6D and High Dynamic Range Measurementsof Hadron Beam Phase-Space
12th International Beam Instrumentation Conference

Sasha Aleksandrov
Spallation Neutron Source, ORNL
September 14th, 2023

ORNL is managed by UT-Battelle, LLC for the US Department of Energy

,DRIn lieu of outline

log 𝐷𝐷𝐷𝐷 ≈ 𝑎𝑎 − 𝑘𝑘𝑘𝑘

courtesy of K. Ruisard,dA. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'2IBIC 2023, Saskatoon , Canada
September 10-14, 2023

Beam dynamics in real 3d space can be represented as evolutionof distribution function in 6d phase space

𝑁𝑁~108 ÷ 109

particle #coordinates

1𝑥𝑥, 𝑥𝑥 ′ , 𝑦𝑦, 𝑦𝑦 ′ , 𝑧𝑧, 𝑧𝑧′

2.
.
𝑁𝑁𝑥𝑥, 𝑥𝑥 ′ , 𝑦𝑦, 𝑦𝑦 ′ , 𝑧𝑧, 𝑧𝑧′.
.
𝑥𝑥, 𝑥𝑥 ′ , 𝑦𝑦, 𝑦𝑦 ′ , 𝑧𝑧, 𝑧𝑧′

6𝑁𝑁 numbers, e.g. 6 � 109

Cannot measure individual particles positions (yet), need something else
distribution function
Distribution function representation requires 𝑛𝑛6 numbers in 6D

number of particles per
bin in phase space

𝑓𝑓 𝑥𝑥, 𝑥𝑥 ′ , 𝑦𝑦, 𝑦𝑦 ′ , 𝑧𝑧, 𝑧𝑧 ′ =1 2…….. n𝑁𝑁(𝑥𝑥 ± ∆, 𝑥𝑥 ′ ± ∆, 𝑦𝑦 ± ∆, 𝑦𝑦 ′ ± ∆, 𝑧𝑧 ± ∆, 𝑧𝑧 ′ ± ∆)=𝑁𝑁𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 � ∆6e.g. 6 � 107 , for n=20

Next best representation after actual particles coordinates
Most important, it’s measurable

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

All commonly used beam parameters can be calculated from 6d
distribution function, but not vise versa
1D profiles:∞𝑝𝑝 𝑥𝑥 = � 𝑓𝑓(𝑥𝑥, 𝑥𝑥 ′ , 𝑦𝑦, 𝑦𝑦, 𝑧𝑧, 𝑧𝑧 ′ ) 𝑑𝑑𝑥𝑥 ′ 𝑑𝑑𝑑𝑑𝑑𝑑𝑦𝑦 ′ 𝑑𝑑𝑑𝑑𝑑𝑑𝑧𝑧 ′−∞Sum from Emittance

Amplitude (arb. unit)

Direct Measurement

15202530

Y (mm)∞

2D emittances: 𝑝𝑝 𝑥𝑥, 𝑥𝑥 ′ = � 𝑓𝑓(𝑥𝑥, 𝑥𝑥 ′ , 𝑦𝑦, 𝑦𝑦, 𝑧𝑧, 𝑧𝑧 ′ ) 𝑑𝑑𝑑𝑑𝑑𝑑𝑦𝑦 ′ 𝑑𝑑𝑑𝑑𝑑𝑑𝑧𝑧 ′σ matrix:

𝑥𝑥
𝑥𝑥 ′
𝑦𝑦
𝑦𝑦 ′
𝑧𝑧𝑧𝑧 ′

𝑥𝑥

−∞

𝑥𝑥 ′

𝑦𝑦𝑦𝑦 ′

𝑧𝑧𝑧𝑧𝑧<xx> <xx’> <xy> <xy’> <xz> <xz’><x’x> <x’x’> <x’y> <x’y’> <x’z> <x’z’><yx> <yx’> <yy> <yy’> <yz> <yz’><y’x> <y’x’> <y’y> <y’y’> <y’z> <y’z’><zx> <zx’> <zy> <zy’> <zz> <zz’><z’x> <z’x’> <z’y> <z’y’> <z’z> <z’z’>

And much more,including generating particle coordinates
to initialize PIC simulations

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

Dynamic range is ratio of maximum density at the peak tominimum density resolvable above noise
𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚

𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚
𝐷𝐷𝐷𝐷 =𝑡𝑡

Maximum amplitude
thresholdSome fraction r is lost due to applying threshold𝑡𝑡

Fraction of particles eliminated by applying threshold depends on threshold,distribution shape, and dimensionality
Example: Gauss distribution, t=10-6
Dimensionality, d1
2
3
4
5
6
Rejected fraction, r2 � 10−7

