Precise calculation of traveling-wave periodic structure

The effects of the round edge beam hole on the frequency and wake field are studied using variational method, which allows for rounded iris disk hole without any approximation in shape treatment. The frequency and wake field of accelerating mode and dipole mode are studied for different edge radius cases, including the flat edge shape that is often used to approximately represent the actual structure geometry. The edge hole shape has weak effect on the frequency, but much effect on the wake field. Our study shows that the amounts of wake fields are not precise enough with the assumption of the flat edge beam hole instead of round edge.