### No Slide Title

```Study of X-ray Harmonics of the
Polarized Inverse Compton Scattering
Experiment at UCLA
Adnan Doyurana, Joel Englanda , Chan Joshib , Pietro
Musumecia , James Rosenzweiga, Sergei Tochitskyb , Gil
Travisha, Oliver Williamsa
a UCLA/Particle
b
Beam Physics Laboratory
UCLA/Laser Plasma Group
Los Angeles, CA 90034, USA
PBPL
Particle Beam Physics Lab
UCLA
Introduction
a0 
e A0
me c 2
a0 is the normalized amplitude of the vector potential of
the incident laser field (just like K, undulator parameter)
a0  0.85 10 0 [m] I 0 [W / m ]
5

2
I0 is the intensity and 0 is the
wavelength of the incident laser
0 2  2 (1   z 0 )
2
a
2
1 0   0  2
2
Frequency of the scattered photons where
0 is the frequency of the incident laser, 0
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.
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Particle Beam Physics Lab
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rb
ICS Calculations
N

N0 
3
 N 0 a0
2
(1   z ) c T
0
2
(1  a 0 / 2)(1   z 0 ) The total number of photons radiated
(1   z )
Where N0 is the number of periods of the
laser field with which electrons interacts
 z 0  a0 2 / 4  0 h0
z 
2
1  a0 / 4  0 h0
 = 1/137
by a single electron
the average axial electron velocity
Fine structure constant
h0   0 (1   z 0 )
L0 2 Z r 2 w0
1
T  min(
,
,
) Interaction time
c
1   z  z  0
 w0 2
Rayleigh range where w0 is the waist radius of the laser
Zr 
0
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Particle Beam Physics Lab
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Gaussian beam
w  2
w0
zM 
w( z )  w0 1  

Z
 r 
2
2
1
F# 
2M 2
Radius of the beam
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Particle Beam Physics Lab
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 Zr
0
F number is f/D
~z/2w(z)
Incident Laser focusing
properties
75 mm waist radius using an F3 and 50 mm 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 .
PBPL
Particle Beam Physics Lab
UCLA
Time duration of the scattered
photons
For head configuration the pulse duration will be determined by either the
electron bunch length if Lb<L0, Zr or by the pulse length of the laser pulse if
electron bunch length is longer than the laser pulse length. So we can
express the duration of the scattered photons as
 
1
min[ Lb , ( 4 Z r  L0 )]
c
For transverse scattering duration of the scattered photons is again
determined by electron bunch length if electron is short or by transverse
dimension and Rayleigh range of the laser pulse along with the pulse
length if electron is long. Thus we can express duration of scattered
photons as
1
   min[ Lb ,2Z r  L0 , L0  2 rb ]
c
PBPL
Particle Beam Physics Lab
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Inverse Compton Scattering Experiment
Design Parameters
Electron and Laser Beam Parameters
TABLE 1). Electron and Laser Beam Parameters
Parameter
Electron Beam Energy
Value
Beam Emittance
Electron Beam Spot size (RMS)
Beam Charge
Bunch Length (RMS)
Laser Beam size at IP (RMS)
CO2 laser wavelength
CO2 laser Rayleigh range
CO2 laser power
CO2 laser pulse length
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Particle Beam Physics Lab
UCLA
14 MeV
25 mm
300 pC
4 ps
25 mm
10.6 mm
0.75 mm
500 GW
200 ps
Design Scattered Photon
Properties
Transverse scattering
Parameter
Value
Parameter
Scattered photon wavelength
5.3 nm
Scattered photon wavelength
10.7 nm
Scattered photon energy
117.7 eV
Scattered photon energy
235.3 eV
Scattered photon pulse duration
(FWHM)
Interaction time
10 ps
Number of periods that electrons
see (N0)
Number of photons emitted per
electron (N)
283
Total number of photons
Half Opening Angle
Bandwidth
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Particle Beam Physics Lab
5 ps
3.34
6.3.109
10 %
UCLA
Scattered photon pulse duration
(FWHM)
Interaction time
Number of periods that electrons
see (N0)
Number of photons emitted per
electron (N)
Total number of photons
Half Opening Angle
Bandwidth
Value
10 ps
0.33 ps
10
0.11
2.108
10 %
Nonlinear Harmonics

n
 
n 

1
n N0
Bandwidth where N0 is the number of
periods that electrons interact.
10% bandwidth is estimated for the
fundamental
(1  a0 / 2)
2
 2 n
Half opening angle of the harmonics
15 mrad half angle is estimated
0 n 2  2 (1   z 0 )
n 
2
a0
1
 2 2
2
Frequency of harmonics
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Particle Beam Physics Lab
s
n
Wavelength of harmonics
UCLA
Double Differential Spectrum of
Nonlinear Harmonics
2
d In
e k0  sin k 0 
2
2

 2 
[
A
J

A
(
J
/
b
)
]
2
n
t
 1 n
d d  c  k 
2
2
2
circularly polarized laser
beam*
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
d I n
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*
*Ride, Esarey, Baine, Phys. Rev. E, Vol 52, p 5425 (1995)
PBPL
Particle Beam Physics Lab
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2
Note: All the variables are defined in the paper
DDS plots for circularly
polarized laser
n=1
n=2
n=3
1800
geometry
n=1
n=2
n=3
900
geometry
PBPL
Particle Beam Physics Lab
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DDS plots for linearly polarized
laser
n=1
n=2
n=3
1800 geometry
n=1
n=2
n=3
900 geometry
parallel
polarization
n=1
n=2
n=3
900 geometry
perpendicular
polarization
PBPL
Particle Beam Physics Lab
UCLA
(PMQ) System for Final Focus
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 mm axis offset which is quite reasonable.
The cubes are measured and sorted to reduce possible errors.
PBPL
Particle Beam Physics Lab
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Beam Transport for Inverse
Compton Scattering
IP
PBPL
Particle Beam Physics Lab
UCLA
F-Cup
Permanent Magnet Dipole (PMD)
for Energy Spectrometer
Field distribution inside the PMD gap
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 90 o 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
PBPL
Particle Beam Physics Lab
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Trajectory in the PMD
Trajectory of the electron beam in PMD
Angle of the trajectory
Inside
the Magnet
X[mm]
Inside
the Magnet
Outside
the
Magnet
Outside
the magnet
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.
PBPL
Particle Beam Physics Lab
UCLA
Angle of the 14 MeV electron
trajectory in the PMD gap. Angle linearly
changes from /4 to -/4 inside the magnet.
ICS Box design
PBPL
Particle Beam Physics Lab
UCLA
Current Status





PBPL
PMQ design is complete and
manufacturing is underway
PMD design is complete and
manufacturing is in progress
Box design is in progress
Soft X-ray camera may come from
Argonne
Polarization measurement is being
researched
Particle Beam Physics Lab
UCLA
```