SLAC-PROPOSAL-E166
October 22, 2002
A Two-Stage Proposal to Test Production of Polarized
Positrons with the SLAC 50-GeV Beam in the FFTB
Stage I:
Production and Polarimetry of Polarized γs with a Helical Undulator in
SLAC’s FFTB
Stage II:
Production of Polarized e+ with the Polarized γs from Stage I, and their
Polarimetry
G. AlexanderDE , P. AnthonySL , Y. BatyginSL , T. BehnkeDE , S. BerridgeU T , W. BuggU T ,
R. CarrSL , G. ChudakovJL , F.-J. DeckerSL , Y. EfremenkoU T , T. FieguthSL ,
K. FloettmannDE , M. FukudaT O , V. GharibyanDE , T. HandlerU T , T. HiroseW A ,
R. IversonSL , I. KamychkovU T , C. LuP R , K. McDonaldP R, 1 N. MeynersDE ,
R. MichaelsJ L , A. MikhailichenkoCO , K. MoffeitSL , M. OlsonSL , T. OmoriKE ,
D. OnoprienkoBR , G. PetratosSL , R. PitthanSL , M. PurohitSC , L. RinolfiCE , P. SchulerDE ,
J. SheppardSL, 1 S. SpanierU T , J. TurnerSL , D. WalzSL , A. WeidemannSC , J. WeisendSL
BR
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
CE
CERN, CH-1211 Geneva 23, Switzerland
CO
Cornell University, Ithaca, NY 14853
DE
DESY, D-22063 Hamburg, Germany
JL
Thomas Jefferson National Accelerator Facility, Newport News, VA 23606
KE
KEK, Tsukuba-shi, Ibaraki, Japan
PR
Joseph Henry Laboratory, Princeton University, Princeton, NJ 08544
SC
University of South Carolina, Columbia, SC 29208
SL
Stanford Linear Accelerator Center, Stanford, CA 94309
TO
Tokyo Metropolitan University, Hachioji-shi, Tokyo, Japan
UT
University of Tennessee, Knoxville, TN 37996
WA
Waseda University, 389-5 Shimooyamada-machi,Machida,Tokyo 194-0202
1
Spokesman
1
Abstract
The full exploitation of the physics potential of future linear colliders such as
NLC and TESLA will require the development of polarized positron beams. In the
proposed scheme of Balakin and Mikhailichenko [1] a helical undulator is employed to
generate photons of several MeV with circular polarization which are then converted
in a relatively thin target to generate longitudinally polarized positrons.
In order to test and develop this concept, we propose to put a short test-undulator
in the FFTB 50 GeV beam line at SLAC. The first stage of this experiment will focus
on the flux and the spectrum of the undulator photons, and will measure their circular
polarization. The second stage will focus on the positrons produced, and will measure
their spectrum and polarization.
2
Contents
1 Executive Summary
5
2 Introduction
2.1 Why is Positron Polarization Needed at All? . .
2.2 Why Not Wait 5 Years? . . . . . . . . . . . . .
2.3 Advantage of Using External γs . . . . . . . . .
2.4 A Brief History of Understanding Polarized Pair
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3 Polarized γ and Positron Production
3.1 Concepts and Methods . . . . . . . .
3.2 Choices Made for E-166 . . . . . . .
3.2.1 Polarized γ Production . . . .
3.2.2 Polarized Positron Production
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4 Concepts of Polarimetry
4.1 Polarimetry below 10 MeV . . . . . . . . . .
4.2 Polarimetry for γ 0s . . . . . . . . . . . . . .
4.2.1 The Compton Transmission Method
4.2.2 The Compton Scattering Method . .
4.2.3 Comparison of the Methods . . . . .
4.3 Polarimetry for Positrons . . . . . . . . . . .
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Production
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5 The FFTB Experiment – E-166
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 The Beamline . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Layout . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Beam Parameters . . . . . . . . . . . . . . . . .
5.2.3 Synchrotron Background . . . . . . . . . . . . .
5.2.4 Collimators . . . . . . . . . . . . . . . . . . . .
5.2.5 Alignment . . . . . . . . . . . . . . . . . . . . .
5.2.6 Instrumentation . . . . . . . . . . . . . . . . . .
5.3 The Undulator . . . . . . . . . . . . . . . . . . . . . .
5.4 Photon Spectrum and Rates . . . . . . . . . . . . . . .
5.5 The Polarization Monitoring - PMON . . . . . . . . . .
5.6 Polarimetry - Overview . . . . . . . . . . . . . . . . . .
5.7 Signal Rates; Flux and Spectra Measurements . . . . .
5.7.1 Undulator Photons . . . . . . . . . . . . . . . .
5.7.2 Positrons . . . . . . . . . . . . . . . . . . . . .
5.8 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Polarization Measurements . . . . . . . . . . . . . . . .
5.9.1 The Photon Compton Transmission Polarimeter
5.9.2 The Photon Compton Scattering Polarimeter .
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5.10 Positron Polarization Measurements . . . . . . . . . . . . . . . . . . . . . . . 48
5.10.1 Transmission Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.11 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6 Resources and Requests
49
6.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.2 Requested Assistance from SLAC to E166 . . . . . . . . . . . . . . . . . . . 49
6.3 Manpower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
7 Appendix
50
8 Acknowledgements
51
9 Bibliography
52
4
1
Executive Summary
The full exploitation of the physics potential of future linear colliders such as NLC and
TESLA will require the development of polarized positron beams. In the proposed scheme
of Balakin and Mikhailichenko [1] a helical undulator is employed to generate photons of
several MeV with circular polarization which are then converted in a relatively thin target
to generate longitudinally polarized positrons.
To advance progress in this field, we propose an experiment, E-166, in the SLAC FinalFocus Test beam (FFTB), using a meter-long, short-period (λu = 2.4-mm, K=0.17), pulsed
helical undulator and the SLAC low emittance electron beam at 50 GeV, to produce circularly polarized photons in the energy range of a few MeV up to a cutoff energy of about
10 MeV. Those photons are converted to polarized positrons in targets of varying radiation
lengths. We plan to study targets of titanium (Ti) and tungsten (W), which are both candidates for collider positron targets. 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.
Because of the uncertainty in the level of detector backgrounds, the experiment will be
done in two stages. The goals for these stages are:
Stage I
• measure flux, spectra and polarization of undulator gammas
Stage II
• positron polarimetry after studying and solving eventual background problems
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 target thickness and material are used as in the linear collider;
• The polarization of the produced positrons is expected to be in the same range as in
the linear collider;
• The simulation tools being used to model the experiment are the same as those being
used to design the polarized positron system for a next linear collider.
This experiment directly tests the validity of the present design considered for polarized
positron production. It will also benchmark the design codes: undulator radiation models
for photon characterization, undulator design codes for undulator fabrication, EGS4 and
a GEANT modified for spin effects for polarized e+ production, and BEAMPATH for
collection and transport.
This test will provide confidence that the design proposed for the next generation of
linear colliders is based on solid, demonstrated principles all working together at the same
time. It will test and compare two approaches to measure photon polarization – transmission and scattering Compton polarimetry. To measure the photon polarization seems to
be the necessary prerequisite to measure positron polarization. Furthermore, by exploring
5
positron production with γs with an energy below the (γ,n) threshold, we make an important step toward the realization of targets with reduced radiation damage, even if we do
not test the actual damage in this experiment.
This experiment, however, will not address all conceivable issues related to polarized
positron production. For example, it will not test capture efficiency, target thermal hydrodynamics, radiation damage in the target, nor does it test operational positron polarization
diagnostics at the GeV level, as envisioned for the actual collider.
2
Introduction
2.1
Why is Positron Polarization Needed at All?
The importance of beam polarization in general has been demonstrated at the Stanford
Linear Collider (SLC), where 75% polarization provided an effective luminosity increase by
a factor of ≈ 25 for many Z 0 asymmetry observables. It enabled the SLC/SLD to make the
world’s best measurement of the weak mixing angle at Z-pole energies, an essential element
for predictions of the Higgs mass. The addition of positron polarization will be of great
importance for future linear electron-positron (e+ e− ) colliders because it allows increased
precision in many important measurements [2]. These questions have also been discussed
in [3].
The most-often given explanation is that a sizeable positron polarization is equivalent to
an increase in the effective electron polarization [2], as shown in Fig. 1. If two measurements
of the cross section are made with a different sign for the polarizations P− and P+ , then
the difference of the two measurements normalized to the sum is:
NL − NR
NL + NR
where
Peff =
≡
Peff ALR ,
P− − P+
.
1 − P− P+
(1)
(2)
At the SLC/SLD, the systematic error in the polarization measurement was the dominating error; with the increased luminosity in future colliders this systematic error will
be even more dominant. A higher effective polarization translates directly into a lower
systematic error. For example, with 0.25% systematic error on the individual e− and e+
polarized beams, the systematic error on the effective polarization can be 0.1% or smaller.
This will be particularly important in the proposed revisiting of Z0 -properties, the so-called
Giga-Z experiment [2]
In other words, asymmetries to be measured are proportional to the polarization, and
thus their errors decrease with increased (effective) polarization, allowing measurements
with smaller systematic errors.
Among the many other reasons making positron polarization desirable are[3]:
6
Effective Polarization vs. Positron Polarization
1
0.98
0.96
P(e−) = 0.9
0.94
Peffective
0.92
0.9
0.88
0.86
P(e−) = 0.8
0.84
0.82
0.8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
e+ Polarization
Figure 1: Effective polarization vs. positron polarization, for electron polarizations of 90% and
80%. The desirability of positron polarization is visible here as shown, the effective polarization
rises steeply even with modest positron polarization, and a larger effective polarization decreases
the systematic polarization error.
• Direct polarization determination from physics measurements in the main detector,
the Blondel scheme [4]. This way, measurement of the luminosity weighted polarization is direct; the result can be different from the average beam polarization measured
by the polarimeter.
• Suppression of W-pair background;
• Reduction of errors in the determination of the Higgs coupling, triple gauge boson
couplings;
• Extension of the discovery reach for a hypothetical Z’, W’, or extra dimensions;
• Discrimination among various super symmetrical particles, suppression of Standard
Model backgrounds.
However, there has not yet been an experimental demonstration of a viable scheme to
produce enough of the polarized γs needed. By viable, we mean based on technology on
hand now, not relying on future R&D to be successful, and without adding a costly second
high energy-electron accelerator to the design.
In the following, we will briefly discuss several possible methods for polarized photon
production. We will give reasons later why a test experiment with undulator-produced γs
7
seems to be the most practical at the present time, notwithstanding what will happen in
5-10 years with the technology of polarized γ production itself.
2.2
Why Not Wait 5 Years?
It is clear that an experimental effort should be started now to explore production of
polarized positrons and to master the polarimetry of γs and e+ at the 10-MeV range. It
took experimenters about 10 years to advance the electron polarization measurement at
SLC to the 0.3% level at GeV energies; a similar learning curve can be expected for a
future collider to reach a 0.1% accuracy for the electron polarization. However the SLC
effort was based on experience at SLAC since 1975 to measure polarization of electrons
with many GeV of energy.
The experts agree that operational (nonintrusive) measurements of the positron polarization should be done with Laser Compton scattering after acceleration to the easier GeV
range, in front of the damping ring probably, and at the interaction point. But the positron
source will be a complicated apparatus, so in the case of disagreements between simulation
and measurement one will be forced to go upstream to the source itself, and its very low
positron energy. Therefore, it is also of importance to develop methods and expertise in
the measurement of polarization of positrons in the 5-50 MeV energy range.
As we are approaching serious linear collider proposal time, is it important to understand
the proposed schemes now.
2.3
Advantage of Using External γs
Even without the polarization aspect, there is a very good reason to look into positron
production with externally produced γs. It is useful to have a short review of the classical
method. Traditionally, positrons have been produced by impinging electrons on a heavy Z
target, typically tungsten-rhenium (W-Re) alloys of many radiation lengths thickness. In
the case of the SLC 30 GeV electrons were used.
