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“PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 [email protected]@cern.ch Page...

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“PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 [email protected] Page 1/28 M A G N ETIC M EA SU REM EN T SECTIO N cern.ch /m m Contents 1 – The PS B-train today 2 – Why upgrade ? 3 – CERN-wide B-train upgrade project 4 – The new PSB system 5 – Outlook PS Booster B-train upgrade M Buzio , R Chritin, D Giloteaux, D Oberson (TE/MSC/MM)
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Page 1: “PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 marco.buzio@cern.chmarco.buzio@cern.ch Page 1/28 Contents 1 –The PS B-train today 2 –Why upgrade ?

“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

Page 1/28

MAGNETIC MEASUREMENT SECTION cern.ch/mm

Contents

1 – The PS B-train today2 – Why upgrade ?3 – CERN-wide B-train upgrade project4 – The new PSB system5 – Outlook

PS Booster B-train upgradeM Buzio, R Chritin, D Giloteaux, D Oberson (TE/MSC/MM)

Page 2: “PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 marco.buzio@cern.chmarco.buzio@cern.ch Page 1/28 Contents 1 –The PS B-train today 2 –Why upgrade ?

“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

Page 2/28

MAGNETIC MEASUREMENT SECTION cern.ch/mm

The PS B-train today

Page 3: “PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 marco.buzio@cern.chmarco.buzio@cern.ch Page 1/28 Contents 1 –The PS B-train today 2 –Why upgrade ?

“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

History of B-train versions

Mark I 1972 – 1981no details known

Mark II 1981 – 1998 1 G resolution, 10-3 (10 G) stabilityUsed by beam diagnostics (longitudinal pick-up, display …)

Ion cycles new NMR field markers («peaking strip» mode)

Mark III 1998 – New electronics by P Dreesen (same as for the PS, LEIR, AD)0.1 G resolution (peak BUP rate = 220 kHz @ 2.2 T/s), Main users: RF, beam DCCT (MPS + trims in open loop)

All rings assumed to have same field: measurements show that up to 6 kA |B1

1/B14-1|, |B1

2/B13-1|< 410-4

SPARE chain calibrated to give same results as OP (NMRs set slightly apart to trigger at the same time in non-uniform field)

Current system works satisfactorily, no major problems (interventions since 2006: missed NMR trigger solved by lowering threshold from 150 mV to 100 mV; pulse repeater replaced; over range noise on Ḃ solved by filtering new

switched-mode converters)

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Current B-train system (361-1-201)

(original) reference pick-up coil

combined pick-up coilsfor fringe field detection

(unused)

spare pick-up coil(unused)

Metrolab NMR probes2× inrection (op + spare)

1× flat-top (unused)

B-train crates (op + spare)

Frequency generator(marker resonance)

GPIB controlled by … ?

NMR output buffer power supplies: new, old (scrap ?)

NMR signal scope

NMRteslameters

empty(available for on-line tests)

free space ?

Vcoil ( Bdot)split towards

op/spare chainsvia isolation amps

coil T sensors(unused)

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Why upgrade ?

Page 6: “PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 marco.buzio@cern.chmarco.buzio@cern.ch Page 1/28 Contents 1 –The PS B-train today 2 –Why upgrade ?

“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Motivation for B-train system upgrade

Hard constraints

• Present electronics cannot cope with 2× field ramp rates dB/dt = 45 T/s BUP/BDOWN rate = 400 500 kHz (PS tests fail between 250 and 500 kHz)reasons: the ADC-based integrator (AFEC card) saturates (register overflow)

the pulse repeaters (TTL24V) have not enough bandwidth

Severe impact on accuracy

• Higher saturation 2× difference between inner and outer rings + larger cycling history-dependent fluctuations fixed (or even f(I)) trims will not work second system in the outer ring needed

• Stronger eddy current effects + saturation-induced field profile change fringe field more important integral coils to get all the required information

Strategic considerations

• Replace ageing electronics and sensors

• Improve maintainability: conformity to upcoming CERN-wide B-train standard; stock fresh spares (in common with other machines); advanced in-built diagnostics and alarms; remote diagnostics and configurability via WhiteRabbit/FESA

