Energy Modulation in LINAC 4

Reported by Anirban Krishna Bhattacharyya CERN-BE-RF-FB

Anirban Krishna Bhattacharyya, Philippe Baudrenghien CERN-BE-RF-FB

Model/Simulation Parameters

ZTT = 22.2 MΩ/mL = 1.548 mQ0 = 20100β = 2.1Φ = 90°Z0 = 50 Ω

Debunching

ZTT = 25.5 MΩ/mL = 1.54 m/1.524 mQ0 = 20000β = 1.2Φ = -20°Z0 = 50 Ω

Module 11/12

Triangular phase modulation in debunching cavity with swing from -71.5° to 71.5°, -81.45° to 81.45° and -112° to 112° each with a voltage of 0.7 MV ± 25%.Time periods: 20 μsec.Beam currents: 20 and 40 mA.

Triangular amplitude modulation in PIMS 11/12 with swing from 4.08 MV to 5.36 MV.Time periods: 20 μsec.Beam currents: 20 and 40 mA.

Klystron saturation limits are 1.1 MW, 1.3 MW and 75 KW respectively

Psat

Start-up conditions300 μsec are allowed for Low Level RF (LLRF) loops stabilization. The sequence leading to beam injection is as follows:

• Filling of cavity open-loop using feed forward set point (SPFF ) for 50 μsec. This set point can be computed from the saturation power of the klystron and is given by

For the first 10 μsec of the process the feed forward set point value is ramped from 0 to SPFF .•The feed back is then switched on and for 50 μsec the loop gains Kp and Ki are ramped to the desired values. The job of the controller is thus to follow the cavityvoltage set point by correcting for the error produced by the feed forward set point.•After 200 μsec the beam is injected.

SPFF=Vcav

1mW

Controller GainsThe loop has a delay of 1.1 μsec arising from computation and cable lengths. This limits the gains of the controller.The Nyquist plots of the loop transfer function are shown below .

Controller GainsGain margin ~ 10 dBPhase margin ~ 60°

Loop gain = 3Corner frequency = 35 KHz.

Debuncher: Icav = 20 mA, ±71.5°

Debuncher: Icav = 20 mA , ±71.5°

Debuncher: Icav = 20 mA , ±71.5°

Debuncher: Icav = 20 mA , ±71.5°

Debuncher: Icav = 20 mA , ±81.45°

Debuncher: Icav = 20 mA , ±81.45°

Debuncher: Icav = 20 mA , ±81.45°

Debuncher: Icav = 20 mA , ±81.45°

Debuncher: Icav = 20 mA , ± 112°

Debuncher: Icav = 20 mA , ± 112°

Debuncher: Icav = 20 mA , ± 112°

Debuncher: Icav = 20 mA , ± 112°

Debuncher: Icav = 40 mA , ±81.45°

Debuncher: Icav = 40 mA , ±112°

PIMS 11/12: Icav = 20 mA, Psat = 1.1MW

PIMS 11/12: Icav = 20 mA, Psat = 1.1MW

PIMS 11/12: Icav = 20 mA, Psat = 1.1MW

PIMS 11/12: Icav = 20 mA, Psat = 1.1MW

PIMS 11/12: Icav = 20 mA, Psat = 1.3MW

PIMS 11/12: Icav = 40 mA, Psat = 1.3MW

Conclusions•For a period of 20 μsec the klystron for the debuncher goes into saturation with a limit of 75 KW.•For PIMS 11/12 the saturation is avoided with a cavity current of 20 mA anda saturation limit of 1.3 MW.•Saturation can be avoided in all cases for a period of 40 μsec (results presentedin previous meeting)•Due to the delay the controller gain has to be limited which limits the ability totrack the set points. This needs to be corrected by the adaptive feedforward.•The controller gains can be pushed higher by taking into consideration the differential gain of the loop around the operating point set by the feedforward.