Echoes of Plasmas in the World of Synchrotrons

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Echoes of Plasmas in the World of Synchrotrons

• P. Colestock
• Los Alamos National Lab

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Plasma Echoes as a PrecisionParticle Beam
Diagnostic Tool

• Synchrotron basics
• The ideal one-dimensional plasma
• How echoes are formed and measured
• Theoretical framework
• Connection to diffusion
• Experimental results

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What is a synchrotron?
particles confined radially by average minimum-B
longitudinal and transverse degrees of freedom
strongly decoupled
Unbunched beam storage
Bunched beam acceleration
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Relativistic Effects lead to Negative Mass
Slip Factor
Revolution Frequency
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Wakes are the Basis for Particle Interactions
The energy change per turn is given by the Wake
Potential.
is the deviation from synchronous energy
The Fourier transform of the wake field in the
beam frame is the Impedance.
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Longitudinal Modes in a Coasting Beam
Vlasov Equation for Longitudinal DoF
Fourier analyze
Dispersion relation for longitudinal modes
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Longitudinal Modes
n 0
n 1000
Df 47.7 kHz
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What makes an echo?
First impulse
Second impulse
Nonlinear interaction term
Phase cancellation occurs when
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Experimental Setup
In a synchrotron, it is possible to see every
particle (limited only by bandwidth).
Gap Detector
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Solve using the perturbation techniquesof plasma
physics
Nonlinear term
Fokker-Planck drag and diffusion terms (Su and
Oberman, PRL, 20, 9, (1968))
Echo Current
Decay due to collisions
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First Measurements of Longitudinal Echoes
Fermilab Antiproton Storage Ring
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Decay rates yield precise measures of diffusion
n 1x10-4 Hz
Collision frequencies as low as 10-9 Hz have been
observed !
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Many other types of echoes have now been studied
Transverse echoes Bunched beam echoes Even
spin echoes
Bunched beam echo
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Summary

• Echoes have become a standard tool for measuring
  weak diffusion rates in synchrotrons
• Both the concept and mathematical techniques have
  come from plasma physics
• Many other nonlinear phenomena in intense beams
  await analysis