1 � 10−6

4� 10−6

2 � 10−5

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'54 � 10−5

1 � 10−4
IBIC 2023, Saskatoon , Canada
September 10-14, 2023

∆�∆
𝐿𝐿

𝑠𝑠2

𝑠𝑠1𝑖𝑖𝐹𝐹𝐹𝐹 = 𝑓𝑓2 (𝑦𝑦, 𝑦𝑦𝑦)

slit 1

Slit-slit technique is well suited for measuring charge
density in phase space𝑦𝑦 = 𝑠𝑠1
𝑠𝑠2 − 𝑠𝑠1′
𝑦𝑦 =𝐿𝐿A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

6IBIC 2023, Saskatoon , Canada
September 10-14, 2023

6d phase scan principle
SLIT_Y_2
SLIT_Y_1

SLIT_X_2

BENDINGMAGNET

SLIT_X_1

SLIT_X_3
RF deflector

Magnetic spectrometer for energy determination
SLIT_X_4

RF deflector or other time resolving device fortemporal degree of freedom

FARADAY CUPor otherdetector

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'7

IBIC 2023, Saskatoon , Canada
September 10-14, 2023

“Curse of dimensionality” for multi-dimensional scans
What looks simple in low-dimension problem can become
ridiculously difficult in higher dimensions• High-dimensional spaces have very large volume: V~𝑎𝑎 𝑑𝑑– Large scan time

𝑁𝑁𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 𝑛𝑛𝑑𝑑

– Low charge density– Large data sets

Total numberof bins

∆Beam current attenuation by 1 slit ~𝜎𝜎Maximum amplitude after 𝑑𝑑 slits 𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 ~log 𝐷𝐷𝐷𝐷 ≈ 𝑎𝑎 − 𝑘𝑘𝑘𝑘

slit widthbeam size∆ 𝑑𝑑𝜎𝜎dimensionality

Number of steps
per degree offreedom

Example: 𝑛𝑛 = 10, 𝑑𝑑 = 6
Total scan time at 1
Example:𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠:𝑠𝑠𝑠𝑠𝑠𝑠∆� ≈ .2 ,𝜎𝜎

𝐴𝐴𝑚𝑚𝑚𝑚𝑚𝑚 ≈ 64𝜇𝜇𝜇𝜇

2……..

n

𝑁𝑁𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 106

𝑇𝑇 = 106 𝑠𝑠𝑠𝑠𝑠𝑠 ≈ 280 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜

𝑑𝑑 = 6,𝐼𝐼𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 30𝑚𝑚𝑚𝑚

𝑡𝑡 < 64 𝑓𝑓𝑓𝑓 To achieve DR=106

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'81IBIC 2023, Saskatoon , Canada
September 10-14, 2023

Beam Test Facility at SNS

Ion Source

RFQParticles

H-Energy

2.5 MeV

Current< 50 mA

Pulse width< 1 ms (50µs)

Rep rate< 60 Hz (10Hz)

Beam Power< 7.5 kW

MEBT

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

9

IBIC 2023, Saskatoon , Canada
September 10-14, 2023

6d phase scan apparatus at SNS Beam Test Facility
Quadrupoles

90-DEG. BENDING
MAGNET (spectrometer)

Beam1mBunch ShapeMonitor (z)2 pairs of movable slits forx, x’, y, y’ selection

Movable slitfor energyselection (z’)

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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Faraday Cup

IBIC 2023, Saskatoon , Canada
September 10-14, 2023

X-Y Slits arrangement

200-by-200 μm
aperture
A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

Energy selection and measurement
video camera

Energy view screen and slit

Bunch energy spectrum∆𝑝𝑝[𝑎𝑎𝑎𝑎𝑎𝑎. 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢]
𝑝𝑝

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

12

IBIC 2023, Saskatoon , Canada
September 10-14, 2023

Bunch Shape Monitor principle of operation
Deflecting 2.5MeV proton beam directly with an RF cavity is expensive therefore
we use Beam Shape Monitor aka “Feschenko monitor”

PhosphorscreenMCP

VideoCamera

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

6d scan results
Date

Duration
[hr]

#pts

Effectiverep. rateFilesize

Dynamicrange

201832~6M

2.5 Hz2021

31~6M2.8 Hz

370G~1002021

27~6M

3.4 Hz447G~100~20Main outcome:o It can be done !
o Distribution function is much more
complex than we prepared foro Identified problems to work ono No useful data for beam dynamics
study, in short term

Very large files, but mostly empty
52% in 3D

8% in 6D!

