Muon Beam Design And Low Energy Muon Experimental Set-Up Study Based On The Proton Accelerator

Since the discovery of muon tracks in cosmic rays, the research and the applica-tion of muons attracted scientists’attention gradually. Muons in cosmic rays are of low intensity, very energetic and uncontrollable, these characteristics limit the research of the muon science. With the development of the proton accelerator and the discov-ery of the basic properties of muons, high-intensity muons have played an important role in the research of particle physics, materials science, life science. Spin polarized muons are used as magnetic probes in the condensed matter, this method is named as the μSR (muon spin rotation/relaxation/resonance) technique. The basic principle of the μSR technique is as follows:when the spin polarized muons stop in the sample, the muon spins can interact with the local magnetic field where muons stay, then de-cay to positrons, these positrons are emitted preferentially along the spin direction of the muons due to the parity violating decay. By measuring the spatial and temporal characteristics of the anisotropic distribution of these decay positions, one can deter-main the magnetic information of the materials. The high-intensity polarized muons are achieved by the high-power proton bombarding the graphite target. Protons can produce pions when they interact with the nucleus of the target. Muons produced by the rest pions called surface muons with momentum of 29.8 MeV/c and high spin polar-izability-100%. Muons which obtained by the decay of the pions in flight have a lower spin polarizability than surface muons, these muons are called decay muons. The spin polarizability of these muons can be higher (about 70%) when they are collected with an appropriate momentum selection. These two kinds of muons are energetic (MeV) and used to study the properties of bulk materials. By moderating surface muons, low energy muons (keV) can be achieved, these muons can study nano-materials, thin-film materials, the surface of the sample and so on. High-intensity muons are necessary for low energy muons because of the low moderation effeciency, and they are also necessay for small beam spot muons and micro muon beams by the collimation method.The monte carlo simulation softwares and matrix multiplication computer soft-wares are used to study the muon beam design based on the proton accelerator and related research in this thesis. China Spallation Neutron Source (CSNS) is a high beam power proton accelerator complex, it is composed of a linac and a rapid cycling syn-chrotron and can accelerate the proton to the energy of 1.6 GeV with power of 100 kW at the first phase. In this thesis, a high-intensity pulsed muon beam line was proposed using superconducting solenoids to collect and transport muons based on CSNS. The highest-intensity continuous muon sources were developed at Paul Scherrer Institute (PSI) in Switzerland. PSI also constructed a low energy muon (-keV) beam in the world, it is the only low energy muon beam that can provide μSR meansurements. The micro-muon beam can study the extremely small samples (beam size<1 mm2) and for a position sensitive μSR technique; so PSI considers to construct a micro-muon beam line. The magnetic field and electric field applied at the experiment area are for the μSR meansurements and to accelerate/decelerate the muon energy, respectively. But these applied magnetic and electric fields can influence the muon beam spot at the experiment area and these effects of the external fields to the beam spot are analyzed in this thesis. The methods to reduce the beam size are also given. As mentioned before, the high spin polarizability is very important for surface muons, the effect that the magnetic field of the superconducting solenoids to the surface muon spin polarizability is also studied.The main achievements in this thesis are shown as follows:1) The superconducting solenoid collect system was desgined to achieve high-intensity pulsed muons based on CSNS. Geant4 and Fluka were used to simulate the momentum distribution of muons and pions of low Z (Be and Graphite)and high Z ( Ni and Cu) target materials. The production rates of surface muons and pions with different momenta and the angle distributions of these particles’momenta to the proton beam were calculated using Geant4. The energy deposition distributions in four differ-ent target materials were simulated by Fluka. The graphite is the best target material to produce muons and pions according to these results. The superconducting solenoid collect and transport system was proposed based on the layout of the High Energy Pro-ton Experimental Area (HEPEA) at CSNS. The surface and decay muon phase space distributions were calculated by G4beamline at the exit of the decay solenoid. Using these phase space parameters as an initial beam source, the envelops of the surface and decay muons after the decay solenoid were simulated by TRANSPORT. Finally, the phase space distributions and production rates of surface and decay muons were given by TURTLE at the experiment areas.2) The first continuous micro muon beam line was proposed at the πE3 beamline of PSI. As a first step, the focus of the two quadrupole triplets was studied by TRANS-PORT and TURTLE with different kinds of inital muon beam spots. The simulation resluts showed that the angular divergence and beam size of the inital beam influence the micro muon beam transmission. The angular divergence of the inital beam has a stronger influence than the beam size. According to the Liouville theorem, the muon beam should better be close to a parllel beam and of a larger beam size before the pair of quadrupole triplets. After beam optics simulation optimization, the total πE3 beamline has a transmission efficiency of 10-4～-5 at the area of 200×200μm2 at the sample position. The intensity at the experimental area of the micro beam is about 103/s or 104/s, which can be used to measure samples.3) The effects of the applied longitudinal/transverse magnetic and electric fields at the sample to the beam spot were studies at low energy muon beam of PS I. External magnetic fields at the sample are necessary for transverse and longitudinal field μSR experiments. An electric field along the muon momentum can be applied to acceler-ate/decelerate the muons to different energies (0.5～30keV) at the sample to investi-gate materials at different depths. These external fields can affect the beam spot at the sample position, which has been analysed using the Monte Carlo toolkit Geant4. These effects on the beam spot can be minimized reduced significantly by optimizing settings of the conical lens before the sample through simulation analysis. The present LEM beam has a relatively large beam spot at the sample position, where in routine operation beam sizes with root-mean-square (RMS) values in x and y of about 6 mm are achieved. This practically limits the application of LEM to sample sizes of 1 cm2. As a first step to overcome these limitations we present beam transport simulation results using Geant4 to investigate several options to generate a smaller beam spot. We studied in detail the effect of the muon start detector-where the muons pass through a 10-nanometer-thin carbon foil-on the beam spot. Without the detector the RMS values of the beam spot can be reduced to 3.5～4.0 mm. Additionally, beam collimation before the start detec-tor and at the source of the low energy muon beam (a cryogenic moderator target) were considered to reduce the beam size.4) The spin polarizability and production rates of the surface muons collected by the superconducting solenoid were studied. Muons precess around the magnetic field, the radial components of the magnetic field of the solenoid can influence the spin direction of muons. The spin polarizability and production rates were calculated by G4beamline with different target lengths, solenoid magnetic fields and angles (0) be-tween the target and the solenoid axes. The results showed that the solenoid magnetic field could reduce the surface muon spin polarizability by about 5%, it has little influ-ence on the surface muon experiments. To achieve high-intensity surface muons, the target length should better be larger than 350 mm, the capture solenoid magnetic field should be larger than 4 T and the best θ is larger than 20°. The surface muon focus in the solenoid was aslo simulated, the radial component of the solenoid magnetic field is low, so it almost could not influence the surface muon spin polarizability. Large magnetic fields can make a better focus for surface muons, the simulation result shows that the transport solenoid magnetic field should be larger than 2 T.