COMPTON POLARIMETRY - USPAS€¦ · COMPTON POLARIMETRY Abraham Meles New Mexico State University...
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COMPTON POLARIMETRY
Abraham Meles New Mexico State University
For USPAS Jan 2013 Laser Applications to Accelerators
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Outline • RHIC
• Basis for Compton polarimetry
• Kinematics
• Compton Asymmetry
• polarization of the electron
• Summary
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RHIC
NSRL LINAC
Booster
AGS
Tandems
STAR 6:00 o’clock
PHENIX 8:00 o’clock
10:00 o’clock
RF 4:00 o’clock
2:00 o’clock
EBIS
ERL Test Facility
RHIC
The Relativistic Heavy Ion Collider (RHIC)
RHIC • 3.83 km circumference • (polarized)proton, heavy ion, light ion Aim: 1) produce and study Quark Gluon Plasma (QGP) ( ~ 250,000 X hotter than sun, few µs after big-bang) 2) measure the spin structure of the nucleon. (the only polarized proton collider in the world)
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Basis for Compton polarimetry
• The scattering of a photon off an electron
• The cross section for this interaction depends on the relative alignment of the spins of the two interacting particles
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• Individual electrons, moving along the z-axis with an energy E, p = (E; 0, 0, p) • incoming photon, denoted by k = (k;- k sinα, 0, −k cosα), where α is the
angle of the incoming photon with respect to the beam axis. • The photon source is a high-power green laser. • The electron imparts some of its energy to the photon, and is deflected
from the main beam line by an angle θe
• The recoil electron thus has 4-momentum p’ = (E’; -p’ sinθe, 0, p’ cosθe). • The photon scatters at an angle θϒ ; K’ = (k’; k’ sinθϒ, 0, k’ cos θϒ) • . • .
Kinematics
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Applying conservation of 4-momentum,
• The energy of the scattered photon can be found in terms of the incident photon and electron parameters as;
• The energy of the recoil electron is;
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Compton Asymmetry
• The theoretical longitudinal asymmetry, Al, for the Compton scattering of electrons and photons with spins parallel, σ+, and spins anti-parallel, σ−, is given by
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The experimentally measured asymmetry, Aexp
n+ is the number of Compton scattering events with electron and photon spins parallel, and
n− with the spins anti-parallel.
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• The experimentally measured asymmetry Aexp
is related to the theoretical asymmetry Al
through the polarizations of the electron beam, Pe, and the scattering photons in the laser beam Pϒ, by
• The longitudinal polarization of the electron beam is therefore
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Compton scattering from proton (RHIC)
• The cross-section for Compton scattering from protons is small.
• smaller than the analogous electron cross section by a factor of (me/mp)3
• Modern lasers, with their high power densities and pulse energies, stand a chance of making up this difference in rate.
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Summary • Given the polarization of laser (Pϒ) the
polarization of the electron beam (Pe) can be measured by – Calculating the cross section (theoretical) Al
– counting the number of Compton events (experimental) Aexp
Reference: Compton Polarimetry; Douglas W. Storey (The Qweak experiment, at Thomas Jefferson National Accelerator Facility) LASER COMPTON POLARIMETRY OF PROTON BEAMS
Arnold Stillman, Brookhaven National Laboratory, Upton, NY 11973-5000 USA
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The Compton scattering cross section
•
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