Field and Phase Error Studies in Normal Conducting Structures

LLRF and Beam Dynamics in Hadron Linacs – EuCARD2 Workshop

Ciprian Plostinar01.06.2015

Overview

• Context• Projects• Structures• Errors Studies• Conclusions• Acknowledgements

Context

• HIPPI – High Intensity Pulsed Proton Injectors– European R&D collaboration aimed at developing a

common European technology base for the construction of high intensity hadron linacs

– Completed in 2008– Linac4, FAIR Proton Injector, ISIS Upgrade Linac.– Several WP, including beam dynamics and cavity

development. – Comparative assessment of several structures

• Work extended to include SNS and J-PARC

Projects – Linac4

Ion Species H-

Output Energy 160 MeVFrequency 352.21 MHzPulse Length 0.4 msPeak Current 40 mAProtons per Pulse 1.0 x 1014

Repetition Rate 2 HzDuty Cycle 0.08 %Average Beam Power 5.1 kWAccelerating Structures RFQ, DTL, CCDTL, PIMS (*CCL)Accelerator Length ~80 m

Projects – ISIS Linac

Ion Species H-

Output Energy 180 MeV Frequency 324/648 MHz Pulse Length 0.1 – 1 ms Peak Current 60 mA Repetition Rate 50 Hz Duty Cycle 0.5 – 5 % Average Beam Power 54 - 540 kW Accelerating Structures RFQ, DTL, CCL Accelerator Length ~99 m

Projects – FAIR Proton Injector

Ion Species ProtonsOutput Energy 70 MeVFrequency 325.244 MHzPulse Length 36 μsPeak Current 35 mAProtons per Pulse 7.88 x 1012

Repetition Rate 4 HzDuty Cycle 0.0144 %Average Beam Power 3.53 kWAccelerating Structures RFQ, CH-DTLAccelerator Length ~31 m

Projects – J-PARC

Ion Species H-

Output Energy 400 MeVFrequency 324/972 MHzPulse Length 0.5 msPeak Current 30/50 mAProtons per Pulse 9.4 x 1013/ 1.5 x 1014

Repetition Rate 25 HzDuty Cycle 1.25 %Average Beam Power 80/133 kWAccelerating Structures RFQ, DTL, SDTL, ACSAccelerator Length ~244 m

Projects – SNS

Ion Species H-

Output Energy 1 GeVFrequency 402.5/805 MHzPulse Length 1.0 msPeak Current 38 mAProtons per Pulse 1.5 x 1014

Repetition Rate 60 HzDuty Cycle 6 %Average Beam Power 1.4 MWAccelerating Structures RFQ, DTL, CCL, SCLAccelerator Length ~257 m

Structures – DTL

Structures – SDTL

Structures – CH-DTL

Structures – CCDTL

Structures – PIMS

Structures – CCL

Structures – ACS

Field and Phase Error Studies- Method -

• RF errors at the klystron level translate directly into accelerating voltage errors

• Impact on the beam quality • Precise tuning of RF amplitude and phase is

indispensable to reduce uncontrolled beam loss and beam quality deterioration.

• Tuning goals at the klystron level can be different for different structure types

Field and Phase Error Studies- Method -

• Tracking a Gaussian distribution containing 100000 macro-particles over 1000 - 2000 runs, with random errors uniformly distributed

• Transmission, beam phase jitter, energy jitter and RMS emittance at the end of the structure analysed.

• Two different types of dynamic errors (“Klystron errors”) have been applied: – an error in RF phase– an error in amplitude

• Errors appear at the RF power source and are applied coherently to all RF gaps powered by the same source

• Cannot be “cured”

Field and Phase Error Studies- Linac4 DTL -

Errors:

Eklystron [%], φklystron [deg]

Phase Jitter [deg]

1 sigma

Energy Jitter [keV]

1 sigma

RMS emittance

[deg.MeV]

Nominal - - 0.167 ± 0.5% - 0.5 ±deg 0.8 13 0.169±0.003

± 0.5% - ±1deg 0.9 18 0.171±0.004 ± 0.5% - ± 2deg 1.1 31 0.175±0.009 ± 1% - ± 0.5deg 1.6 23 0.1707±0.005 ± 1% - ± 1deg 1.6 28 0.1719±0.006 ± 1% - ± 2deg 1.8 36 0.1772±0.011 ± 2% - ± 0.5deg 5.1 43 0.179±0.014 ± 2% - ± 1deg 5.7 46 0.180±0.017 ± 2% - ± 2deg 8.6 49 0.187±0.024

Field and Phase Error Studies- Linac4 DTL -

• Amplitude errors have more impact than the phase errors• For small errors, the phase jitter is dominated by

amplitude errors, while energy deviation by phase errors.• A variation of ±2% in amplitude causes an emittance

growth and an energy jitter above what is tolerable• A control of the amplitude and phase within ±0.5% and

±0.5 degrees would be ideal• But, ±1% and ±1 degree is also acceptable• The same procedure was repeated for the SNS, J-PARC

and RAL DTLs with similar conclusions

Field and Phase Error Studies- Linac4 CCDTL -

• Just like for the DTL, the results confirm the Klystron’s amplitude and phase should be controlled ideally to ±0.5 % and ±0.5 deg to control energy and phase jitter at the CCDTL output

• However, values of ±1% and ±1 deg are still acceptable

Errors:

Eklystron [%], φklystron [deg]

Phase Jitter [deg]

1 sigma

Energy Jitter [keV]

