1. The cyclotron accelerates positively charged particles, while the betatron accelerates negatively charged electrons.

2. The betatron and synchrotron oscillation are measured frequently during the period of the machine commissioning, operation and machine study.

3. This thesis introduces in detail how to keep betatron electron track radius invariable in two conditions of typical magnetic field distribution.

4. The betatron tunes are measured frequently during the period of the machine operation and machine studies.

5. In the betatron, a single magnetic field is harnessed for both purposes.

6. Extending the equations in linear regime of free-electron laser particle model to include arbitrary Betatron motions of electrons.

7. Its' radiant intension higher tenfold to hundredfold compare with the betatron, spending shorter time on radiogram. higher resolution rate. Hope stream to strong, spot to small commonly.