Beam dynamics simulations with the measured SPARC gun-solenoid field

1. Beam dynamics simulations with the measured SPARC gun-solenoid field G. Bazzano, P. Musumeci, L. Picardi, M. Preger, M. Quattromini, C. Ronsivalle, J. Rosenzweig, C. Sanelli SPARC review committee, Frascati 16/11/05

2. July ’05: • gun-solenoid magnetic field measurements (at 100,200,250 A) • Preliminary PARMELA/TREDI beam dynamics computations based on the measured maps put in evidence: • a significant emittance growth (depending by the excitation current) due to additional fields in the solenoid • a different focusing in x and y planes • Numerical and/or measurements errors effect? Physical effects? • September ’05: • 1. Coils alignment and new magnetic field measurements at 140 A (working point) • 2. Testing and optimizing of the accuracy of the data analysis method in order to evaluate and minimize the effect of the numerical errors • 3. New beam dynamics calculations

3. 3D MAP COMPUTATION FROM MEASURED MAGNETIC FIELD DATA • Available measured data : • Bz (x,y,z) for -10 mm < x,y < 10 mm (5 mm stepsize)and -350 mm < z < 350 mm: 5x5=25 points at each z • In order to construct the input 3D map for the beam dynamics codes we need Bx and By • The max. rms beam radius in the gun region is 2.2 mm, so a great accuracy is required near the axis (the measurements have been done far from the axis)

4. Used approach: Least square fit Bz(z) = b0(z) + b1(z) x + b2(z) y + b3(z) x2 + b4(z) y2 From rot B=0 These expressions agree with the first terms of a3D multipole expansion that is solution of Maxwell equations only if the correct relations between the coefficients are satisfied

5. In our fit the relation (4) can be written as: (b3+b4)= -b0”/2 that for an ideal solenoid gives the well known expansion of the on-axis field It is very easy to demonstrate that the condition: (b3+b4)= -b0”/2 gives div B=0 near the axis

6. If in our fit the coefficients are free the condition div B =0 near the axis is not verified within the tolerances required by beam dynamics codes. The error on divB is given by: where The problem has been solved combining Bz(z) = b0(z) + b1(z) x + b2(z) y + b3(z) x2 + b4(z) y2 and (b3+b4)= -b0”/2 Bz(z) = b0(z) + b1(z) x + b2(z) y + b3(z) (x2-y2)- (b0”(z)/2) y2 Conditioned least square fit

7. Test of the accuracy of the method: simulation of the measurement by using the solenoid field map as computed by POISSON (converted to a 3D map) divB on axis Emittances vs z in the post-gun drift

8. Analysis of the measured maps: coefficients Ideal field (pure solenoid) b0= on axis field b1,b2=0 b3=-b0”/4 b4=-b0”/4 Measured field b0= on axis field b1,b20 (dipolar terms) b3=-b0”/4+ b4=-b0”/4-  dz give a skew quadrupole

9. this means: added transverse fields Focal length (at 5.6 MeV)8 m

10. Beam dynamics results (PARMELA): post-gun drift • Emittance growth at the linac entrance1.7 • Asymmetric beam at the linac input • The max. effect of the dipolar components on the emittance is only 12% • The main effect of the dipolar component is a beam steering All terms included No dipolar terms (b1=b2=0) centroid

11. Beam dynamics results (PARMELA): linac (b1=b2=0) Output beam: nx=2.2 mm-mrad ny=1.6 mm-mrad instead of 0.8 mm-mrad (design value) Emittances and envelopes vs z Phase spaces Linac input Linac output

12. Mechanism of emittance growth: quadrupole-induced x-y coupling • Quadrupole kicks applied inside solenoid are Larmor rotated after application of kick • Coupling between x and py, y and px produces “uncorrelated” looking added phase space area • Estimates, from projections after Larmor rotation: • Normal quad • Skew quad • Example: f=10 m, x=1.4 mm, =11,z=10 cm • It doesn’t matter if it comes from skew or normal

13. Correcting the problem A linear x-y coupling can be corrected downstream by a skew quad Skew quad parameters (PARMELA model: an horizontal focusing hard edge q-pole rotated of 45°): G=5 gauss/cm, Lq=5 cm, Focal length=8 m, z-position=80 cm Corrector off Corrector on

14. Correcting the problem: slice (300 m) analysis at linac output Corrector off Corrector on The correction brings again also the slice emittance below 1 mm mrad

15. November ’05: Start of SPARC solenoid 3D modelization by CST EM STUDIO Aim:investigation of sources of m-poles (coils misalignments, cross-overs in coil windings, iron geometry, manufacturing errors) and possible improvements to SPARC solenoid. • Advantages respect to RADIA code (used for design): • Short computing time: 30’ (on PC WXP, 3GHz, 2GB Ram) for the complete geometry – no symmetry imposed • High accuracy • iron geometry from drawings inserted • only ideal coils (the exact coils geometry has been required to manufacturer)

16. Multi-pole components due to solenoid imperfections have been observed experimentally at GTF Asymmetric beam on phosphor screen immediately downstream of the solenoid. Source of asymmetry (initially attributed to a non-uniform laser beam and cathode quantum efficiency): m-poles in solenoid. Rotating coil measurements showed the presence of an unexpected q-pole component.

17. Based on the the magnetic measurements, operational experience and beam tests with the GTF gun solenoid, it was decided to include in LCLS correctors mounted inside the gun solenoid horizontal and vertical dipole correctors normal and skew 4 wire quadrupole correctors OD=2.85”

18. CONCLUSIONS • In simulations a quadrupole superimposed on SPARC solenoid field gives a “tilted beam” emittance growth due to x-y phase plane coupling • Next activities after beam tests • Continue to work on solenoid improvements • (very accurate 3D modelization) • Direct measure of m-poles by rotating coil • Design and test of external corrector magnets • * Post gun steering already exists for dipole correction • * Quad (similar to the already used skew quads in FNAL “flat-beam” converter experiments) • Design and implement inside solenoid correctors