# Can someone explain head to tail bunch differential acceleration?

1. May 3, 2007

### ballistikk

I was given an assignment involving finding the head to tail bunch differential acceleration of a beam of muons loading onto an RF cavity, and it occurred to me that my understanding of the concept might be keeping me from working the problem. Can somone concisely explain it to me?

2. May 3, 2007

### ZapperZ

Staff Emeritus
You did not give any clear info on what are the parameters of the bunch and the RF.

Is your bunch length shorter than the RF period? What is the geometry of the RF pulse? Is it a TM mode?

If all you have is a finite length bunch shorter than the RF, and you have the E-field along the direction of propagation (z-direction typically), then you can easily assume that the E-field has a sinusoidal profile both in space and in time. Since the Lorentz force is simply qE, you then have the actual force acting on each length segment of the muon bunch. That automatically tells you the acceleration of each part of the muon bunch.

Zz.