The acceleration which increases the speed is provided by an electric force ##F_E=qE##. Since ##q## of a particle is small, in order to have a strong ##F_E## you need strong electric field ##E##. But there are limits to how strong an electric field can be generated, and this limits the acceleration. So, to reach the high speed you need more time, that is more distance. This distance can be either a long line, or a circle that is traversed multiple times. To make the trajectory a circle you need a centripetal force that is provided by a magnetic force ##F_B = q(v \times B)##, but this is also limited by the maximum strength of the magnetic field ##B## provided by the superconducting magnets, so the circle has a large radius.