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Related Experiment Videos

Longitudinal instability for a purely inductive wake function.

Y Shobuda1, K Hirata

  • 1KEK, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

A physically defined wake function resolves the Haissinski equation’s non-existence issue beyond a threshold. This study proves solution existence and identifies a lower stability threshold for particle beam dynamics.

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Area of Science:

  • Plasma physics
  • Particle accelerator physics
  • Electromagnetism

Background:

  • The Haissinski equation models charged particle beam behavior in accelerators.
  • A purely inductive wake function previously led to a non-existent solution beyond a threshold.
  • This non-existence was attributed to an ill-defined wake function treatment.

Purpose of the Study:

  • To investigate the existence of solutions to the Haissinski equation with a physically defined wake function.
  • To re-evaluate the threshold beyond which solutions were previously considered non-existent.
  • To determine the stability threshold for the solution.

Main Methods:

  • Mathematical analysis of the Haissinski equation.
  • Physical definition and incorporation of the wake function.

Related Experiment Videos

  • Analysis of solution existence and stability.

    • Main Results:

    • The Haissinski equation solution is proven to exist beyond the previous threshold when the wake function is physically defined.
    • A stability threshold for the solution exists.
    • This stability threshold is lower than the previously identified non-existence threshold.

    Conclusions:

    • A physically meaningful wake function is crucial for the Haissinski equation.
    • The existence of solutions is confirmed under physically realistic conditions.
    • Understanding stability thresholds is vital for particle beam dynamics and accelerator design.