Reducing shock in the Neutrino Factory target Goran Skoro (University of Sheffield) UKNF Meeting 11 January 2006

Contents: Short reminder (Stress vs. macro pulse length) New results (Effect of additional target material) Pbar target Neutrino Factory target Summary, Plans

Short reminder The target is bombarded at up 50 Hz by a proton beam consisting of ~1ns long bunches in a pulse of a few micro-s length. The target material exposed to the beam will be ~ 20cm long and ~2cm in diameter. Energy density per pulse ~ 300 J/cc. Thermally induced shock (stress) in target material (tantalum).

Geometry: NF target 2cm 20cm Boundary conditions: freeThermal load of 100K (equivalent energy density of ~ 300 J/cc) T initial = 2000K

Material model used in the analysis Temperature Dependent Bilinear Isotropic Model  'Classical' inelastic model  Nonlinear – Uses 2 slopes (elastic, plastic) for representing of the stress-strain curve – Inputs: density, Young's modulus, CTE, Poisson's ratio, temperature dependent yield stress,... Element type: LS-DYNA Explicit Solid Material: TANTALUM, Graphite (T2K)

~10-20% effect< 3% effect Stress vs. pulse length micro-pulse macro-pulse Fixed: 1 us

Stress vs. pulse length micro-pulse macro-pulse

~ RAL proton driver Important parameters: Energy deposition rate and shock transit time! Stress vs. pulse length micro-pulse macro-pulse 10

“Old” Pbar test results In this case 'Damage' = reduction of pbar yields The tantalum target (disc, ~ few mm height) was bombarded by a proton beam (up to 5e12 ppp, pulse length = 1.6 us) The beam width was extremely small (down to sigma = 0.15 mm) -> Energy density per pulse up to J/cc !!!! Expectation: 1 pulse should damage the target......but, tantalum survived thousands of pulses with 'no damage' ! Here, only (relatively) small volume of the material was heated. Is that important? NO DAMAGE for tantalum target (WHY?) Graphite Tantalum Graphite beam Pbar target assembly

Simulations of Pbar target (tantalum cylinder case) Patrick Hurh (FNAL) about the beam parameters:  “the area where we could put a tantalum test target (before 2009) has beam parameters something like 0.5 mm sigma and 5e12 protons per pulse (120 GeV) 1.6 microsecond pulse length with a repetition rate of once every 2 seconds If you need finer resolution on the pulse structure, I believe it is dependent upon the Booster batches per pulse and I'll have to find that out later.” I have simulated the target response keeping the same geometry as in NF target case (beam centreline = centreline of the cylinder) with target radius a = 3sigma = 1.5mm......and then repeated it with more material around the heated part of the cylinder a b Approximation !!! But, stress is maximal along the beam (centreline).

a b It looks like oscillation around 'quasi-static' stress value (with much smaller amplitude than for b=0 case) End of pulse Characteristic time ~ 2b / speed of sound Pbar energy density conditions Temperature rise (peak) = 500 K Origin of damage? Stress absolute value or “tension-compression” oscillations or both?

Neutrino Factory case 'quasi-static' stress value + reflected “shock wave” every t_char (for 2b = 10a = 10cm it is ~ 33 us) this cannot be avoided......but the first peak (usually the highest one) is reduced End of pulse If both preferable situation when having more material! Let's say cross-section of toroid to be bigger than 1cm in radius (if heated area has 1cm radius) or smaller beam sigma!

Neutrino Factory case stress is higher at a when additional material is present... a b it is radially constrained 'plateau' – new equilibrium position corresponds to quasi-static stress

Neutrino Factory case stress reduction because of longer macro-pulse (~5x) stress reduction because of additional material (~ 2x) 'Elimination' of the first peak, definitely! Maybe, tests at FNAL with different target dimensions (heights)? Is it a bigger toroid a problem?

Neutrino Factory case Stress pattern dependence on material parameters values (Yield stress in this case) Need for experiments to determine material model data Current pulse through wire!

fitting formula: Details, progress, etc... see URL: Target Studies Thermal Shock Simulations Extraction of material data (first steps)

Summary: Simulations: Non-negligible stress reduction in the NF targets by varying the macro-pulse length and target/beam dimensions looks possible Experiments needed for better understanding of the material behavior (properties) Tests: Possible Pbar target tests have problems with diagnostics but some qualitative picture about the damage as a function of target dimensions/energy density can be obtained (hopefully) Current pulse – wire test