• Improved resolution and accuracy free up margins elsewhere e.g. radial position loop long-term operational flexibility

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

0.3400

0.3405

0.3410

0.3415

0.3420

0.3425

0.3430

0.3435

0.3440

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Tm/k

A

Cycle Index

Integrated Dipole Transfer Function vs Cycle History (INNER ring)

2 Gev stable, puis 5 fois 1.4 Gev, puis 2 Gev jusqu'à stabilisation1.4 Gev stable, puis 5 fois 2 Gev, puis 1.4 Gev jusqu'à stabilisation1.4 Gev stable, puis 5 fois 1 Gev, puis 1.4 Gev jusqu'à stabilisation1 Gev stable, puis 5 fois 1.4 Gev, puis 1 Gev jusqu'à stabilisation

Repeatability – Inner rings

Repeatability as a function of cycling hystory: 210-4 @ 1 1.4 GeV

510-4 @ 2 1.4 GeV

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Repeatability – outer rings

Repeatability as a function of cycling history: 110-4 @ 1 1.4 GeV

710-4 @ 2 1.4 GeV

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

Page 9/28

MAGNETIC MEASUREMENT SECTION cern.ch/mm

Why are fringe fields important ?

0.990

0.995

1.000

1.005

1.010

1.015

1.020

0 50 100 150 200 250

I [A]

BdL

B0

Tran

sfer

fun

ction

nor

mal

ized

@ 1

30 A

saturation

815

816

817

818

819

820

821

822

823

0 50 100 150 200 250Lm

[mm

]I [A]

High field - saturation

Low field - linear range

𝓁𝑚(𝐼 )= 1𝐵0(𝐼 )

∫−∞

𝐵 ( 𝐼 ,𝑠 ) 𝑑𝑠

B, Ḃ

BendḂend

• end eddy currents, in-plane of the end laminations, due to the leaking normal field component

• effect dominant in short aspect ratio magnets

• eddy currents in the laminations (normally negligible)

2

8

1t

R

L

e

ee

t

wtR

L

e

ee

0

8

1

• High-field saturation longitudinal field profile flattens out extrapolation from central to integral become less accurate

• In short magnets, eddy currents in the end regions become the dominant dynamic effect

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Repeatability of magnetic length

• Recent tests for MedAustron B-train evidence clearly that the magnetic length is much more history-dependent at low than high field increased precision by marking at the flat-top for drift correction

• To be evaluated: trade-off with larger integrator drift during ramp-up • To be evaluated: trade-off with smaller dynamic range for gain correction (mid-level marker is best ?)

Courtesy G. Golluccio

Page 11: “PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 marco.buzio@cern.chmarco.buzio@cern.ch Page 1/28 Contents 1 –The PS B-train today 2 –Why upgrade ?

“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

CERN-wideB-train upgrade

project

Page 12: “PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 marco.buzio@cern.chmarco.buzio@cern.ch Page 1/28 Contents 1 –The PS B-train today 2 –Why upgrade ?

“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Functional specifications

Project originally motivated by performance limits of the PS system + need of long-term consolidation

• Reliability new markers as a long-term alternative for difficult-to-replace peaking strips reduction of down time due to timing conflicts

(synchronization between peaking strip window and current cycles; internal integrator recalibration)

more robust signal transmission remote diagnostics

• Operational flexibility sensors in both F/D halves to recover full information mitigate B-train errors due to the imbalance induced by specific operation sequences that today are best avoided

(e.g. F8 degaussing cycles, certain combinations of cycles) allow higher flat-bottoms and thus shorter cycles

(NB: the current very low 5 mT value is imposed by the peaking strips !) remote switching between OP and SPARE chains

• Precision and accuracy 5 µT resolution (currently limited by the integrator and repeaters)

more accurate integration, drift correction more flexibility in the calibration and in adapting to new operation modes

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

New B-train systems

Main design choices:

1. Modern electronics (integrator, marker trigger generator) based upon CERN-supported solutions (Industrial PICMG1.3 PC FE, OpenHardware SPEC PCIe carried card & FMC mezzanine)