The electrons first produce bremsstrahlung γs in the field of the high-Z nuclei in the
target material, which then produce electron-positron pairs in a cascade. This cascade in
turn produces copious giant resonance neutrons, which lead to radiation damage in the
target. This process produces both large energy deposition and radiation damage.
The demands for several 1010 positrons in one pulse with the length of a few picoseconds at the SLC, pushed the material strength of W-Re to the limit, and the SLC target
eventually failed. This classical target route for the NLC, which requires 1012 positrons in
a total of 200 bunches in 300 nanoseconds, would require several targets in parallel for the
NLC. It is all but impossible for the intensity requirements of TESLA.
If the γs for pair production are produced external to the target, be it by undulators
or Compton back scattered lasers, and not in the target, a light material like Ti or carbon
composites can be used for the target material. These materials can have a higher damage
threshold than the heavy Z materials used in the past. For example, in the case of the
NLC pulse format, the fatigue stress in W-Re occurs at an energy deposition of about 40
J/gm. But for Ti-alloy, the fatigue stress is reached at an energy deposition of 340 J/gm [5].
8
Long. Positron Polar. vs. E; 10 MeV MonoE γs
1
Longitudinal Polarization, ξ3
0.8
0.6
0.4
0.2
0.05 r.l. Ti
0.1 r.l. Ti
0.25 r.l. Ti
0.5 r.l. Ti
Olsen&Maximon
0
−0.2
−0.4
0
1
2
3
4
5
6
7
8
9
10
Positron Energy (MeV)
Figure 2: Polarization of positrons produced by 10MeV circular-polarized photons on targets of
0.05, 0.1, 0.25 and 0.5 radiation length thickness. The zero-thickness formalism of Ref. [7] is
compared to Monte Carlo calculations based on the EGS4 [8] program. Olsen and Maximon’s
analytical calculations agree well with the extrapolation of EGS4 toward zero thickness, giving us
confidence in the Spin-Monte-Carlo calculations. It is also evident that a thicker target initially
leads to higher polarization. For 10 MeV γs this is true up to a thickness of 0.25 r.l.
Linear thermal expansion coefficients and heat capacity of the materials conspire to make
Ti a better suited material for positron targets than W-alloy, even though the mechanical
yield strength of W-Re alloy is higher than that of Ti-alloy. However, this advantage of
Ti only holds below the neutron production threshold. Above it, more complicated factors
play a role [5], which could negate the advantage of Ti.
2.4
A Brief History of Understanding Polarized Pair Production
The foundation for the theory of polarized positron (and electron) production, and how
to conceptually measure their polarization, was laid in the 1950’s by Tolhoek [6] and by
Olsen and Maximon [7]. Plotting the formulas of Reference [7] and comparing them with
modern EGS4 [8] simulation shows that the zero thickness calculations agree very well (Fig.
2), giving us confidence in the EGS4 simulations with the inclusion of spin.
The concepts of polarimetry were further developed by Goldhaber et al. [9] and by
Schopper [10] and Ullmann et al. [11]. The definitive papers about helical undulators have
been written by Alferov [12], Kincaid [13] and Blewett and Chasman [14].
The basic concept of polarized positron production for linear colliders through polarized
γs has first been proposed by Balakin and Mikhailichenko [1]. Independently, Amaldi and
9
Pellegrini considered a scheme for positron production while researching energy recovery in
linear colliders [15], mentioning the polarized γs as an aside.
These concepts are the foundation for the base plan of TESLA for positron production
[16]. The Japanese Collider team has put effort into experimental exploration of polarized
laser light, backscattered from the KEK-ATF electron linac, as a source for polarized γs
[17]. Most recently, they succeeded for the first time to measure the polarization of the γs
produced at the 5% level [18].
In the last decade, the idea of the production and polarimetry of positrons with undulator radiation, and their possible polarization, has led to several Ph.D. theses. References
[19] and [20] deal with production issues; polarimetry of low-energy γs and charged particles
are dealt with in [21].
3
3.1
Polarized γ and Positron Production
Concepts and Methods
In principle there are several methods of producing polarized positrons, whether directly
through radioactive processes, or indirectly though the use of polarized γs.
• The oldest, and most ‘natural’ “production” is from radioactive decay. A measurement
from µ-decay is the only polarization measurement of positrons in the energy range
of interest for collider positron production (5-50 MeV) we could find in the literature
[22]. To use radioactive decay of any kind to produce enough positrons for a linear
collider would require megacuries of radioactivity, a proposition which generally has
been rejected as dangerous and impractical.
• Also time honored is γ production through coherent bremsstrahlung, like scattering of
the lattice of a diamond or of silicon crystals. This method was used at SLAC in the
1970’s [23]. It will be used again for a new series of experiments through the SLAC
Real Photon Collaboration [24]. For the needs of a linear collider positron source, it
is believed that it can not deliver enough intensity, or perhaps better expressed the
rapid destruction of the crystals make this scheme infeasible.
• The Backscattered Compton Scattering method is based on the production of polarized γ-rays through Compton Scattering of circular polarized laser light off relativistic
electron beams. The attractive feature here is that for submicron wavelength lasers
only 1 GeV electron beams are needed to produce tens of MeV of γ-rays. On the
negative side is that the average power of the solid-state lasers needed is in excess of
≈ 10 MW [17]. The proposal to use a CW Linac-based intra-cavity FEL needs R&D
[25].
• (Polarized) γ production from a (helical) undulator [16] is the basis for the TESLA
positron source. In order to be able to use the primary beam a gap of ≈ 0.5 cm
in the undulator is needed to avoid wake field emittance dilution. Since the ratio
10
of gap:period has to be at least 1:2, cm-large gaps and periods are the consequence,
leading to ≈ 200-GeV energy needed. So the negative aspect here is that one has
to use the primary beam, short of building a second 200-GeV accelerator, and that
one needs 200 GeV for positron production, even if the colliding beam energies are
lower, as forseen for the Giga-Z [2]. On the positive side, once the decision to use the
primary beam for positron production has been made, the system is self-consistent
inasmuch as the emittance and energy spread of the primary beam will not be diluted
much[19].
• Recently, the E-157 experiment at SLAC has shown that an ion channel in a plasma
can be a powerful wiggler [26] with large K (K=18 in this case) and copious production of X-rays. In this experiment, the ion channel was created by the electron
beam itself. This limited the plasma density to be less than that of the electron
beam. A laser pulse could generate a much denser plasma and ion channel, such
that a 3-GeV electron beam would produce 30-MeV γs with a yield of 10-100, i.e.,
10-100 photons per electron at a K of several hundred. This could happen through
relativistic self-channeling in plasma or transverse laser wake fields [27]. These surprising results come about through wiggler periods of only a few tens of microns and
magnetic fields in the thousand-tesla region. This technology is probably on hand for
unpolarized γ production, but so far there is no clear path to polarization. External
helical magnetization of the plasma might be possible [28].
Looking at all the possibilities, we plan to investigate the undulator based method as
the one which looks most realistic at present.
3.2
Choices Made for E-166
3.2.1 Polarized γ Production
The goal of our test is to measure the spectrum and longitudinal polarization of the photon
beam produced by the undulator (γs), in a first stage, and in a second stage to measure
characteristics of the positrons, which are derived from the photon beam. We hesitate to
call these positrons “beam,” because of the large energy and angular spread they will have.
Since SLAC has a 50-GeV electron beam available, the use of a helical undulator is
practical, it is available now, at low cost and buildable in a short time frame. The electron
beam does not need to be polarized, the polarization comes solely from the circular motion
of the electrons in the helical undulator.
In the case of TESLA [16] a planar undulator for their positron source is part of the base
plan, with plans to expand this to polarized positrons at a later stage. The backscattered
laser method is being actively pursued for the JLC linear collider; the presently available
flux of positrons for polarization measurement tests is about 1000/second and first measurements have taken place [18]. The key players of the TESLA and of the KEK-ATF effort
are members of this collaboration.
While the flux of photons in the FFTB will exceed what can be reached with other
methods at the present time, there are certain other limitations on what we can reach in
11
E-166. These limits are the maximal γ energy (≈ 10 MeV) and the wiggler parameter K
(≈ 0.2), see Eq. 6. But these limitations turn out to be an advantage as 10 MeV keeps us
comfortably below the onset of the giant resonance neutron background 1 , neutrons being
the most important cause of radiation damage in positron targets. And as we will see
later, the asymmetry measured in polarized iron (Fe), which determines the polarization,
increases with lower energy, also an advantage in measurement error.
The maximum energy reached by the first harmonic is described by [13]
h̄ωmax =
2γ 2 mc2λC /λu
2.4 [MeV]
2γ 2 mc2 λC /λu
≈
≈
,
2
2
1 + K + 2γλC /λu
1+K
λu [cm](1 + K 2 )
(3)
where λC = 2.4 × 10−10 cm is the Compton wavelength of the electron, and the last form
holds for electrons of γ = 105 (≈ 50 GeV). The relation between energy and angle of
emission of the photons (of an order whose peak energy is h̄ωmax) is given by
h̄ω ≈
h̄ωmax
,
1 + (γθ)2/(1 + K 2 )
(4)
so the upper half of the energy spectrum is emitted into a cone of angle θ =
√
1 + K 2 /γ.
Kincaid eq 24, K=0.17, 2.4 mm, 50 GeV
Kincaid eq 25, K=0.17, 2.4 mm, 50 GeV
1
st
1st Harmonic
2nd Harmonic x10
Sum of first 4 Harmonics
1 Harmonic
nd
2 Harmonic x10
Sum of first 4 Harmonics
0.9
1.2
0.8
0.7
dI(θ)/dθ (arb. units.)
dI(E)/dE (arb. units)
1
0.8
0.6
nd
2
0.4
x 10
0.6
0.5
0.4
2nd x 10
0.3
0.2
0.2
0.1
0
0
2
4
6
8
10
12
14
16
18
0
20
E (MeV)
0
0.2
0.4
0.6
0.8
1
γθ
1.2
1.4
1.6
1.8
2
Figure 3: (a) The intensity spectrum of undulator radiation, integrated over angle, for a 50GeV electron beam incident on an undulator with period λu = 2.4 mm and strength parameter
K = eB0 λu /2πmc2 = 0.17. The peak energy of the first harmonic radiation is 9.62 MeV. (b)
Intensity vs. angle γθ. Due to the low K, most of the γs are produced by the first harmonic,
and are peaked at forward angle. The 2nd harmonic contributes little and is “peaked” at a wider
angle.
Details and kinematics of undulator radiation are described in Reference [30] and are
summarized later in this Proposal.
1
The central energy of the giant dipole resonance (E1), responsible as a doorway state for the neutron
background, follows quite accurately the equation EE1 = 80 A−1/3 , where A is atomic mass. This results
in 22 MeV for 48 T i. [32]
12
The energy of the γs produced depends quadratically on the energy of the electron
beam, and is inversely proportional to the period:
E[keV ] =
0.95 E 2 [GeV ]
λu [cm]
(5)
Therefore, to produce 10 MeV γs, we need a very short undulator, with a period λu
≈ 2 mm. The shortest pulsed undulators ever designed before are slotted copper-tube
undulators of 3-mm period at Los Alamos [33].
In general, in undulator-based γ production, the push is for an undulator factor K ≈ 1.
To reach a K of this magnitude is precluded in our test case, because the undulator period
enters the definition of K (we use here the practical units favored by the X-ray community
[34]) as follows:
K = 0.934 λu [cm] B0 [T ] ,
(6)
so that with a field of B0 ≈ 1 T and a period of λu ≈ 2 mm,Kwill be of the order of
0.2. Previous studies [33] have shown that for undulator dimensions below ≈1 cm, pulse
technology is more advantageous than superconductivity to reach K≈1.
Thus, while the “low” γ energy may be advantageous for lowering radiation damage
to future collider targets, a lower K can also be advantageous; at lower K the undulator
radiation is more forward directed, and the higher order modes are suppressed. Capture
of positrons in all positron sources is limited to a finite momentum band; 20% capture is
regarded as very good.
