Electron-Beam-Based Sources of Ultrashort X-ray Pulses

TLDR: A review of various methods for generation of ultrashort X-ray pulses using relativistic electron beam from conventional accelerators is presented in this article, where spontaneous and coherent emission of electrons are considered.

Abstract: A review of various methods for generation of ultrashort X-ray pulses using relativistic electron beam from conventional accelerators is presented. Both spontaneous and coherent emission of electrons are considered.

Figures

Figure 5. (a) A low signal gain as a function of delay between the laser pulse and the electron bunch (at optimum wiggler gap). Solid line is a Gaussian fit with σz =16.6 ps. (b) Spectral dependence of the gain as a function of wiggler emission wavelength (adjusted via the wiggler gap). Solid line is the gain predicted from Eq. (3) with Ipeak=23 A, dots are the measured values.

Figure 26. A schematic of the generation of two attosecond x-ray pulses, where W1, W2, and W3 are wiggler magnets; C1, C2, and C3 are dispersion sections; R1 and R2 are xray undulator radiators; ω1 is the carrier frequency of the long laser pulse; and ω2 is the carrier frequency of a few-cycle laser pulse that is split into two pulses. ARTICLE IN PRESS

Figure 25. Calculated power of x-ray radiation of the electrons in the undulator radiator. The FWHM pulse length is 20 attoseconds.

Figure 14. A schematic for generating sub-ps x-ray pulses via Thomson scattering.

Figure 21. Calculated angular modulation of the 14-GeV electron bunch with the normalized emittance of 10-6 meters and beta function in the wiggler βx0 = 200 m, e.g.,

Figure 8. A calculated 2D electron density distribution (as a function of time and horizontal displacement normalized on the rms size) after electron bunch propagation through 1.5 arc sectors at the ALS from the wiggler to the bend magnet.

Full text

ANL/APS/LS-320
Electron beam-based sources of ultrashort x-ray pulses
Alexander Zholents
Advanced Photon Source, Argonne National Laboratory
Argonne, IL 60439
(September 7, 2010)
To be published in Reviews of Accelerator Science and Technology
The submitted manuscript has been created by UChicago Argonne, LLC, Operator of
Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy
Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357.
The U.S. Government retains for itself, and others acting on its behalf, a paid-up
nonexclusive, irrevocable worldwide license in said article to reproduce, prepare
derivative works, distribute copies to the public, and perform publicly and display
publicly, by or on behalf of the Government.

2
Electron beam-based sources of ultrashort x-ray pulses
*
Alexander Zholents
Argonne National Laboratory, Advanced Photon Source,
9700 South Cass Ave., Argonne, IL 60439
Abstract
A review of various methods for generation of ultrashort x-ray pulses using
relativistic electron beam from conventional accelerators is presented. Both spontaneous
and coherent emission of electrons is considered.
Introduction
The importance of the time-resolved studies of matter at picosecond (ps),
femtosecond (fs), and atttosecond (as) time scales using x-rays has been widely
recognized including by award of a Nobel Prize in 1999 [Zewa]. Extensive reviews of
scientific drivers can be found in [BES1, BES2, BES3, Lawr, Whit]. Several laser-based
techniques have been used to generate ultrashort x-ray pulses including laser-driven
plasmas [Murn, Alte, Risc, Rose, Zamp], high-order harmonic generation [Schn, Rund,
Wang, Arpi], and laser-driven anode sources [Ande]. In addition, ultrafast streak-camera
detectors have been applied at synchrotron sources to achieve temporal resolution on the
picosecond time scale [Wulf, Lind1].
In this paper, we focus on a different group of techniques that are based on the use
of the relativistic electron beam produced in conventional accelerators. In the first part
*
Work supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences,
under Contract No. DE-AC02-06CH11357.

3
we review several techniques that utilize spontaneous emission of electrons and show
how solitary sub-ps x-ray pulses can be obtained at existing storage ring based
synchrotron light sources and linacs. In the second part we consider coherent emission of
electrons in the free-electron lasers (FELs) and review several techniques for a generation
of solitary sub-fs x-ray pulses. Remarkably, the x-ray pulses that can be obtained with the
FELs are not only significantly shorter than the ones considered in Part 1, but also carry
more photons per pulse by many orders of magnitude.
Part 1: Spontaneous emission
1. Generation of Ultrashort X-ray Pulses from an Electron Storage Ring
1.1. Preamble
Modern synchrotron light sources based on electron storage rings operate with
electron bunches whose rms bunch length in the zero-current approximation is defined by
the total gap voltage V of the radio frequency (rf) accelerating cavities, harmonic number
h of the rf field, electron bunch energy spread
σ
Ε
, and momentum compaction factor
α
c
:
s
bc
r
E
z
hV
E
cT
E
φπ
ασ
σ
cos2
0,
=
.
Here E
b
is the electron beam energy, T
r
is the revolution time and
φ
s
is the synchronous
phase of the rf field, c is the speed of light, and e is the electron charge. Typically
σ
z,0
/c
is of the order of a few tens of ps. However, as the electron beam current increases to a
few mA per bunch, the bunch length also increases due to impact of the self-induced
fields [Pell, Bane] and microwave instability [Gao, Chao]. Therefore, most of the light
sources operate with electron bunches whose length is greater than
σ
z,0
. Several

4
approaches to shorten the electron bunch have been tried, and one that takes advantage of
a small (close to a zero)
α
c
had been found to be the most successful [Feik1, Feik2].
However, the synchrotron tune
b
c
s
E
Ve

