Simulation of a LINAC RF Simulation of a LINAC RF station station - - PowerPoint PPT Presentation

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Simulation of a LINAC RF Simulation of a LINAC RF station station - - PowerPoint PPT Presentation

Oct 14, 2023 213 likes •453 views

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

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SLIDE 1

Julien Branlard – 11/20/2008 1/23

Simulation of a LINAC RF station Simulation of a LINAC RF station

  • J. Branlard, B. Chase

FNAL, AD/RF department

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SLIDE 2

Julien Branlard – 11/20/2008 2/23

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 QL, Pfwd, ψ for all cavities ? – Enough klystron power ?

  • HINS:

– High power vector modulators (bw & slew rate limitations) – Mixing NC and SC cavities (for 1 klystron) ?

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SLIDE 3

Julien Branlard – 11/20/2008 3/23

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
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SLIDE 4

Julien Branlard – 11/20/2008 4/23

Simulation Model Simulation Model

Standard RLC cavity model: Klystron FF SP table/FB loop: A/Φ α1/ϕ1 α2/ϕ2 Δω1/QL1 Δω2/QL2 Δωn/QLn

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SLIDE 5

Julien Branlard – 11/20/2008 5/23

Solving the RLC electrical model of a cavity 2nd order differential equation 1st order solution to the equation above: Vcav = (Vr + j.Vi) is a function of the cavity detuning Δω, the cavity half bandwidth ω1/2, the cavity loaded resistance RL and the current inside the cavity It = Ig + Ib = (Ir + j.Ii)

Simulation Model Simulation Model

* “Vector Sum Control of Pulsed Accelerating Fields in Lorentz Force

Detuned Superconducting Cavities” , T. Schilcher PhD Thesis, 1998

*

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SLIDE 6

Julien Branlard – 11/20/2008 6/23

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

  • v/ILC-public/DocDB/DocumentDatabase

/DocumentDatabase

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SLIDE 7

Julien Branlard – 11/20/2008 7/23

Cavity fill time and beam compensation Cavity fill time and beam compensation

interrupt cavity fill and use the beam loading to

  • btain flat top

let cavity reach steady state use FF A/Φ modulation to compensate for beam loading

CAVITY BEAM

PFWD

CAVITY BEAM CAVITY BEAM

PFWD PFWD

during steady state during transient

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SLIDE 8

Julien Branlard – 11/20/2008 8/23

  • each cavity has its own: Q0, V0, Φs, ψ, QL
  • Pfwd

A/Φ modulation is unique to each cavity

  • using one FVM for each cavity

A Re { } Im { } Gf

Beam loading compensation: Approach A Beam loading compensation: Approach A

2

4 2

π θ θ + + − = Φ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = 2 cos

4 2

θ θ A 1 ≤ ≤ A π π + ≤ Φ ≤ −

Using high power ferrite vector modulators (FVM)

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SLIDE 9

Julien Branlard – 11/20/2008 9/23

HINS with FVM: individual Cavity Feedback Control HINS with FVM: individual Cavity Feedback Control

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SLIDE 10

Julien Branlard – 11/20/2008 10/23 Beam current Ibo = 20 mA

  • “warm” cavity QL ~ 5000
  • rise time τ ~ 30 usec
  • beam arrival during steady state
  • slow FVM response time

+1%

  • 1%

HINS with FVM: simulation results HINS with FVM: simulation results

  • ramping beam over 50 μsec
  • anticipate FVM response
  • introduce pole cancellation
  • ability to regulate beam loading

±1% amplitude

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SLIDE 11

Julien Branlard – 11/20/2008 11/23

Amplifier request for beam compensation Amplifier request for beam compensation

22 x 15V = 330V

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SLIDE 12

Julien Branlard – 11/20/2008 12/23

Using FF klystron amplitude and phase modulation

Beam ON Beam ON Beam OFF Beam OFF Icav Igen

ψ

ψ = cavity detuning angle Assuming nominal beam loading, there is no need to modulate the klystron forward power using the ferrite vector modulator if Itot(beam OFF) = Itot(beam ON) Icav Ibeam Ibeam Igen Itot

Φ Φs

Igen(beam) = Igen(no beam) x AeiΦ

Φs

Itot No dynamic use of FVM

Beam loading compensation: Approach B Beam loading compensation: Approach B

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SLIDE 13

Julien Branlard – 11/20/2008 13/23

A, Φ α1 , ϕ1

ψ1 ψ2 ψN

α2 , ϕ2 αN , ϕN

HLRF

Find each cavity’s unique α, ϕ, ψ and QL

Using FF klystron amplitude and phase modulation Beam loading compensation: Approach B Beam loading compensation: Approach B

dynamic set once adjustable

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SLIDE 14

Julien Branlard – 11/20/2008 14/23

18 normal conducting cavities Cavity 12 is matched (Pref = 0 ) A = 1.25 , Φ = 10° Total Pfwd = 480 kW Total Pref = 6.85 kW

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SLIDE 15

Julien Branlard – 11/20/2008 15/23

Verification using a time dependent simulation HINS – 18 cavity warm section

Using FF klystron amplitude and phase modulation Beam loading compensation: Approach B Beam loading compensation: Approach B

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SLIDE 16

Julien Branlard – 11/20/2008 16/23

Matched cavity

Power analysis

Steady state power during beam loading Power variations during a pulse

Using FF klystron amplitude and phase modulation Beam loading compensation: Approach B Beam loading compensation: Approach B

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SLIDE 17

Julien Branlard – 11/20/2008 17/23

Introducing variations in detuning (δω) and in loaded Q (δQL ) Introducing variations in detuning (δω) and in loaded Q (δQL )

δω = 2π x 2.5kHz (~6%) δQL = 500 (~12%)

vector sum amplitude error: 2% vector sum phase error: 0.5°

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SLIDE 18

Julien Branlard – 11/20/2008 18/23

0.008% peak-to-peak 0.006° peak-to-peak

with PI feedback KP = 1.5 KI = 106

18 cavity vector sum set point 18 cavity vector sum set point

2% error 0.4° error

no feedback

Introducing feedback Introducing feedback

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SLIDE 19

Julien Branlard – 11/20/2008 19/23

FB is on Vsum only Individual cavities might still show beam loading

Introducing feedback Introducing feedback

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SLIDE 20

Julien Branlard – 11/20/2008 20/23

beam ON (900 usec) Fill time ~ 600-700 usec Total Pfwd = 2.5 MW Total Pref = 620 kW Pref matched for cavity #12

warm cold warm cold

Mixing warm and cold cavities Mixing warm and cold cavities

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SLIDE 21

Julien Branlard – 11/20/2008 21/23

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
  • ne klystron
  • Simulations can predict:

– individual / optimal QL, PK, ψ settings – required PFWD , expected PREF – 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
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SLIDE 22

Julien Branlard – 11/20/2008 22/23

Conclusions and Suggestion for HINS Conclusions and Suggestion for 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

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SLIDE 23

Julien Branlard – 11/20/2008 23/23

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