Since, to first order, the e+ polarization is dependent on the fractional energy carried
in the pair creation process, positrons, which are created by the higher energy harmonic
γs, have a lower polarization at the energy range of interest just below E1 , where the
most highly polarized positrons occur. Fig. 3a shows the intensity spectrum of undulator
radiation, integrated over angle, for the parameters of E-166. Fig. 3b shows that most of
the γs are produced by the first harmonic, and are peaked at the forward (zero) angle. The
2nd harmonic contributes little and is “peaked” at a wider angle.
In Fig. 4a we show the photon number spectrum, which looks very different from the
intensity spectrum in Fig. 3a, and in Fig. 4b the photon polarization as a function of
energy. It is important to keep these two figures in mind.
3.2.2 Polarized Positron Production
As shown in Fig. 4b, in the case of a helical undulator, photons radiated with energy near
the maximum energy (of the first harmonic) have a longitudinal polarization P ≈ 1, those
with very low energy have P near −1, and those with energy near the middle have P ≈ 0
[7]. The energy dependence of the longitudinal γ polarization is P ≈ − cos(πE/Emax ).
However, due to the effect of bremsstrahlung and ionization in the target (more detailed
explanation see below) the polarization of the produced positrons does not follow these
rules, as can be seen in Fig. 2.
13
Photon Helicity to 4th order
Photon Number Spectrum, E =9.62 MeV, K=0.17
1
1
1.4
0.8
1.2
Photon Polarization, Stokes ξ
3
0.6
dN(E)/dE (arb. units)
1
0.8
0.6
0.4
0.4
0.2
0
−0.2
−0.4
−0.6
0.2
−0.8
0
0
5
10
15
20
25
30
35
40
−1
0
5
10
15
20
25
30
35
40
Photon Energy (MeV)
Photon Energy (MeV)
Figure 4: (a) The photon number spectrum, intensity spectrum, of undulator radiation, integrated
over angle, for the parameters of Fig. 3. The peak energy of the first harmonic radiation is 9.62
MeV. (b) The helicity of the undulator radiation as a function of energy. Fortunately, as explained
in the text, the negative helicity dependence at low energy does not transfer to the positrons, see
Fig. 2.
Fig. 5a and 5b show the number of positrons produced and integrated polarizations as
a function of energy, and a polarization scatter plot, respectively. The blue curves in Fig.
5a and 5b represent a yield × polarization integration with a 1-MeV gliding energy window
(equal the average polarization in this energy window). The γs from the 2nd (and higher)
harmonic, the reason for the counts between 10 and 20 MeV, contribute very little to the
numbers, but have a large influence on the integrated polarization down to 9.62-1.02 MeV.
For example, if we capture the positrons between 6 and 8 MeV, the average polarization
would be about 80%.
If the photon beam could be collimated to angles smaller than 1/γ ≈ 10−5 , its average
polarization could be increased. However, this is difficult in practice; at 50 GeV a radius
of 100 µm is required for a collimator 10 m from the undulator. Since the goal is high
average polarization of positrons, and not of photons, it suffices to make an energy cut on
the positrons, since the polarization of the positrons is strongly energy dependent, as shown
in Fig. 2.
One important parameter for (polarized) positron production is the target thickness. If
optimized, the thickness can not only increase the polarization (Fig. 2), it also can increase
the yield, see Fig. 6 and Fig. 7.
Positrons loose energy inside the target due to bremsstrahlung and ionization loss.
Bremsstrahlung leads also to a degradation of the polarization, however, the energy loss is
faster than the polarization loss. Positrons which are produced with low energy have a low
or even negative polarization [7]. These particles are likely to be stopped in a somewhat
thicker target, while the higher energy region is repopulated by positrons starting with
high polarization at higher energy. Thus the average polarization increases with the target
14
E =9.62 MeV, K=0.17, γθ
c1
Longitudinal Polarization vs. E; K=0.17, γθ
=none
cut
cut
= None
1
3
1
Longitudinal Polarization, ξ
Longitudinal Polarization ξ3 and Relative Number in Bin
1.2
0.8
0.6
0.4
0.8
0.6
0.4
<ξ (E)>
3
0.2
0
0.5 r.l. Ti
0.2
0
0
−0.2
2
4
6
8
10
12
Positron Energy (MeV)
14
16
18
20
−0.4
0
1
2
3
4
5
6
Positron Energy (MeV)
7
8
9
10
Figure 5: (a) The expected spectrum of positron energies obtained by conversion in a 0.5-X0
titanium target of photons of 9.26 MeV, the maximum energy of the first harmonic. The gammas
from the 2nd (and higher) harmonic, the reason for the counts between 10 and 20 MeV, contribute
very little to the numbers, but have a large influence on the integrated polarization. The blue
curves in both parts of the figure represents a yield × polarization integration with a 1-MeV
energy bin (equal to the average polarization in this energy bin). For example, if we capture
the positrons between 7 and 8 MeV, the average polarization would be about 80%. (b) Positron
polarization vs. energy (scatter plot).
thickness as shown in Fig. 2
The uncollimated beam of undulator radiation is not monoenergetic and its longitudinal
polarization decreases with energy. However, due to the falling cross section of pair production, the low energy photons will not contribute to the positron production. Since K¿1
there will also be no contribution from higher harmonics. Another factor related to the target thickness is multiple scattering in the target which leads to an increased angular spread
of the positrons. A thinner target reduces this effect. In conclusion the target thickness
has to be optimized taking into account the limited energy and angular acceptance of the
positron spectrometer and the number and average polarization of the positrons reaching
the polarimeter. While it might be desirable for NLC/TESLA to maximize the positron
flux rather than the positron polarization by going to a thick target, the real measure of the
success of the FFTB experiment is the statistical significance of the measured asymmetry.
A thicker target initially gives a larger yield, shown in Fig. 6, and larger polarization,
shown in Fig. 2, but this relation does not hold for very thick targets. It might be desirable
for NLC/TESLA to maximize the positron flux rather than the positron polarization by
going to relatively thick targets (≈ 1X0), but the real measure of the success at the FFTB
is the statistical significance of the measured asymmetry, not the yield achieved.
For the low average energy of 5 MeV available in the FFTB, a thick target may be
defined as larger than about 0.1 radiation lengths. So, while a thinner target produces
less positron flux, it also has less multiple scattering, and consequently higher rates in the
detector(s).
15
E =9.62 MeV, K=0.17, γθ
1
300
0.05 rl Ti
200
0.1 rl Ti
250
N+tot =1719
∆N+/∆E+
∆N+/∆E+
250
N
= 500,000
γin
150
100
50
0
= none
cut
300
N+tot =2329
200
N
γin
100
50
0
5
10
15
0
20
0
Positron Energy (MeV)
10
15
20
300
0.25 rl Ti
250
N
γin
0.5 rl Ti
250
N+tot =2549
200
∆N+/∆E+
∆N+/∆E+
5
Positron Energy (MeV)
300
= 500,000
150
100
50
0
= 500,000
150
N+tot =2274
200
N
γin
= 500,000
150
100
50
0
5
10
15
20
Positron Energy (MeV)
0
0
5
10
15
20
Positron Energy (MeV)
Figure 6: Positron energy spectrum for Ti targets of thickness 0.05, 0.1, 0.25, and 0.5 r.l. As
the target thickness increases, initially the yield goes up, and the energy spread of the emanating
positrons becomes somewhat smaller. As the thickness grows further, the yield goes down again.
For the less complex design of E-166, we depend on the angular spread being modest,
so that we can transport the positrons without undue losses, and so that we can make
good polarization measurements. For the energy (momentum) spread, collimators in the
spectrometer can cut out an appropriate momentum bite for measurement; no such remedy
is obvious for the angular spread except using a thin target.
4
4.1
Concepts of Polarimetry
Polarimetry below 10 MeV
Measuring the polarization of electrons is a well-established skill at very low energies
(up to ∼1 MeV) and then again at very high energies (several GeV). At SLAC, Mott
Scattering was used at low energies to qualify polarized cathodes in gun test labs [35]. At
high energies, many GeV, Møller scattering [36] and backscattered Compton scattering [37],
[?] were used at the end of the linac, in End Station A , and at the SLD experiment. It is
the intermediate range between a few MeV and a few GeV, which is difficult.
For ease of operation operational (noninvasive) measurement for a collider should be
planned to happen where the beam has an energy of a few GeV, before the Damping Ring
for example. Investigative, invasive, polarimetry is a different story.
For this experiment we have no choice but to do polarimetry at ≤10 MeV. The question
arises, is this a lost effort, which has no future application? We think no, naturally provided
16
Yield vs. Target Thickness, MonoEγ’s
0.1
0.09
0.08
30 MeV γs
Raw Yield: Ne+/Nγ
0.07
0.06
0.05
20 MeV γs
0.04
15 MeV γs
0.03
0.02
10 MeV γs
0.01
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Target Thickness (r.l. of Ti)
Figure 7: Positron yields vs. target thickness, for incident, monoenergetic photons of 10, 15, 20,
and 30 MeV (bottom to top curves). This figure, when used by itself, could lead to the conclusion
that higher γ energy is always better for polarized positron production. The truth is more subtle
and there is an optimum. In addition, when the γ energy reaches the (γ,n) threshold, target
lifetime comes into play, see text.
future colliders successfully make gammas in the 10-MeV range, and positrons with them.
. From SLAC’s experience with polarized cathodes [35] and with positron production [39]
the lesson is that it is important to be able to track the yield and the polarization back to
the inception. When yield and polarization are not as large as expected, as has happened
in the past, each stage of the positron system, from γ production, positron production,
positron capture, and positron acceleration will be suspect. Consequently, to determine
where yield and polarization are being lost, these quantities need to be measured close to
the source (undulator and target in the polarized positron case), at low energy. For this
reason, the low energy polarimetry experience gained at E-166 in the MeV region could be
invaluable for future colliders.
4.2
Polarimetry for γ 0s
Two different approaches have been taken to determine the γ polarization: (1) an Iron
Transmission Polarimeter (ITP) using a massive block of Fe and staying on the axis of the
photon beam, and (2) scattering off a thin foil of magnetized Fe in a Compton Scattering
Spectrometer, off axis. This concept can also be applied to e+ polarimetry by converting
the polarized e+ back to a polarized γ.
The first technique has been employed recently by experiments for analyzing the circular
polarization of MeV photons at KEK-ATF as a test for linear colliders, see, e.g., [18] and
will be developed further, for our parameters. The second technique has been proposed for
the same series of experiments [41] and is discussed further below.
17
The Compton cross section used is given by
σ = σ0 + f Pe σe
(7)
where σ0 is the unpolarized cross section, and f is the fraction of polarized electrons (naively
2 out of 26 for Fe, but more accurately determined to be Z f = ν = 2.06, or 7.92% for iron
at saturation). Pe is +1 (-1) for parallel (anti-parallel) photon and electron spins. σe is the
polarized cross section given by
σe = 2πr02
(
)
1 + 4k0 + 5k02 1 + k0
ln (1 + 2k0)
−
2k02
k0 (1 + 2k0 )2
(8)
where r0 is the classical electron radius (2 π r02 = 0.5 barn) and k0=Eγ /(0.511 keV).
σe is the cross section per electron as defined in Equation 8. On the other hand, σ and
σ0 in Equation 7 are the cross sections per Fe-atom.
The polarized Compton cross section for Fe, σe , is plotted in Fig. 8a, and the total
(unpolarized) photon cross section (including pair-production etc.) for Fe, σtot , is plotted
in Fig. 8b [51]. We use these cross sections later (Fig. 21 on p. 41) to calculate the
attenuation length in Fe, L0 , for unpolarized photons and for left- and right-polarized
photons.
