1. Optical level manipulations of beams
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“Beam by design”
As you will see in the talk, much can be accomplished in making desirable beams by using lasers. This has implication of bringing two different communities to join forces and work together and it will have a profound impact on the future of accelerator field.
Alexander Zholents
Argonne National Laboratory
Workshop on Methods in Collective and Nonlinear Affects in Bright Charged Particle Beams, University of Chicago, October 27, 2017
Also reported at Workshop on nonlinear dynamics and collective effects in particle physics Arcidosso, Italy, September 18, 2017

2. Basics of the laser beam interaction with the electron beam
In what will follow, I will show several examples with the increased level of complexity, but all based on the same fundamental physics. Therefore, I want to spend few minutes to refresh these fundamentals using the most simple approximation of the laser plane wave.

3. Laser e-beam interaction in undulatorLu
Undulator parameter
Undulator/Modulator
Electron motion in undulator

4. Laser e-beam interaction in undulator (cont’d)
Laser field
(plane wave approximation)
kL=2p /lL
laser wave vector
Energy gain or loss by the electron
FEL resonant energy
where
After averaging over the undulator period
where
PL is the laser peak power
where
P0 = 8.7 GW

5. Beam manipulation using modulator- Magnetic chicane modules

6. Combination of One modulator and one magnetic chicane
Coherent Harmonic Generation1
High Gain Harmonic Generation2
for A>>1 Ds =
p=DE/sE
Intensity modulation
s/lL
Jn is Bessel function of order n
Bunching
1) Girard et al., 1984; Kinkaid et al., 1984
2) Ben-Zvi et al., 1991; Yu et al., 1991; Allaria et al., 2013

7. Example: generation of attosecond x-ray pulses
SASE FEL
Current Enhanced Self Amplified Spontaneous Emission (ESASE)*
electric field
current, (kA)
10 mJ
1010ph
one laser
two lasers
250 asec
Understanding how to create artificial photosynthesis, flexible high-temperature superconductors, or better solar cells, or a myriad other advances, will only be possible when we have the ability to image electrons by freezing time within a few quintillionths of a second.
t (fs)
t (fs)
Nearly Fourier transform limited x-ray pulse
Carrier-envelop phase stabilized few cycle laser pulse
*) Zholents, 2005; Zholents and Penn, 2005; Y. Ding et al., 2009; Marinelli, 2016.

8. Tapered undulator method*
generation of attosecond x-ray pulses (cont’d)
Tapered undulator method*
Hard x-rays
Soft x-rays
Energy chirp is compensated by the undulator taper in the central slice
Wigner transform
of the on-axis far field
-2.5 -5
t, fs
7.9
7.6
7.8
Wavelength, nm
Chirp
x ≈ 0.5
7.7
2.5
Frequency chirp definition
~ 200 as
Contrast ≈ 1
Energy modulation
lx=0.15 nm
Fourier transform limited pulse ~ 1.5 fs (FWHM)
W.M. Fawley, Nucl. Inst. and Meth. A 593, 111(2008).
With two lasers one can manipulate the energy chirp and, thus, the frequency chirp
*) E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, Phys. Rev. ST-AB 9, (2006).

9. Combination of two modulators and one magnetic chicane*
Partial reduction of the energy spread induced by first modulator
After second modulator
Jia et al.
After the chicane
Energy spread histogram
Favorable for HGHG
Bunching
*) McNeil et al., 2005; Allaria and De Ninno, 2007; Jia, 2008

10. Combination of two modulators and two magnetic chicanes*
Echo Enabled Harmonic Generation (EEHG)
s/lL 1 2 3 4 5 6 p
0.36
Efficient bunching
Evolution of the longitudinal phase space through an EEHG system
Intensity of COTR
Radiation wavelength (nm)
Only 1590 nm modulation, w1
experimental results
Both 1590 nm and 795 nm modulations, w2
7th harmonic
*) Stupakov, 2009; Xiang and Stupakov, 2009; Xiang et al., 2012; Zhao et al., 2012

11. Synthesis of radiation with an arbitrary waveform*
Cascaded laser manipulations for tailoring the harmonic content of the radiation
Quadrupoles are used in chicanes to control the sign of R56
Generation of odd-harmonic bunching for emission of square waveform fields
Bunching factor
harmonic p
current
Deleterious effects:
Incoherent synchrotron radiation
Intrabeam scattering
Coherent synchrotron radiation
Recently proposed schemes employing several modulator-chicane cascades also allow one to precisely tailor the harmonic content of the electron peak current distribution and radiation at the scale of the optical wavelength, often using only one laser wavelength. Such systems can behave as optical analogs of conventional rf function generators, suggesting new ways to produce radiation with customized waveforms.
*) Hemsing and Xiang, 2013

12. Beam angular modulation using the laser

13. Using TEM10 laser field mode
Second order solution of paraxial wave equation can be used to impart an optical-scale angular kick to the electrons* x y
TEM10
TEM10
Gouy phase
(1) -2
energy modulation
electron horizontal offset
applying Panofsky-Wenzel theorem
obtain angular modulation
*) Zholents and Zolotorev, 2008

14. Application of angular modulation
unwanted spikes
Generation of a high-contrast attosecond x-ray pulses using a few-cycle laser pulse
2 mm laser
TEM00
TEM10
2 mm laser
TEM10
Due to transverse oscillations electrons acquire additional phase shift:
LG is the FEL gain length
kx =2p/lx is the x-ray wave number
Slippage caused by transverse oscillations can increase or even “kill” the FEL gain