2. Front-End software compatible with ACCOR accelerator control systems (CERN Scientific Linux + FESA)

3. Field markers based on commercially available components (FMR resonator / NMR probes)

4. Optical-fibre serial transmission of numerical measurement results(OpenHardware White Rabbit)

5. New timing-independent, streaming integration and drift/gain correction algorithms

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

N different marker levels up to 4 N corrections per cycleCorrections smeared over a certain t to avoid sudden rumps

ADC offset ( integrator drift) updated every time the same marker level is reached

Integrator gain error updated every time a different marker level is reached

𝐵=𝐵0+1𝐴∫0

𝑡

(1+𝜀(𝑡))(𝑉 (𝑡 )−𝑉 0(𝑡)¿)𝑑𝑡 ¿

t1low time

B

t2low t1

hi t2hi

field markers

ܤ

ܤ ௪

New concept: continuous digital distribution of B(t) on a fast serial line to replace old pulse train• Output stream continuously updated with current B(t) values

no need for complex triggering and reset logic; no B0 initialization burst

• Adaptive auto-calibration of gain and offset using field markers on flat-top and flat-bottom fully transparent correction of measurement error

fast and robust transmission, no more timing conflictsbut: drift correction must be applied continuously on-the-fly

Streaming integration

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Prototype electronics in U101

2× AnaPico 20 GHz signal generators for F,D FMR (local frequency setting only)

Front End industrial PC

Switching chassis - simulated/measured B-train (based on POPS being on/off)- OP/SPARE B-train (HW signal from CCC)

B-train chassis including: 8-page multi-function display,analog and digital I/O, RF amplifier, power supplies

New high quality PFW/I8 DCCT outCourtesy O. Michels

OP

syst

emSP

ARE

syst

em

SPEC FMC 2-ch. integrator card- “classic” integration reset at c0 + weighted sum of F/D integrals- basic offset correction- software-configured ADC/preampli calibration with internal voltage reference, automatically done during zero cycles (NB yearly offline calibration still necessary)

SPEC FMC 2-ch. marker card- trigger generation with high-Q FMR- trigger generation with NMR (tested in MedAustron)

tested

Commercial White Rabbit switch

Page 16: “PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 marco.buzio@cern.chmarco.buzio@cern.ch Page 1/28 Contents 1 –The PS B-train today 2 –Why upgrade ?

“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

White Rabbit distribution in the PS

• All cabling + spares in place • Broadcast mode with two switches tested @ 250 kHz (50 design target, 300 theoretical max.)

first test results: 5.6 µs latency seen by POPS receiver • P.C. broadcast internally measured current 1 kHz, 1% on-the-fly B(I) simulation for:

- timing-independent marker trigger enable- telegram-independent cycle recognition- internal diagnostics and alarms- simulated B-train in case of measured B-train failure (?)

lab testsOK

field testsOK

coming in 2015:same as RF

In operationImplemented now Large headroom for expansion

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Diagnostic PS “spy” system

• System operating at ½ channel capacity, debug ongoing

• New high-quality F8 + PFW current readout from DCCT (courtesy of O. Michels) under test

• Based on National Instruments hardware: PXIe chassis, RT controller, 2 6368 DAQ cards (162 MHz parallel 16-bit channels + 3210MHz digital I/O channels)

• Acquisition of all sensors and B-train signals • Introduced in 2010 to track the magnetic state in F/D halves • Used to check the consistency of sensor and B-train signals,

timing and currents• Testbed for the design of new sensors and acquisition

algorithms

Currents: Imain, IF8L, 8 × IPFWFlux coils: 3 × F + 3 × D

Peaking strips: 3 × F + 3 × DPeaking strip currents: 3 × F + 3 × D

NMR/FMR markerDistributed Bdot: 2 × channel

Distributed B-trains: 2 × channel (up + down)Cycle/Supercycle timing signals

analog signals

digital signals

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Ongoing & planned activity

1. Finalization of the FPGA code• Integrator: VHDL timing registers to check and control + DMA transfer data• Dynamic (smoothed) adjustment of the integrator offset/gain upon reception of marker triggers • Dynamic adjustment of calibration coefficients, marker gate (enable) etc… as a function of

I via an internal approximated magnet model B=B(I,t)• Automatic self-calibration during zero-cycles according to telegram index or I(t) history

