Halo Formation and Emittance Growth of Positron Beams in Long, Dense Plasmas

1. Halo Formation and Emittance Growth of Positron Beams in Long, Dense Plasmas Patric Muggli and the E-162 Collaboration: C.D. Barnes, F.-J. Decker, M. J. Hogan, R. Iverson, C. O’Connell, P. Raimondi, R.H. Siemann, D. Walz Stanford Linear Accelerator Center B. Blue, C. E. Clayton, C. Huang, C. Joshi, K. A. Marsh, W. B. Mori, M. Zhou University of California, Los Angeles T. Katsouleas, S. Lee, P. Muggli University of Southern California

2. IP2: Ionizing Laser Pulse (193 nm) IP0: e-, e+ Streak Camera (1ps resolution) ∫Cdt Li Plasma ne≈21014 cm-3 L≈1.4 m E-162: Quadrupoles Bending Magnet X-Ray Diagnostic N=21010 sz=0.7 mm E=28.5 GeV Cherenkov Radiator Optical Transition Radiators Dump Imaging Spectrometer 25 m y y E-157: x x y,E y,E x x EXPERIMENTAL SET UP • Optical Transition Radiation (OTR) • CHERENKOV (aerogel) - Spatial resolution ≈100 µm - 1:1 imaging, spatial resolution <9 µm - Energy resolution≈30 MeV - Time resolution: ≈1 ps

3. e- Back Back Blow Out Front 3s0 beam 3s0 beam Front e+ e- & e+ BEAM NEUTRALIZATION 3-D QuickPIC simulations, plasma e- density: r=35 µm r=700 µm N=1.81010 d=2 mm e-: ne0=21014 cm-3, c/p=375 µm e+: ne0=21012 cm-3, c/p=3750 µm • Uniform focusing force (r,z) • Non-uniform focusing force (r,z)

4. z (µm) z (µm) -3750 0 3750 -3750 0 3750 e- e+ 700 1500 x (µm) 0 x (µm) 0 -700 -1500 Ex (GV/m) Ex (GV/m) e- e+ e- & e+ FOCUSING FIELDS* x0=y0=25 µm z=730 µm N=1.91010 e+/e- ne=1.51014 cm-3 *QuickPIC Non-linear, abberations Linear, no abberations

5. r=r r=3r r=r r=3r e- & e+ FOCUSING FIELDS QuickPIC: x0≈y0≈25 µm, Nx≈39010-6, Ny≈8010-6m-rad, N=1.91010 e+, z≈730 µm, ne=1.5 10-6, L≈1.1 cm Front Back Front Back • Non-uniform focusing force (r,z) • Uniform focusing force (r,z) • Stronger focusing force • Weaker focusing force • e+: focusing fields vary along r and z!

6. ne=0 ne≈1014 cm-3 2mm •Ideal Plasma Lens in Blow-Out Regime e- 2mm •Plasma Lens with Aberrations e+ FOCUSING OF e-/e+ •OTR images ≈1m from plasma exit (x≠y) • Qualitative differences

7. UV Energy (mJ) EXPERIMENT / SIMULATIONS x0=y0=25µm, Nx=39010-6, Ny=8010-6m-rad, N=1.91010 e+, L=1.4 m Downstream OTR Experiment Simulation • Excellent experimental/simulation results agreement!

8. EXPERIMENTAL/SIMULATION RESULTS x0≈65 y0≈48 µm, Nx≈11510-6, Ny≈18410-6m-rad, N≈1.91010 e+, L≈1.4 m Downstream OTR Experiment Simulation UV Energy (mJ) • Defocusing in x and y “low” e in both planes, larger s • No distinctive features (b-tron oscillations) • Excellent experimental/simulation results agreement!

9. y,E UV Energy (mJ) x EXPERIMENTAL RESULTS e+ x0≈y0≈25 µm, Nx≈39010-6, Ny≈8010-6m-rad, N=1.91010 e+, L≈1.4 m Cherenkov/Plasma Exit Resolution Limit? • Strong focusing in x (large ), defocusing in y (low ) • No distinctive features (-tron oscillations)

10. FIT FOR BEAMS WITH HALO X-profile y-profile Beam Size=FWHM (BAB’) Charge in the Peak=Area(BAB’) Charge in the Halo=2*Area(CDB) Halo

11. HALO FORMATION x0≈y0≈25 µm, Nx≈39010-6, Ny≈8010-6m-rad, N=1.91010 e+, L≈1.4 m •Charge is conserved by the triangular fits •The halo forms at low density

12. HALO FORMATION x0≈y0≈25 µm, Nx≈39010-6, Ny≈8010-6m-rad, N=1.91010 e+, L≈1.4 m Experiment Simulation •Very nice agreement

13. 0.01 mJ (OFF) 1mm ne=21014 cm-3 OFF 0.93 mJ HALO FORMATION x0≈y0≈25 µm, Nx≈39010-6, Ny≈8010-6m-rad, N=1.91010 e+, L≈1.4 m Experiment Simulation •Very similar

14. Radius (cell) BEAM/FIELD EVOLUTION x0=y0=25µm, Nx=39010-6, Ny=8010-6m-rad, N=1.91010 • Beam becomes non-Gaussian • Beam size and focusing field “stop” at z≈0.7 m

15. e-/e+: SLICES SIZE IN THE PLASMA Front Back o=0.34 m, ne matched=1.61013 cm--3 e- e+ • Head diverges ≈0 • Head diverges ≈0 • Coherent betatron motion of the core • Phase mixing of the following slices

16. Front Back e-/e+: SLICE EMITTANCE e- e+ • Increase in the head ... • Increase in the head ... • Blow-out, pure ion column preserves beam emittance • Phase mixing of the following slices

17. CONCLUSIONS • Focusing of e+ by a plasma is qualitatively different from that of e-: •Positron bunches are focused without showing betatron oscillations … • … focusing depends on  and  at plasma entrance… • … show formation of a beam halo. • Focusing force is nonlinear in r and z • Emittance growth is expected • Simulation results confirm the experimental observations • Simulation results show emittance growth, mostly in the front and back of the bunch • Simulation results show “hosing” in the back of the bunch

18. 0.01 mJ (OFF) 0.23 mJ 0.13 mJ 1mm y 0.93 mJ 6.47 mJ x EXPERIMENTAL PROFILES @ OTR x0=y0=25µm, Nx=39010-6, Ny=8010-6m-rad, N=1.91010, ne=0.751014 cm-3 • Focusing in x, not in y, ne “independent” • No halo at low ne • Triangular projected beam profiles (ne≠0)

19. SIMULATION PROFILES x0=y0=25µm, Nx=39010-6, Ny=8010-6m-rad, N=1.91010 ne=0.751014 cm-3 ne=0 @ DS OTR @ Plasma Exit/Cherenkov @ DS OTR • Beam halo, as in experiment • Focusing in x • Triangular projected beam profiles (ne≠0)

20. FOCUSING OF e+: HIGH ne •from OTR images ≈1m from plasma exit s0x=s0y=25 µm N=1.91010 e+ exN≈10eyN≈1010-5 m-rad L=1.4 m • x-size reduction >3, no betatron oscillations • Focusing limited by emittance growth due to plasma focusing aberrations? M.J. Hogan et al., PRL (2003).