energy modulation in linac 4: some preliminary results

Energy Modulation in Linac 4: Some Preliminary Results

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

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

The Klystron Model

2010-05-27 2A. K. Bhattacharyya - Energy

Modulation in LINAC 4

Klystron Transfer Function

Done at reduced power. Maximum power output from klystron 100 KW

Experimental Setup




ExperimentalData

Transfer functionequation

Number of poles

Number of zeros

+-

OptimizerNormerror

Algorithm:

Input is only the expected number of poles and zeros




Transfer function in RFTransfer function

Error: 10%

Number of poles: 14Number of zeros: 18



Klystron Transfer FunctionTransfer function in IQHs(jω) = 1

2H(jω+jω0) + H(jω-jω0) Hc(jω) =-12jH(jω-jω0) - H(jω+jω0)

ω0 = 352.2 MHz

Transfer function from II/QQ Transfer function from IQ/QI

Error: 18%Error: 4%Number of poles: 12Number of zeros: 17

Number of poles: 22Number of zeros: 22



Klystron Gain ModulationThe gain modulation of the Klystron with respect to the input power has to be scaled so that the characteristics remain same but the Klystron saturates for an input of 0 dBm.

Method for scaling:

Find point (Ρi,Gi) where Klystron saturates from experimental data.

Let saturation limit of klystron be Psat.ÞGain at saturation has to be 10log10(Psat /1 mW ).ÞGains from experiments are scaled such that Gi = 10log10(Psat /1 mW ).ÞUsing Z0=50Ω find voltage for Klystron saturation Voutsat=√(2PsatZ0).ÞVinsat=Voutsat/10(Gi/20).ÞScale x-axis such that Pi is equal to Vinsat.

Experimental data



Closed loop simulation

Klystron Simulation Model





Klystron Tuner Loop

Model/Simulation Parameters

ZTT = 23.1 MΩL = 1.3 mQL = 7100Q0 = 17000Φ = -20°Z0 = 50 Ω

Beam coupling = ZTT * L * QL

Q0

Cavity Gain = QL

Q0

√((Q0-QL)*2*ZTT*L)√(QL*Z0)

Triangular output voltage in the cavity 1 with Vmin = 4.08 MV and Vmax = 5.36 MVTriangular phase modulation in cavity 12 with swing from -81.45° to 81.45° and voltage of 0.7 MV ± 25%.Time periods: 20 μsec and 40 μsec.



PIMS 11/12

ZTT = 23.1 MΩL = 1.55 mQL = 6000/8000/1200Q0 = 19227Φ = -20°Z0 = 50 Ω

Debunching

Results

Gain characteristics for Psat=1.1 MW

Gain characteristics for Psat=1.3 MW



Results: Voltage Modulation Beam current: 40 mA Saturation power: 1.1 MW (10.488 kV)



A. K. Bhattacharyya - Energy Modulation in LINAC 4 162010-05-27

Results: Debuncher Beam current: 40 mA Saturation power: 1.1 MW (10.488 kV) Q = 6000


Results: Debuncher

Simplifications made No delay in the loop (in reality there is a total loop

delay of 1100 ns) Cavity model has single peak in frequency response Cavities on tune for PIMS and detuned for Debuncher

These simplifications allow the controller gain to be pushed so that effective control can be obtained.However this is not real and hence will call for some sophisticated control strategy.



Scopes of improvement Large error in Klystron transfer function estimation (18%), in

spite of quite a large number of poles and zeros. Hence, use of fractional order systems, proposed as virtually an infinite number of poles and zeros can be tackled with a finite number of parameters.

Inclusion of delays in the loop, and tuning of PID controller to achieve optimal performance.

Inclusion of noise model from HV power supply. Inclusion of observer in feed back loop to reduce noise. Design and comparison of various predictive schemes for

control The non-linearity in the system provides opportunity to design

and implement non-linear control strategies.



Thank You



energy modulation in linac 4: some preliminary results

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