Simulation of a LINAC RF Simulation of a LINAC RF station station J. Branlard, B. Chase FNAL, AD/RF department Julien Branlard – 11/20/2008 1/23
Introduction Introduction System consists of one klystron for many cavities • Motivations: – How to handle cavities with different gradient ? – Can a flat top vector sum be achieved ? Which gradient ? – How to choose Q L , P fwd , ψ for all cavities ? – Enough klystron power ? • HINS: – High power vector modulators (bw & slew rate limitations) – Mixing NC and SC cavities (for 1 klystron) ? Julien Branlard – 11/20/2008 2/23
Outline Outline • Introduction: need for simulations, scope of this study • Model description and parameters • Compensate for beam loading during steady state � with high power vector modulator � using only klystron amplitude and phase modulation • Mixing warm and cold cavities � simulation of the entire RF section � power analysis • Conclusions Julien Branlard – 11/20/2008 3/23
Simulation Model Simulation Model Standard RLC cavity model: Klystron FF SP table/FB loop: α 2 / ϕ 2 α 1 / ϕ 1 Δω 2 /Q L2 Δω n /Q Ln Δω 1 /Q L1 A/ Φ Julien Branlard – 11/20/2008 4/23
Simulation Model Simulation Model * Solving the RLC electrical model of a cavity � 2 nd order differential equation 1 st order solution to the equation above: V cav = ( V r + j. V i ) is a function of the cavity detuning Δω , the cavity half bandwidth ω 1/2 , the cavity loaded resistance R L and the current inside the cavity I t = I g + I b = ( I r + j. I i ) * “Vector Sum Control of Pulsed Accelerating Fields in Lorentz Force Detuned Superconducting Cavities” , T. Schilcher PhD Thesis, 1998 Julien Branlard – 11/20/2008 5/23
MATLAB simulation code MATLAB simulation code Available for download from the ILC database: doc # 481 (zipped Matlab files) Related paper: ILC DB doc # 480 http://docdb.fnal.g http://docdb.fnal.gov/ILC-public/DocDB ov/ILC-public/DocDB/DocumentDatabase /DocumentDatabase Julien Branlard – 11/20/2008 6/23
Cavity fill time and beam compensation Cavity fill time and beam compensation during steady state during transient CAVITY CAVITY CAVITY BEAM BEAM BEAM P FWD P FWD P FWD use FF A/ Φ let cavity reach interrupt cavity modulation to steady state fill and use the compensate for beam loading to beam loading obtain flat top Julien Branlard – 11/20/2008 7/23
Beam loading compensation: Approach A Beam loading compensation: Approach A Using high power ferrite vector modulators (FVM) each cavity has its own: Q 0 , V 0 , Φ s , ψ , Q L • A/ Φ modulation is unique to each cavity • P fwd Im { } G f • using one FVM for each cavity A Re { } θ − θ ⎛ ⎞ = A cos ⎜ 2 4 ⎟ ≤ A ≤ 0 1 ⎝ 2 ⎠ − π ≤ Φ ≤ + π θ + θ + π Φ = − 2 4 2 Julien Branlard – 11/20/2008 8/23
HINS with FVM: individual Cavity Feedback Control HINS with FVM: individual Cavity Feedback Control Julien Branlard – 11/20/2008 9/23
HINS with FVM: simulation results HINS with FVM: simulation results +1% -1% Beam current I bo = 20 mA • ramping beam over 50 μ sec • “warm” cavity Q L ~ 5000 • rise time τ ~ 30 usec • anticipate FVM response • beam arrival during steady state • introduce pole cancellation • ability to regulate beam loading • slow FVM response time ±1% amplitude Julien Branlard – 11/20/2008 10/23
Amplifier request for Amplifier request for beam compensation beam compensation 22 x 15V = 330V Julien Branlard – 11/20/2008 11/23
Beam loading compensation: Approach B Beam loading compensation: Approach B Using FF klystron amplitude and phase modulation I gen I beam Φ s I gen Φ I tot I tot ψ I cav I cav Φ s I beam ψ = cavity detuning angle I gen (beam) = I gen (no beam) x Ae i Φ � No dynamic Beam OFF Beam ON Beam OFF Beam ON use of FVM Assuming nominal beam loading, there is no need to modulate the klystron forward power using the ferrite vector modulator if I tot (beam OFF) = I tot (beam ON) Julien Branlard – 11/20/2008 12/23
