Active plasma lenses at 10 GeV

Transcription

1 Active plasma lenses at 1 GeV Jeroen van Tilborg, Sam Barber, Anthony Gonsalves, Carl Schroeder, Sven Steinke, Kelly Swanson, Hai-En Tsai, Cameron Geddes, Joost Daniels, and Wim Leemans BELLA Center, LBNL 216 FACET-II Science Workshop, Oct Office of UNIVERSITY OF Science CALIFORNIA

2 Magnetic lenses play a critical role in accelerator applications. Strength & tunability desirable. FEL driven by a Laser Plasma Accelerator Undulator Magnet Grating FEL light LPA Active Plasma Lens Chicane 2nd Lens Seed e-beam LPA drive laser Discharged capillary Accelerator applications à transport line Magnetic lens for collimation, focusing Focal length ~ gamma / (db/dr) High gradient à compact applications High gradient à high energy applications Ideal: tunable, radially symmetric Active Plasma Lens meets these criteria e-beam

3 Discharge current flowing through a capillary: linear B-gradient for uniform current distribution beam in Ampere s law 2πrB(r) = µ R 2πrJ(r)dr = I r 2πr'J(r')dr' J B courtesy of A. J. Gonsalves Uniform current J(r) = J J = I /πr 2 B(r) = µ I 2πR r 2 B r = µ I 2πR 2 ~ r ~ 1/r R r R r

4 Active plasma lens an old concept for ion beams. Attractive due tunability, symmetry, and strength Active Plasma Lens Introduced 195s (ion beams) Radial symmetric focusing Tunable, up to ~1 ka ( active ) Gradients >3 T/m Panofski et al. RSI 195 Field gradient Strength parameter Focal length B r = µ I 2πR 2 k = q m γc F =1/(kL) B r Example D=.5mm, L=6cm 5 MeV I=43 A (14 T/m) Example D=.5mm, L=6cm 1 GeV I=695 A (22 T/m) 1 mrad & 25cm à σ=25 µm

5 Experimental demonstration on Laser-Plasma Accelerated electron beams in 215 van Tilborg et al. PRL 115, (215)

6 Energy-dispersed beam size diagnostic reveals oscillations within plasma lens D.25mm capillary, L=33mm, tape protection Agreement with à 3 T/m 2 nd and 3 rd oscillation inside lens observed van Tilborg et al. PRL 115, (215)

7 Transverse scan useful to measure focusing gradient µm kick/µm offset Averaged data Gradient fit Good technique regardless of imaging geometry D.5mm capillary, L=15mm, 3mm drift, no tape protection Under investigation: measured current ~36 Amps Cap wider (on average) by 21%? y LPA source Lens y E y E E

8 Where active plasma lenses can provide unique solutions: 1. Ultra-relativistic e-beams Quadrupole doublet: Asymmetric focusing For 3 MeV e-beam Solenoid (2 T, L=2 cm): F=5 cm Quad doublet (5 T/m, L=3 cm): F=13 cm Active plasma lens (2 T/m, L=3 cm): F=1.7 cm For 1 GeV e-beam Quad doublet (5 T/m, L=3 cm): F=4.5 m Active plasma lens (2 T/m, L=6 cm): F=.28 m k = (also of interest to ion beams) Panofski et al. RSI 195, Boggasch et al. Proceedings EPAC 92 q m γc B r

9 Where active plasma lenses can provide unique solutions: 2. Rapid capture for compactness, mitigation ε growth Barber et al. Proceedings AAC 216 ε n = ε 2 +σ θ 4 σ γ 2 z 2 /γ 2 Migliorati et al. PRSTAB 213 ( ) [ ] -> ( ) Compact (staging) Quick capture à emittance mitigation for Δγ/γ~% Quick capture à matching in undulator for larger Δγ/γ Steinke et al. Nature 216