78% in 2D<1 %100% of points in 1D rectilinear grid contain signal
A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'14

IBIC 2023, Saskatoon , Canada
September 10-14, 2023

5d scan provides usable dynamic range and resolution inexchange for sacrificing one dimension

beam

𝑥𝑥2 ~ 𝑥𝑥𝑥

X’ [mrad]𝑥𝑥1 = 𝑥𝑥𝑦𝑦1 = 𝑦𝑦

Grid size:
Scan time:
File size:

32 x 23 x 23 x 258 x 346~3 hours~20Gb

𝑦𝑦2 ~ 𝑦𝑦𝑦

viewscreen

X [mm]

Comparison of 2 datasets taken 2 weeks apart𝑥𝑥3 ~Δ𝐸𝐸

courtesy of K. Ruisard

5D scan (integrated along other 3 dimensions)
2D scanA. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'15

IBIC 2023, Saskatoon , Canada
September 10-14, 2023

yy'Figure shows 4D transverse phasespace for each energy slice,
Linear color scale
Courtesy of Austin Hooverx momentum

There is a lot of complexity in highdimensional beam distribution that isnot apparent in “typical” 2D
projections

Hoover et al, submitted, https://arxiv.org/abs/2301.04178.
Hoover et al, [Data set]. Zenodo.
https://doi.org/10.5281/zenodo.7517479

courtesy of K. Ruisard
A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'16X position

IBIC 2023, Saskatoon , Canada
September 10-14, 2023

yy'

Figure shows 4D transverse phasespace for each energy slice,
Linear color scale
Courtesy of Austin Hooverx momentum

There is a lot of complexity in highdimensional beam distribution that is
not apparent in “typical” 2D
projections

Hoover et al, submitted, https://arxiv.org/abs/2301.04178.
Hoover et al, [Data set]. Zenodo.
https://doi.org/10.5281/zenodo.7517479

courtesy of K. Ruisard
A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'17X position

IBIC 2023, Saskatoon , Canada
September 10-14, 2023

2d scan provides dynamic range usable for halo study

Threshold level is found by visual examination
A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

Integration
windowTT [us]Synthesized high dynamic range is achieved by charge-to-light
conversion and stitching images with variable gain

T0
T0 [us]Grid size:# of averaging# of gains
Rep. rate
Scan time:

100 x 100
1025Hz~12 hours

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'19IBIC 2023, Saskatoon , Canada
September 10-14, 2023

2D high dynamic range scans reveal features at halo level
100Chopper off0-1

5-2xp [mrad]

30mA0-3-5-4-10-10-5-5

5010x [mm]10Chopper on0-1

5xp [mrad]-2-60-3-5-10-10-4-5-50

510x [mm]A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

20IBIC 2023, Saskatoon , Canada
September 10-14, 2023

Scan speed
improvement

Dynamic rangeincrease

Comments

Data collection rate ->10Hz✓✓

Dedicated camera server

2d BSM✓

Dedicated HDR detector✓✓

BSM light collectionimprovement✓

Fiber coupled camera?

BSM direct e- image readout✓

Timex, 200-300k$

Proton RF deflector

✓

>1M$

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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being
implemented

Ways for scan speed and dynamic range improvement

IBIC 2023, Saskatoon , Canada
September 10-14, 2023

2-dimensional Beam Shape Monitor to reduce time of 6d scan
𝐸𝐸 − 𝑊𝑊 plane is measured inone shot, reducing numberof dimensions to scan to 4

courtesy of K. Ruisard

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

22IBIC 2023, Saskatoon , Canada
September 10-14, 2023

Electron optics simulations, top view

Electron optics simulations, side view
Δx = 33 mm

Δy = ~0.4 mm

courtesy of Adam Moro, RadiabeamPartnered with industry to develop 2d BSM (Radiabeam)

Horizontal position on screen vs. position on wire
x-y image on screen
courtesy of Aurora Araujo, Radiabeam

Drop-in compatible with old BSM vacuum chamber,electronics and software
Expect delivery in November 2023

BSM assembly
Wire and RF deflector assembly

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

2-camera synthesized dynamic range light detector toreduce time of 2d scan and improve dynamic range•

Shorter camera to screen
distance for better lightcollection•

Two cameras for
simultaneous
measurements at two gains•

Possibility of using PMT incounting mode•

View screen at 45 degrees
to reduce peak density

Camera 1,
low gain
Camera 2,
high gainor PMT
A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

6D and HDR diagnostics is integral part of high intensity beam
dynamics experiment at SNS BTF
Full-6D
measurement

High-dynamic range
measurement

5D-capable
diagnostics

Ion Source

2.5 MeV
acceleration

Periodic focusing

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

Plan to resume operation of SNS BTF in November 2023

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

What is beyond?
Reach one-particle-per-bin-per-bunch when 𝐷𝐷𝐷𝐷 ≈ 109 in 2d measurement
and even earlier for higher dimensionality
Does it mean ~ infinite DR after that?
Switching to measuring individual particles coordinates instead ofdistribution function?
Most advanced simulations are unlikely to reach similar DR anytime soon

1 bunch in simulations…
…

1000s of bunches in measurements…

…

millions of bunches in real linac

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023

In lieu of summary

2024

A. Aleksandrov. '6D and High Dynamic Range Measurements of Hadron Beam Phase-Space'

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IBIC 2023, Saskatoon , Canada
September 10-14, 2023