1. Outline of the method to find an approximate region of electrons that enter the detector in a quadrupole field after kicked by a point bunch
K. Kanazawa
KEK
22 June 2009

2. Magnetic field Coordinate y x
Approximation of the initial condition (B ~ 0 near the center) x
First, determine the initial region in the phase plane (v, 0) for those electrons that enter the detector. Then translate the region into the real plane (r, 0).

3. Equation of motion
Introduction of lK
The final form of equations.

4. Solution when u<<1.
Asymptotic solution with the form similar to the last equation

5. Analysis of the electron motion near the detector (u>>1)
The conditions to enter the detector
Aperture condition
Energy condition

6. Conditions expressed with actual parameters
Numerical example

7. Final result