PBPL
Study of X-ray Harmonics of the Inverse
Compton Scattering Experiment at UCLA
Particle Beam Physics Lab
UCLA
Adnan Doyurana, Joel Englanda , Chan Joshib , Pietro Musumecia , James Rosenzweiga, Sergei Tochitskyb , Gil Travisha, Oliver Williamsa
a UCLA/Particle
doyuran@physics.ucla.edu
Beam Physics Laboratory, b UCLA/Laser Plasma Group, Los Angeles, CA 90034, USA
Design Electron, Laser and Scattered Photon Beam Parameters
Abstract
Electron and Laser Beam Parameters
We propose an Inverse Compton Scattering experiment, which will investigate nonlinear properties of the
scattering utilizing the terawatt CO2 laser system in Neptune Laboratory at UCLA. When the normalized amplitude
of the vector potential a0 is larger than unity the scattering occurs in the nonlinear region; therefore, higher
harmonics are also produced. We discuss the experimental setup and procedure to measure the angular and spectral
distribution of the higher harmonics scattered from 14 MeV electron beam. We also present a calculation tool for
the Double Differential Spectrum (DDS) distribution and total number of photons produced for both head-on and
90o scattering. We decided to do the experiment at 90o to avoid complications due to strong diffraction of the
incoming laser. We discuss the electron and laser beam parameters for the experiment.
Scattered Photon Beam Parameters
Parameter
Electron Beam Energy
Beam Emittance
Electron Beam spot size (RMS)
Value
14 MeV
5 mm-mrad
25 m
Beam Charge
300 pC
Bunch length (rms)
4 ps
Inverse Compton Scattering
UCLA/NEPTUNE Laboratory Accelerator consists of a photo-injector
RF Gun (BNL/SLAC/UCLA), a solenoid, PTW Linac, a chicane
compressor, Three triplets for final focusing, 10 steering magnets, two
integrating current transformers (ICT) for charge measurements and a
number of pop in monitors for beam measurements. The accelerator can
deliver up to 15 MeV Electron beams with ~5 mm-mrad emittance and
300 pC charge. We plan to do the experiment with 14 MeV electrons.
The photo-injector gun is driven by
Achieved beam parameters for NEPTUNE.
10 ps long UV laser at 266 nm. A
1024 nm mode locked Nd:YAG
Parameter
Value
Beam Energy
15 MeV
laser is amplified by Nd:Glass
Energy spread
<0.5%
regenerative amplifier and then
Energy jitter
<1%
quadrupled which yields up to 200
Beam size (rms)
100 µm
J pulse energy.
Beam Charge
300 pC
Bunch length (rms)
CO2 Laser Power
4 ps
500 GW
CO2 Rayleigh range
2.2 cm
Pointing jitter
<100 µm
Alignment precision
<1 mrad
UCLA/NEPTUNE Laboratory
houses a Terawatt CO2 laser system
which delivers 10.6 m CO2 pulses
with 200 ps pulse length and up to
100 J energy pulses (500 GW)
I0 is the intensity and 0 is the
wavelength of the incident laser
a0  0.85 105 0 [m] I 0 [W / m2 ]

0 2  2 (1   z 0 )
2
a0
1
 2 2
2
Frequency of the scattered photons where 0 is
the frequency of the incident laser,  is the
relativistic factor of electron beam, z0 is
component of the electron initial velocity in the
direction of laser pulse. (z0=1 for head on
scattering and z0=0 for 90o scattering.
10
CO2 laser wavelength
10.6m
Number of Photons per electron
0.11
CO2 laser Rayleigh Range
0.75 mm
Total Number of Photons
CO2 Laser Power
500 GW
Opening angle (deg)
15
CO2 waist size (RMS)
25 mm
bandwidth (%)
10
CO2 laser pulse length
200 ps
rb
n 
High intensity CO2 laser can be focused to achieve
the normalized laser strength parameter a0  1 .
Therefore it is possible to investigate the nonlinear
properties of the Inverse Compton Scattering. In
order to avoid the additional nonlinearities due to
diffraction we choose a transverse scattering
geometry (I=90o).
a0  1
0 n 2  2 (1   z 0 )
Frequency of harmonics
2
a0
1
 2 2
2
2
2
2
d In
e k
 20
d d  c
2
 sin k  0 
2
2

[
A
J

A
(
J
/
b
)
]
2
n
t

 1 n
 k 
Radiation Spectrum for circularly
polarized laser beam*
75 m waist radius using an F3 and 50 m waist radius using
F2 focusing geometries are achieved experimentally in
Neptune.
The M factor is estimated to be 1.93.
For F2 geometry the Rayleigh range is 0.75 mm. 500 GW laser
yields an intensity of 1.25x1016 W/cm2 and a0  1. Since a0 is
proportional to 0 wavelength it is advantageous to use CO2
laser compared to YAG lasers.
For F3 geometry the Rayleigh range is 1.7 mm. 500 GW laser
yields an intensity of 5.5x1015 W/cm2 and a0  0.67 .