10 Possible limitation: emittance degradation from beam-driven wakefields for dense e-beams Esarey et al. Rev. Mod. Phys mrad, L=3cm, 2 pc, L=1/2/4mu Effective field gradient [T/m] L=1 micron Linear regime: e-beam Zeta [micron] (E r B ϕ )(r,ζ) = π(k pl) n b 1 sin k E π 2 k 2 p L 2 n k p ζ L p 2 Effective field gradient [T/m] L=2 µm L=1 µm Density [cm-3] L=4 µm + L πζ cos π L 2r 2 r + 2k pi '(k p r)k 2 (k p r b ) b

11 Possible limitation: emittance degradation from beam-driven wakefields for dense e-beams Effective field gradient [T/m] Zeta [micron] To minimize wakefield effect: Let e-beam divergence more Operate at highest current (shortest cap) à reduce relative effect Emittance degradation ~1/γ Away from resonant density (weak effect, low density most practical) Wakefields play role for >2pC sub-gev <1µm beams Emittance [micron] MeV,.25 micron source, 1.5 mrad L=2 micron, Lprop=3 cm, σ=45 micron nbeam=1.3e15 cm-3 (25pC) Lens= T/m front-end variation Emittance increase x2.5 Cap lens Drift q m γc B r = Propagation (m) q m γc µ I 2πR +η(ζ ζ s) 2 2

12 Possible limitation: emittance degradation from non-uniform current Radial current distribution dominated by temperature Towards peak of current pulse: more current on-axis! Bobrova et al. PRE 22 From Helsinki University online lecture

13 Possible limitation: emittance degradation from non-uniform current Density.4 Density [1e18] T e [ev] B [Tesla] Uniform J r [micron] Hotter plasma on-axis More current on-axis Stronger gradient on-axis (shorter focal length) Curved gradient à emittance degradation r [micron] Simulation by Bobrova

14 On-axis current concentration reveals itself as donut mode when beam is over-focused Experiment I=64 A I=48 A I=27 A Simulations Experiment

15 On-axis current concentration reveals itself as donut mode when beam is over-focused Energy [MeV] Y (mm) B-field [T] Energy (MeV) #1-4 Radius [m]

16 Stability:.5% rms jitter in current at e-beam timing Jeroen van Tilborg, Sam Barber, Carl Schroeder, and Wim Leemans BELLA Center, LBNL 216 FACET-II Science Workshop, Oct At fixed timing, 2 Amps 45 Amps (.5% rms) for 5 consecutive shots 16 UNIVERSITY OF CALIFORNIA

17 Conclusion Jeroen van Tilborg, Sam Barber, Simulations by Bobrova Carl Schroeder, and Wim Leemans BELLA Center, LBNL 216 FACET-II Science Workshop, Oct Bfield [Tesla] Bfield [Tesla] D 1.mm cap early timing.15.1 D.5mm cap Radius [micron] Radius [micron] Active Plasma Lens: Strong gradients observed Ideal for compact & GeV applications Understand limits wakefields and non-uniform current More uniform for optimized timing, pressure, diameter, beam size UNIVERSITY Nov 216: DESY collaboration at MainzOFaccelerator 17 CALIFORNIA

18 End Jeroen van Tilborg, Sam Barber, Carl Schroeder, and Wim Leemans BELLA Center, LBNL 216 FACET-II Science Workshop, Oct UNIVERSITY OF CALIFORNIA

19 45 Size=51.3 micron 45 Size= micron Number of particles Number of particles Amps, uniform Y (micron) Y (micron) 3 Size=45.3 micron 3 Size= i micron Number of particles Number of particles Amps, actual Y (micron) Y (micron) 6 MeV 4 MeV

20 Effect of on-axis current (stronger near-axis B-field gradient) J(r) = J exp( 2r 2 /w 2 ) R 2I 2πJ(r)rdr = I J = πw 2 1 exp 2R 2 /w 2 2πrB(r) = µ r [ ( )] 2πJ(r')r'dr' B(r) = µ J w 2 4r [ 1 exp( 2r 2 /w 2 )] # Current density wà w=.3mm Bfield [Tesla] w=.3mm wà r [micron] Example: R=1mm, I = 16 Amps r [micron]

21 Title Y (mm) Y (mm) Energy (MeV) Energy (MeV) # #1-4