1. Emittance measurements for LI2FE electron beams
LI2FE Diagnostic

2. Emittance It is a measurement of the quality of the beam.
It measures the area of the phase space occupied by the beam
A beam of particles can be characterized in detail by its density in the six-dimensional phase space, (x; px; y; py; z; pz), where p is the canonical momentum.
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3. Liouville
The utility of a such a description derives from the discovery by Liouville that the density in phase space of a system of non-interacting particles subject to a Hamiltonian (such as that of an electromagnetic field) is constant in time. Accordingly, the extent of the beam in phase space, termed its emittance, is also constant in time, at least under ideal conditions.
LI2FE Diagnostic

4. Definitions of Brightness
For many practical application it is more meaningful to know the total beam current that can be in a 4 dimensional trace space V4.
For particle distribution whose boundary in 4D trace space is defined by an hyperellipsoid
[A/(m-rad)2]
Normalized Brightness
LI2FE Diagnostic

5. Standard techniques Quadrupole Scan Multiple screens Pepper pot
High energy spread leads chromaticity
It needs a lot of space
Multiple screens
Beam dominated by angular divergence
Pepper pot
Problems related to the mask
Insensitive to original beam spot size if the mask is placed at more than few mm from the plasma
LI2FE Diagnostic

6. Quadrupole scan k1 P1 P2 k2
Beam k3
Quadrupole
Schermo
It is possible to measure in the same position changing the optical functions
The main difference respect to the multi screen measurements is in the beam trajectory control and in the number of measurements
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7. Pepper pot
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8. Emittance measurements with pepper-pot like structures
To measure the emittance for a space charge dominated beam the used technique is know 1-D pepper-pot
The emittance can be reconstructed from the second momentum of the distribution
C. Lejeune and J. Aubert, Adv. Electron. Electron Phys. Suppl. A 13, 159 (1980)
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9. Design issues
The contribution of the slit width to the size of the beamlet profile should be negligible (in our case L greater than few cm)
The angular acceptance of the slit cannot be smaller of the expected angular divergence of the beam (in our case l< 1-5 cm)
The material thickness (usually tungsten) must be long enough to stop or heavily scatter beam at large angle
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10. Electron range in W
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11. In our case…
Any method Must be sensitive to the initial beam size to retrieve the emittance at the beginning
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12. A chance?
If the correlation at the beginning is zero the measurements of s and s‘ are enough to retrieve the emittance value.
Being the angular divergence a constant in a drift it can be measured everywhere
The only challenging measurement is the beam spot size at the origin X’ X
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13. 3 possibilities so far… Laser Wire Incoherent transition radiation
Coherent transition radiation (A. R. Rossi)
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14. Laser Wire
Rayleigh range of the laser beam : distance between the focus and the point where the laser spot-size has diverged to of its minimum value
Not intercepting device
Multi shot measurement (bunch to bunch position jitter, laser pointing jitter, uncertainty in the laser light distribution at IP)
Setup non easy
Resolution limited from the laser wavelength
Several effects to take into account
I. Agapov, G. A. Blair, M. Woodley, “Beam emittance measurement with laser wire scanners in the International Linear Collider beam delivery system”, Physical review special topics- accelerators and beams 10, (2007)
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15. Shintake monitor
Tsumoru Shintake, “ Proposal of a nanometer beam size monitor for e+e- linear collider”, Nuclear Instruments and methods in Physics Research A311 (1992) 453
Yamanaka et al. “Status of the first commissioning of the Shintake monitor for ATF2”, Proceeding of PAC09, Vancouver (Canada) 2009
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16. Critical issues Q-Switched 40 MW 532 nm, pulse length 8 ns (FWHM)
Stabilization of the system
It needs a lot of space for the setup
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17. OTR (Optical Transition Radiation)
It is emitted when a particle cross the boundary between two medium with different index of refraction
The radiation is emitted in a narrow cone with aperture 2/g
It is weak (~ 1 photon per 100 electrons in the optical wavelenght)
It is linear in the number of particles
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18. Equivalence of a metal interface
C. B. Schroeder, E. Esarey, J. van Tilborg, and W. P. Leemans, Theory of coherent transition radiation generated at a plasma-vacuum interface, PHYSICAL REVIEW E 69, (2004)
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19. Moving charge
At rest
moving
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20. Radiation field K1(x) Natural length
The intensity is proportional to the total charge
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21. TR angular distribution
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22. OTR for beam diagnostic
Both the angular distribution (giving information on the energy and the angular divergence of the beam) and the beam image (giving information on the beam size) can be measured (optical resolution, diffraction limited l/q)
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23. Problems so far
Realization of a compact optical system with at least 10X
Radiation is emitted on axis
Electron must be separated from the light
Band pass filter to avoid photons from the laser
LI2FE Diagnostic