THE RADIAL STABILITY OF ORBITS IN A SPIRAL RIDGE CYCLOTRON

Abstract

Contents: Axial stability The conventional fixed frequency cyclotron Vertical focussing in a spiral ridge cyclotron: choice of units Thomas-effect Laslett effect Alternating gradient effect Generalization for nonsinusoidal flutter Orbital frequencyAnalytic approximation to radial oscillations Qualitative discussion Equations of motion Equilibrum orbit Deviations from the equilibrum orbit Frequency of small radial oscillations Motion of the orbit center Perturbation by nonlinear terms Expansion of orbits due to acceleration More than four sectors Radial stability limits Order-of-magnitude estimate of stability limits Combined effect of acceleration and orbit precession (four sectors) Numerical integration of the orbit equations

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1957
Accession Number
AD0252888

Entities

People

  • Peter Stahelin

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Cyclotrons
  • Equations
  • Equations Of Motion
  • Frequency
  • Mathematical Analysis
  • Mathematics
  • Motion
  • Numerical Analysis
  • Numerical Integration
  • Numerical Methods And Procedures
  • Oscillation
  • Perturbations
  • Precession

Fields of Study

  • Physics

Readers

  • Control Systems Engineering.
  • Pulsed Power and Plasma Physics.
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • Space
  • Space - Hall-Effect Thruster
  • Space - Orbital Debris