could shed additional light on the problem of target length optimisation. MARS: beam energy = 10 GeV; beam radius = target radius. - If the pulse length is below 250 s*, stress is NOT a determining factor for the target length** (it IS for the diameter of the target). Iso-yield line Length of 2 cm diameter target [cm] Length of 3 cm diameter target [cm] **) Assuming that we can dictate the beam time-profile. If not (if the pulse length is defined from ‘outside’) we will have to optimise the target diameter in order to reach the minimal peak stress. *) Above this value, the stress (vs. pulse length) starts to depend on longitudinal shock transit time. The effect is not very prominent but the calculation should be repeated if we face such a long pulse length. Target length (conclusions) MARS