1 sigma

RMS emittance

[deg.MeV] Nominal - - 0.196 ± 0.5% - ± 0.5deg 0.5 39 0.196±0.003 ± 1% - ± 1deg 1 63 0.196±0.005 ± 2% - ± 2deg 2 115 0.198±0.009 ± 5% - ± 2deg 4 237 0.200±0.015

Field and Phase Error Studies- J-PARC SDTL -

• SDTL results comparable with DTL• ±1% error in amplitude and ±1 deg error in phase are

acceptable

Errors:

Eklystron [%], φklystron [deg]

Phase Jitter [deg]

1 sigma

Energy Jitter [keV]

1 sigma

RMS emittance

[deg.MeV] Nominal - - 0.126 ± 0.5% - ± 0.5deg 0.8 42 0.126±0.004 ± 1% - ± 1deg 1.5 75 0.128±0.005 ± 2% - ± 2deg 3.1 125 0.130±0.008

Field and Phase Error Studies- Linac4 CCL -

• Again, for the CCL, the ±1% - ±1 deg case is acceptable, but it also depends on requirements for energy painting at injection into PSB.

• SNS and RAL CCL study also indicates a similar error budget.

Errors:

Eklystron [%], φklystron [deg]

Phase Jitter [deg]

1 sigma

Energy Jitter [keV]

1 sigma

RMS emittance

[deg.MeV] Nominal - - 0.18 ± 0.3% - ± 0.3deg 0.6 73 0.1827±0.0036 ± 0.6% - ± 0.6deg 1.12 144 0.1926±0.036 ± 1% - ± 1deg 1.92 239 0.2106±0.0324

Field and Phase Error Studies- J-PARC ACS -

• J-PARC ACS comparable with CCL (Pi/2 structures)• ±1% error in amplitude and a ±1 deg error in phase

acceptable from a beam dynamics point of view.

Errors:

Eklystron [%], φklystron [deg]

Phase Jitter [deg]

1 sigma

Energy Jitter [keV]

1 sigma

RMS emittance

[deg.MeV] Nominal - - 0.140 ± 0.5% - ± 0.5deg 0.8 102 0.141±0.003 ± 1% - ± 1deg 1.2 217 0.145±0.005 ± 2% - ± 2deg 2.5 315 0.148±0.009

Field and Phase Error Studies- Linac4 PIMS -

• For the PIMS structure, klystron phase and amplitude should ideally be controlled to ±0.5% and ±0.5 deg to limit energy and phase jitter

• Values of ±1% and ±1 deg are still acceptable. However, this is a hard limit as for successful energy painting at injection into the PSB, the maximum energy jitter acceptable is 125 keV.

Errors:

Eklystron [%], φklystron [deg]

Phase Jitter [deg]

1 sigma

Energy Jitter [keV]

1 sigma

RMS emittance

[deg.MeV] Nominal - - 0.180 ± 0.3% - ± 0.3deg 0.3 65 0.181±0.00088 ± 0.5% - ± 0.5deg 0.4 78 0.181±0.00094 ± 1% - ± 1deg 0.66 126 0.181±0.0012 ± 2% - ± 1deg 0.85 220 0.181±0.0013

Field and Phase Error Studies- FAIR Linac CH-DTL -

• The probability that the degradation of the emittance due to errors is within 1% or 5% is presented.

• ±1deg error in phase is tolerable• However, due to the distinctive characteristics of the

KONUS focusing scheme, a reduction in voltage is not desirable, that is why the design aims for a ±0.2% error in voltage at the klystron level.

Errors:

Eklystron [%], φklystron [deg]

|Δεx/εx|

Probability

|Δεy/εy|

Probability

|Δεz/εz|

Probability ± 1% <5% 80.3

<10% 96.9

<5% 82.3

<10% 97.8

<5% 60.5

<10% 80.6 ± 1deg <5% 100 <5% 97.4

<10% 100

<5% 67.1

<10% 87.6

DTL SDTL CH-DTL CCDTL PIMS CCL ACS

Ideal ±0.5%±0.5 deg

- - ±0.5%±0.5 deg

±0.5%±0.5 deg

±0.5%±0.5 deg

-

Acceptable ±1%±1 deg

±1%±1 deg

±0.2%±1.0 deg

±1%±1 deg

±1%±1 deg

±1%±1 deg

±1%±1 deg

Conclusions

Conclusions

• For most structures a ±1% error in amplitude and ±1 deg error in phase is tolerable.

• The control should ideally be to within ±0.5% in amplitude and ±0.5 deg in phase

• CH-DTL has tighter requirements for amplitude control• Some limitations might come from downstream

machines (i.e. injection).• Sensitivity to input jitter from upstream structures

could also alter the “error budget”

Acknowledgements

• Linac4 error studies done as part of HIPPI by A. Lombardi, M. Baylac, G. Bellodi, M. Eshraqi, J‑B Lallement, E. Sargsyan and others at CERN, LPSC.• M. Baylac et al., “Statistical Simulations of Machine Errors for

Linac4“, “Proceedings of HB'06", Tsukuba, Japan (2006).• G. Bellodi et al., “Effects of RF Errors on the Linac4

Performance“, “HIPPI 2008 Annual Meeting", Geneva, Switzerland (2008).

• FAIR Proton Linac error studies done by G. Clemente and others at GSI and Frankfurt University.• G. Clemente et al., “Beam Dynamics Layout and Loss Studies

for the Fair P-Injector”, Proc. of EPAC’08, Genoa, Italy (2008).