Enge background study

The detailed Enge optics study explained in section 3.3.1 and 3.3.2 shows the background for the direct electrons originating from bremsstrahlung and M$\phi$ller scattering can be controlled in the rate of a few MHz by the tilt method. However, it means the collimators and the Enge magnet pole are hit by those very high-rate electrons. Therefore, it is important to estimate the rate of the in-direct electrons (for example, scattered-in electrons). For this purpose, a GEANT Monte Carlo simulation was performed. The magnetic field of the Enge is simplified to be a dipole field in this simulation, but the pole and collimator materials are taken into account and physics processes of the electrons in those materials are simulated.

The result of this simulation shows $1.6 \times 10^{-5}$ electrons / one bremsstrahlung electron, and $5.8 \times 10^{-4}$ electrons / one M$\phi$ller electron reach the focal plane.

In our experimental condition (1.8 GeV, 30$\mu$A electron beam and 100mg/cm$^2$ carbon target) the bremsstrahlung and M$\phi$ller electron rates for the momentum range of $190 - 442$ MeV/$c$ and 4$\pi$ solid angle are 3.4 GHz and 0.75 GHz. Therefore, the indirect bremsstrahlung electron and M$\phi$ller electron rates are respectively expected to be less than 54kHz and 500kHz; they are not serious.