Electron Polarization in ELIC Figure8 Ring

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Electron Polarization in ELICFigure-8 Ring

• P. Chevtsov and Ya. Derbenev

EIC Collaboration Meeting, Hampton University,
19-23 May 2008
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Outline

• Motivation
• Spin Rotation and Stabilization in E-ring
• (Future) Work on Spin Depolarization Effects
• Summary

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Electron spin and electron beam polarization
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The spin precession of relativistic electrons (in
a laboratory frame) is given by the Thomas-BMT
equation. For typical conditions in electron
storage rings, for example, this equation can be
written as
the spin precession due to B? depends on the
beam energy (?)
the spin precession due to B is
energy-independent
B
V

a 0.0011596
is anomalous magnetic moment of the electron
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• Bending magnets (dipoles)
• The spin precession ?sp with respect to
  the electron momentum vector
• p (or V) is equal to a?a, where a
  is the dipole bending angle
• a) a0.022 (ELIC vertical crossing bends)
  ? ?sp 0.45 at 9 GeV
• 
  0.15 at 3
  GeV
• b) ?sp p/2 at 9 GeV ? a0.077

a?E(GeV)/0.44065
?sp a?a
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• Solenoids
• spin rotation angle ?sp (1a) BL/B0? ?
  BL/B0?
• where
  B0? (T.m) 3.3356 P (GeV/c)
• ?sp p/2 ? BL 15p T.m

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ELIC Conceptual Design
30-225 GeV protons 15-100 GeV/n ions
prebooster
12 GeV CEBAF Upgrade
3-9 GeV electrons 3-9 GeV positrons
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ELIC Design Goals

• Energy
• Center-of-mass energy between 20 GeV and 90 GeV
• energy asymmetry of 10,
• ? 3 GeV electrons on 30 GeV protons/15 GeV/n
  ions up to
• 9 GeV electrons on 225 GeV protons/100 GeV/n
  ions
• Luminosity
• 1033 up to 1035 cm-2 s-1 per interaction point
• Ion Species
• Polarized H, D, 3He, possibly Li
• Up to heavy ion A 208, all striped
• Polarization
• Longitudinal polarization at the IP for both
  beams
• Transverse polarization of ions
• Spin-flip of both beams
• All polarizations gt70 desirable

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Spin Rotation and Stabilization in E-Ring
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Electron Polarization in ELIC

• Polarized electrons are produced in CEBAF
  electron polarized source
• High polarization is preserved during
  acceleration in CEBAF
• Polarized beams are injected into the ELIC
  Figure-8 ring with
• vertical polarization

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Electron Polarization in ELIC

• Spin is vertical in arcs and longitudinal at IPs

IP
IP
IP
IP
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Electron Polarization in ELIC

• Spin is vertical in arcs and longitudinal at IPs
• Vertical crossing bends cause energy-dependent
  spin
• rotations

a0.022
IP
IP
IP
IP
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Electron Polarization in ELIC

• Spin is vertical in arcs and longitudinal at IPs
• Vertical crossing bends cause energy-dependent
  spin
• rotations

a0.022
IP
IP
IP
IP
We need spin rotators that do not change the beam
orbit and provide longitudinal spin at IPs at all
available electron beam
energies (3-9 GeV)
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Spin dynamics in the ELIC electron ring
2
1
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a0.022
?sp a?a 0.45 at 9 GeV

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a0.022
SR1
?sp a?a 0.45 at 9 GeV

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Sol1
Sol2
a0.022
B1
B2
a2
a1
SR1
Example B2 ?aa2p/2 at 9 GeV
- a20.077 B1
a12a2
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SR1
SR2
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SR1
SR2
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SR1
SR1
SR2
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Electron Polarization in ELIC

• High polarization of electron beams in the ELIC
  ring is maintained
• by self-polarization (S-T)
• To remove spin resonances, SC solenoids are used
  in straight sections
• Additional solenoids at the end sectors of arcs
  (acting together with arc bends) provide spin
  rotators, which do not change the beam orbit at
  all available beam energies

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Electron Polarization in ELIC
Electron/positron polarization parameters
Time can be shortened using high field
wigglers. Ideal max equilibrium polarization
is 92.4. Degradation is due to radiation in spin
rotators.
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PROBLEMS.

• The S-T effect is a very convenient way to
  obtain
• highly polarized beam but it is useful only if
  depolarization
• is not too big.
• Beam optics misalignments, uncompensated
  solenoids
• or skew quadrupoles, beam-beam interaction
  effects, etc.
• can cause significant depolarization.

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PROBLEMS

• The S-T effect is a very convenient way to
  obtain
• highly polarized beam but it is useful only if
  depolarization
• is not too big.
• Beam optics misalignments, uncompensated
  solenoids
• or skew quadrupoles, beam-beam interaction
  effects, etc.
• can cause significant depolarization.

To estimate beam depolarization factors, we need
a spin modeling tool.
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ELIC Polarization Modeling Tool
SLICK - is based on a linear
approximation of orbital and spin motion,
which reveals only
first order spin-orbit resonances
SLICKTRACK - one of the most advanced spin
tracking codes describing
full 3-D spin dynamics
including the results of non-linear
orbital motion
and beam-beam interactions
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Summary

• A concept of spin rotators, which do not change
  the beam orbit for the ELIC electron ring at all
  available energies has been developed
• Such rotators and spin stabilizing solenoids
  build up a spin manipulation system for the ELIC
  electron ring, which makes it possible for us to
  begin our work on
• - complete beam transport optics design
• - spin dynamics simulations
  (depolarization
• due to optics misalignments, non-linear
  orbital motion)

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Sol1
Sol2
B1
a0.022
B2
a2
a1
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Sokolov-Ternov effect
Radiative self-polarization of relativistic
electrons. Spins of particles are oriented in
the same way under the influence of synchrotron
radiation when they circulate in storage rings
for a long time. This provides a unique
capability for creating polarized beams of
high-energy electrons.