The injection of laser-generated protons through conventional drift tube linear accelerators (linacs) has been studied numerically. For this, we used the parameters of the proton source produced by ultraintense lasers, i.e., with an intrinsic high beam quality. The numerical particle tracing code PARMELA [L. M. Young and J. H. Billen, LANL Report No. LA-UR-96-1835, 2004] is then used to inject experimentally measured laser-generated protons with energies of 7+-0.1 MeV and rms un-normalized emittance of 0.180 mm mrad into one drift tube linac tank that accelerated them to more than 14 MeV. The simulations exhibit un-normalized emittance growths of 8 in x direction and 22.6 in y direction, with final emittances lower than those produced using conventional sources, allowing a potential luminosity gain for the final beam. However, the simulations also exhibit a limitation in the allowed injected proton charge as, over 0.112 mA, space charge effect worsens significantly the beam emittance

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