After review of the timing diagram (shown as the left schematics), we decided to adjust the time delay between the firing angle and the thyratron firing.
The scope traces are shown below. The lower trace shows that the charging current pulses are nearly constant in amplitude. This does not lead to constant power charging of the capacitors as evidenced by the exponential rise of the voltage in the middle trace. This exponential rise is further aggravated by the fact that the firing angle of the top trace is decaying in time whereas it should be probably be increasing in time.