Total Photon Cross Section in Fe
Compton Cross Section in Fe
0
−0.005
6
Total cross−section (barns/atom)
Polarized cross−section (barns/electron)
7
−0.01
−0.015
5
4
3
2
−0.02
1
−0.025
0
1
2
3
4
5
6
7
8
9
0
10
E (MeV)
0
1
2
3
4
5
6
7
8
9
10
E (MeV)
Figure 8: (a) Polarized Compton cross section (b) Total unpolarized photon cross section in Fe
4.2.1 The Compton Transmission Method
A transmission type Compton polarimeter, as first used by Goldhaber et al. [9], employs a
thick magnetized-iron target in the photon beam. A similar device was recently operated
in tests at KEK-ATF in Japan [18]. In our case we employ a very narrow beam with low
divergence going in, and we only accept “unscattered” photons by using a narrow collimator
behind the block. One could call this the “one-scatter-and-you-are-out” principle. This setup lends itself to analytical treatment, but we also have compared the result to GEANT
18
Monte Carlo simulation, which were modified for spin effects by the KEK-ATF polarized
positron collaboration [18]. Those results are shown later in Table 7 on p. 42.
Scale in inches
10.00
Movable Target
Ti, W 0.5 RL
Positron Spectrometer
Collimator
End vacuum
Sweep Magnet
Pb Converter 1mm Pb
Calorimeter
Collimator
90 deg Bend
Magnet
Flux Counter
Pb Converter 1mm Pb
End vacuum
Fe Reversible
Magnetization
Cerenkov Detector
Pb Shielding
Sweep Magnet
Collimator
Fe Reversible
Magnetization
Sweep Magnet
Collimator
Flux Detector
Calorimeter
Pb Shielding
Figure 9: Concept for γ and the e+ polarimetry, using the reverse iron method, see [18]. The
undulator photon beam enters from the left through the collimator. For photon polarimetry it
goes forward through a flux counter, a reversible-magnetization iron block, a sweep magnet to
remove charged background, and another collimator. Finally, it is measured in Cerenkov counters
of different thresholds and a calorimeter, to establish a spectrum. For positron polarimetry the
photons strike a thin, removable, pair production target. The generated polarized positrons are
bent by a magnet (see discussion of possible angles in the text), and then are back-converteed
into photons. The helicity of these photons is then measured, similarly to the set-up in the
straight-ahead beam.
The asymmetry in the transmission of polarized photons through a block of magnetized
iron, when the magnetization of the iron is reversed, is given as δ in Reference [40] by
equations (2.5.64) and (2.5.67). Equation (2.5.67),
δ = tanh(NLf Zσe Pe )
(9)
is plotted in Fig. 10 for different thicknesses of iron, L. Equation 9 is different from that
in Reference [40] by a factor of 2, in keeping with the modern definition of polarization.
Although the flux decreases with increased length L0, the asymmetry increases.
For the detector we use an arrangement similar to the one used in [18]; ours is shown
in Fig. 9.
19
Methods of Exp. Phy. Vol 5, Part B, Eq. 2.5.672 ÷ 2
0.06
0.04
δ
0.02
0
−0.02
−0.04
L = 3 cm Fe
0
L = 7 cm Fe
0
L = 10 cm Fe
0
L = 15 cm Fe
−0.06
0
0
5
10
15
Photon Energy (MeV
20
25
30
Figure 10: Asymmetry δ as a function of target thickness following equation 2.5.67 of [40]. Although clearly the flux goes down with increased length L0 , the asymmetry increases.
The analyzing power, AP, for the transmission polarimeter is defined to be
Ã
−l/ +
e L0
!
Ã
−l/ −
e L0
!
−
T+ − T−
AP = +
=Ã
! Ã
!
T + T−
−l/L+
−l/L−
0
0
e
+ e
(10)
where T + (T − ) is the transmission for parallel (anti-parallel) photon and electron spins, L+
0
(L−
)
is
the
attenuation
length
for
parallel
(anti-parallel)
spins,
and
l
is
the
length
of
the
0
magnetized Fe.
4.2.2 The Compton Scattering Method
In this section we describe a scattering-type Compton polarimeter which employs a thin
ferromagnetic foil target in the photon beam. Arichev, Potylitsyn, and Strikanov [41]
have proposed a polarimeter of this type for tests at KEK-ATF. In their study they proposed to detect the recoil Compton electrons. This section is based on recent work at
DESY [42]which, however, came to the conclusion that it is vital to detect the scattered
photons instead.
The reason is that multiple scattering of low energy electrons (∼ 5 MeV ) is so large,
even in very thin target foils, as to essentially destroy the kinematic information of interest. Fortunately, this problem can be avoided if we detect the scattered photons instead.
Furthermore, we can eliminate the pair-production background that would be significant
in the case of electron detection, by use of a simple sweeping magnet.
20
PR
SM
Det
H
H
C3
C2
C1
Tgt
MeV Gamma Compton Polarimeter
1m
Figure 11: Experimental Layout of the Scattering Compton Spectrometer, for more details see
p. 44. The undulator photon beam enters from the left and is collimated by C1 . It then strikes
a Møller-type thin ferromagnetic foil (Tgt), whose magnetization can be reversed by Helmholtz
coils (H). Charged particles from pair-production background are swept out by a sweeping magnet
(SM), finally the scattered photons are detected a detector. This detector may consist of Cerenkov
threshold counters and a calorimeter.
The experimental layout of the scattering polarimeter is simple, and is shown in Fig.
11. The undulator beam is collimated by a small aperture C1 before it strikes the iron foil
target (Tgt). The electron polarization of the target can be flipped by reversing a modest
external field that is generated by a pair of Helmholtz coils (H). A calorimetric detector
(Det) is mounted behind apertures C2 and C3 which define a fixed scattering angle. A small
sweeping magnet removes any charged component from the scattered photon beam axis.
In Subparagraph 1 of this section we will review some basic kinematic features, as well
as the cross sections and spin asymmetries of the Compton process. In Subparagraph
2 we describe the undulator photon spectrum, its angular distribution and polarization
behavior. In Subparagraph 3 we will concoct this into observable detector signals and spin
asymmetries.
• 1 Kinematics, Cross Sections, Spin Asymmetry
We review briefly some of the basic features of the Compton scattering process.
21
Definitions:
ω0 and ω are the initial and final photon energies;
E0 = mc2 and E are the initial and final energies of the recoil electron;
θ and θe are the scattering angles of the photon and the electron.
The energies are related through energy conservation
ω0 + mc2 = ω + E .
(11)
Furthermore, from momentum conservation follows
ω =
ω0
.
1 + (ω0 /mc2) (1 − cos θ)
(12)
The scattered photon and the scattered electron angles relative to the photon beam
direction are
mc2
cos θ = 1 −
ω0
and
tan(θe ) =
Ã
!
ω0
− 1
ω
,
(13)
cot(θ/2)
.
1 + ω/mc2
(14)
The spin-dependent differential Compton cross section is
dσ0
dσ
=
(1 + Pγ Pe A)
dΩ
dΩ
(15)
with the unpolarized part
dσ0
r0 2
=
dΩ
2
Ã
ω
ω0
!2 Ã
ω0
ω
+
− sin2 θ
ω
ω0
!
(16)
where r0 is the classical electron radius, and Pγ and Pe are the longitudinal polarizations or helicities of the initial beam photon and the target electron.
The spin asymmetry is given by
A =
dσ1/2 − dσ3/2
(ω0 /ω − ω/ω0) cos θ
=
.
dσ1/2 + dσ3/2
ω0 /ω + ω/ω0 − sin2 θ
(17)
mc2
,
=
2 + mc2 /ω0
(18)
The energy spectra of the scattered photons and electrons are mirror images of each
other because of equation 11. The spectra are continuous and extend from a minimum
photon energy ωmin for backward scattering (θ = 180o )
ωmin
all the way up to the beam energy ω0 for forward scattering (θ = 0).
In Fig. 12 a,b we give, for a monochromatic beam energy of 5 MeV (9.6 MeV), the
differential cross sections dσ/dΩ as a function of the photon scattering angle θ for
22
75
75
50
50
25
25
0
1
0
1
0.5
0.5
0
0
-0.5
-0.5
-1
10
-1
10
5
5
0
0
10
4
5
2
0
0
0 20 40 60 80 100 120 140 160 180
0 20 40 60 80 100 120 140 160 180
Figure 12: (a) The differential cross sections dσ/dΩ as a function of the photon scattering angle θ
for Pγ Pe = +1, −1, and 0; the spin asymmetry A, the figure of merit A2 dσ/dΩ, and the photon
and electron energies (for a monochromatic beam energy of 5 MeV). (b) The same quantities for
9.6 MeV.
Pγ Pe = +1, − 1, and 0; furthermore the spin asymmetry A and the figure of merit
A2dσ/dΩ.
The same quantities are shown in Fig. 13 as a function of the scattered photon and
electron energies.
• 2 Undulator Spectrum
For the purpose of this polarimeter study, we need to know the energy spectrum and
polarization behavior of the undulator photons. These parameters are determined
by the geometry of the undulator and the beam energy; they are collected in Table 1. Some of the resulting polarimetry physics description is repeated in different
sections in the proposal, because different schools of polarimetry are using different
nomenclature.
The first harmonic of the undulator spectrum is given by
23
5
4
3
2
1
0
10
100
100
50
50
0
1
0
1
0.5
0.5
0
0
-0.5
-0.5
-1
10
-1
10
7.5
5
2.5
0
150
7.5
5
2.5
0
150
100
100
50
50
0
8
6
4
2
0
0
0
1
2
3
4
5
0
2
4
6
8
10
Figure 13: (a) Same quantities as in 12 (a) (for 5 MeV) but as a function of the scattered photon
energy. (b) The same quantities for 9.6 MeV.
where s = ω0 /ω0max
and α = 1/137.
dNγ
K2
1
= 4πα M
×
(1 − 2s + 2s2 )
ds
1 + K2
2
is the reduced energy variable, ω0max = 9.613 M eV ,
(19)
Numerically we have then
dNγ
1
= 1.078 × (1 − 2s + 2s2) ,
ds
2
(20)
with the total number of undulator photons (per 50 GeV electron) given by
Nγ =
Z
0
1
dNγ
ds = 0.359 .
ds
24
(21)
Table 1: Undulator Parameters
0.06
Polarisation
dN/dE
Electron Beam Energy 50 GeV
Magnetic Field
0.760 T
Undulator Period
2.4 mm
K Value
0.1704
Length of Undulator
1m
M (Number of Periods)
417
0.05
0.5
0.04
0
-0.5
0.03
-1
2 4 6 8 10
Energy E (MeV)
Polarisation
0
Angle (mrad)
1
0.15
0.1
0.05
0
0.02 0.04
Angle (mrad)
1
0
-1
0
0
2 4 6 8 10
Energy E (MeV)
0
2 4 6 8 10
Energy E (MeV)
Figure 14: Energy spectrum, polarization, and angular distribution of undulator photons
The relation between the emission angle θ and the energy variable s is
s =
1
,
1 + γ 2θ2 /(1 + K 2 )
(22)
θ =
1q
(1 + K 2 ) (1 − s)/s
γ
(23)
or
with γ = 50 GeV /mc2 = 105 .
The circular polarization of the undulator radiation is given by
Pγ =
2s − 1
1 − 2s + 2s2
25
(24)
These distributions are shown in Fig. 14. Contributions from higher order harmonics
may be neglected.
• 3 Detector Signals and Asymmetries
We shall assume that we will detect Compton scattered photons behind a suitable
collimator aperture (designated C2 in Fig. 11 on p. 21), which subtends a solid
angle dΩ at a fixed scattering angle θ. If the photon beam were monochromatic, the
detector would then be illuminated with photons of a fixed energy ω = f (θ, ω0 ), with
the function given by Equation 12.
Actually, the undulator photons are not at all monochromatic, but cover a broad
spectrum of parabolic shape that reaches from zero to ω0max = 9.613 MeV as shown
in Fig. 14. Furthermore, the circular polarization of these undulator photons changes
from -1 to +1 over this energy range, with a zero crossing at the midpoint energy of
4.807 MeV.
As the detector will not be able to count individual photon events, it will record an
analog signal which is the superposition of all the single photon signals as obtained
after integration over the entire undulator spectrum (dNγ /dω0)(ω0 ).
S =
X
Z
si = dΩ
ω0max
ω0min
dσ0
dNγ
(θ, ω0 ) [1 + Pe Pγ (ω0 )A(θ, ω0)] dω0 .