15. Application of angular modulation (cont’d)
Central peak
10-10 Px-ray (W)
t (fs)
Peak power
Contrast > 100
(compare to ~ 1)
115 as, 10 mJ
lx = 0.15 nm
Peak power
100 GW

16. Application of angular modulation (cont’d)B QD QF
z → x and x → z emit. exch.
Emittance exchange (EEX) beamline with deflecting cavity*
TM110
TM010
Deflecting cavity B QD QF
Laser assisted EEX with angular modulation by the laser**
CO2
*) Cornacchia and Emma, 2002; Emma et al., 2006; Sun et al., 2010; Xiang and Chao, 2011; Zholents and Zolotorev, 2011.
**) Xiang, 2010

17. Application of angular modulation (cont’d)
EEX for regular spaced clusters of electrons
Initial x-x’ phase space
x’(s) after interaction with laser
High brightness electron clusters
Final phase space
x(s) after EEX
Energy chirp before EEX and collimator after EEX can be used to select a single cluster
Furthermore, the increased longitudinal emittance after EEX is helpful for suppressing the microbunching instability, which can also degrade the FEL performance.
Such small transverse emittances enable the operation of an x-ray FEL at lower energy if one manage to build the undulator with a small period.
Representative beam phase space evolution in EEX with a laser
*) Xiang, 2010

18. Diagnostics with lasers

19. Application of angular modulation (cont’d)
Optical oscilloscope: combination of the rf deflector and laser deflector*
(TEM10) mode
Simulation: a fragment of the electron bunch on the YAG screen
RF streaking
*) Andonian et al., 2011
Laser streaking

20. Laser heater* An effective tool to suppress microbunching instability
The laser heater works by introducing a correlated microstructure in the phase space of the beam on the scale of the laser wavelength that is effectively washed out through transport, resulting in an increase in the uncorrelated energy spread.
*) Saldin, Schneidmiller, Yurkov, 2004; Huang et al., 2004; Huang et al., 2010

21. Optical replica synthesizer*
modulator, By
radiator, Bx
Polarizer
FROG e-
Evolution of the longitudinal phase space in a simplified ORS scheme
To measure the temporal dependence of the charge, emittance and energy spread distributions within the bunch using frequency resolved optical gating (FROG).
Assumed that longitudinal dynamics in the undulators and dispersion section is governed by purely single-particle effects where the results do not depend on the presence of other particles.
So, measuring electron current profile, const*I(t); for a single ultrashort electron pulse is reduced to the problem of a single-shot, ultrafast laser pulse-shape measurement.
A two dimensional (2-D) phase retrieval algorithm is used to extract the intensity and phase of a pulse from its spectrogram
Measuring I(t) as a function of R56 allows to measure the energy spread
FROG trace maps bunch shape:
Electric field (a.u)
t (fs)
slice energy spread
energy modulation
*) Saldin et al., 2005; Salén et al., 2011;

22. Acknowledgement
Many examples given in the presentation are taken from the paper: “Beam by design: Laser manipulation of electrons in modern accelerators” published in Rev. of Modern Phys., V. 86, p.897, (2014).
And I benefited from many fruitful discussions with Erik Hemsing, Gennady Stupakov and Dao Xiang during the work on the paper.

23. Conclusion
Beam manipulations on the microscale, in particular those using the laser, have shown a tremendous potential for preparing the better beams
Many techniques have been adapted in practice and the number of newly proposed techniques continue to grow
The outlook for a future is very bright as new possibilities like transverse laser modulation and beam shaping are awaiting further explorations

24. Thank you for your attention

25. Beam manipulation using two modulators

26. BEAM CONDITIONING FOR FREE-ELECTRON LASERS*
MODIFYING BEAM PROPERTIES BY IMPOSING USEFUL CORRELATIONS ON A MICROSCALE
*) Sessler, Whittum, Yu, Phys. Rev. Lett., 68, 309 (1992).

27. What “beam conditioning” does
Addresses the problem of de-bunching due to electron transverse oscillations in FEL
microbunch z y
undulator z y z y
DE/E y
debunching happens
DE/E y
no debunching
Solution of the problem:
Provide correlation between the amplitude of electron transverse oscillation and electron energy to speed up the electron
Beam conditioning relaxes requirements on the beam emittance in FELs

28. Laser-assisted electron beam conditioning*
(extension of a time delay method proposed by Vinokurov)
e-beam
By utilizing laser and wiggler for electron energy modulation this scheme gives a factor of 105 better conditioning than equivalent scheme based on RF cavities:
!!!
*) Zholents, Phys. Rev. ST–Acc. and Beams, 8, , (2005)

29. Laser-assisted electron beam conditioning cont’d
e-beam
Caution:
approximately one half of electrons have wrong sign of correlations
Best choice of parameters to achieve conditioning
short ~ 20 mm electron bunch,
single cycle 1.5 THz, ~15 mJ light pulse*) to chirp and de-chirp the electron bunch
one period wiggler
*) feasible with the accelerator-based coherent emission THz source, i.e, like TeraFermi

30. Laser-assisted electron beam conditioning cont’d
Example: LCLS-like FEL with ~5 times of LCLS emittance
GENESIS simulations
Beam parameters:
energy = 14 GeV
peak current = 3.4 kA,
energy spread = 1.2 MeV, emittance = 2.4 mm-mrad,
beta-function = 20 m.
- no conditioning, 2 - ideal conditioning (all electrons),
3 - partial conditioning.