在直线坐标系\(xoy\)中,曲线\(C_{1}\)的参数方程为\(\begin{cases} & x=a\cos t \\ & y=1+a\sin t \end{cases}(t\)为参数,\(a > 0)\)。在以坐标原点为极点,\(x\)轴正半轴为极轴的极坐标系中,曲线\(C_{2}\):\(ρ=4\cos θ\).
\((1)\)说明\(C_{1}\)是哪一种曲线,并将\(C_{1}\)的方程化为极坐标方程;
\((2)\)直线\(C_{3}\)的极坐标方程为\(θ=α_{0}\),其中\(α_{0}\)满足\(\tan α_{0}=2\),若曲线\(C_{1}\)与\(C_{2}\)的公共点都在\(C_{3}\)上,求\(a\)。