# Consider a beam of high-energy cosmic ray protons streaming along a uniform background magnetic field in a collisionless plasma. Let

## Question:

Consider a beam of high-energy cosmic ray protons streaming along a uniform background magnetic field in a collisionless plasma. Let the cosmic rays have an isotropic distribution function in a frame that moves along the magnetic field with speed u, and assume that u is large compared with the Alfvén speed but small compared with the speeds of the individual cosmic rays. Adapt our discussion of the emission of Langmuir waves by a bump-on-tail distribution to show that the growth rate is given to order of magnitude by Eq. (23.68).

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**Related Book For**

## Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics

**ISBN:** 9780691159027

1st Edition

**Authors:** Kip S. Thorne, Roger D. Blandford

**Question Details**

Chapter #

**23**Section: Exercises

Problem: 8

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