Emittance Measurements

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Randy Thurman-Keup

Fermilab

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Joseph Liouville

Outline

• Theory
• Three-screen
• Quadrupole scan
• Aperture Based
• Slits
• Pepper Pot
• Allison Scanner
• Deflecting Mode Cavity / Spectrometer
• Tomographic Methods
• Other methods of interest

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R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Theory

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Theory

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Emittance

• Emittances have the dimensions of (length x angle)ⁿ
• mm-mrad, cm-mrad, m-rad, etc…
• radian is dimensionless so some people just drop it
• m, mm, μm, nm, etc… 🡪 mm-mrad = μm
• From M. Stockli talk

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

For semi-axis-products it is common to write

π⋅mm·mrad, π⋅cm·mrad, or π⋅m·rad

The π is supposed “to assure the reader that the π has been factored out of the phase space area (Sanders, 1990).” However, if the π was factored out, it was factored out in the definition. The π in the unit has no clear meaning. It is neither a real unit, nor a true multiplier. It is a one-of-a-kind object that has no precedent in the physics literature! It has created as much confusion as it intended to eliminate.

Confusion can be avoided by stating whether the quoted emittance value is a volume, an area, or a semi-axis-product!

Specify the Emittance Definition

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

I think I’ll just include�the beam core

Maybe 100% of�the particles…

We have an emittance of 0.2 𝜇m.

That’s amazing!! Ours is 100 𝜇m.

Phase Space

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Enrico Bravin CAS

Courant-Snyder Parameters

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Enrico Bravin CAS

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Theory

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Only true for trace �space emittance

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Canonical emittance�(p_x not x’) is always

constant

Matrix Transport of Phase Space

• Remember Day 1???
• Take the x – x’ space as an example
• A single particle can be transported as follows

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• The beam matrix can be transported as

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R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Drift Transfer Matrix

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

E.Wildner NUFACT08 School

Quadrupole Transfer Matrix

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

E.Wildner NUFACT08 School

Outline

• Theory
• Three-screen
• Quadrupole scan
• Aperture Based
• Slits
• Pepper Pot
• Allison Scanner
• Deflecting Mode Cavity / Spectrometer
• Tomographic Methods
• Other methods of interest

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R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Three Screen Emittance

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Three Screen Emittance

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Three Screen Emittance

• This gives us 3 equations and 3 unknowns

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• Can solve for emittance
• This assumes an elliptical phase space
• It also assumes no space charge
• Also have the option of fitting profiles with accelerator simulations

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Outline

• Theory
• Three-screen
• Quadrupole scan
• Aperture Based
• Slits
• Pepper Pot
• Allison Scanner
• Deflecting Mode Cavity / Spectrometer
• Tomographic Methods
• Other methods of interest

​

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Quadrupole Scan

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Quadrupole Scan

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Quadrupole Scan

• More than 3 measurements form a redundant system of equations from which systematic errors can be extracted

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Outline

• Theory
• Three-screen
• Quadrupole scan
• Aperture Based
• Slits
• Pepper Pot
• Allison Scanner
• Deflecting Mode Cavity / Spectrometer
• Tomographic Methods
• Other methods of interest

​

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Slit and Profile Method

• The principle behind slit and profile methods is to select a subset of the beam (x) and measure its angular profile (x’)

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• Scan the slit across the beam�collecting x’ profiles
• The position of the slit is the x value for �the x’ profile
• Space charge distortions are generally minimal

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

x

x’

Slit Devices

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

FNAL FAST Electron Linac

Single 50 𝜇m Slit

Multislit and Profile Method

• Similar to single slit method, but no scanning of slit is required
• Spacing of data in x is set by the slit spacing
• No fine tuning possible

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Multislit and Profile Method

• FNAL A0 photoinjector, 15 MeV electrons

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Correlations between horizontal and vertical

Multislit Devices

• FNAL FAST Electron Linac

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Allison Scanner

• Another variation of a slit method is the Allison Scanner
• The scanner has a slit at the entrance
• An electrostatic deflector plus slit at the exit to select a particular angle
• And a faraday cup at the end to measure intensity

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Allison Scanner

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

SNS LEBT, 65 keV ions

Pepperpot Method

• Like the slit and profile, but instead of one or more slits, this has many, many small holes
• Advantage is the potential to measure correlations between the x and y dimensions and possibly the �4-D emittance

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R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Radiabeam Website

Pepperpot Method

• FETS Ion Source

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Simon Jolly, Imperial College

Blue X’s are hole locations�Red is image spot location

Raw Image

Difference in positions gives the angles x’ and y’

Outline

• Theory
• Three-screen
• Quadrupole scan
• Aperture Based
• Slits
• Pepper Pot
• Allison Scanner
• Deflecting Mode Cavity / Spectrometer
• Tomographic Methods
• Other methods of interest

​

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Deflecting Cavity plus Dispersion

• This is a longitudinal emittance measurement technique
• Combines a transverse deflecting cavity with a spectrometer
• First the beam is deflected horizontally (x – t) and then it enters a vertical spectrometer (y – 𝛥E/E)
• t – 𝛥E/E 🡪 x – y

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Horizontal Deflection�x – t correlation

Vertical Dispersion�y – 𝛥E/E correlation

Deflecting Cavity plus Dispersion

• LCLS XTCAV

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Deflecting Cavity plus Dispersion

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

LCLS Data

No Microbunching

Microbunching

Outline

• Theory
• Three-screen
• Quadrupole scan
• Aperture Based
• Slits
• Pepper Pot
• Allison Scanner
• Deflecting Mode Cavity / Spectrometer
• Tomographic Methods
• Other methods of interest

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R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Tomography

• The reconstruction of an object by using projections of it
• Radon Transform is one method for accomplishing it
• CAT scan (Computer Aided Tomography)
• X-ray images from different directions
• Reconstruct phase space via projections of it onto the time axis for instance

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Tomographic Techniques

• Pseudo-tomography
• For a synchrotron storage ring, the longitudinal phase space density is constant in time and along phase space trajectories
• Uniformly populate rings in phase space such that the projection of phase space onto the time axis matches the data
• Emittance can be calculated since�the phase space distribution has been �determined

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Tomographic Techniques

• Rapid-cycling synchrotron, phase space not evenly distributed
• Collect time distributions throughout a synchrotron period (time period that particles rotate once around the longitudinal phase space)

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Rotation of density variations in longitudinal phase space

Tomographic Reconstruction

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

FNAL

Main

Injector

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Tomographic

reconstruction�of longitudinal�phase space

Outline

• Theory
• Three-screen
• Quadrupole scan
• Aperture Based
• Slits
• Pepper Pot
• Allison Scanner
• Deflecting Mode Cavity / Spectrometer
• Tomographic Methods
• Other methods of interest

​

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

6-D Phase Space

• SNS Beam Test Facility, after RFQ (radio frequency quadrupole)

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024

Extras

R. Thurman-Keup --- USPAS Hampton, VA

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February 1, 2024