The FFTB Experiment
We are proposing an experiment in the FFTB, using a meter-long, short-period, pulsed
helical undulator (u = 2.4 mm, K=0.17) and the SLAC low emittance electron beam at
50 GeV, to produce polarized photons in the energy range of a few MeV up to a cutoff
energy of about 10 MeV. Photons are converted to polarized positrons in a target which is
0.5 radiation lengths in thickness (targets of both Ti and W will be studied). The goal of
the experiment is to measure the yield, spectrum, and polarization of the photons and
positrons, and to compare the results to expectations from simulations.
This test is a 1% length scale demonstration of undulator-based production of polarized
positrons for linear colliders:
 Photons are produced in the same energy range and polarization characteristics as
for the collider;
 The same slab target geometry and material are used as in the linear collider;
 The polarization of the produced positrons is in the same range as in the linear
collider;
 The simulation tools being used to model the experiment are the same that are
being used to design the polarized positron system for the NLC.
Table 1 shows a comparison between the FFTB experiment, the NLC polarized positron
source design, and the unpolarized TESLA positron source system.
Table 1: TESLA, NLC, FFTB Polarized Positron Parameters
Parameter Units TESLA
NLC
FFTB
GeV 150-250
150
50
Eb
3x1010
8x109 1x1010
N-/bunch
2820
190
1
Nbunch/pulse
Hz
5
120
30
Pulses/s
1
1
0.17
K
cm
1.4
1.0
0.24
u
MeV
9-25
11
9.6
Ec10
N/m/e
0.72-2
2.6
0.37

%
1-5
1.8
0.5
Y+
m
135
132
1
L
12
12
8.5x10
1.5x10
2x107
N+/pulse
10
9
3x10
8x10
2x107
N+/bunch
%
40-70
40-70
40-70
Polarization
Figure 1 shows the layout of the proposed experiment in the SLAC FFTB. 50 GeV, low
emittance electrons are sent through a helical undulator to produce circularly polarized
1
photons. After the undulator, the 50 GeV electrons are bent vertically downward and sent
to the FFTB dump. The photons drift in the zero-degree line for a distance of about 20 m
where they are either analyzed or converted to positrons in a thin target. A nominal, low
emittance beam of 1x1010 e-/bunch, 1 bunch/pulse, 30 pulses/second at 50 GeV is
available for the experiment.
Figure 1: Conceptual layout of the experiment to demonstrate the production of polarized
positrons in the SLAC FFTB. Toro= beam current toroid; BPMi= beam position monitor;
PRi=beam profile monitors; Ai=aperture limiting collimators; HSB="hard" soft bend;
SSB="soft" soft bend; D1=FFTB primary beam dump bend magnet string; D2=analyzing
magnet.
Radiation shielding considerations limit the maximum beam power in the FFTB
enclosure to less than 2.5 kW. 30 Hz, 50 GeV operation corresponds to a beam current of
less than about 1x1010 e-/pulse. The emittances of the electron beam for fully coupled
damping ring operation and low beam charge is expected to be about x = y = 1.5x10-5
m-rad. For 10 m , the corresponding beam size is about 40 m, rms; the angular
divergence of the beam is about 4 rad, rms. Table 2 lists the beam parameters for the
experiment.
Table 2: FFTB Beam Parameters
Eb
Nb
GeV
50
e1x1010
x=y
xy
m-rad
m
-5
1.5x10
10,10
x,y
x',y'
D
m

rad

m
20
 σ 2x
2 
 2 + σ x' 
D

rad

1
2
1
γ
rad

For small values of K, the number of photons emitted per meter from the helical
undulator is dN dL :
2
dN
dL

4 
K2
30.6
K2

photons / m / e 
2
2
3 u  m  1  K
u  mm  1  K
(1)
where
K  0.00934B0  kG  u  mm .
(2)
The average energy of the photons for small K is
h
Eavg  0.5  Ec10  4.74 10
3
Ee2  GeV 
u  mm  1  K 2 
MeV / photon .
(3)
The radiated power per meter of undulator is dPu dL :
E 2  GeV  K 2
dPu
 qEn  2.32 104 e 2
n p 1010 f rep  Hz  Watts / m
dL
u  mm 