2. Development of C++ FESA classes/Linux device drivers• develop the classes to exchange measurement and control signals as agreed with OP team• Local FMR frequency control (e.g. for dynamic marker point adjustment)

3. Component-level tests• Statistical analysis of drift/gain error vs. machine cycling sequence, ambient conditions definition

of optimal marker levels, frequency of internal correction• White Rabbit communication to/from all users (latency and jitter vs. data rate)

4. System-level tests• Systematic offline comparison of old/new sensors, old/new system in different conditions• Offline correlations with beam behaviour (radial instability) during different cycle combinations to

validate measurement principle• Online (with beam) tests in parallel with existing system, by feeding back one user at a time• Online tests with the new system replacing completely the old

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

UpgradedPSB B-train

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Specifications

Parameter Value Unit

Max. magnetic field B 1.2 T

Min. magnetic field B 0.1 T

Max. field ramp rate dB/dt 4.0 T/s

Absolute measurement uncertainty 100 µT

Max. measurement resolution 10 µT

Min. cycle duration 1.2 s

Field broadcast rate 400 kHz

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Outer B-train OP

Inner B-train OP

Inner B-train SPARE

Outer B-train SPARE

RF R2

MPC 2&3

MPC 1&4

RF R1

CCC reference magnet users

FESA classes

NMR probe (low + high)

switch flags (FESA)

integral fluxmeter

DCCT R2

DCCT R1

RF R3

RF R4

DCCT R3

DCCT R4

Overall system architecture

Main advantages of PCB fluxmeters:- industry-made, multiple units relatively inexpensive- accurate measurement of (much higher) saturation/eddy current effects (avoid high-field RF corrections ?)- 10-4 surface accuracy absolute energy calibration possible- real-time field harmonics as a by-product

LLRF/DCCT: - inner/outer rings share B(t) from the corresponding OP chain - or each ring is fed all the time with its own B(t): more information, but 2× failure risk

redundancy: 2× (OPerational + hot SPARE) chains, always running, remotely switchable - OP sensors in rings 3 (for historical continuity …) and 4- SPARE sensors in rings 1 and 2: get full magnetic information, but switching chains may entail more complex calibration - or SPARE sensors in rings 3 and 4 (as today): easier cross-calibration, less fluxmeters, two empty rings remain available

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

NMR marker

• Continuous-Wave Nuclear Magnetic Resonance probe: absorption peak at signal demodulated by teslameter threshold comparator trigger pulse

• 10-6 metrological reference (fundamental constants, essentially T-independent, weak chemical shifts)

• Noise sensitivity of demodulated signal (gating and repetition suppressor needed; threshold lowered in 2006 to 150 mV)

• Main limits: B 450 G, B/B<0.02/m, 20<dB/dt< 50 mT/s• Ramp rate limitation could be mitigated (FMR resonator) or avoided

(DC NMR on a plateau) at the price of added complexity, reduced accuracy

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

0 200 400 600 800 1000 1200

T, T

/s

Time (ms)

1.4 GeV PSB Cycle

B

dB/dt

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

100 150 200 250 300

T, T

/s

Time (ms)

1.4 GeV PSB Cycle - Initial acceleration ramp

B

dB/dt

NMR markert 187 ms

B = 1107 G (Ring 3)

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Interface signals (proposal)

Real-time (10 s) serial distribution (White Rabbit @ 400 kHz ) - From the B-train: B1

3, Ḃ13, B1

4, Ḃ14

- From the PC: Imain14, Imain23, Itrim1, Itrim2, Itrim3, Itrim4

Quasi real-time (~1 s) low-bandwidth (5 kHz) distribution (FESA + OASYS/SAMPLER ?)- From the B-train: B1

r, Ḃ1r, B2

r, B3r, VNMR

r , tNMRr for r=1…4

- total estimated uncertainty on all distributed measurements- Deviation from synthetic model Bj=Bj(Ik,t)

Configuration parameters (FESA)- From the CCC/bldg. 30: Marker levels, windows, chain status (active/spare),

calibration parameters (extrapolation from reference magnet to whole ring)