(ω0 )
dω0
dΩ
(25)
If the detected signal is not proportional to the number of photons, but instead to the
sum of their energies (as would be obtained with a calorimetric detector), we have to
integrate an energy weighted expression,
Z
ω0max
dNγ
dσ0
(θ, ω0 ) [1 + Pe Pγ (ω0 )A(θ, ω0)] ω(θ, ω0) dω0 .
(ω0 )
dω0
dΩ
(26)
These expressions depend on the polarization of the electron target Pe . We can
operate the target with positive (+) and with negative (-) polarization, where we
assume equal magnitudes so that Pe (+) = −Pe (−) = Pe .
We can then form the following experimental signal asymmetry
W =
X
wi = dΩ
AS
ω0min
1 S+ − S−
1 Z
=
=
Pγ (ω0 )A(θ, ω0 ) dω0 ,
Pe S+ + S−
S0
(27)
and similarly for the energy weighted signals
AW
1 Z
1 W+ − W−
=
Pγ (ω0)A(θ, ω0 ) ω(θ, ω0) dω0 ,
=
Pe W+ + W−
W0
26
(28)
where the normalizations S0 and W0 are just the unpolarized parts in Equations 25
and 26.
S0 = dΩ
Z
dσ0
dNγ
(ω0 )
(θ, ω0 ) dω0 ,
dω0
dΩ
(29)
W0 = dΩ
Z
dNγ
dσ0
(ω0 )
(θ, ω0 ) ω(θ, ω0 ) dω0 .
dω0
dΩ
(30)
80
400
60
300
40
200
20
100
0
1
0
1
0.5
0.5
0
0
-0.5
-0.5
-1
-1
10
2
5
1
0
0
0
20
0
40
20
40
Figure 15: (a) Integrated count signals for cross-section, asymmetry, and figure-of-merit as measured in a detector which measures the sum of single photon signals. (b) The same properties for
a calometric detector which gives the sum of the energies.
We have evaluated the asymmetries AW and AS in Fig. 15a and Fig. 15b as a
27
function of the scattering angle θ. The different curves shown correspond to different
undulator collimation angles.
Undulator collimation will eliminate all beam photons below a corresponding threshold (see Equation 23) and will therefore control the lower integration limit ω0min . For
example, an undulator collimation of 10 µrad would eliminate the lower half of the undulator spectrum with its undesirable negative polarization. The degree of undulator
collimation that can be applied has a dramatic effect on the mean photon polarization
and the observable polarimeter asymmetry.
Also shown are the spin-averaged signals S0 and W0 (labeled as dσ/dΩ) and the
statistical figures of merit A2S S0 and A2W W0 (labeled as A2 dσ/dΩ), corresponding to
either unweighted or energy-weighted photon detection. Energy-weighted detection
favors higher photon energies and thus slightly smaller scattering angles. A scattering
angle of 17o appears to be a reasonable compromise that would accommodate useful
asymmetry measurements with both detection techniques for all possible collimation
cases.
4.2.3 Comparison of the Methods
While the transmission polarimeter and the scattering polarimeter are both based on the
Compton process, they are nevertheless very different in the way they exploit this. In order
to address the relative merits of both methods, it will be useful to compare
• the analyzing powers of the physical processes as well as those of the instruments;
• the energy acceptance functions;
• potential effects of background reactions;
• the required measurement time for a certain statistical precision;
• systematic uncertainties of the target electron polarization.
The analyzing power of the elementary physical process is defined as the cross-sectional
asymmetries for parallel and antiparallel beam and target spins with complete (100%) polarization. For the scattering polarimeter this is an asymmetry of differential cross sections
which peaks at a certain scattering angle. For example, for a photon beam energy of
5 MeV this analyzing power reaches a maximum of 72%, see Fig. 12. For the transmission
polarimeter this is an asymmetry of the total cross sections which amounts to 22% at the
same beam energy of 5 MeV.
In order to obtain the instrumental analyzing powers, we must account for the fact
that only 2/26 ∼ 0.08 of the electrons in iron can be polarized. This factor applies to
both polarimeters equally. Therefore, it will likely be the knowledge on the target electron
polarization that will determine the overall precision of the beam polarization measurement.
The target electron polarization is determined from published values of the gyromagnetic
ratio g 0 [50] and the magnetization M which can be measured with pickup coils upon field
28
reversals. For standard Møller experiments with thin tilted foils, an error of about 3% must
be assumed for the target electron polarization.
However, the transmission polarimeter can boost its effective analyzing power through
multiple successive interactions in a sufficiently long target. With a 15-cm-long target, one
obtains the same instrumental analyzing power of 6% as for the scattering polarimeter.
The beam energy acceptance of the scattering polarimeter is relatively flat in the region
of interest. For the transmission polarimeter it drops steeply for energies below 5 MeV.
With regard to counting statistics, the transmission method is ahead with a factor of
4
10 . However, this appears to be no real advantage, as none of the instruments is in any
way limited by statistics.
Early publications on the transmission method reported problems in quantifying the
extent of the magnetization near the ends of the long target cylinder. More recent measurements with this method at ATF showed also large differences for opposite target polarities.
As the required resources for either polarimeter are quite modest on the scale of the
overall effort, and since the polarization measurement is the most essential part of the experiment, we propose to implement both techniques so that they can be tested concurrently.
4.3
Polarimetry for Positrons
If using the concept of an Iron Transmission Polarimeter, we must reconvert the polarized positrons with a lead target back into polarized γs, which are measured in an ITP
similar to the one shown in Fig. 9 on p. 19 for the γs.
By bending the charged particles out of the central beam, we hope to be better able to
control background created by the 50-GeV original beam. In experiment E-144 [43], it was
found that the background was tolerable for 15-MeV particle detection as soon as one was
outside the immediate straight ahead beam envelope.
Further simulations, and background measurements will show if we can use a simple
dogleg geometry (as proposed in reference [18]) , or will need to bend the beam 90o away
from the beam (as shown in Fig. 9 on p. 19). We do not anticipate to have to go outside of
the FFTB housing, but this would be a further possibility.
Although a Transmission Polarimeter seems to be the obvious choice, since it has been
used more often in the past, we explore other choices for Stage II, like measuring the
positron annihilation γs.
29
5
The FFTB Experiment – E-166
Target
A1
Toro
e-
A2
PR1
BPM1
PR2
HSB SSB
BPM2
eDump
A3
Undulator
PR3
BPM3
D1
PR4
D2
γ
Diag.
SSB HSB
e+
Diag.
- to
e
D
um
p
Figure 16: Conceptual layout (not to scale) 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.
5.1
Overview
The experiment will be done in two stages because of the uncertainties in the backgrounds in the FFTB. In the first stage the flux, spectrum , and polarization of the undulator photons will be characterized. In addition, the backgrounds will be measured and a
preliminary measurement of the positron polarization will be made. Both Compton transmission and Compton scattering polarimetry measurements will be taken because of the
importance to develop these photon diagnostics for a new linear collider. In the second
stage of the experiment, the positrons will be characterized in terms of yield, spectrum ,
and polarization. If the back grounds are found to be initially low, the second stage of
the experiment can follow the first in short order. Additional time may be required to
reposition and to shield the detectors if the backgrounds are found to be high.
Table 2 shows a comparison between the TESLA positron source system [16], the NLC
positron source design, and E-166. The TESLA baseline design uses a planar undulator
for unpolarized positron production; the NLC design and FFTB experiment use helical
undulators.
5.2
The Beamline
5.2.1 Layout
Fig. 16 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
photons. After the undulator, the 50-GeV electrons are bent vertically downward and sent
30
Table 2: TESLA, NLC, FFTB Polarized Positron Parameters
Parameter
Beam Energy, Ee
Ne /bunch
Nbunch /pulse
P ulses/s
Undulator T ype
UndulatorP arameter, K
UndulatorP eriod, λu
1st Harmonic Cutoff , Ec10
dNγ /dL
UndulatorLength, L
T arget Material
T arget T hickness
Y ield
Capture Eff iciency
N+ /pulse
N+ /bunch
P olarization
Units
TESLA
GeV
150-250
3 × 1010
2820
Hz
5
planar
1
cm
1.4
MeV
9-25
photons/m/e−
1
m
135
T i − alloy
r.l.
0.4
+
e /photon (%)
1-5
%
25
8.5 × 1012
3 × 1010
%
-
NLC
150
8 × 109
190
120
helical
1
1.0
11
2.6
132
T i − alloy
0.5
1.8†
20
1.5 × 1012
8 × 109
40-70
FFTB
50
1 × 1010
1
30
helical
0.17
0.24
9.6
0.37
1
T i − alloy
0.5
0.5
2 × 107
2 × 107
40-70
† Including the effect of photon collimation at γθcut = 1.414.
to the FFTB dump. The photons drift in the zero-degree line for a distance of about 35 m
where they are either analyzed or converted to positrons in a thin target.
5.2.2 Beam Parameters
Radiation shielding considerations limit the maximum beam power in the FFTB enclosure
to less than 2.5 kW. At 50 GeV, 30 Hz operation corresponds to a beam current of less than
about 1×1010 e− /pulse. The emittances of the electron beam for fully coupled damping ring
operation, and low beam charge, are expected to be about γ²x = γ²y = 1.5 × 10−5 m − rad.
For 10 m β, the corresponding beam size is about 40 µm rms; the angular divergence of
the beam is about 10 µrad rms. Table 3 lists the beam parameters for the experiment.
Table 3: FFTB Beam Parameters
Ee
GeV
50
Ne
e−
1 × 1010
γ²x = γ²y
m-rad
1.5 × 10−5
βx , βy
m
10,10
σx , σy
µm
39
31
σx0 , σy 0
µrad
3.9
2
D ( Dσx2 + σx20 )1/2
m
µrad
35
4.1
1/γ
µrad
10
5.2.3 Synchrotron Background
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 used successfully in the E144 experiment [29], albeit the
soft bend magnets are different magnets due to space limitations. Table 5 lists expected
photon parameters from the undulators and bend magnets in the immediate vicinity of the
experiment. As seen in Table 5, the expected flux from the undulator is significantly higher
in photon energy and number. In Table 5, h̄ωc is the critical energy of the synchrotron
radiation emitted by the bends; ∆L(3/γ) is the length of bend required to produce a 3/γ
angular deflection in the beam; and the ∆Nγ and ∆PB are the radiated flux and power
from the bends for the ∆L(3/γ) length segment of bend.
5.2.4 Collimators
Fig. 16 shows three aperture-limiting collimators for the experiment, A1 , A2 and A3 . These
devices are 30-cm-long (∼20 r.l.) cylinders of copper with 0.85 mm ID through holes for
electron beam transmission in A1 and A2; A3 has a 3 mm ID aperture for the photon
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 fault. 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.
5.2.5 Alignment
Absolute component alignment tolerances of 100 µm 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 requires remote mover capability. Because of the long
lever arm ( ∼ 35 m) from the end of the undulator to the measurement area, remote
movers for A3 are incorporated into the design. The 100-µm tolerance does, however,
require consideration in the design of various supports and 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.
32
5.2.6 Instrumentation
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 current on
a pulse-to-pulse basis with an absolute accuracy of less than a few per cent and a relative
accuracy of a few tenths of a 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. PR4 has been included in front of A3 for
observation of the photon beam. In addition to set up, the PRs will be used to monitor
the beam quality over the duration of the experiment. The PRs are invasive monitors. A
wire scanner is also available for noninvasive (with the possible exception of backgrounds)
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
supplies and instrumentation) will be controlled and monitored through the existing SLAC
accelerator control system.
5.3
The Undulator
Figure 17: A 23-cm-long Test Section (only the end is shown), which fulfills the demands in
current and stability required.
The undulator shown in Fig. 16 is an in-line pair of 0.5-m-long undulators with opposing
helical windings [30]. Use of opposing undulators is being adopted to help reduce possible
systematic errors in the polarization measurements. Discussion of this topic is presented in
Section 5.5. Each undulator consists of a copper wire bifilar helix, wound on a 1.068 mm
OD, stainless steel (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 0.6 mm
wire diameter has been chosen. Fig. 17 shows an actually built model: three G10 rods and
rings hold the helical coil in place.
