Longitudinal instability for a purely inductive wake function.
A purely inductive wake function was the only known case where a solution of the Haissinski equation did not exist beyond a certain threshold. This is due to the ill-defined treatment of the wake function. The solution is proved to exist beyond the threshold, if we define the wake function physically. The threshold of the stability for the solution exists but is lower than the former "threshold."
Shobuda
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Y
KEK, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan.
Hirata
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