Dynamics of Liquid Metal Jets Penetrating a Strong Magnetic Field in High-power Colliders

One very important problem of future high-power colliders, such as the muon collider, is to create an effective and reliable target system that is able to withstand a harsh environment and generate effective high-flux muon beams. Liquid metal jets (pulsed or continuous) are proposed as potential target candidates. Such a proposal poses two critical problems: penetration of a free liquid jet inside the required strong inhomogeneous magnetic field (20 T) and the fragmentation of liquid due to the intense sudden heating by the proton beam and the resultant magnetohydrodynamic instabilities. In this study, we analyzed the dynamic motion of a free liquid metal jet entering a strong inhomogeneous field by using a new two-dimensional numerical model implemented in the HEIGHTS package for arbitrary jet parameters. INTRODUCTION To realize a μ+μcollider, high-Z targets are necessary [1]. Solid targets made from tungsten, platinum, or lead would be a good choice, but the heat load could not be easily removed and the stresses from thermal-shock wave propagation can seriously damage the target. Therefore, more sophisticated targets, such as a tungsten powder flow or rotating band, are suggested [1]. Rapidly flowing liquid metal targets have been considered an option because the heat energy can be removed along with the moving liquid [1]. Theoretical and experimental studies of liquid metal target flow in magnetic field are underway. There are mainly three important problems of using liquid metal targets in these environments. First, as the liquid jet penetrates the magnetic field of the cylindrical coil, perturbations in jet motion and deceleration can because of the large field gradients at the entrance and exit of the solenoid and because of J x B forces [2]. Second, during the intense pulse of energy deposited in a short time (a few ns), the strong resultant stress waves could damage the target and adjacent components [3]. Third, the liquid jet can develop instabilities during both liquid motion in the strong inhomogeneous magnetic field and after beam energy deposition because of RayleighTaylor and magnetohydrodynamic (MHD), balloon mode, instabilities. These instabilities can change the jet shape into a significantly less efficient target for pion production. Tolerance to capillary instabilities can be achieved by an improved nozzle shape that has been proved experimentally for lithium and water jets [4]. 2 BEAM/TARGET SYSTEM The parameters of the proton beam and solenoid coil system are determined by the required conditions of pion and muon production rates [1]. Basic system parameters consist of a proton energy Ep = 16 GeV, number of protons in one bunch Np ≈ 10 , bunch beam power of 280 kW, with frequency f = 15 Hz and total power of 4 MW. Only 10% of the beam power is absorbed inside the target. The solenoid has a length Lcoil = 20 cm, radius Rcoil = 10 cm, and a maximum magnetic field Bo = 20 T. The beam arrives at an angle αbeam = 100 millirad and interacts with the liquid jet of radius Ro ≈ 0.5 cm, coming at an angle αjet = 67 millirad; therefore, the angle between the beam and the jet is α = αbeam αjet = 33 millirad = 1.89 °, as schematically shown in Fig. 1. Liquid metal jet proton beam coil