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 µs current pulse, the temperature rise is about 4o C/pulse
33
Table 4: FFTB Helical Undulator System Parameters
Parameter
Units
Value
Number of Undulators
2
Length
m
0.5
Inner Diameter
mm
0.89
Period
mm
2.4
Field
kG
7.6
KUndulator Parameter
0.17
Current
Amps
1800
Pulse Width
µs
30
Inductance
H
1.8 × 10−6
Wire Type
Cu
Wire Diameter
mm
0.6
Resistance
ohms
0.125
Repetition Rate
Hz
30
Power Dissipation
W
225
0
C
∆T /pulse
4
and the average power dissipation for 30 Hz operation is about 225 W. The undulators are
immersed in an oil bath for cooling. The presence of the SS support tube reduces the
field by < 3%. Modeling of the undulators has been done using MERMAID [31]. Table 4
lists various undulator system parameters. Fig. 18 shows the back-to-back undulator
configuration with power supply connections.
50 cm left
helicity
50 cm right
helicity
Beam
Saturated
choke
Thyristors
Charging
choke
Recharging
inductance
c
c
Power
supply
Figure 18: Back-to-back pulsed undulator concept.
5.4
Photon Spectrum and Rates
For small values of K, the number of photons emitted per meter from the helical undulator is dNγ /dL:
34
Table 5: FFTB Experiment Photon Flux
Parameter
Ee
ne
frep
Pe
B0
K
dNγ /dL
Ec10 (h̄ωc )
hν Eavg
dPu,B /dL
∆L(3/γ)
∆Nγ
∆Pu , ∆PB
Units
GeV
×1010 e−
Hz
kW
kG
photons/m/e−
MeV
MeV
mW/m
m
photons/s
mW
Undulator D1 Bend
50
50
1
1
30
30
2.4
2.4
7.58
4.45
0.17
0.37
2.75
9.62
(0.739)
4.81
0.228
87
30
1
0.01
11
1.1 × 10
9.5 × 109
87
0.35
SS Bend
50
1
30
2.4
0.066
0.04
(0.011)
0.003
0.007
0.77
9.5 × 109
0.005
HS Bend
50
1
30
2.4
0.660
0.41
(0.110)
0.034
0.7
0.08
9.5 × 109
0.05
4 πα
30.6
K2
K2
dNγ
=
=
photons/m/e−
dL
3 λu [m] 1 + K 2
λu [mm] 1 + K 2
(31)
where α is the fine structure constant, λu is the undulator period and K is the undulator
parameter, as defined in Eq. 6.
The average energy of the photons for small K is
−3
Eavg = 0.5 × Ec10 = 4.74 × 10
Ee2[GeV ]
MeV /photon ,
λu [mm] (1 + K 2)
(32)
wherein Ec10 is the cutoff energy of the first harmonic radiation and Ee is the electron
energy.
The radiated power per meter of undulator is dPu /dL
E 2 [GeV ]K 2
dPu
ne [×1010]frep [Hz] W/m
= q∆E ṅ = 2.32 × 10−4 e 2
dL
λu [mm]
(33)
in which ne is the number of electrons per pulse and frep is the pulse repetition rate.
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 of arbitrary size. In the case of 0.5 r.l. of Ti (or W), the outgoing
beam size is dominated by the multiple scatter and target thickness in comparison to the
expected input size of about 350 µm, rms. Expected undulator photon flux and power are
listed in Table 5.
35
For the parameters of E-166, Fig. 4a on p. 14 shows the expected photon number
spectrum and Fig. 4b on p. 14 shows the corresponding circular polarization spectrum.
The low K value limits the flux to essentially only the first harmonic. To produce the
curves in Fig. 4a and 4b, the undulator radiation has been integrated over all emission
angles up to π/2. Since the characteristic opening angle of the radiation is 1/γ ≈ 10 µrad,
the finite aperture of the undulator does not effect the calculation.
On p. 15, Fig. 5a and 5b show the spectrum and polarization of positrons, as a function
of energy, produced in 0.5 r.l. of Ti by the photons of Fig. 4a and 4b. The EGS4 code was
used to simulate the positron production shown in Fig. 5.
5.5
The Polarization Monitoring - PMON
The triggers for the left undulator and right undulator current pulses will come from
a polarization monitor (PMON) system. PMON refers to a set of SLAC-built custom
electronics, which are controlled through the accelerator controls system software. It has
been used extensively over the last 10 years at SLAC for many experiments, including SLD
and E-158, to control the left-right helicity sequence for the polarized electron beam [47].
PMON generates a pseudorandom helicity sequence and imposes a quadruplet structure on
this, in which two consecutive pulses have randomly chosen helicities and the subsequent
two pulses are chosen to be their complements. For example, a possible sequence could be
LRRL LLRR.
In the data analysis, asymmetries can be calculated for pairs of events. Pairs are formed
from the first and third members of the quadruplet, and from the second and fourth members. The pseudorandom sequence used is described in [48]. Observing the helicity state of
33 consecutive pairs allows one to predict the helicity state of future pairs. For 30 Hz beam
operation, PMON will be set up to generate 20 Hz of triggers with a pseudorandom helicity
sequence. The remaining 10 Hz will be used for 9 Hz of beam pulses with no undulator
pulses (for background measurements) and 1 Hz of no beam (for pedestal measurements).
The second feedback will zero the left-right flux asymmetry measured by the flux counter
shown in Fig. 9. We will measure the average radiation flux from the left undulator, FL , and
the average flux from the right undulator, FR . We compute the left-right flux asymmetry,
−FR
AF = FFLL +F
, for mini-runs of ∼ 2000 beam pulses. AF will be nulled by adjusting the
R
pulsed currents to the left and right undulators. This feedback is identical to an existing
charge asymmetry feedback used by the E-158 experiment. We plan to duplicate this for
E-166, replacing the toroid measurement for charge asymmetry with AF .
A third fast feedback system may be necessary to accommodate the data acquisition
(DAQ) planned for the experiment. We plan to use fast feedback software to acquire data
from 2 ADCs that will contain measurements from the photon and positron detectors.
This third process does not control actuators in the conventional sense of feedback. This
is discussed further in Section 5.11.
5.6
Polarimetry - Overview
Fig. 9 on p. 19 shows the experimental setup as it would be located ∼35 meters
downstream of the undulator. The initial collimator, with an aperture of 1.5-mm radius,
36
selects the forward undulator photons and should reject most of the synchrotron radiation
from bend magnets near the undulators.
This collimator is sized to transmit undulator photons with energies above 1 MeV, while
allowing for tolerances in beam targeting and alignment. One MeV undulator photons have
an angle of ∼30 µrad and a radius of ∼1 mm at this location.
The undulator photons continue forward for measurements of their flux, circular polarization and total energy. An insertable thin radiator converts a portion of the photons to
electron-positron pairs.
A dipole magnet is used to sweep charged particles out of the neutral beamline and to
select positrons for further analysis (described below). The undeflected photons continue
forward, through a thin exit vacuum window to the photon diagnostic hardware. A quartz
Cerenkov counter measures the photon flux. The degree of circular polarization of the
photons is measured with a transmission Compton polarimeter. The magnetized iron target
is reversible allowing the transmission to be measured with the photon and target electron
spins parallel (J=3/2) and anti-parallel (J=1/2). Following the magnetized iron target,
charged particles are deflected by a sweep magnet and a subsequent collimator selects the
transmitted photons. This collimator will have a 2-mm radius.
The transmitted undulator photons will be analyzed in two detectors: a threshold
Cerenkov counter, with a thin lead converter before it, followed by a silicon-tungsten sampling calorimeter with 1 X0 sampling.
The calorimeter consists of unit cells each composed of a layer of high resistivity silicon,
300-µm thick, mounted on a 900-µm layer of G-10 followed by a 1 X0 Heavimet absorber.
Such a calorimeter has a sampling fraction of ∼0.75%, which varies less than 0.02% over
the energy range of undulator photons. A 13 X0 calorimeter has a containment of ∼90%,
also constant over the full energy range to within 3%. The response of this calorimeter to
104 photons with energies ranging from 1 to 10 MeV has been simulated and is plotted in
Fig. 19 (for a LeCroy 2249W ADC with 1/4 pC per count).
A small nonlinearity is apparent as might be expected from the use of a sampling
calorimeter at these low energies. However, the absolute scale of the energy flux can be
measured to a few percent. For the threshold Cerenkov counter, data runs with different
radiator materials and thresholds will be used to probe the energy spectrum of the undulator radiation. Quartz, aerogel, isobutane and propane are the radiator materials being
considered.
Positrons are produced in a thin production target and are deflected 90 degrees in a
dipole field that selects the desired momentum interval, e.g. 5-7 MeV/c for analysis. For
polarization analysis, the positrons then pass through a thin radiator to generate polarized
photons, whose polarization is measured in a transmission Compton polarimeter similar to
that described above for the undulator photons.
For measurements of the positron flux and energy spectrum we will remove the thin
radiator and magnetized iron target. The positron flux will be measured, with the threshold
Cerenkov and calorimeter detectors shown, in different energy intervals by tuning the field
in the 90o dipole. A quartz Cerenkov counter can be used for this application. An active
calorimeter, such as NaI or BaF, is required because the low energy positrons lose energy
37
Si:Tungsten Calorimeter
Si:Tungsten adc counts
1500
1000
500
0
0
2
4
6
8
10
12
Photon Energy (MeV)
Figure 19: Response of Si:Tungsten calorimeter to 104 photons vs. photon energy
very quickly due to ionization losses and stop within 1 or 2 X0 .
This setup should provide a good determination of the total positron flux and energy
spectrum. Good measurements of the average polarization and polarization spectrum are
also possible though this will depend on how well backgrounds can be reduced. The positron
flux will be significantly lower than the photon flux, making the positron polarization
measurement significantly more difficult than that for the photons.
If the signal-to-background ratio achieved for the experimental configuration shown in
Fig. 9 on p. 19 proves too low for positron polarimetry, we plan to modify the configuration
in one of two ways. First, we can compromise on the measurement of the polarization
spectrum by having a smaller bend angle and allowing larger apertures to transmit a wider
momentum bite of the positrons. This significantly will increase the positron yield for
analysis. Second, we can consider the use of a strong solenoid magnet to contain the
angular spread of the positrons and/or to transport them a few meters into a new shielded
alcove to significantly reduce the background. We do not intend to implement this second
solution for the first stage of the experiment, because it might not be necessary.
It is easy to propose to add a flux concentrator and short accelerator section to obtain
better collection efficiency for the positrons and make a beam with a reasonable emittance.
This would, however, require a significant investment of at least five times the budget of
the present proposal. We think we can learn what we need to learn without this extra cost.
5.7
Signal Rates; Flux and Spectra Measurements
5.7.1 Undulator Photons
The expected undulator photon spectrum is shown in Fig. 20, for photon energies from
1-9.6 MeV. As always this spectrum corresponds to a K = 0.17 helical undulator with
a 2.4-mm period for a 50-GeV electron beam with 5 × 109 electrons/pulse (1st harmonic
cutoff energy is 9.62 MeV). The undulator length assumed is 0.5 m. Integrated over the
full spectrum, 9.25 × 108 photons are emitted with a mean energy of 4.81 MeV.
38
8
2
1
x 10
0.8
1.8
0.6
1.6
Undulator photon helicity N=1
Photons per MeV
1.4
1.2
1
0.8
0.4
0.2
0
0. 2
0.6
0. 4
0.4
0. 6
0.2
0. 8
0
0
1
2
3
4
5
E (MeV)
6
7
8
9
1
10
0
1
2
3
4
5
E (MeV)
6
7
8
9
10
Figure 20: (a) Undulator photon spectrum (b) Undulator photon helicity spectrum
Over the primary energy region of interest from 1-9.6 MeV, there are 8 × 108 photons
emitted. The photon helicity spectrum in this energy range is shown in Fig. 20.