Quasi real-time (~1 s) diagnostic parameters/alarms (FESA)- From the B-train: for each cycle, for r=1…4: ADC gain error, integration chain drift/gain error,

difference between inner/outer rings, difference between spare and operational chains;

Diagnostic parameters (offline analysis in the Spy system)- standard magnetic cycle analysis (as a function of current + previous users): remanence,

hysteresis width, saturation amplitude, linear transfer function, ripple vs. frequency,

apparent and differential magnet inductance etc …

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Outlook

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

CERN-wide B-train upgrade deployment

PS P rototype systeminstalled

System & component testsCalibration

Tests with beamVHDL finalizationFESA for CCC

P roductionelecronics

Tests with beamRemove oldsystem

Additional sensors

Componenttests

Operation withnew system

PSB Design finalized Offline testsP CB fluxmeterSpy system

New sensors in existing ref. MB

Online tests Tests with beamInstallation in new ref. MB

Componenttests

Operation withnew system

ELENA P CB fluxmetersOffline tests

Installation of Btrain + Spy

Tests with beamOperation withnew system

SPS Spy system

LEIR Spy system (?)

AD Spy system (?)

2020LS1

2014 2015 2016 2017LS2

2018 2019

• Offline tests: on regular/modified BZH/MQ spare in bldg. 867

• Online tests: Installation of additional sensors in free Ring 4 + new electronic components & diagnostic (spy) in the free slots in the B-train racks (LLRF available now, DCCT in 2015, MPS ?)

• tests with beam must be envisaged before LS2

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Open questions for the WG

• Overall architecture: where to put SPARE sensors / use SPARE as OP ?

• NMR frequency programming: how is it done now, who will do it in operation ?

• 3 full-height racks needed for the production system (as close as possible to the ref magnet)can we fill in free space in the B-train racks now ?

• 2 × IMPS (+ 4 × Itrim ) broadcast via White Rabbit: in parallel or merged ?

• define signals, variable and alarms to be exchanged with the CCC

• what about the synthetic B-train ? Define uses and tolerances

• are there any other users ?

• Internal drift/gain correction may generate steps in the distributed B-train.Maximum acceptable step size ( need to smooth out over a certain time)

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“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Ongoing & planned activities

Foreseen in the next 6-12 months:

• B-train sensors- design and procurement of fluxmeters- status of coils in ring 1 and 2

• B-train electronics:- White Rabbit communication lab tests with LLRF- installation of Spy system in the B-train racks

• Offline (bldg. 867) magnet tests

- impact of higher saturation levels on the field quality (harmonics) of bending/quads- evaluation of history- and field-dependent differences between inner and outer rings- evaluation of coupling between inner and outer rings in split-coil mode- effectiveness of laminated side plates to equalize inner and outer rings- magnetic behavior of the insertion dipoles evaluation of trim currents

Page 28: “PS Booster B-train upgrade” LIU-PSB WG, 16.10.2014 marco.buzio@cern.chmarco.buzio@cern.ch Page 1/28 Contents 1 –The PS B-train today 2 –Why upgrade ?

“PS Booster B-train upgrade”LIU-PSB WG, 16.10.2014 [email protected]

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MAGNETIC MEASUREMENT SECTION cern.ch/mm

Summary & conclusions

• Large saturation + eddy current effects expected to impact severely the reproducibility of the magnetic behaviour of the bendings

• The proposed B-train upgrade solves this problem to first order:- integral coils measure high field and dynamic effects in the end regions- twin parallel chains measure inner and outer rings

• Second-order effects not addressed for now (but object of planned study):- history dependence of field profile @ marker level- differences between rings 1/4, 2/3

• State-of-the-art instrumentation takes advantage of many years of R&D + extensive on-line tests carried out in the PS before deployment during LS2.

• Added value: - 10-4 absolute energy calibration possible- real-time field harmonics measurement for free

• Need to coordinate (and test) details of excitation current:- NMR marker compatibility: need 515 ms with dB/dt = 20 40 mT/s (dI/dt = 200 400 A/s)- “Zero cycles” with short dips to I=0 as in POPS: possible impact on reproducibility, to be assessed- ripple, overshoot, undershoot, oscillations at end of cycle, ground loops: ditto- implications of coupling between inner and outer rings


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