salİm oğur Velİ Yildiz

1. salİm oğur Velİ Yildiz BogaziciUniversity, Department of Physics

2. Outline • Emittance • Why we need to measure the emittance at the exit of the ion source ? • Quadrupole Variation Method • Our calculations and results • Forward Method • Forward Method using Quadrupole • Forward Method using Solenoid

3. 1. Emittance A particle’s properties can be figured out via Lagrange Mechanics, however a system of particles had better be defined in Hamiltonian Mechanicswhich requires Phase Space. Phase Space includes position and (combination of) derivative of position (velocity, momentum).

4. 1. Emittance In Accelerator Physics, we define 3 phase spaces for 3 dimensions (x,y,z). Again, phase space includes position(i.e. x) and itsgradient (x’). where α,β,γare twiss parameters which enables me to define the areauniquely. A= π. ϵ

5. 1. Emittance Emittance with determined α,β,γ values gives information about the beam as a whole, and this information is used through the beam propagation simulations. This is why we had to figure out the emittance and twiss parameters.

6. 2- Quadrupole Variation Method ϵ_rms = 1.0000 π.mm.mrad β=0.2000 mm/π.mrad α=-2.0001 P.S: Beam pipe is taken with infinite radius such that all created particles can travel and are not annihilated. Also, no effect of space charge ! This figure was drawn by a multiparticle simulation program PATH, and considered as the beam exiting the ion source. Due to radial symmetry at the exit of the ion source both xx’ and yy’ have the same emittance and twiss parameters.

7. 2- Quadrupole Variation Method

8. 2- Quadrupole Variation Method

9. Beam Dynamics Transfer Matrices

10. 2- Quadrupole Variation Method We have 10 cm of quadrupole with effective length and 20 cm of drift space. Therefore our transfer matrix R(k)can be calculated, and notice that although focusingquadrupole stands before the drift , in transfer matrix they are in backwards sequence.

11. 2- Quadrupole Variation Method

12. 2. Quadrupole Variation Method So far we have seen that the emittance and twiss parameters are very close those ones simulated, but this is the case for 0 mA (No space charge effect). Normalized solutions are given for trials with equations more than the unknowns.

13. 2. Quadrupole Variation Method In 2 mA space charge effect does not play such an important rule but in 10 mA, the beam emittance measurement blows up dramatically. What about beam pipe with physical length ?

14. 2. Quadrupole Variation Method What is the effect of the beam pipe? Table is meant to give a taste about what is happening in the case of a 3 cm radiusof beam pipe. Notice for small gradient x_rms values are close.

15. 3. ForwardMethod • In QVM, wecalculate emittance viaanalyticalwaysuchthatfrom x_rmsandgradientvalues, wegobackwardby transfer matricesandfindoutthe emittance and twiss parameters. • In FM, wehave an inceptionbeam, andwefeedthis emittance intosimulationstogetclosetothe x_rmsand y_rmsvaluesusingTRAVEL.

16. 3. Forward Method (Quadrupole)

17. 3. Forward Method (Quadrupole) • Now we insert our parameters to create a beam after analyses • We draw the beam with PLOTWIN

18. 3. ForwardMethod (Quadrupole) We used inception beam in simulations and the beam from FM is at good agreement with real beam. Notice that inception does not fit well with real beam.

19. 3. Forward Method (Solenoid)

20. 3. ForwardMethod (Solenoid) We have good agreement with real beam parameters by using solenoid, as well.

21. Conclusion • Quadrupole Variation Method is useful and gives accurate results at 20 keV and 2 mA with shortcomings in beam transmission rate for 3 cm of radius beam pipe. • Forward Method are both applicable with Quadrupole and Solenoid magnets. Moreover, transmission rate does not follow since the particles do not hit solenoid surface.

22. Thanks for your kind attention …