For the initial detector design study in this proposal, photons with energies above 9.6
MeV have been ignored, but they have been included in the EGS4 simulations, see Fig. 4a
and 4b on p. 14. Properly accounting for these in the detector simulations will be done
soon, but is not expected to impact the detector design.
The total energy per pulse of the undulator photons incident on the iron target is 4400
TeV. Following the 15-cm iron target, the energy per pulse is reduced to 120 TeV, with a
corresponding flux of 1.8 × 107 photons and a mean photon energy of 6.7 MeV. This photon
signal at the detectors is very large and we do not expect to experience any problems due
to backgrounds. Results from the calorimeter and Cerenkov counters will provide a good
determination of the total flux and average polarization of the undulator radiation. Some
information on the energy-dependence of the flux and polarization will also be provided
from the different energy responses of the detectors.
5.7.2 Positrons
The positron yield for an 0.5 radiation length titanium target is ∼0.007 positrons per
incident photon for the undulator photons considered in Section 3.2.1. Positrons are
momentum-selected with a 90o bend as shown in Fig. 9. A bend radius of 17-cm is chosen,
as well as collimation to achieve an effective aperture in the bend of 1.75-cm × 1.75-cm.
We simulated polarized positron transmission through this geometry as a function of the
bending field. The results are presented in Table 6. The positron flux and energy spectrum
will be measured by an active calorimeter and a flux counter. As an example, we consider
the positron rate available for a B-field of 0.11 tesla. The expected positron yield is 9.7×104
per pulse with an average energy of 5.3 MeV, corresponding to a total energy per pulse of
515 GeV. This signal size is expected to be adequate for measurements of the total flux
and spectra, although it may be marginal for polarimetry.
39
Table 6: Simulation results for transmission of polarized positrons, produced by an 0.5 X0 Ti
target, through a 90o bend with 17-cm radius.
B (tesla) Mean Energy(MeV) Energy spread, σE /E
0.05
2.8
0.21
0.09
4.8
0.17
0.11
5.3
0.17
0.13
6.5
0.16
0.15
7.2
0.13
0.17
7.8
0.12
5.8
Transmission(%) Polarization
0.38
0.28
1.1
0.53
1.5
0.67
1.5
0.76
1.3
0.84
0.97
0.87
Backgrounds
The measurements planned are all integrating flux measurements and we do not plan
to identify and measure single particles in the energy range 1-10 MeV. Though such measurements would be valuable for detailed measurements of the energy-dependent flux and
polarization of the photons and positrons, we consider counting measurements impractical
in this environment with 5 × 109 50-GeV electrons only a few feet away. We do not have
too much guidance from earlier FFTB experiments to indicate the level of backgrounds we
might expect for the planned photon and positron measurements.
There is some guidance from the air threshold Cerenkov counter in the neutral beam
used in the laser interferometer spot size measurement [49]. This counter, with a 25MeV threshold and 1” lead pre-radiator had a measured signal:background of ∼10:1 for an
incident signal flux of ∼200 10-GeV photons from Compton backscattering. The ∼200 GeV
per pulse of background had typical pulse-to-pulse fluctuations of (50-100)%. To achieve
this low level of background a significant amount of tuning of upstream collimators in
the FFTB and Linac was required, as well as very good beam emittance. In a more recent
experiment, E-150, backgrounds were more typically ∼40 TeV per pulse with ∼100% pulseto-pulse fluctuations.
Fortunately, these background levels are still small compared to the 4400 TeV undulator
radiation signal. The transmission Compton detectors for the undulator photons should be
easy to shield well, and we do not anticipate much difficulty with their signal-to-background
ratio. Detectors used after any scattering process (e.g. all the positron detectors), require
larger apertures and active areas, and care is needed to adequately shield them.
A significant source of background can be the small aperture at the undulator itself.
The inner radius of the undulator is only 0.45 mm, ∼11 beam σ. This is by far the
smallest aperture of any element in the FFTB beamline and the neutral beamline for the
detector apparatus has a direct line-of-sight to it. Very good beam emittances and primary
collimation well upstream of this location are needed to minimize any beam loss at the
undulator location. A significant amount of tuning time will likely be needed to achieve
acceptable backgrounds.
40
5.9
Polarization Measurements
It will be possible to measure the polarization of the undulator photons with a transmission Compton polarimeter as shown in Fig. 9 on p. 19, or with a scattering Compton
polarimeter as shown in Fig. 11. A comparison has been made in Section 4.2.3 on p. 28.
5.9.1 The Photon Compton Transmission Polarimeter
We defined the cross-sections in Section 4.2. The polarized Compton cross section, σe , was
plotted in Fig. 8a, and the total (unpolarized) photon cross section for Fe, σtot , was plotted
in Fig. 8b.
Photon Attenuation Length in Fe
5
4.5
Attenuation Length in Fe (cm)
4
3.5
3
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
7
8
9
10
E (MeV)
Figure 21: Photon attenuation length vs. energy in Fe
We use these cross sections to calculate the attenuation length in Fe, L0, for unpolarized
photons and for left- and right-polarized photons. It is plotted in Fig. 21 as L0 versus the
photon energy in the region of interest for this experiment, from 1-10 MeV.
The analyzing power, AP, for the transmission polarimeter is defined to be
Ã
−l/ +
e L0
!
Ã
−l/ −
e L0
!
−
T+ − T−
AP = +
=Ã
! Ã
!,
T + T−
−l/L+
−l/L−
0
0
e
+ e
(34)
where T + (T − ) is the transmission for parallel (anti-parallel) photon and electron spins, L+
0
(L−
)
is
the
attenuation
length
for
parallel
(anti-parallel)
spins,
and
l
is
the
length
of
the
0
magnetized Fe.
Fig. 22a plots the (unpolarized) transmission, T0 , versus photon energy for a 15-cm
length of magnetized Fe, while Fig. 22b plots the analyzing power vs. energy for this
target.
41
Analyzing Power in 15 cm of Magnetized Iron
Transmission through 15 cm of Iron
0.08
0.06
0.03
Analyzing Power
Transmission
0.04
0.02
0.02
0
0.02
0.01
0.04
0.06
0
0
5
E (MeV)
0.08
10
0
1
2
3
4
5
6
E (MeV)
7
8
9
Figure 22: (a) Photon transmission through iron as function of γ energy. (b) Analyzing power of
15 cm of fully magnetized iron as function of γ energy, following [10]
The transmission and analyzing powers obtained here analytically, using Equation 34,
have also been checked in a GEANT simulation with the modified GEANT program used
at the ATF [18] and found to be in good agreement, see Table 7.
We can define a figure-of-merit (FOM) to be FOM=(AP)2T and this is plotted versus
l in Fig. 23 for 7.5 MeV γs. While this indicates the optimal length to be 8 cm, we choose
instead a length for this experiment of 15 cm. This enhances the measured asymmetry by
a factor of ∼2, while reducing the measured flux of photons by a factor ∼0.16 compared to
a 7.5-cm length. Given the large flux of photons, this reduction is not expected to impact
significantly the signal-to-background ratio.
The configuration for the transmission polarimetry is given in Fig. 9. The polarized
Table 7: Analytical calculations and GEANT simulations, for 5 MeV monochromatic gammarays. 100% polarization and saturated iron is assumed.
Analytical
Fe [cm]
3.0
15.0
GEANT
3.0
15.0
Energy [MeV]
5.0
5.0
T+
T−
0.484 0.473
0.027 0.024
Asymmetry
0.011
0.057
5.0
5.0
0.483 0.472
0.026 0.024
0.012
0.055
42
10
−4
2
x 10
1.8
1.6
Figure of Merit
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
Length (cm)
12
14
16
18
20
Figure 23: Figure of Merit vs. length of Fe target
target will be a 15-cm length of Fe with radius of 5 mm in a field of 2.2 tesla. Following the
target will be a sweep magnet and collimator with a 2-mm radius. We will employ three
detectors for the polarization measurement: quartz and isobutane threshold Cerenkov flux
counters; and a Si:tungsten sampling calorimeter.
We have simulated the expected asymmetry measurements in these detectors. We use
as input the undulator photon flux spectrum, shown in Fig. 20a, and the corresponding
helicity spectrum, shown in Fig. 20b.
The expected asymmetry spectrum of photons at the detectors following the magnetized Fe target is shown in Fig. 24. For a 15-cm length of magnetized Fe, we expect the
calorimeter to observe an asymmetry of 3.3%. The asymmetry measured by a threshold
flux counter is plotted in Fig. 24 as a function of the energy threshold.
0.05
0.08
0.045
0.06
0.04
Flux Counter Meassured Asymmetry
0.1
Measured Asym Spectrum
0.04
0.02
0
−0.02
−0.04
0.035
0.03
0.025
0.02
0.015
−0.06
0.01
−0.08
0.005
−0.1
0
1
2
3
4
5
Energy (MeV)
6
7
8
9
0
10
0
1
2
3
4
5
6
Threshold Energy (MeV)
7
8
9
10
Figure 24: (a) Intensity asymmetry of undulator photons after 15-cm iron target (b) Intensity
asymmetry measured by a threshold flux counter
A flux counter with a 200-keV threshold (e.g. quartz) would observe a 2.3% asymmetry,
43
Table 8: Summary of Detector Measurements
Detector†
Calorimeter
Quartz Cerenkov
Isobutane Cerenkov
Threshold Energy Mean Energy‡ Asymmetry
7.4 MeV
3.3%
0.2 MeV
6.7 MeV
2.3%
8.1 MeV
8.9 MeV
4.7%
†These results are for idealized flux counters and calorimeter and will need to be updated
with corrections for the energy response of the actual detectors .
‡For the calorimeter, the mean energy is determined by weighting by both spectrum and
energy. For the threshold Cerenkov counters, the weighting is by the spectrum only.
while a counter with an 8-MeV threshold (isobutane has an 8.1 MeV threshold) would
observe an asymmetry of 4.7%. The mean photon energy observed by a calorimeter would
be 7.4 MeV (weighted by spectrum and energy), while the mean photon energy observed
by a flux counter with a 200-keV threshold would be 6.7 MeV (weighted by spectrum only).
We can also consider a threshold Cerenkov counter with a threshold above the N=1 cutoff
energy of 9.62 MeV, such as propane with an 11-MeV threshold. However, we have not yet
simulated the expected results from this counter.
The detector measurements expected are summarized in Table 8. These correspond to
the expected undulator spectra and helicity given in Fig. 20a and 20b. With measurements
from these detectors, we expect to check the predicted photon polarization with ∼5%
accuracy.
5.9.2 The Photon Compton Scattering Polarimeter
This section deals with the configuration specific aspects of the concept described in Section
4.2.2 on p. 20.
• 1 Experimental Configuration
We refer to Fig. 11 on p. 21 for a graphical description of the set-up.
The undulator photon beam enters from the left and is collimated by C1. This
collimator must be located at a considerable distance from the undulator in order
to achieve the very small collimation angles that would be desirable. For example, a
10 µrad collimation angle could be realized with an aperture diameter of 0.5 mm at a
distance of 25 m.
The collimated undulator beam then strikes the polarized electron target (Tgt) which
consists of a thin ferromagnetic foil which is tilted by a shallow angle of 20o against
the beam direction. The foil is magnetized by a modest external field from a pair
of Helmholtz coils (H) which may be reversed every few minutes. Such a target has
been employed since 1975 in numerous Møller scattering experiments in End Station
A at SLAC. This device would need a somewhat larger exit flange to accommodate
a scattering angle of 17o ± 1o . Recently it has been demonstrated that Møller target
44
Table 9: Standard Assumptions and Parameters for the Monte Carlo Simulations
Electron Beam
Energy
50 GeV
Electrons per bunch
1 × 1010
Bunches per second
30 Hz
Undulator
Photons per e−
0.359
ωmax
9.613 MeV
Spectrum
Eq. 20, fig. 14
Angular distribution Eq. 23, fig. 14
Collimation angle
variable
Polarization
Eq. 24, fig. 14
Target
Material
Fe
Thickness
100 µm
Tilt angle
20o
Polarization
0.08
Spectrometer
Scattering angle θ
17o
∆θ
±1o
∆φ
±1o
∆Ω
3.56 × 10−4
foils can also be oriented square to the beam direction under certain conditions, but
this requires very high external fields [44] [45].
