EMMA Meeting: Longitudinal Simulations

1. EMMA Meeting:Longitudinal Simulations 18/11/10 Jimmy Garland The University of Manchester The Cockcroft Institute

2. EMMA Meeting:Longitudinal Simulations • Built a simulation code which derives from a ToF per cell curve obtained using a particular lattice in S. Machida’s code. This parabolic shape of the time of flight curve as a function of energy can be approximated by a 2nd order Taylor expansion:

3. EMMA Meeting:Longitudinal Simulations • Scaled the ToF curve acquired from Machida’s code with respect to the data measured from EMMA.

4. Synchrotron Tune • An example of EMMA synchrotron tune measurements…

5. Synchrotron Tune • Data agrees very well with my simulation (e.g. 1.3MV per turn)

6. Synchrotron Tune as a Function of Cavity Voltage (in bucket) • Synchrotron tune is proportional to the square root of the cavity voltage • Can use synchrotron tune to measure the actual MV per turn in EMMA.

7. Phase Errors • Modeled the effect of phase errors in the cavities. Added a random phase error within a specified percentage limit to the phase of each cavity. • If the phase errors produce a vector sum of voltages in 1 turn that is under the voltage needed to open the serpentine channel, we will not see acceleration! • I calculate the minimum voltage gain per turn needed to open the gutter channel is 0.9MV at the current 1.301GHz operating frequency.

8. Phase Errors • 1000 samples of random errors were simulated for each given limit of phase error up to ±90 degrees. • Repeated for several values of total voltage gain per turn. Phase error tolerance increases with higher voltage gain per turn as a higher voltage gain per turn widens the serpentine channel in phase space.

9. Phase Errors • Phase error limit for serpentine acceleration as a function of voltage gain per turn.

10. Gutter Width • Gutter size increases with increasing voltage gain per turn:

11. Gutter Width • Gutter size increases with increasing voltage gain per turn:

12. Conclusions • We haven’t seen convincing acceleration in EMMA yet! • My simulations can predict the threshold voltage above which the serpentine channel opens up. • If we have some phase error on the cavities in EMMA then the vector sum of the voltages may NOT add up to the voltage per turn necessary for acceleration in the machine. • Initial simulations show that when a random phase error is added to the cavities that sometimes we have serpentine acceleration and sometimes we do not. I have simulated the tolerances. • Need to find out accurately what the phases are in the cavities and compare this with the simulations to determine whether it is phase errors which are preventing serpentine acceleration in EMMA before run2.

13. Back-up Slides:RF Buckets • If an RF frequency is chosen which corresponds to a point on the ToF curve we can select acceleration buckets at particular energies.

14. Back-up Slides:Buckets and the Gutter • In fact in an ns-FFAG we can allow the particles to be accelerated in the so called “gutter” between buckets. This is known as “serpentine acceleration”.

15. Back-up Slides:Buckets and the Gutter • Above some voltage the serpentine channel is opened up…

16. Back-up Slides:Buckets and the Gutter • Modeled the acceleration as a function of voltage in the cavities…