The muon source with small phase-space produced from the compressed target for muon-muon collider

For the muon-muon collider, we proposed using a target compressed by high intensity laser or heavy-ions irradiation, to collect the pions produced in very small phase-space and then to cool them by another high intensity laser in the PAC 97. Although the pions are produced initially with small phase space, they will be spread transversely in a short time because of their large transverse momentum; consequently a broad high-intensity laser irradiation is needed to collect and accelerate them, and thus the process is not economical. To keep the transverse dimension small, a high solenoidal magnetic field is needed. This field can be created using circularly polarized laser irradiation to the target´s surface. A magnetic field of mega-tesla order of magnetic field can be created by the laser intensity of 10¹⁵ watt/cm² , using approach developed Eliezer (1995); the Lahmer radius of the produced pions becomes less than 0.01 mm, and they can be accelerated by another laser irradiation while in this confined state. Since the target is compressed at not a high temperature, the energy required for this compression is much smaller the inertial confinement fussion-device, and the higher density reduces the target´s mass. This approach is more effective than the one used in the RF field for producing cold muons. This approach also can be applied for anti-baryon production