1. Echoes of Plasmas in the World of Synchrotrons P. Colestock Los Alamos National Lab

2. Plasma Echoes as a Precision Particle Beam Diagnostic Tool Synchrotron basics –The ideal one-dimensional plasma How echoes are formed and measured Theoretical framework –Connection to diffusion Experimental results

3. What is a synchrotron? particles confined radially by average minimum-B longitudinal and transverse degrees of freedom strongly decoupled Bunched beam: acceleration Unbunched beam: storage

4. Relativistic Effects lead to Negative Mass Slip Factor: Revolution Frequency:

5. Wakes are the Basis for Particle Interactions The Fourier transform of the wake field in the beam frame is the Impedance. The energy change per turn is given by the Wake Potential. is the deviation from synchronous energy

6. Longitudinal Modes in a Coasting Beam Vlasov Equation for Longitudinal DoF Dispersion relation for longitudinal modes Fourier analyze:

7. Longitudinal Modes n = 0n = 1000  f = 47.7 kHz

8. What makes an echo? First impulse Second impulse Nonlinear interaction term Phase cancellation occurs when

9. Experimental Setup In a synchrotron, it is possible to see every particle (limited only by bandwidth). Gap Detector

10. Solve using the perturbation techniques of plasma physics Nonlinear termFokker-Planck drag and diffusion terms (Su and Oberman, PRL, 20, 9, (1968)) Echo Current Decay due to collisions

11. First Measurements of Longitudinal Echoes Fermilab Antiproton Storage Ring

12. Decay rates yield precise measures of diffusion  1x10 -4 Hz Collision frequencies as low as 10 -9 Hz have been observed !

13. Many other types of echoes have now been studied Bunched beam echo Transverse echoes Bunched beam echoes Even… spin echoes

14. 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