FACILITY FORM 602 N66-10878 GPO PRICE $ ___ CFSTI PRICE(S) $ ___ Hard copy (HC) Microfiche (MF) ___ ff 653 July 65 RESEARCH LABORATORY a division of AVCO CORPORATION A LIMIT ON STABLY TRAPPED PARTICLE FLUXES C. F. Kennel and H. E. Petschek RESEARCH REPORT 219 July 1965 supported jointly by HEADQUARTERS NATIONAL AERONAUTICS AND SPACE ADMINISTRATION OFFICE OF SPACE SCIENCES Washington, D. C. under Contract No. NAS w-837 DEPARTMENT OF THE NAVY OFFICE OF NAVAL RESEARCH Washington 25, D. C. under Contract No. Nonr-2524(00) $^{*}$ Submitted to Journal of Geophysical Research, July 27, 1965. ## TABLE OF CONTENTS Abstract v 1. Introduction 1 2. Linear Propagation and Stability of the Whistler and Ion Cyclotron Modes 5 3. Whistler and Ion Cyclotron Turbulence 22 4. Steady State Diffusion into a Loss Cone: "Drizzle" 30 5. Whistler Mode Upper Limit to Stably Trapped Electron Flux 36 6. Limitation Upon Trapped Proton Intensities 43 7. Consistency of Lifetime and Observed Pitch Angle Profiles 44 8. Discussion of Equatorial VLF Wave Intensity 51 9. Summary and Discussion 54 References 59 ## ABSTRACT Whistler mode noise leads to electron pitch angle diffusion. Similarly, ion cyclotron noise couples to ions. This diffusion results in particle precipitation into the ionosphere and creates a pitch angle distribution of trapped particles which is unstable to further wave growth. Since excessive wave growth leads to rapid diffusion and particle loss, the requirement that the growth rate be limited to the rate at which wave energy is depleted by wave propagation allows an estimate of an upper limit to the trapped equatorial particle flux. Electron fluxes >40 keV and proton fluxes >120 keV observed on Explorers XIV and XII respectively obey this limit with occasional exceptions. Beyond L=4, the fluxes are just below their limit, indicating that an unspecified acceleration source sufficient to keep the trapped particles near their precipitation limit exists. Limiting proton and electron fluxes are roughly equal, suggesting a partial explanation for the existence of larger densities of high energy protons than electrons. Observed electron pitch angle profiles correspond to a diffusion coefficient in agreement with observed lifetimes. The required equatorial whistler mode wideFACILITY FORM 602 N66-10878 GPO PRICE $ ___ CFSTI PRICE(S) $ ___ Hard copy (HC) Microfiche (MF) ___ ff 653 July 65 RESEARCH LABORATORY a division of AVCO CORPORATION A LIMIT ON STABLY TRAPPED PARTICLE FLUXES C. F. Kennel and H. E. Petschek RESEARCH REPORT 219 July 1965 supported jointly by HEADQUARTERS NATIONAL AERONAUTICS AND SPACE ADMINISTRATION OFFICE OF SPACE SCIENCES Washington, D. C. under Contract No. NAS w-837 DEPARTMENT OF THE NAVY OFFICE OF NAVAL RESEARCH Washington 25, D. C. under Contract No. Nonr-2524(00) $^{*}$ Submitted to Journal of Geophysical Research, July 27, 1965. ## TABLE OF CONTENTS Abstract v 1. Introduction 1 2. Linear Propagation and Stability of the Whistler and Ion Cyclotron Modes 5 3. Whistler and Ion Cyclotron Turbulence 22 4. Steady State Diffusion into a Loss Cone: "Drizzle" 30 5. Whistler Mode Upper Limit to Stably Trapped Electron Flux 36 6. Limitation Upon Trapped Proton Intensities 43 7. Consistency of Lifetime and Observed Pitch Angle Profiles 44 8. Discussion of Equatorial VLF Wave Intensity 51 9. Summary and Discussion 54 References 59 ## ABSTRACT Whistler mode noise leads to electron pitch angle diffusion. Similarly, ion cyclotron noise couples to ions. This diffusion results in particle precipitation into the ionosphere and creates a pitch angle distribution of trapped particles which is unstable to further wave growth. Since excessive wave growth leads to rapid diffusion and particle loss, the requirement that the growth rate be limited to the rate at which wave energy is depleted by wave propagation allows an estimate of an upper limit to the trapped equatorial particle flux. Electron fluxes >40 keV and proton fluxes >120 keV observed on Explorers XIV and XII respectively obey this limit with occasional exceptions. Beyond L=4, the fluxes are just below their limit, indicating that an unspecified acceleration source sufficient to keep the trapped particles near their precipitation limit exists. Limiting proton and electron fluxes are roughly equal, suggesting a partial explanation for the existence of larger densities of high energy protons than electrons. Observed electron pitch angle profiles correspond to a diffusion coefficient in agreement with observed lifetimes. The required equatorial whistler mode wide