α
π
ν
2
1
=
also decreases with
α
c
, and less frequent change of particle positions inside the electron
bunch leaves more time for instabilities to build up. As a result, short bunches of the
order of 1 ps can only be obtained along with a dramatic reduction of the electron bunch
current [Feik1, Limb]. This seems to be acceptable for generation of coherent
synchrotron radiation (CSR) in the THz part of the radiation spectrum [Wüst] but not for
spontaneous emission of photons in the x-ray part of the spectrum. Also, the lattice of x-
ray sources is always optimized to yield the smallest electron beam emittance, but low
α
c
storage rings need a negative dispersion function in a large number of bending magnets,
and this is incompatible with a lowest-emittance lattice.
Up to this point we presumed that the x-ray pulse should have the same lengths as
the electron bunch. However, one can obtain a much shorter x-ray pulse if one can select
the radiation emitted by electrons from a short section of the electron bunch and separate
it from the radiation of all other electrons. One way to achieve this is to use ultrafast
streak camera detectors [Wulf, Lind1]. Another way is to force an ultrashort slice of the
electron bunch to emit photons in a different direction than other electrons. Two variants
of the latter approach will be discussed next.

5
1.2. Laser Energy Modulation of Electron Bunches
The “slicing” technique proposed in [Zhol1] uses a femtosecond optical pulse to
generate sub-ps x-rays pulses. Figure 1 shows a schematic of this technique. A
femtosecond optical pulse of moderate energy (~1 mJ) modulates the energy of an
ultrashort slice of a stored electron bunch as they co-propagate through a wiggler (Fig.
1a). The energy-modulated electrons within this slice are spatially separated from the
main bunch in a dispersive section of the storage ring (Fig. 1b) and can then be used to
generate femtosecond x-rays (Fig. 1c) at a bend-magnet (or insertion-device) beamline.
Note that energy modulation of an ultrashort slice will leave behind a hole or dark pulse
in the main electron bunch (see Fig.1c). This will be manifested in the generated x-rays
and, in principle, can be used for time-resolved spectroscopy in the same manner as a
bright pulse. The original electron bunch is recovered due to synchrotron radiation
damping, leaving no impact from energy modulation on the electron beam lifetime.
Figure 1. Schematic of the laser slicing method for generating sub-ps synchrotron
pulses.
Effective energy modulation of the electrons is accomplished using the high peak
electric field (~10
9
V/m) of a femtosecond laser pulse. Electrons that co-propagate with
the optical pulse through a wiggler are accelerated or decelerated depending on the
optical phase
φ
,
as seen by each electron at the entrance of the wiggler. The energy

Frequently asked questions

Q1. What are the contributions in "Electron beam-based sources of ultrashort x-ray pulses" ?

A review of various methods for generation of ultrashort x-ray pulses using relativistic electron beam from conventional accelerators is presented. In this paper, the authors focus on a different group of techniques that are based on the use of the relativistic electron beam produced in conventional accelerators. 

Q2. Why do electrons accumulate toward the head of the bunch?

due to path-lengthdifferences (caused by time-of-flight properties of the storage ring), electrons with ∆E<0accumulate toward the head of the bunch while electrons with ∆E>0 accumulate towardthe tail of the bunch, giving rise to the time-skew observed in the electron distribution. 

Q3. What is the x-ray yield at shallow scattering angles?

At shallow scattering angles, the x-ray pulse duration scales as ψ; however, the x-ray yield also scales with the scattering angle. 

Q4. How can phase advance error be compensated?

Phase advance error can be compensated by changing the relative voltage of the first and second sets of cells of the second cavity. 

Q5. How can one regulate the length of the x-ray output?

by changing the duration of the laser pulse and adjusting the number of active wiggler periods, one can regulate the length of the WS and therefore the duration of the x-ray output. 

Q6. How was the synchronization between laser pump and x-ray probe pulses obtained?

A synchronization between laser pump and x-ray probe pulses in this techniquewith a sup-ps jitter can be obtained by linking the laser pulse to a zero crossing phase of the deflecting cavity. 

Q7. What is the optimum time interval between the laser and the bunch?

since the bunch slice is only a small fraction of the total bunch, an interaction interval corresponding to 30% of the storage ring damping time (e.g., of the order of a few ms) is sufficient to allow recovery of the electron beam between laser interactions. 

Q8. What is the benefit of operating at longer wavelengths?

The benefit of operating at longer laser wavelengths is cancelled by the corresponding reduction in ML (assuming fixed laser and x-ray pulse durations). 

Q9. How does the laser interact with the bunch?

By arranging the timing such that the laser interacts sequentially with each bunch in the storage ring, the time interval between interactions is given by NB/fL, where NB is the number of bunches in the ring. 

Q10. How many diffractionlimited x-ray beams can be sliced?

In fact, if the angle between the head and tailtrajectories is sufficiently large, the radiation fan can be sliced into many diffractionlimited x-ray beams that can be spatially separated. 

Q11. How can one create a vertical dispersion bump in a bend magnet?

One can use the natural horizontal dispersion or create a vertical dispersion bump in a bend magnet or an undulator [Stei] and take advantage of the smaller vertical beam size. 

Q12. What is the way to have a group of pulses with a controlled time delay?

It will also be possible to have groups of two or more attosecond pulses with a controlled time delay between individual pulses and variable wavelengths for individual pulses. 

Q13. What is the effect of the acceleration on the energy modulation of the electrons?

This acceleration does not affect the energy modulation introduced in the wiggler and does not produce noticeable relative longitudinal motion of electrons because of the ultra-relativistic electron energies.