(4)
in which n p is the number of electrons per pulse in units of 1010 and f rep is the pulse
repetition in hertz.
The conversion yield of photons to positrons is calculated using the EGS4 code. An
EGS4 user code has been modified to allow introduction of arbitrary photon spectra and
polarization as data inputs. In addition, the modified version allows the user to input a
gaussian transverse beam size of arbitrary size. In the case of 0.5 r.l of Ti, the outgoing
beam size is dominated by the multiple scatter and target thickness in comparison to the
expected input size of about 80 m, rms.
Expected fluxes (photons and positrons) are listed below in Table 4.
For the FFTB experiment, Figure 2a shows the expected photon number spectrum and
figure 2b shows the corresponding circular polarization spectrum. The low K value limits
the flux to essentially only the first harmonic. Circular polarization of the photons is
taken as the third Stokes parameter. To produce the curves in Figures 2a and 2b, the
undulator radiation has been integrated over all emission angles. Since the characteristic
opening angle of the radiation is 1/ 4 rad, the finite aperture of the undulator does not
effect the calculation. Figure 2c shows the spectrum and longitudinal polarization of
positrons as a function of energy produced in 0.5 r.l. of Ti by the photons of Figures 2a
3
and 2b. The EGS4 code was used to simulate the positron production shown in Figure 2c.
Figure 2a: Photon number spectrum for the FFTB helical undulator: K=0.17, u = 2.4
mm, and assuming a electron beam energy of 50 GeV.
Figure 2b: Circular polarization of the photons in figure 2a.
4
E =9.62 MeV, K=0.17, q
Longitudinal Polarization x and Relative Number in Bin
3
c1
cut
=none
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
14
16
18
20
Positron Energy (MeV)
Figure 2c: Positron spectrum and longitudinal polarization resulting from the conversion
in 0.5 r.l. of photons in Figures 2a and 2b.
The undulator in Figure 1 is an inline pair of 0.5 m long undulators with opposing helical
windings. Use of opposing undulators is being adopted to help reduce possible systematic
errors in the polarization measurements. Discussion of this topic is deferred to the section
on polarimetry. Each undulator consists of a copper wire, bifilar helix, wound on a 1.068
mm OD, SS support tube; the ID of the tube is 0.889 mm. The undulator ID is thus ± 11
times the rms beam size. The period of the undulator is 2.4 mm. A wire diameter 0.6 mm
has been chosen. For 1800 A excitation, the on-axis field in the magnets is 0.76 T,
resulting in an undulator K parameter of K=0.17. For a 30 s current pulse, the
temperature rise is about 40C/pulse and the average power dissipation for 30 Hz operation
is about 225 W. The undulators are immersed in an oil bath for cooling. Table 3 lists
various undulator and power supply parameters. Figure 3 shows the back-to-back
undulator configuration with power supply connections.
Figure 3: Back-to-back pulsed undulator concept.
5
Table 3: FFTB Helical Undulator System Parameters
Parameter
Number of Undulators
Length
Inner Diameter
Period
Field
K
Current
Pulse Width
Inductance
Wire Type
Wire Diameter
Resistance
Repetition Rate
Power Dissipation
T/pulse
Units
m
mm
mm
kG
Amps
s
H
mm
ohms
Hz
W
0
C
Value
2
0.5
0.45
2.4
7.6
0.17
1800
30
1.8x10-6
Cu
0.6
0.125
30
225
4
To avoid noise in the detectors from synchrotron radiation due to upstream bends and
from the dump line magnets, two pairs of soft bends are included in the layout. These
bends all have the same polarity and give a vertical down kick to the electron beam. This
is the same geometry that was successfully used in the E144 experiment, albeit the soft
bend magnets are different magnets due to space limitations. Table 4 lists expected
photon parameters from the undulators and bend magnets in the immediate vicinity of the
experiment.
Table 4: FFTB Experiment Numbers
Parameter
Ee
np
frep
PB
B0
K
dN  dL
Ec10 ( c )
h
E avg
Units
Undulator D1 Bend SS Bend HS Bend
GeV
50
50
50
50
10 
1
1
1
1
10 e
Hz
30
30
30
30
kW
2.4
2.4
2.4
2.4
kG
7.58
4.45
0.066
0.660
0.17
photons/m/e0.37
2.75
0.04
0.41
MeV
9.62
(0.739)
(0.011)
(0.110)
MeV
4.81
0.228
0.003
0.034
6
dPu , B dL
mW/m
87
30
0.007
0.7
L(3  )
N 
m
photons/s
1
0.01
0.77
0.08
Pu , PB
mW
1.11011
87
9.5  109
0.35
9.5  109
0.005
9.5  109
0.05
Figure 1 shows three aperture limiting collimators for the experiment. A 1, A2 and A3.
These devices are 30 cm long (20 r.l.) cylinders of copper with 0.85 mm ID through holes
for beam transmission. A1 and A2 are water cooled because of the possibility of primary
beam interception. A3 does not require water cooling. A1 and A2 serve to protect the
undulator assembly from being hit by the primary electron beam. A2 is the more
important of the two devices which prevent the electron beam from making a head-on
collision with the undulator. The efficacy of A1 is compromised due to the necessity of
placing the soft bends between A1 and A2. A failure of the soft bends could result in the
glancing incidence of the beam into the undulator. Preliminary calculations indicate that
such interception should not damage the undulator in a single shot; the beam can be
turned off after detection of a single shot error. Collimator A3 is located just upstream of
the conversion target. A3 serves to limit extraneous halo (both photons and charged
particles) from entering into the detector region of the experiment.
Absolute component alignment tolerances of 100 m, rms in the transverse dimensions
for the beam line devices are required for the experiment. With the exception of the
photon collimator, A3, none of the devices required remote mover capability. Because to
the longish level arm ( ~20 m) from the end of the undulator to the measurement area,
remote movers for A3 are incorporated into the design. The 100 m tolerances do
however require consideration in the design of various supports and this has been taken
into account. As expected, the tolerances in z, along the beam line, are very loose and are
essentially set by what is required to match up and seal the vacuum chambers.
A variety of beam line instrumentation is shown in the layout. Three beam position
monitors (BPMs) are required for steering the primary beam through the undulators and
are used in the automated beam steering feedback to keep the beam away from the
undulator and on the dump. A beam current toroid (Toro) is used to measure the electron
currrent of a pulse to pulse basis with an accuracy of less than a few per cent. A number
of transverse beam profile monitors (PRi) are shown. These are used in the initial optical
set up of the beam line to adjust to the requisite beam size through the undulator. PR 4 has
been included in front of A3 for observation of the photon beam. In addition to set up, the
PR's will be used to monitor the beam quality over the duration of the experiment. The
PR's are destructive monitors. A wire scanner is also available for nondestructive, beam
size monitoring and may be substituted for PR1, PR2, or PR3. Ion chambers located along
the beam line are used to detect beam interception.
The precision and accuracy of the required instrumentation does not exceed the normal
performance of the standard FFTB equipment. All of the beam line hardware (power
7
supplies and instrumentation) will be controlled and monitored through the existing
SLAC accelerator control system.
8