Scattered photons are then detected by a single calorimeter channel that measures
the integrated energy deposition per accelerator pulse. The scattering angle and the
covered solid angle are fixed by the position and aperture of collimator C2 : θ =
(17 ± 1)o , ∆φ = 2o , ∆Ω = 3.56 × 10−4 .
Finally, a small sweeping magnet with about 0.01 T m would be sufficient to deflect
any charged component out of the scattered photon beam path. This will remove
recoil Compton electrons, but also pair production background.
• 2 Event Rates and Statistical Errors
In order to understand the response of the polarimeter as well as possible, we have
generated Monte Carlo events which simulate the undulator spectrum and the Compton scattering process as described in the previous chapters.
For the simulation we used the standard assumptions and parameters shown in Table
9.
The results of the simulations are shown in Fig. 25 for six different undulator collimation from 5 µrad to 100 µrad. Two-dimensional event distributions in scattered
45
46
Figure 25: Monte Carlo results described in the text
10
10
10
8
8
8
6
6
6
4
4
4
2
2
2
20
40
20
40
20
0.1
0.1
0.1
0.05
0.05
0.05
0
0
2
4
6
8
10
0
0
2
4
6
8
10
0
10
10
10
8
8
8
6
6
6
4
4
4
2
2
2
20
40
20
0.1
0.05
0.05
0.05
2
4
6
8
10
0
0
2
4
6
8
4
6
20
0.1
0
2
40
0.1
0
0
40
10
0
0
2
4
8
10
40
6
8
10
P
Table 10: Photon Energy hωi, the Energy Sum
ω/pulse, the Number of Detected Photons
N/pulse, and the Statistical Error ∆P/P for One Minute of Data Taking.
P
Collimation Angle
hωi
(µrad)
(M eV )
5
5.1
10
4.6
15
4.0
30
3.1
50
2.8
100
2.7
P
ω/pulse
(GeV )
7.69
16.82
22.49
28.17
28.88
28.92
P
N/pulse ∆P/P per min.
(%)
1570
1.2
3848
1.1
5847
1.5
9602
1.9
11081
1.8
11502
1.8
photon energy vs. angle are shown in the upper plot. The lower plot shows the detected photon event spectrum. For each of the six simulations we generated a total
of 2 × 109 beam electrons and thus 0.72 × 109 undulator photons, equally divided
between the two target polarization states.
Table 10 gives, for each of the simulations, the mean detected photon energy hωi,
P
P
the energy sum ω/pulse, the number of detected photons N/pulse, where these
numbers had to be scaled from the obtained Monte Carlo statistics and finally, the
statistical error ∆P/P in the polarization measurement obtained in one minute of
data taking.
In order to avoid misunderstandings we want to emphasize that the high photon
statistics materializes in the form of an analog signal during the very short bunch
length, i.e., these photons can not actually be counted. Nevertheless, we may use
these simulated numbers to calculate statistical errors. We may conclude that errors
based on event statistics will be exceedingly small in comparison with systematic
effects.
We will not attempt a discussion of systematic errors in this proposal, except to state
that we expect an overall systematic uncertainty of the order of 3% as typical for
standard Møller target experiments.
• 3 Summary and Conclusion
We have presented a design of a scattering type Compton polarimeter for the measurement of circular polarization of very high intensity undulator photons. The experimental configuration is quite simple and can be quickly implemented from existing
components. The precision of the polarization measurement is expected to be determined by systematic errors at the level of 3%.
47
5.10
Positron Polarization Measurements
5.10.1 Transmission Simulation
For the geometry of Fig. 9 on p. 19 and for a 90o bend field of 0.11 tesla, we expect
9.7 × 104 positrons per pulse with a mean energy of 5.3 MeV incident on the thin radiator.
We are still in the process of simulating and optimizing the geometry for this polarization
measurement and expect to have results soon.
But we can estimate the expected signal rates at the detectors. We will likely choose
an ∼0.1 X0 radiator, which is a compromise to obtain sufficient photon yield while not
introducing too much multiple scattering and depolarization of the positrons. The length
of the magnetized Fe target is expected to be ∼7.5 cm to give an average transmission of
∼10% for the photons. We plan to implement a geometry to achieve ∼10% acceptance of
photons generated in the converter. Thus the photon yield at the detectors is expected to
be ∼100 photons per pulse with a mean energy of ∼3 MeV, giving a total signal of 300
MeV per pulse. This may be marginal because of backgrounds, which would necessitate
reoptimizing the geometry as was already discussed in Section 4.1. The uncertainty about
this expected background level and the desire to measure the polarization spectrum of the
positrons, not just an ensemble polarization, is what drives the request for having two stages
for this experiment.
5.11
Data Acquisition
.
We plan to use the Accelerator SCP (SLAC Control Program) hardware and software
for the data acquisition system (DAQ). This will be done as part of a fast feedback, as
indicated in Section 5.5. The fast feedback will acquire data from ∼20 detector channels
in 2 analog-to-digital converters (ADC) at the machine repetition rate of 30 Hz.
Additionally, we will record the polarization state of the undulator radiation, some beam
diagnostics (BPM and toroid information), and some Hall probe readings for the magnetic
fields in some of the detector analyzer magnets. We expect to run the beam in a mode
with ∼10-Hz left pulses, 10-Hz right pulses, 9-Hz background (undulator not pulsed), and
1-Hz pedestal (no beam) pulses. The 9-Hz background pulses will be used to subtract
beam-related background in the detectors not associated with the undulator radiation. A
dedicated process will run to transfer data accumulated in the fast feedback buffers to a
storage disk for offline analysis.
48
6
6.1
Resources and Requests
Resources
The following list gives a breakdown of the projects needed for this experiment and an
assignment of manpower.
BEAMLINE
SLAC
UNDULATOR
Undulator Body
Cornell
Power supply
Cornell, SLAC
TRANSMISSION POLARIMETRY JLAB, KEK, SLAC, Tokyo Metropolitan, Waseda
SCATTERING POLARIMETRY
DESY, JLAB
CALORIMETER
Tennessee, South Carolina
ONLINE DATA ACQUISITION
Princeton, SLAC, South Carolina
MAGNETS (to be built)
Princeton, Tennessee
SIMULATION
Cornell, KEK, SLAC, South Carolina,Tokyo Metro,Waseda
6.2
Requested Assistance from SLAC to E166
We request that SLAC make available equipment needed to run in the FFTB, such as
the soft bend, SLAC-type wire scanners, BPMs, profile monitors, and associated power
supplies and controls packages. SLAC effort will be required to help tie the E-166 DAQ
into the accelerator controls system for required beam data transfer. We request assistance
from SLAC for the installation and check out of the beam line and associated beam line
instrumentation.
We assume that beam running will take place in between PEP-II fills resulting in a
beam delivery efficiency of about 50% of clock time.
We believe that one week of general checkout can be done parasitically at the 30 GeV
needed for PEP-II fills.
49
Prior to data taking, we request one week assistance in setting up the 50 GeV, low emittance beam. We estimate that this one week is required to first establish 30 Hz operation at
50 GeV, low emittance, stable, and focused beams in the FFTB as well as commissioning
of all the beam-line hardware. During this time, further beam check out of the undulator
and the data acquisition system will take place.
After establishment of 50 GeV beam operation, an additional week of running is requested for Stage I of E-166. At least a week of “dead time” is requested to permit data
analysis and equipment improvement. After which, another week days of running is requested.
The STage II request is similar except that we request 4 one-week periods seperate by
appropriate pauses, which should be at least one week.
Upon approval a parasitic T-experiment is requested in the FY03 machine cycle so as to
take a first look at the background situation in the FFTB. This parasitic running will use
whatever beam is available and is largely noninvasive other than for possible, brief requests
for access to the equipment and for adjustments to the beam steering, collimation, etc. for
the purpose of understanding the sources of backgrounds. Coordination of the parasitic
operation will be made with the scheduled, primary users of the beam line.
6.3
Manpower
The collaboration is a strong one. It includes many of the world’s recognized experts in
polarimetry.
Many of the collaborators have had experience in FFTB experiments (E-144, E-150 and
others). The SLAC contingent includes personnel with much experience in setting up and
running End Station A and FFTB of experiments.
7
Appendix
Recent design studies indicate the realistic possibility of the production of positron
beams for the NLC which meet the full NLC beam specifications and which have an overall
positron polarization of about 60%. The basic concept is to produce circularly polarized
photons which are in turn converted in a thin target to longitudinally polarized positrons.
Positrons are captured with the same type of systems as are used in a conventional positron
source (multi-GeV electrons, targeted into thick converter targets); positron polarization is
maintained in the subsequent capture and acceleration. The phase-space of the captured
positrons needs to be damped using a pair of damping rings prior to injection to the main
linac for acceleration and transport to the collision region.
Photons are generated by sending the primary electron beam through a helical undulator. The electrons are redirected into the linac for additional acceleration to the collision
region. The photons are converted to polarized positrons in 0.5 r.l. thick targets. At this
time, target materials of both high strength Ti-alloy and W-Re alloy are under investigation.
Preliminary studies show that for a 150-GeV primary electron beam, a K=1, 1 cm period
helical undulator, photon angular collimation at γθ = 1.414, a 0.5 r.l. Ti-alloy target, and
50
a positron capture efficiency of 20%, the required active length of the undulator for a unity
gain system is about 130 m and the overall polarization of the captured positrons is 60%.
Photon coherency is not required; hence, the tolerances on the undulator are very loose
in comparison to what is required for a FEL. In addition, the undulator is composed of a
number of short sections that are likely several meters in length each. Capture efficiency
of 20% is based on simulations using the modeled phase space of the positrons emitted
from the target. The actual length of the undulator will of course be longer to provide
engineering margin. Fig. 26 depicts the layout for an NLC polarized positron source.
Detailed optimization studies are continuing with particular emphasis on the thermal
hydrodynamics in the target, anticipated radiation damage to the target, and positron
capture efficiency. Design investigations for the undulator systems have begun. Codes
have been developed to model all of the various components in the design. These include
programs for undulator radiation models, undulator design, polarized positron production,
and positron capture and transport. Additional simulations are used to study the effects
of energy deposition and radiation in candidate target materials. The key features of
each system are in hand; the task of overall system performance optimization, including
component tolerances and operational considerations, has begun.
Electron Main Linac
Electron Main Linac
Undulator Bypass Line
150 G
eV
eV e150 G
e-
1.8 GeV L-Band Linac
Helical Undulator
Photon Drift
Redundant Targets and
Polarized Electron Gun
To Positron Pre Damping Ring
Figure 26: Layout of the NLC Polarized Positron Source. The 150-GeV primary electron beam
is sent through a helical undulator to produce circularly polarized photons in the energy range
of a 0-20 MeV. After transmission through the undulator, the electrons are directed back into
the remainder of the main linac for further acceleration and transport to the interaction point.
The photon beam transverse size grows above the target damage threshold in the drift between
the end of the undulator and the conversion target. The conversion target is a rapidly spinning
annulus of high strength Ti-alloy that is 0.5 r.l. thick. Positrons are captured using a magnetic flux
concentrator, high field solenoid, and an initial 250 MeV of acceleration. After initial acceleration,
the positrons are injected into a 1.8-GeV linac for additional acceleration up to 1.98 GeV and
transport to the positron predamping ring. An inline, redundant target and initial capture section
are included in the design to improve system availability in the event of a target system failure. An
electron injector is used for commissioning of the downstream systems (positron linac, predamping
ring, and damping ring). The electron source can be polarized for use in the γγ collider option.
8
Acknowledgements
We thank Clive Field, Ralph Nelson, Helmut Wiedemann, Maury Tigner, Mike Woods,
and many others for useful discussions and other assistance.
51
9
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