Beam loading compensation: Approach B Beam loading compensation: Approach B Using FF klystron amplitude and phase modulation � Find each cavity’s unique α , ϕ , ψ and Q L α 1 , ϕ 1 α 2 , ϕ 2 α N , ϕ N set once HLRF A, Φ ψ N ψ 2 ψ 1 dynamic adjustable Julien Branlard – 11/20/2008 13/23
18 normal conducting cavities Cavity 12 is matched ( P ref = 0 ) A = 1.25 , Φ = 10 ° Total P fwd = 480 kW Total P ref = 6.85 kW Julien Branlard – 11/20/2008 14/23
Beam loading compensation: Approach B Beam loading compensation: Approach B Using FF klystron amplitude and phase modulation � Verification using a time dependent simulation HINS – 18 cavity warm section Julien Branlard – 11/20/2008 15/23
Beam loading compensation: Approach B Beam loading compensation: Approach B Using FF klystron amplitude and phase modulation � Power analysis Matched cavity Steady state power during beam loading Power variations during a pulse Julien Branlard – 11/20/2008 16/23
Introducing variations in detuning ( δω ) and in loaded Q ( δ QL ) Introducing variations in detuning ( δω ) and in loaded Q ( δ QL ) δω = 2 π x 2.5kHz (~6%) δ Q L = 500 (~12%) vector sum amplitude error: 2% vector sum phase error: 0.5 ° Julien Branlard – 11/20/2008 17/23
Introducing feedback Introducing feedback no feedback 0.4 ° error 2% error 18 cavity vector sum 18 cavity vector sum set point set point with PI feedback K P = 1.5 0.006 ° peak-to-peak 0.008% peak-to-peak K I = 10 6 Julien Branlard – 11/20/2008 18/23
Introducing feedback Introducing feedback FB is on V sum only � Individual cavities might still show beam loading Julien Branlard – 11/20/2008 19/23
Mixing warm and cold cavities Mixing warm and cold cavities cold warm beam ON (900 usec) Fill time ~ 600-700 usec Total P fwd = 2.5 MW Total Pref = 620 kW P ref matched for cavity #12 cold warm Julien Branlard – 11/20/2008 20/23
Conclusion Conclusion • Development of a powerful simulation tool • Multi-cavity steady-state and transients analysis is possible • Investigation of issues associated with driving many cavities with one klystron • Simulations can predict: – individual / optimal Q L , P K , ψ settings – required P FWD , expected P REF – FVM required characteristics to meet specs for gradient and phase stability • Warm and cold cavities use up to 2.5 MW of power without FVM Julien Branlard – 11/20/2008 21/23
Conclusions and Suggestion for Conclusions and Suggestion for HINS HINS • Issues with using the klystron as an un-modulated RF power source and using FVMs as the only modulator for both feedback and feedforward with a step function of beam current – Feedback BW and gain are limited by the FVM – Feedforward correction is limited by FVM slew rate – Meeting vector regulation specifications over the full beam time is not possible • Ramping up the beam current over 50 microseconds may allow regulation but will push the system to the limit • By proper choice of cavity detuning and power coupling, it is possible to obtain perfect beam loading compensation for all cavities using klystron RF vector modulation – FVM slew rate requirement could be relaxed – FVM BW may be able to be increased – better for FB Julien Branlard – 11/20/2008 22/23
Issues with Mixing NCRF and SCRF within a single RF System • It appears that power requirements for all 47 cavities come close to the 2.5 MW for the klystron – This is only made worse by adding the losses of the FVM (2dB?) – Fill time is long in our simulations so far – Microphonics and LFD will complicate the picture • All cavities driven by one klystron does not look promising at this time Julien Branlard – 11/20/2008 23/23
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