1

n n N 0
 2 
Bandwidth where N0 is the number of
periods that electrons interact.
10% bandwidth is estimated for the
fundamental
(1  a0 / 2)
n 
s
2
e k0  sin k  0  k g
b1
b2
2

[
B

B

2
B
]
0
1
2


d d 4 2 c  k  k0 


2
2
d I n
2
2
e k0  sin k 0  b1
b2
2

[
B

2
B
]
1
2


d d 4 2 c  k     
   
2
2
2
d 2I n
d d

d 2 I n
d d

d 2 I n
d d 
Radiation Spectrum for linearly polarized
laser beam*
2
 2 n
Half opening angle of the harmonics
15 mrad half angle is estimated
Permanent Magnet Quadrupole (PMQ) System for Final Focus
For circularly polarized laser at 90o geometry
n=2
Four permanent magnet cubes (NdFeB) are
positioned to produce Quadrupole field at the axis.
Radia Program is used to design the magnet to
produce 110 T/m gradient. Octagonal iron yoke
provide proper field flow and hyperbolic iron tips
produce perfect quadrupole field inside the magnet.
The prototype was build and it is good agreement
with the simulation.
1% field error in the magnetization of the cubes in
worst orientation causes 10 m axis offset which is
quite reasonable. The cubes are measured and
sorted to reduce possible errors.
n=3
Permanent Magnet Dipole (PMD)
for Energy Spectrometer
Beam Transport for Inverse
Compton Scattering
A Permanent magnet Dipole is designed to serve
as energy spectrometer and dump for the
electron beam. It bends the beam by 90o. The
geometry is chosen so that beam always exits
the dipole at 90o for various energies only with
some offset.
Iron Yoke is designed for proper field flow
Magnets are made out of NdFeB high grade
magnets which can yield 1.2-1.4 T
magnetization.
The Magnetic field inside the gap is ~0.85 T. For
14 MeV energy design electrons the bend radius
is about 55mm
For linearly polarized laser at 90o geometry where electron’s velocity is parallel to plane of polarization
PMD
F-Cup
IP
Beam size plot along the Neptune beamline for Inverse
Compton experiment simulated by MAD program.
Angle of the trajectory
Trajectory of the electron beam in PMD
For linearly polarized laser at
2
Experimental Setup
Normalized intensity distribution of the scattered photons of the first three harmonics
The detector is centered at zo along z (=0) axis. The distances in x and y are measured in units of (x/zo)~ 
90o geometry
2.00E+08
Wavelength of harmonics
n
d 2 I n
*Ride, Esarey, Baine, Phys. Rev. E, Vol
52, p 5425 (1995)
Nonlinear Harmonics Spectrum
n=1
0.33 ps
No of periods that electrons see
Note: All the variables are defined in the paper
a0 is the normalized amplitude of the vector
potential of the incident laser field (just like K,
undulator parameter)
Interaction time
Nonlinear Harmonics
Inverse Compton Calculations
e A0
a0 
me c 2
Value
10.7 nm
117.7eV
10 ps
25 m
Laser beam size at the IP (rms)
Introduction
Parameter
Scattered Photon wavelength
Scattered Photon Energy
Scattered Photon Pulse duration
where electron’s velocity is perpendicular to plane of polarization
Inside
the Magnet
Inside
the Magnet
X`[rad]
X[mm]
Outside
the
Magnet
Outside
the magnet
Field distribution inside the PMD gap
simulated by Radia
Trajectory of the 14 MeV electron
beam in the PMD gap. Beam enters the
magnet by 45 o angle and exits by 45 o
angle. Y axis is the length of the magnet and
x axis is width.
Angle of the 14 MeV electron
trajectory in the PMD gap. Angle linearly
changes from /4 to -/4 inside the magnet.